Xinzhi Liu

Xinzhi Liu
University of Waterloo | UWaterloo · Department of Applied Mathematics

PhD

About

591
Publications
22,822
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12,377
Citations
Citations since 2016
205 Research Items
5625 Citations
201620172018201920202021202202004006008001,000
201620172018201920202021202202004006008001,000
201620172018201920202021202202004006008001,000
201620172018201920202021202202004006008001,000

Publications

Publications (591)
Article
Full-text available
Owing to the weak observability of the azimuth misalignment angle, alignment accuracy and time are always the contradictory issues in the initial alignment process of Strapdown Inertial Navigation System ( SINS) , which requires a compromise between them. In this paper, a combined alignment mechanism is proposed to construct an observable and contr...
Article
This paper studies the problem of practical synchronization for delayed neural networks via hybrid-driven impulsive control in which delayed impulses and external disturbance are taken into account. Firstly, a switching method which establishes the relationship between error signals and a threshold function is introduced, which determines whether t...
Article
This article studies congestion control of wireless access networks. In a wireless access network, it is necessary to design a robust active queue management (RAQM) technique to control congestion occurrence and to make the network robust simultaneously against some issues in the wireless link aspects, such as packet error rate (PER) and fading eff...
Article
Full-text available
This paper investigates the input-to-state stability (ISS) and integral input-to-state stability (iISS) of switched stochastic nonlinear systems with time delays and random impulses. Different from the existing researches on ISS and iISS, random impulses with both high intensity and density are taken into account. More practically, these impulses a...
Article
This article addresses a class of large-scale stochastic impulsive systems with time delay and time-varying input disturbance having bounded magnitude. The main interest is to develop sufficient conditions for the input-to-state stability (ISS) and stabilization in the presence of impulsive effects. The method of Razumikhin–Lyapunov function is use...
Article
This is to reply the concerns about our NAHS paper ”Lyapunov and external stability of Caputo fractional order switching systems” pointed out by Hu in ”Comments on ’Lyapunov and external stability of Caputo fractional order switching systems’” recently.
Article
There are various methods designed for solving the distributed optimization problem with only local computation and communication. This letter discusses a continuous-time and distributed version of the gradient descent method for solving the distributed optimization problem. We prove that the convergence rate of this method matches those of the cen...
Article
Full-text available
In this paper, the problem of the robust tracking for two-arm condenser cleaning crawler-type mobile manipulators (CCCMM) with delayed angle-velocity uncertainties is original investigated. The two-arm condenser cleaning crawler-type mobile manipulators are composed of a crawler-type mobile platform and two-arm industrial manipulators.The uncertain...
Chapter
This paper investigates mean-square stability of stochastic systems with time-varying parameters, impulses and unbounded delay. Applying the characteristics of stabilizing and destabilizing impulses, stochastic analysis techniques and mathematical deduction, the two conclusions on mean-square stability analysis of the considered systems are obtaine...
Chapter
This paper addresses the problems of input-to-state stability/stabilization (ISS) and designing a robust reliable \(H_{\infty }\) control for a class of switched systems with state delay and time-varying, bounded disturbing input. The methodology of Razumikhin with multiple Lyapunov functions is used to establish the ISS property. The importance of...
Chapter
This paper investigates the Exponential Stabilization (ES) problem for Markov Jumping Neural Networks (MJNNs) with Additive Time-varying Delays (ATDs). To further mitigate the “unnecessary” waste of networks resources, a Sample-based Event-triggered Impulsive Control (SEIC) scheme is employed. A novel Lyapunov-Krasovskii functional is constructed b...
Chapter
This study aims at investigating the problem of stability and stabilization of chaotic systems on the basis of Takagi–Sugeno (T–S) fuzzy model under aperiodic sampling. A modified Lyapunov-Krasovskii functional (LKF), which fully captures the information of the sampling pattern, is constructed to the chaotic systems. Together with free-weighted mat...
Chapter
In this paper, we discuss the distance-based formation control problems for double-integrator multi-agent system (MAS) via impulsive protocols. The proposed controller allows all agents to attain the desired formation shape by controlling the inter-distances and velocities. Unlike the common conditions in most literatures associated with distance-b...
Article
We propose a nonsmooth Filippov refuge ecosystem with a piecewise saturating response function and analyze its dynamics. We first investigate some key elements to our model which include the sliding segment, the sliding mode dynamics and the existence of equilibria which are classified into regular/virtual equilibrium, pseudo-equilibrium, boundary...
Article
Designing a robust active queue management (RAQM) is mandatory to avoid congestion in networks with wireless access links, because transmission control protocol (TCP) can detect congestion after its occurrence in a communication network and wireless links suffer from bottleneck capacity variations caused by fading and packet error rate (PER) in the...
Article
In this study, a novel spatiotemporal graph convolutional networks model is proposed for traffic flow prediction in urban road networks by fully considering an information geometry approach and attention-based mechanism. Accurate traffic flow prediction in real urban road networks is challenging due to the presence of dynamic spatiotemporal data an...
Article
This paper addresses the problems of exponential mean‐square stability and reliable sampling data control design for nonlinear switched systems. First, a common model of actuator fault is used to give a description of the nonlinear of controller. The packet loss is assumed to be affected by multiple sampling periods. By input delay method, probabil...
Article
In this article, the sampled-data-based event-triggered synchronization control for fractional and impulsive complex networks (CNs) with time-varying delay is investigated and a class of more general network structure based on the switching topologies at impulsive instants is considered. First, a class of novel fractional-order integral inequalitie...
Article
A novel sampled-data event-triggered control (SDETC) for multi-agent systems (MASs) is proposed in this study, which is a more general form with the advantages of more flexible triggering techniques such as LIoDT, EIoDT, LT described in Remark 2.1, 2.2 covering many existing cases [1, 2, 3, 4]. It eliminates the Zeno behavior based on itself struct...
Article
Full-text available
This paper deals with the point control problem for a class of distributed parameter systems with time varying delay induced by the network. To eliminate the effect of time delay, a predictor with the time‐varying gain is designed to predict the state based on the sampled data. Meanwhile, the prediction error vanishes exponentially with the desired...
Article
Full-text available
We propose an impulsive stabilization method for delay equations based on a reduction to the centre-unstable manifold. Our approach does not make use of the constructions of Lyapunov’s direct method, such as Lyapunov functions or functionals. Necessary and sufficient conditions for when a system can be stabilized by impulses are derived based on th...
Article
This paper studies the finite-time stability (FTS) for a class of hybrid dynamical systems with deviating argument. An improved hybrid control scheme including sampled-data control as well as impulsive control is presented. Based on the theory of differential equations with piecewise constant argument of generalized type (PCAG) and the method of av...
Article
This paper studies the input-to-state stabilization problem of nonlinear time-delay systems. A novel event-triggered hybrid controller is proposed, where feedback controller and distributed-delayed impulsive controller are taken into account. By using the Lyapunov-Krasovskii method, sufficient conditions for input-to-state stability are constructed...
Article
Full-text available
This paper investigates the problem of cluster synchronization of complex dynamical networks with noise and time-varying delays by using a delayed pinning impulsive control scheme. Different from the traditional impulsive control schemes without the effects of input delays, it designs a pinning impulsive control scheme to successfully address the a...
Article
This paper studies the problem of the distributed networked sampled-data control for a class of distributed parameter systems with spatially-dependent diffusion term. In view of limited fixed sampling spatial points, the distributed sensor network is proposed to obtain the sampled-data measurements of the state which can efficaciously circumvent bl...
Article
The stability and synchronization problems are addressed in this study for the memristor-based fractional-order fuzzy cellular neural networks with multiple delays. By using the Laplace transform method, fractional-order calculus approach and the method of complex function, three exponential stability criteria are derived. Compared with the existin...
Book
Full-text available
This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independ...
Chapter
A follow-up to Chapter 5, this chapter is devoted to computational aspects of centre manifold theory. This includes a concrete representation of the centre manifold in Euclidean space, Taylor expansions, and an explicit ordinary impulsive differential equation for the dynamics on the manifold.
Chapter
The centre manifold reduction provides a framework in which bifurcations of fixed points and periodic solutions can be studied. In this section we will explain how the centre manifold reduction can be adapted to take into account parameters, prove two generic bifurcation patterns and present a general recipe for how one might study smooth local bif...
Chapter
In this final chapter, we study an in-host viral infection model with impulsive drug treatment. We first restrict to the disease-free subspace and prove the existence of a disease-free periodic solution and a compact, invariant global attractor. Next, we move to the full model and show that solutions are bounded and the positive orthant is invarian...
Chapter
Here we analyze a susceptible-infected-removed (SIR) model with pulse vaccination and temporary immunity modeled by a discrete delay. We complete an analysis of the disease-free equilibrium and the transcritical bifurcation of periodic orbits that occurs as the basic reproduction number crosses through unity. A cylinder bifurcation at the endemic p...
Chapter
In the theory of impulsive dynamical systems, impulses are often interpreted as idealized discrete jumps associated with a process that is continuous in time but occurs on a negligibly small time scale. The intuition is that one can ignore the transient small-time intermediate dynamics and consider only the change in state. In this chapter, we expl...
Article
This article investigates the hybrid event-triggered and impulsive consensus problems for leaderless and leader-following multiagent systems (MASs) with switching topologies. Based on the state information of neighboring agents at event-triggered moments and impulsive instants, a hybrid event-triggered and impulsive control strategy (HETICS) is des...
Article
This paper studies a class of multi-agent systems (MASs) subject to deception signal and communication interference. The objective of the present work is to establish a flexible and generalized distributed dynamic event-triggered control (DDETC) with impulsive signal to make the investigated MASs achieve secure consensus under redundant signal and...
Article
This paper studies the stability and L1-gain problems for impulsive positive switched systems (IPSS) consisting of both unstable and stable subsystems, and proposes a mode-dependent impulsive control (MDIC) method for the first time. By means of a piecewise linear co-positive Lyapunov function (PLCLF) and using average dwell time (ADT) approach, so...
Article
This paper studies the stochastic dynamic behaviors and pulse control strategy for a vegetation ecosystem with switching parameters. First, a novel stochastic switching ecosystem is built by the variable perturbation, where the parameters are assumed to be time-varying functions. Then, based on the stochastic Ito^ formula and the theory of switched...
Chapter
We study the dynamics resulting from impulsive damping or driving forces applied to a classical rigid pendulum. The impulse effect adjusts the angular velocity at fixed times based on either a point measurement or an average. In the latter, the result is that the impulse effect contains a delayed term. We complete a stability analysis and prove the...
Chapter
This chapter will be devoted to the invariant manifold theory of impulsive differential equations. At the theoretical level, we will assume only that the reference bounded solution has exponential trichotomy, but when we move into computational aspects we will assume that the dynamics are periodic. This will allow us to take advantage of the Floque...
Chapter
This chapter presents analogues of the classical codimension-one bifurcations of flows and maps. Specifically, this includes analogues of the fold (saddle-node), period-doubling, and Hopf (Neimark-Sacker) bifurcation. Additionally, we present the transcritical and pitchfork bifurcations.
Chapter
We prove the existence of a transcritical bifurcation in the pulse-harvested Hutchinson equation. Specifically, we prove the bifurcation with respect to the period of impulse effect. The proof requires a reduction to a non-smooth centre manifold and a careful fixed-point argument.
Chapter
We study bifurcations in a stage-structured predator prey system with pulsed birth. We determine the stability of the extinction equilibrium. Next, we establish the existence and uniqueness of a predator-free periodic solution and determine its stability. We then prove that the latter periodic solution can pass through the extinction equilibrium by...
Chapter
We discuss the existence and smoothness of unstable, stable and centre-stable manifolds, thereby establishing the classical hierarchy of invariant manifolds for impulsive functional differential equations.
Chapter
This chapter contains a proof of the principle of linearized stability for nonlinear impulsive functional differential equations, in addition to some auxiliary results on smooth dependence on initial conditions.
Chapter
In this chapter, we cover existence and uniqueness of solutions, evolutions families, phase-space decompositions and the variation-of-constants formula for linear impulsive functional differential equations.
Chapter
This chapter contains proofs of the existence, smoothness, and reduction principle of centre manifolds for impulsive functional differential equations. We also derive the abstract dynamics equations on the centre manifold.
Chapter
In this chapter, we develop theoretical and computational aspects of Floquet theory for periodic linear systems.
Chapter
In this chapter we will be interested in bifurcations that result from two “non-smooth” phenomena: perturbations in the sequence of impulses andcrossings of discrete delays across impulse times. perturbations in the sequence of impulses and crossings of discrete delays across impulse times.
Chapter
This chapter is devoted to some preliminary background on ordinary impulsive differential equations. This includes existence and uniqueness of solutions and dependence on initial conditions and parameters.
Chapter
This chapter contains the essential theory of linear impulsive differential equations. This includes the variation-of-constants formula, Floquet theory, and stability.
Chapter
In this chapter we will discuss some methods of proving stability for nonlinear systems.
Article
Full-text available
In this paper we analyse some epidemic models by considering a time-varying transmission rate in complex heterogeneous networks. The transmission rate is assumed to change in time, due to a switching signal, and since the spreading of the disease also depends on connections between individuals, the population is modelled as a heterogeneous networks...
Article
Full-text available
Transmission control protocol, in the transport layer of a network, can usually detect congestion after its occurrence. Therefore, designing a robust active queue management (RAQM) is imperative to prevent congestion along with being robust against wireless environment issues such as packet error rate and fading. Moreover, a communication network s...
Article
This paper studies the reliable H∞ control on stochastic delayed Markovian jump systems (SDMJSs) with asynchronous jumped actuator failure and uncertain transition rates (TRs). It is assumed that the actuator failure occurs randomly under a Markov process with its jumping mode different from the system’s one. A generalized functional Itô’s formula...
Article
This paper analyzes the problem of extended dissipative asynchronous filtering for Markov jump T–S fuzzy systems (MJTSFSs) with sensor failures and incomplete measurements. The highlight of this work lies in the fact that we introduce an asynchronous filter (AF) in which mode transition probability matrix (TPM) is non-homogeneous. “Asynchronous” me...
Article
This paper addresses multi-group formation tracking (MGFT) control problems for second-order nonlinear multi-agent systems (MASs) with multiple leaders via distributed impulsive control methods. The objective is to design formation tracking protocols such that agents divide into multiple subgroups with following different leaders while maintaining...
Article
This work deals with the robust D-stability test of linear time-invariant (LTI) general fractional order control systems in a closed loop where the system and/or the controller may be of fractional order. The concept of general implies that the characteristic equation of the LTI closed loop control system may be of both commensurate and non-commens...
Article
Full-text available
In this paper, we study the continuation of solutions to systems of Caputo fractional order differential equations. The continuation is constructed and proven by using the Schauder Fixed Point Theorem. As a necessary prerequisite to the continuation, the existence and uniqueness results generalized for systems are also reviewed.
Article
This paper studies input-to-state stability (ISS) of general nonlinear time-delay systems subject to delay-dependent impulse effects. Sufficient conditions for ISS are constructed by using the method of Lyapunov functionals. It is shown that, when the continuous dynamics are ISS but the discrete dynamics governing the delay-dependent impulses are n...
Article
This study addresses a new approach to generalized dissipativity analysis for fuzzy systems with coupling memory sampled-data (CMSD) control. Based on the information of the time derivative of membership functions (MFs), an improved time-dependent Lyapunov–Krasovskii functional (LKF) is proposed to commendably capture the available information rela...
Article
This paper investigates the general decay stability on systems represented by stochastic functional differential equations with semi-Markovian switching and Lévy noise (SFDEs-SMS-LN). Based on functional Itô’s formula, multiple degenerate Lyapunov functionals and nonnegative semi-martingale convergence theorem, several new pth moment and almost sur...
Article
Full-text available
A time-delayed SIR model with general nonlinear incidence rate, pulse vaccination and temporary immunity is developed. The basic reproduction number is derived and it is shown that the disease-free periodic solution generically undergoes a transcritical bifurcation to an endemic periodic solution as the vaccination coverage drops below a critical l...
Article
A non-smooth Filippov ecosystem with group defense is proposed to investigate the effects of threshold and intermittent control strategy for IPM. The proposed model has been analyzed theoretically using the qualitative analysis techniques related to Filippov non-smooth systems in the first place. In particular, the existence and stability of equili...
Article
A more advanced two-sided looped-functional is adopted for the stability analysis of the linear impulsive system. Compared with existing methods based on functionals relying on Lyapunov’s theorem, the positivity requirement of the functional is relaxed by the looped-functional. The other highlight is the full utilization of information on both the...
Article
Full-text available
This article investigates the stochastic robust finite‐time boundedness problem for semi‐Markov jump uncertain (SMJU) neutral‐type neural networks with distributed and additive time‐varying delays (TDs). To derive less conservative stability criteria, a generalized reciprocally convex combination inequality (RCCI) is first proposed, which includes...
Article
Optimization of power management in plug-in hybrid electric vehicles (PHEVs) with dual-power-source plays a critical role in achieving higher fuel economy and less pollutant emissions. In this study, power management and optimal control strategies in PHEVs have been investigated subject to uncertain driving cycles of individual drivers for particul...
Article
This article studies the nonfragile sampled-data filtering problems for Takagi-Sugeno fuzzy systems with uncertainties and delays. By introducing two delay-product-type terms and other augmented terms, a novel Lyapunov-Krasovskii functional containing more detailed information of time delays is constructed. With the help of some new bounding inequa...
Article
This work concerns the stability and stabilization problems on switched impulsive positive system. A single-inductor dual-output (SIDO) buck converter is employed for investigation and evaluation, which is a typical switched system. Then, considering the complex dynamical behaviour, a novel control scheme applying proportional with asynchronous int...
Article
This paper investigates the general decay stability on systems represented by stochastic functional differential equations with semi-Markovian switching and Lévy noise (SFDEs-sMS-LN). Based on generalized multidimensional Itô’s formula and multiple Lyapunov functions, a new pth moment stability criterion with general decay rate is established. Mean...
Article
This paper investigates the problems of exponential stability and robust H∞ control for a general class of uncertain singular nonlinear switched systems subject to impulsive perturbations. An effective computational method is introduced for designing switched linear feedback controllers, which is based on the novel conditions on the solvability of...
Article
This paper studies a class of quasi-linear impulsive systems of functional differential equations with infinite time delay. By employing the contraction principle, several criteria on uniform stability and asymptotic stability are established. The proposed approach utilizes the idea of averaging instead of the point-wise estimate in the Lyapunov me...
Article
This work mainly concentrates on the finite-time H∞ reliable control for T–S fuzzy systems with aperiodic sampling. By considering the information of the state, an improved Lyapunov–Krasovskii functional (LKF) is structured. Moreover, based on free-weighted method and aperiodic sampling techniques, further criteria are proposed to guarantee that th...
Article
This study focuses on the stabilization analysis for fuzzy systems with the switched sampled-data control. By utilizing the information of the membership functions, an improved time-dependent and fuzzy-membership-function-dependent Lyapunov–Krasovskii functional (LKF) is constructed to commendably capture the available information related to the re...
Article
Full-text available
This paper studies a stochastic predator–prey model for integrated pest management. It shows that the system has a positive solution that exists globally. The long time behavior of the system is investigated, and a condition for the pest to go extinct is given. Then the numerical simulations are carried out to illustrate our theoretical results and...
Article
The almost sure stability of second‐order nonlinear stochastic system with Lévy noise is studied by sliding mode control method. A conventional linear sliding mode surface is first constructed, by employing stochastic analysis technique combined with Lyapunov function method, sufficient conditions are established to ensure the almost sure stability...
Article
This paper studies the synchronization problem of coupled reaction-diffusion neural networks with time-varying delays. A novel pinning impulsive controller is proposed, where distributed delays and discrete delays are taken into account, respectively. By using the Lyapunov–Krasovskii method, the relations among impulsive gains, pinned node numbers,...
Article
This paper studies adaptive control of Markov jump distributed parameter systems via model reference, where a finite dimensional adaptive control approach is used for the distributed parameter systems. In order to obtain the stability criteria, the Galerkin's technique is initially applied to the distributed parameter systems to get a slow system o...
Article
This paper studies impulsive synchronization of a class of nonlinear singular switched complex networks (SSCNs). With the aid of discretized Lyapunov function method and the matrix generalized inverse technique, an impulsive controller is designed, which works on both the slow and the fast state variables to synchronize SSCNs at impulsive instant....
Article
This paper investigates the synchronization of coupled switched neural networks with leakage delay and time-varying delay. The desynchronizing impulses and synchronizing impulses are taken into account in the constructed systems, and they are not required to act simultaneously with the switching behaviors. Moreover, a new concept named mode-depende...
Article
This paper investigates Lyapunov and external stability of Caputo fractional order switching systems. It proves an estimation for the Caputo fractional order derivative of an arbitrary quadratic function whose variable is a function of time with the same differential properties as those given by the most recent smoothness result, and then establish...
Article
This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems is not necessarily required. First, an output derivative-based method and time-varying coordinate transformation are considered...
Article
This paper is concerned with the problem of stochastic synchronization for semi-Markovian jump chaotic Lur’e systems. Firstly, packet dropouts and multiple sampling periods are both considered. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original system is tr...
Article
Fuel cell plug-in hybrid electric vehicles (FC-PHEVs) can have extended range while utilizing cheap grid electricity, but has poor durability of onboard fuel cells due to dynamic loading. In this study, fuel cell durability is enhanced significantly for a novel configuration of FC-PHEVs with three fuel cell stacks through strategic power management...
Article
Full-text available
Based on the centre manifold theorem for impulsive delay differential equations, we derive impulsive evolution equations and boundary conditions associated to a concrete representation of the centre manifold in Euclidean space, as well as finite-dimensional impulsive differential equations associated to the evolution on these manifolds. Though the...