Alexandre Seuret

University of Seville | US · Departamento de Ingeniería de Automática y Sistemas

This article deals with the problem of providing a data-driven solution to the local stabilization of linear systems subject to input saturation. After presenting a model-based solution to this well-studied problem, a systematic method to transform model-driven into data-driven linear matrix inequality (LMI) conditions is presented. This technical...

This paper introduces a data-driven control design approach for power converters modelled as a switched affine system, that guarantees the global stability. Unlike many existing approaches, our contribution does not require a precise identification of a nonlinear model but it rather relies on prior random experimental data, which allows the design...

Este trabajo presenta un método de diseño de control basado en datos para convertidores de potencia que pueden aproximarse como sistemas afines conmutados, proporcionando garantías de estabilidad global. A diferencia de las técnicas convencionales que a priori, requieren una identificación del modelo no lineal, nuestra contribución relaja este requ...

This contribution presents the stabilization of switched affine systems subject to an input delay in the switching signal. The proposed approach extends an existing control Lya-punov function method, which guarantees the stabilization to an a priori defined limit cycle in the case of a constant input delay. The main contribution relies on the defin...

The problem of data‐driven control is addressed here in the context of switched affine systems. This class of nonlinear systems is of particular importance when controlling many types of applications in electronic, biology, medicine and so forth. Still in the view of practical applications, providing an accurate model for this class of systems can...

This paper deals with the problem of providing a data-driven solution to the local stabilization of linear systems subject to input saturation. After presenting a model-based solution to this well-studied problem, a systematic method to transform model-driven into data-driven LMI conditions is presented. This technical solution is demonstrated to b...

The problem of data-driven control is addressed here in the context of switched affine systems. This class of nonlinear systems is of particular importance when controlling many types of applications in electronic, biology, medicine, etc. Still in the view of practical applications, providing an accurate model for this class of systems can be a har...

An important trend about data-driven systems has recently emerged motivated for practical issues, that are the difficulties to identify a model of the plant. In this direction some recent results enhanced the robust control theory to get efficient and relevant solutions. To the best of or knowledge, the existing solutions are rather limited to the...

This letter revisits the $\mathcal {L}_{2}$ stabilization problem for linear systems subject to saturating input and energy-bounded additive disturbance from a data-driven point of view. The backbone of the results resides in writing the stability conditions in a compact dedicated structure allowing to exhibit LMI conditions. Based on the assumpt...

Recently, necessary conditions of stability for time-delay systems based on the handling of the Lyapunov-Krasovskii functional have been studied in the literature giving rise to a new paradigm. Interestingly, the necessary condition for stability developed by Gomez et al. has been proven to be sufficient. It is presented as a simple positivity test...

This paper investigates the stability analysis of time-delay systems through Lya-punov arguments. Using the existence of a complete Lyapunov-Krasovskii functional and relying on the polynomial approximation theory, our main goal is to approximate the complete Lyapunov functional and to take profit of the supergeometric convergence rate of the trunc...

This paper deals with the stability analysis of the reaction–diffusion equation interconnected with a finite-dimensional system. In this situation, stability is no longer straightforward to assess, and one needs to look for dedicated tools to provide accurate numerical stability tests. Here, the objective is to provide a Lyapunov analysis leading t...

This work is dedicated to the stability analysis of time-delay systems with a single constant delay using the Lyapunov-Krasovskii theorem. This approach has been widely used in the literature and numerous sufficient conditions of stability have been proposed and expressed as linear matrix inequalities (LMI). The main criticism of the method that is...

We propose a distributed hybrid observer for a sensor network where the plant and local observers run in continuous time and the information exchange among the sensing nodes is sampled-data. Process disturbances, measurement noise and communication noise are considered, and we prove that under some necessary detectability assumptions the observer g...

Recently, sufficient conditions of stability or instability for time-delay systems have been proven to be necessary. In this way, a remarkable necessary and sufficient condition has then been developed by Gomez et al. It is presented as a simple test of positive definiteness of a matrix issued from the Lyapunov matrix. In this paper, an extension o...

This chapter deals with the stability analysis of the reaction-diffusion subject to dynamic boundary conditions. More particularly, the objective is to propose a linear matrix inequality criterion which ensures the stability of such infinite-dimensional system. By the use of Fourier-Legendre series, the Lyapunov functional is split into an augmente...

This book is an extension of my Ph.D. thesis which is devoted to the methods for the stability (dissipativity) analysis and stabilization of linear systems with non-trivial distributed delays based on the application of the Liapunov- Krasovski\u{i} functional (LKF) approach. https://arxiv.org/abs/2204.08353

This chapter deals with the robust stability analysis of a coupled system made up of an uncertain ordinary differential system and a string equation. The main result states the robust exponential stability of this interconnected system subject to polytopic uncertainties. The Lyapunov theory transforms the stability analysis into the resolution of a...

With a continuous-time formulation of the multihop decomposition, we propose a distributed hybrid observer for a sensor network where the plant and local observers run in continuous time and the information exchange among the sensing nodes is sampled-data. Process disturbances, measurement noise and communication noise are considered, and we prove...

We first study stabilization of heat equation with globally Lipschitz nonlinearity. We consider the point measurements with constant delay and use spatial decomposition. Inspired by recent developments in the area of ordinary differential equations (ODEs) with time-delays, for the stability analysis, we suggest an augmented Lyapunov functional depe...

This paper focuses on the design of both periodic time- and event-triggered control laws of switched affine systems using a hybrid dynamical system approach. The novelties of this paper rely on the hybrid dynamical representation of this class of systems and on a free-matrix min-projection control, which relaxes the structure of the usual Lyapunov...

Observer design for linear systems with aperiodic sampled-data measurements is addressed. To solve this problem, a novel hybrid observer is designed. The main peculiarity of the proposed observer consists of the use of two output injection terms, one acting at the sampling instants and one providing an intersample injection. The error dynamics are...

This paper investigates the stability of a linear finite‐dimensional system interconnected to a single delay operator. From robust approaches, to derive delay‐dependent frequency tests, a characterization of the delay behavior is required. Based on approximation methods, one describes the transported signal by lumped parameters. More precisely, by...

This paper addresses the design of a sampled-data model predictive control (MPC) strategy for linear parameter-varying (LPV) systems. A continuous-time prediction model, which takes into account that the samples are not necessarily periodic and that plant parameters vary continuously with time, is considered. Moreover, it is explicitly assumed that...

Observer design for linear systems with aperiodic sampled-data measurements is addressed. To solve this problem, a novel hybrid observer is designed. The main peculiarity of the proposed observer consists of the use two output injection terms, one acting at the sampling instants and one providing an intersample injection. The error dynamics are aug...

This paper addresses the problem of synchronizing a group of interacting discrete-time switched affine systems with centralized control laws. Two different state-dependent control laws are proposed, based on recent literature on switched affine systems and are evaluated on an academical example with a multi-agent system.

This paper deals with discrete time-varying systems with state-delayed and saturating actuators. A robust state feedback control gain is designed through convex methods ensuring the local stability of the time-varying system with interval time-varying state delay. The estimate of the set of admissible initial conditions is characterized by three co...

This article presents an observer‐based event‐triggering strategy for systems with slope‐restricted nonlinearities that depend on the state. Both the emulation and codesign problems are addressed. To avoid Zeno behavior, a minimum dwell time is considered. By using a looped‐functional approach and the cone‐bounded properties of the nonlinearity, su...

In this paper, we investigate the observation and stabilization problems for a class of linear time-invariant systems, subject to unknown states, and network constraints, including time-delays and event-triggered sampling. A new type of event-triggered mechanism is proposed based on an appropriate storage function, which is chosen larger than the d...

This article focuses on the design of a robust switching control law for uncertain switched affine systems in the discrete‐time domain. More precisely, a novel control law is introduced whose parameters result from an optimization problem, aiming at reducing the volume of the attractive and invariant set, where the solutions to the closed‐loop syst...

This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints (IQCs) and expressed in terms of two linear matrix inequalities with a moderate computational burden. The IQCs are...

This paper proposes a framework to assess the stability of an Ordinary Differential Equation (ODE) which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints (IQCs) and expressed in terms of two linear matrix inequalities with a moderate computational burden. The IQ...

We address distributed estimation of the state of a linear plant by a set of agents. The problem is cast in a setting where the communication capabilities of an agent might be deactivated from time to time, due to failures in the communication devices or malicious attacks. An observer architecture is proposed to achieve our estimation goal, based o...

This paper deals with the stabilization of switched affine systems. The particularities of this class of nonlinear systems are first related to the fact that the control action is performed through the selection of the switching mode to be activated and, second, to the problem of providing an accurate characterization of the set where the solutions...

In this paper, a numerical analysis to assess stability of time-delay systems is investigated. The proposed approach is based on the design of a finite-dimensional approximation of the infinite-dimensional space of solutions of the system. Indeed, based on the dynamical coefficients on the sequence made of the first Legendre polynomials, the origin...

This paper deals with the stabilization of high frequency DC-DC converters. These kind of systems can be modeled as switched affine systems subject to a periodic sampled-data control implementation. The dynamics of these systems is expressed using the δ-operator in order to cope with high frequency switching control constraints. The novelties of th...

By taking advantage of properties of the Laguerre polynomials, we propose a new inequality called Bessel–Laguerre integral inequality, which can be applied to stability analysis of linear systems with infinite distributed delays and with general kernels. The matrix corresponding to the system without the delayed term or the matrix corresponding to...

This chapter deals with the stability analysis of linear systems subject to fast-varying delays. The main result is the derivation of a delay-dependent reciprocally convex lemma allowing a notable reduction of the conservatism of the resulting stability conditions with the introduction of a reasonable number of decision variables. Several examples...

This article deals with the stability analysis of a drilling pipe controlled by a PI controller. The model is a coupled ordinary differential equation/partial differential equation (PDE) and is consequently of infinite dimension. Using recent advances in time-delay systems, we derive a new Lyapunov functional based on a state extension made up of p...

This book contains advances on the theory and applications of time-delay systems with particular focus on interconnected systems. The methods for stability analysis and control design are based on time-domain and frequency-domain approaches, for continuous-time and sampled-data systems, linear and nonlinear systems. This volume is a valuable source...

We present a new approach for the stability analysis of linear coupled differential-difference systems (CDDS) with a general distributed delay. The distributed delay term in this note can contain any $\fL^{2}$ function which is approximated via a class of elementary functions including polynomial, trigonometric and exponential functions etc. Thro...

This paper addresses the stability of continuous-time nonlinear rational systems subject to aperiodically sampled-data control action. By the use of differential algebraic representations and a looped-functional approach to deal with aperiodic sampling, LMI conditions that ensure the regional asymptotic stability of the origin of the closed-loop sy...

This paper deals with the stability analysis of a drilling pipe controlled by a PI controller. The model is a coupled ODE / PDE and is consequently of infinite dimension. Using recent advances in time-delay systems, we derive a new Lyapunov functional based on a state extension made up of projections of the Riemann coordinates. First, we will provi...

This paper addresses the problem of encircling and tracking a moving target with a fleet of unicycle-like vehicles. A new control law is developed to steer the vehicles to an evenly spaced formation along a circumference, the center of which tracks the motion of the target. The strategy proposed relies only on the relative positions of the agents w...

This paper presents an observer-based event-triggered strategy for linear systems subject to input cone-bounded nonlinearities. Both the emulation and co-design problems are addressed. Considering a Lyapunov approach and the cone-bound property of the input nonlinearity, sufficient conditions based on linear matrix inequalities are derived to ensur...

This paper addresses the local stability analysis problem for linear systems subject to input saturation and state delay. Thanks to the construction of a Lyapunov-Krasovskii functional associated to Legendre polynomials and the use of generalized sector conditions, sufficient linear matrix inequalities (LMIs) are derived to guarantee the local stab...

This study provides an overview and in-depth analysis of recent advances in stability of linear systems with time-varying delays. First, recent developments of a delay convex analysis approach, a reciprocally convex approach and the construction of Lyapunov–Krasovskii functionals are reviewed insightfully. Second, in-depth analysis of the Bessel–Le...

This article proposes a distributed algorithm for the compact deployment of robots, using both distanceand angular-based arguments in the controllers' design. Our objective is to achieve a configuration maximizing the coverage of the environment while increasing the graph's connectivity. First, we provide: (i) a dispersion protocol guaranteeing con...

Time-dependent Lyapunov functionals appeared to be very efficient for sampled-data systems. Recently, new Lyapunov functionals were constructed for sampled-data control in the presence of a constant input delay. The construction of these functionals was based on Wirtinger's inequality leading to simplified and efficient stability conditions in term...

The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time‐delay systems, an exact stability result is firstly derived using pole locations. Then, based on the small‐gain theorem and on the quadratic separation framework, some robus...

Various efficient matrix inequalities have recently been proposed to deal with the stability analysis of linear systems with time-varying delays. This paper provides more insights on the relationship between some of them. We present an equivalent formulation of Moon et al.’s inequality, allowing us to discover strong links not only with the most re...

We first propose a nonsmooth hybrid invariance principle with relaxed conditions stemming from the fact that flowing solutions evolve only in the tangent cone, and complete jumping solutions cannot jump ouside the jump and flow sets. We then show an application consisting in the design of eventtriggered rules to stabilize a class of uncertain linea...

This paper deals with the stabilization of an anti-stable string equation with Dirichlet actuation where the instability appears because of the uncontrolled boundary condition. Then, infinitely many unstable poles are generated and an infinite dimensional control law is therefore proposed to exponentially stabilize the system. The idea behind the c...

This paper deals with the stabilization of an anti-stable string equation with Dirichlet actuation where the instability appears because of the uncontrolled boundary condition. Then, infinitely many unstable poles are generated and an infinite dimensional control law is therefore proposed to exponentially stabilize the system. The idea behind the c...

This paper deals with the stability of discrete‐time networked systems with multiple sensor nodes under dynamic scheduling protocols. Access to the communication medium is orchestrated by a weighted try‐once‐discard or by an independent and identically‐distributed stochastic protocol that determines which sensor node can access the network at each...

In this paper, the design of a static feedback gain for a linear system subject to an input delay is studied. This synthesis is based on a stability analysis conducted using Lyapunov-Krasovskii theorem and Bessel-Legendre inequalities expressed in terms of LMIs. Some bilinear non-convex matrix inequalities are obtained to go from analysis to synthe...

The chapter deals with the design of Event-Triggered rules to stabilize a class of uncertain linear control systems where the uncertainty affecting the plant is assumed to be norm-bounded. The event-triggering rule uses only local information, namely the control updates are generated only by the output signals available to the controller. The propo...

This article deals with the stability analysis of a drilling system which is modelled as a coupled ordinary differential equation / string equation. The string is damped at the two boundaries but leading to a stable open-loop system. The aim is to derive a linear matrix inequality ensuring the exponential stability with a guaranteed decay-rate of t...

The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived using pole locations. Then, based on the Small-Gain theorem and on the Quadratic Separation framework, some robus...

This paper deals with the stability analysis of time delay systems based on continuous-time approach. The originality of the present paper relies on the construction of several models for a same time-delay systems using the interconnection of an ordinary differential equation and a transport partial differential equation. The stability analysis is...

This paper deals with the problem of distributedly estimating the state of an LTI plant through an interconnected network of agents. The proposed approach results in an observer structure that incorporates consensus among the agents and that can be distributedly designed, achieving a robust solution with a good estimation performance. The developed...

This paper deals with the stability analysis of a system of finite dimension coupled to a vectorial transport equation. We develop here a new method to study the stability of such a system, coupling ordinary and partial differential equations, using linear matrix inequalities led by the choice of an appropriate Lyapunov functional. To this end, we...

In this paper, the design of a static feedback gain for a linear system subject to an input delay is studied. This synthesis is based on a stability analysis conducted using Lyapunov-Krasovskii theorem and Bessel-Legendre inequalities expressed in terms of LMIs. Some bilinear non-convex matrix inequalities are obtained to go from analysis to synthe...

In this paper, new sufficient stability conditions for the asymptotic stability of time-delay systems are presented using the quadratic separation approach. The time-delay system is modeled as an interconnected closed-loop system involving a linear transformation and delay-dependent functions, representing the uncertainties brought by the delay. Th...

This paper presents a new dissipative analysis method for linear coupled differential-difference systems (CDDS) with general distributed delays in both state and output equation. More precisely, the distributed delay terms under consideration can contain any $\fL_{\mathit{2}}$ functions which are approximated via a broader class of functions in com...

This paper investigates synchronization in complex dynamical networks (CDNs) with interval time-varying delays. The CDNs are representative of systems composed of a large number of interconnected dynamical units, and for the purpose of the mathematical analysis, the leading work is to model them as graphs whose nodes represent the dynamical units....

As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov functional technique. Inspired from recent developments in the area of time delay systems, a new methodology to study...

As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov functional technique. Inspired from recent developments in the area of time delay systems, a new methodology to study...

This paper addresses the stability problem of linear systems with a time-varying delay. Hierarchical stability conditions based on linear matrix inequalities are obtained from an extensive use of the Bessel inequality applied to Legendre polynomials of arbitrary orders. While this inequality has been only used for constant discrete and distributed...

The paper presents an observer-based event-triggered control strategy for linear systems subject to input cone-bounded nonlinearities by using only available measurable variables. Sufficient conditions based on linear matrix inequalities are proposed to ensure the asymptotic stability of the closed loop and the avoidance of Zeno behavior in an emul...

This article investigates the asymptotic stability of impulsive delay dynamical systems (IDDS) by using the Lyapunov–Krasovskii method and looped-functionals. The proposed conditions reduce the conservatism of the results found in the literature by allowing the functionals to grow during both the continuous dynamics and the discrete dynamics. Suffi...

This paper deals with the exponential stabilization of a time-delay system with an average of the state as the output. A general stability theorem with a guaranteed exponential decay-rate based on a Wirtinger-based inequality is provided. Variations of this theorem for synthesis of a controller or for an observer-based control is derived. Some nume...

This paper deals with the problem of encircling a moving target with a fleet of unicycle-like vehicles. A new control law is developed to steer the vehicles to a circular formation whose center tracks the target. The novelty of this paper lies in the fact that the control law only uses the velocity of the target and the relative positions of the ag...