Finite-Time H∞ Control of Switched Nonlinear Systems under State-Dependent Switching

This paper investigates the finite-time H∞ control problem of switched nonlinear systems via state-dependent switching and state feedback control. Unlike the existing approach based on time-dependent switching strategy, in which the switching instants must be given in advance, the state-dependent switching strategy is used to design switching signals. Based on multiple Lyapunov-like functions method, several criteria for switched nonlinear systems to be finite-time H∞ control are derived. Finally, a numerical example with simulation results is provided to show the validity of the conclusions.

Stabilization Control for Linear Switching Stochastic Systems Against Time-Delay in Communication Channel

The paper is concerned with stabilization problem for a class of stochastic switching systems with time-delay in the detection of switching signal. By using binomial model,Poisson process,and Wiener process to describe time-delay, switching signal, and exogenous disturbance, respectively, the system under investigation is entirely set in a stochastic framework. The influence of the random time-delay is combined into reconstructing the switching signal of overall closed-loop system and changes the distribution property of switching points. Therefore,based on the asymptotical behaviors of Poisson processes and Wiener processes,the almost surely exponential stability conditions are established. Furthermore,a design methodology is posed for solving the stabilization control.

Error reachable set based stabilization of switched linear systems with bounded peak disturbances

This paper investigates the error reachable set based stabilization problem for a class of discrete-time switched linear systems with bounded peak disturbances under persistent dwell-time(PDT)constraint.A double-clockdependent control scheme is presented that can split the disturbed switched system into a nominal system and an error system,and assign to each system a controller scheduled by a clock.A necessary and sufficient convex stability criterion is presented for the nominal system,and is further extended to the stabilization controller design with a nominal clock.In the presence of bounded peak disturbances,another stabilization controller with an error clock is developed for the error system,with the purpose of‘‘minimizing’’the reachable set of the error system by the ellipsoidal techniques.It is demonstrated that the disturbed system is also globally exponentially stable in the sense of converging to an over approximation of the reachable set of the error system,i.e.,a union of a family of bounding ellipsoids,that can also be regarded as the cross section of a tube containing the trajectories of the disturbed system.Two numerical examples are provided to verify the effectiveness of the developed results.

Robust Controller Design of a Class of Uncertain Switched Fuzzy Systems with Delays

The robust control problem for a class of uncertain switched fuzzy systems with delays is investigated. Firstly,the model of the switched fuzzy system is presented and the parallel distributed compensation( PDC) technology is employed to design fuzzy controllers. Then, based on the convex combination method, a sufficient condition for robust stabilization in terms of linear matrix inequalities( LMIs) is obtained and a switching law is presented.Meanwhile,the Lyapunov-Krasovskii functional is taken to deal with time varying delays. Moreover,an algorithm is applied to finding a solution for a group of convex combination coefficient. Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.

Distributed H2/H∞ Filter Design for Discrete-Time Switched Systems

This paper addresses an infinite horizon distributed H2/H∞ filtering for discrete-time systems under conditions of bounded power and white stochastic signals. The filter algorithm is designed by computing a pair of gains namely the estimator and the coupling. Herein, we implement a filter to estimate unknown parameters such that the closed-loop multi-sensor accomplishes the desired performances of the proposed H2 and H∞ schemes over a finite horizon. A switched strategy is implemented to switch between the states once the operation conditions have changed due to disturbances. It is shown that the stability of the overall filtering-error system with H2/H∞ performance can be established if a piecewise-quadratic Lyapunov function is properly constructed. A simulation example is given to show the effectiveness of the proposed approach.

Adaptive Consensus of Non-Strict Feedback Switched Multi-Agent Systems With Input Saturations

This paper considers the leader-following consensus for a class of nonlinear switched multi-agent systems(MASs)with non-strict feedback forms and input saturations under unknown switching mechanisms.First,in virtue of Gaussian error functions,the saturation nonlinearities are represented by asymmetric saturation models.Second,neural networks are utilized to approximate some unknown packaged functions,and the structural property of Gaussian basis functions is introduced to handle the non-strict feedback terms.Third,by using the backstepping process,a common Lyapunov function is constructed for all the subsystems of the followers.At last,we propose an adaptive consensus protocol,under which the tracking error under arbitrary switching converges to a small neighborhood of the origin.The effectiveness of the proposed protocol is illustrated by a simulation example.

Global Practical Stabilization of Discrete-Time Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid

This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via statedependent switching rules.Several attempts have been made to solve this problem via different types of a common quadratic Lyapunov function and an ellipsoid.These classical results require either the quadratic Lyapunov function or the employed ellipsoid to be of the centralized type.In some cases,the ellipsoids are defined dependently as the level sets of a decentralized Lyapunov function.In this paper,we extend the existing results by the simultaneous use of a general decentralized Lyapunov function and a decentralized ellipsoid parameterized independently.The proposed conditions provide less conservative results than existing works in the sense of the ultimate invariant set of attraction size.Two different approaches are proposed to extract the ultimate invariant set of attraction with a minimum size,i.e.,a purely numerical method and a numerical-analytical one.In the former,both invariant and attractiveness conditions are imposed to extract the final set of matrix inequalities.The latter is established on a principle that the attractiveness of a set implies its invariance.Thus,the stability conditions are derived based on only the attractiveness property as a set of matrix inequalities with a smaller dimension.Illustrative examples are presented to prove the satisfactory operation of the proposed stabilization methods.

H∞ Tracking Control for Switched LPV Systems With an Application to Aero-Engines

This paper focuses on the H_∞ model reference tracking control for a switched linear parameter-varying(LPV)model representing an aero-engine. The switched LPV aeroengine model is built based on a family of linearized models.Multiple parameter-dependent Lyapunov functions technique is used to design a tracking control law for the desirable H_∞ tracking performance. A control synthesis condition is formulated in terms of the solvability of a matrix optimization problem.Simulation result on the aero-engine model shows the feasibility and validity of the switching tracking control scheme.

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

Adaptive fuzzy tracking control for a class of switched MIMO nonlinear systems

An adaptive fuzzy tracking control scheme is presented for a class of switched multi-input-multi-output (MIMO) nonlinear systems with disturbances under arbitrary switching. Adaptive fuzzy systems are employed to approximate the unknown functions on line,and a systematic framework for adaptive fuzzy tracking controller design is given,where the dynamic surface control (DSC) approach is used to solve the problem of "explosion of complexity"in the backstepping design procedure. According to the common Lyapunov function theory,it is proved that the proposed controller can guarantee the boundedness of all signals in the closed loop system. Finally,the simulation results demonstrate the validity of the control approach.

Robust H_∞ output feedback controller design for linear uncertain discrete-time switched systems via state reset

This paper studies the problem of robust H∞ output feedback controller via state-reset for linear uncertain discrete-time switched systems. Using multiple Lyapunov functions,we address an output feedback controller under arbitrary switching signals,in which an H∞ performance is required. The condition is shown in the form of linear matrix inequalities (LMI). Finally,a numerical example shows the feasibility of the designed controller and illustrates that the new sufficient condition has lower conservation and more optimized H∞ tfperformance.

Output Feedback Robust H_(∞) Control for Discrete 2D Switched Systems

The two-dimensional(2-D)system has a wide range of applications in different fields,including satellite meteorological maps,process control,and digital filtering.Therefore,the research on the stability of 2-D systems is of great significance.Considering that multiple systems exist in switching and alternating work in the actual production process,but the system itself often has external perturbation and interference.To solve the above problems,this paper investigates the output feedback robust H_(∞)stabilization for a class of discrete-time 2-D switched systems,which the Roesser model with uncertainties represents.First,sufficient conditions for exponential stability are derived via the average dwell time method,when the system’s interference and external input are zero.Furthermore,in the case of introducing the external interference,the weighted robust H_(∞)disturbance attenuation performance of the underlying system is further analyzed.An output feedback controller is then proposed to guarantee that the resulting closed-loop system is exponentially stable and has a prescribed disturbance attenuation levelγ.All theorems mentioned in the article will also be given in the form of linear matrix inequalities(LMI).Finally,a numerical example is given,which takes two uncertain values respectively and solves the output feedback controller’s parameters by the theorem proposed in the paper.According to the required controller parameter values,the validity of the theorem proposed in the article is compared and verified by simulation.

Stabilization of Slowly Varying Switched Linear Systems

The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.

Output Feedback Controller Design for Discrete-time Switched Singular Systems

This paper is concerned with the problems of robust admissibility and static output feedback( SOF)stabilization for a class of discrete-time switched singular systems with norm-bounded parametric uncertainties.The objective is to design a suitable robust SOF controller guaranteeing the regularity,causality and asymptotic stability of the resulting closed-loop system under arbitrary switching laws. Based on the basic matrix inequality sufficient condition for checking the admissibility of switched singular systems,together with some matrix inequality convexifying techniques,the SOF controller synthesis is developed for the underlying systems. It is shown that the controller gains can be obtained by solving a set of strict linear matrix inequalities( LMIs). A simulation example is given to show the effectiveness of the proposed method.

Call for Papers:Special Issue on "Recent Advances and New Directions in Switched Control Systems" ——Jounal of Control Theory and Application

Recently, switched control systems have been attracting much attention m the control community because the problems are not only academically challenging for the inherent complexity, but also of practical importance due to its wide ranges of applications in nature, engineering, and social sciences.

Event-Triggered Finite-Time <i>H</i>_∞Control for Switched Stochastic Systems

This paper investigates the problem of event-triggered finite-time H∞ control for a class of switched stochastic systems. The main objective of this study is to design an event-triggered state feedback H∞ controller such that the resulting closed-loop system is finite-time bounded and satisfies a prescribed H∞ level in some given finite-time interval. Based on stochastic differential equations theory and average dwell time approach, sufficient conditions are derived to ensure the finite-time stochastic stability with the prescribed H∞ performance for the relevant closed-loop system by employing the linear matrix inequality technique. Finally, the desired state feedback H∞ controller gain matrices can be expressed in an explicit form.

On the leader-following exponential consensus of discrete-time linear multi-agent systems over jointly connected switching networks

The leader-following asymptotic consensus problem for general discrete-time linear multi-agent systems over jointly con-nected switching networks was solved about a decade ago.Recently,the leader-following exponential consensus was further established using the so-called Krasovskii-LaSalle theorem for a class of discrete-time linear switched systems.But this method involves some advanced concepts such as the weak zero-state detectability of some limiting system.In this paper,we offer a simpler solution to the leader-following exponential consensus problem for general discrete-time linear multi-agent systems over jointly connected switching networks.After converting the solvability of the problem to the establishment of the exponential stability for a class of discrete-time linear switched systems,we first show that this class of linear switched systems is uniformly completely observable.Then,we further conclude that the uniform complete observability for this class of linear switched systems implies the exponential stability for the same class of linear switched systems,thus leading to the solution of the leader-following exponential consensus problem.Moreover,our approach also gives rise to an explicit characterization of the exponential convergence rate of the leader-following consensus problem.

H-infinity filtering for discrete-time switched linear systems under arbitrary switching

This paper is concerned with the problem of H-infinity filtering for discrete-time switched linear systems under arbitrary switching laws.New sufficient conditions for the solvability of the problem are given via switched quadratic Lyapunov functions.Based on Finsler's lemma,two sets of slack variables with special structure are introduced to provide extra degrees of freedom in optimizing the guaranteed H-infinity performance.Compared to the existing methods,the proposed one has better performances and less conservatism.An example is given to illustrate its effectiveness.

Stability of Switched Positive Descriptor Systems with Average Dwell Time Switching

In this paper, the problems of stability for a class of switched positive descriptor systems(SPDSs)with average dwell time(ADT) switching are investigated. First, based on the equivalent switched system and the properties of the projector matrix, sufficient stabilities are given for the underlying systems in both continuoustime and discrete-time contexts. Then, a sufficient stability condition for the SPDS with both stable and unstable subsystems is obtained. The stability results for the SPDSs are represented in terms of a set of linear programmings(LPs) by the multiple linear co-positive Lyapunov function(MLCLF) approach. Finally, three numerical examples are given to illustrate the effectiveness of the obtained theoretical results.