Xinzhi Liu

University of Waterloo | UWaterloo · Department of Applied Mathematics

This article considers exponential stabilization (ES) of switched interval type‐2 (SIT2) fuzzy systems with asynchronous switching control. The SIT2 fuzzy system switches from one mode to another according to transition probabilities (TPs). A general SIT2 fuzzy quantized event‐triggered output controller (QETOC) is designed to save the communicatio...

An ecosystem with anti-predator behavior is established in both deterministic and stochastic environments. This means that adult prey could attack weak predators. Bifurcation diagrams are used to analyze the deterministic case, while a tool called the most probable trajectory, defined by the spatial extreme point of the probability density function...

This paper introduces a switched SQWVEAIR (Susceptible, Quarantined, Weak, Vaccinated, Exposed, Asymptomatic, Infected, and Recovered) epidemic model considering changing contact rates in an infected society. It also takes into account the presence of vulnerable individuals as frontiers in vaccination, recognizing their societal importance. The qua...

Resilient distance regulation process is significantly essential in intelligent transportation systems with connected automated vehicles (CAVs), due to vulnerability of communication links within the vehicles of a platoon. On the other hand, time varying distance regulation process is usually ignored in adaptive cruise control procedures, which yie...

The article investigates the practical finite-time stability (PFTS) issue of continuous-time nonlinear systems with disturbance. Some extended Lyapunov results for semi-global/global PFTS, including attraction domain and settling time estimation are obtained based on a relaxed Lyapunov condition. Especially, for systems with stabilizing delayed imp...

This study investigates finite-time observability of probabilistic logical control systems (PLCSs) under three definitions (i.e., finite-time observability with probability one, finite-time single-input sequence observability with probability one, and finite-time arbitrary-input observability with probability one). The authors adopt a parallel exte...

Resilient control and cyber security are of great importance for multiagent systems (MASs) due to the vulnerability during their coordination through information interaction among agents. Unexpected cyber-attacks on a single agent can spread quickly and can affect critically the safety and the performance of the system. This paper proposes a distri...

Under the framework of a hybrid-index model, this paper investigates safe control problems of state-dependent random impulsive logical control networks (RILCNs) on both finite and infinite horizons, respectively. By using the ξ-domain method and the constructed transition probability matrix, the necessary and sufficient conditions for the solvabili...

This article presents a self-triggered impulsive framework for group consensus of multiagent systems (MASs). Two types of self-triggered delayed impulsive control schemes are proposed to regulate impulsive protocols with sensing and actuation delays, respectively. Here, the Lyapunov-based and comparison-system-based approaches are constructed to ac...

In the realm of Intelligent Transportation Systems (ITSs), ensuring the safety and stability of connected automated vehicles (CAVs) is of paramount importance due to their susceptibility to vulnerabilities in interactions. The potential for system-wide disruption stemming from a cyber-attack on the leader underscores this need. Therefore, this pape...

This paper studies scaled consensus problems of multi-agent systems under fixed and switched topologies. Firstly, the scaled consensus protocols are designed for solving consensus problems of multi-agent systems under fixed topologies. Secondly, the scaled consensus problems of multi-agent systems under switching topologies are considered. Thirdly,...

This paper investigates generalized synchronization of drive–response complex-valued dynamical networks (CVDNs) with time-delay. An effective hybrid controller is designed in the complex field to construct response complex-valued networks for achieving generalized synchronization with drive delayed CVDNs. By employing the Lyapunov method in the com...

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...

This paper studies the leader-following flocking control problem of unmanned aerial vehicle (UAV) systems by integrating a hybrid impulsive framework, where the full exchange of information only occurs at each impulsive time instant. It is also shown that the overall stability can be achieved via impulses while the continuous dynamics remains desta...

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...

This paper studies the flocking control problem of heterogenous multi-agent systems with multi-group tracking various virtual leaders. In particular, hybrid impulsive control protocol is designed based on the partially discrete agents’ information transmission, where full information exchange only occurs at each impulsive time instant. Meanwhile, b...

This article investigates the problem of exponential bipartite synchronization of fractional-order multilayer signed networks via hybrid impulsive control. First, the mathematical model of the networks is established by integrating the fractional dynamics of nodes, the multilayer network edges, and the positive and negative weights (antagonistic re...

The issue of finite-time synchronization (FTS) of complex dynamical networks (CDNs) is investigated in this article. A new control strategy coupling weak finite-time control and finite times of impulsive control is proposed to realize the FTS of CDNs, where the impulses are synchronizing and restricted by maximal impulsive interval (MII), differing...

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...

This paper deals with systems of stochastic differential equations with piecewise constant arguments (SEPCA), where the arguments are of a delay type. To reduce the complexity of the proposed system, SEPCA is treated as a hybrid (or switched) system. This effective approach motivates the applicability of the classical theory of ordinary stochastic...

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...

Previously, impulses were used to model abrupt changes in dynamic biological systems. This paper introduces a hybrid-index model that can characterize instantaneity of the impulsive behavior more effectively, compared with the existing impulsive Boolean network models. Using the hybrid-index model, we investigate the set stabilization of Boolean co...

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...

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...

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.

This paper investigates the master–slave synchronization problem of complex-valued neural networks via event-triggered pinning impulsive control (ETPIC). A time-delayed pinning impulsive controller is proposed based on three levels of event-triggered conditions. By employing the Lyapunov functional method and differential inequality techniques, suf...

Based on the theories of inertial systems, a second-order accelerated neurodynamic approach is designed to solve a distributed convex optimization with inequality and set constraints. Most of the existing approaches for distributed convex optimization problems are usually first-order ones, and it is usually hard to analyze the convergence rate for...

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...

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...

This paper studies the consensus problem of complex-valued multi-agent systems. A complex-valued hybrid consensus protocol with time-delay is proposed, where different network topologies in both continuous-time intervals and impulsive instants are also taken into account. By employing the method of Lyapunov functionals, delay dependent sufficient c...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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.

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...

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.

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.

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.

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.

In this chapter, we develop theoretical and computational aspects of Floquet theory for periodic linear systems.

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.

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.

This chapter contains the essential theory of linear impulsive differential equations. This includes the variation-of-constants formula, Floquet theory, and stability.

In this chapter we will discuss some methods of proving stability for nonlinear systems.

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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...