Exponential quasi‐(Q,S,R)‐dissipativity and practical stability for switched nonlinear systems

In this paper, the problems of exponential quasi‐(Q,S,R)‐dissipativity and practical stability analysis for a switched nonlinear system are addressed. First, the concept of exponential quasi‐(Q,S,R)‐dissipativity for switched nonlinear systems without requiring the exponential quasi‐(Q,S,R)‐dissipativity property of each subsystem is proposed. Then, we show that an exponentially quasi‐(Q,S,R)‐dissipative switched nonlinear system is practically stable. Second, this exponential quasi‐(Q,S,R)‐ dissipativity property for a switched nonlinear system is obtained by the design of a state‐dependent switching law. Third, a composite state‐dependent switching law is designed to render the feedback interconnection of switched nonlinear systems exponentially quasi‐(Q,S,R)‐dissipative. This switching law allows interconnected switched nonlinear systems to switch asynchronously. Finally, the effectiveness of the results is verified by a numerical example.     

Exponentially incremental dissipativity for nonlinear stochastic switched systems

ABSTRACT

In this paper, we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state-dependent switching law and multiple Lyapunov functions approach. Specifically, using incremental supply rate as well as a state dissipation inequality in expectation, a stochastic version of exponentially incremental dissipativity is presented. The sufficient conditions for nonlinear stochastic switched systems to be exponentially incrementally dissipative are given by the designed state-dependent switching law. Furthermore, the extended Kalman–Yakubovich–Popov conditions are derived by using two times continuously differentiable storage functions. Moreover, the incremental stability conditions in probability for nonlinear stochastic switched systems are derived based on exponentially incremental dissipativity. The exponentially incremental dissipativity is preserved for the feedback-interconnected nonlinear stochastic switched systems with the composite state-dependent switching law; meanwhile, the incremental stability in probability is preserved under some certain conditions. A numerical example is given to illustrate the validity of our results.     

Exponentially incremental (Q,S, R)-dissipativity and incremental stability for switched time-varying nonlinear systems

Exponentially incremental (Q,S,R)-dissipativityand incremental stability for switched time-varying nonlinear systems are studied whose subsystems are not required to be exponentially incrementally (Q,S,R)-dissipative. The sufficient conditions for switched time-varying nonlinear systems to be exponentially incrementally (Q,S,R)-dissipative are presented by the design of state-dependent switching laws. Incremental stability for switched time-varying nonlinear systems are derived based on exponentially incremental (Q,S,R)-dissipativity. Exponentially incremental (Q,S,R)-dissipativity is shown to be preserved under feedback interconnection by the design of a composite state-dependent switching law. Two simulation examples are provided to show the effectiveness of the proposed approaches.     

Incremental passivity and output regulation for switched nonlinear systems

This paper studies incremental passivity and global output regulation for switched nonlinear systems, whose subsystems are not required to be incrementally passive. A concept of incremental passivity for switched systems is put forward. First, a switched system is rendered incrementally passive by the design of a state-dependent switching law. Second, the feedback incremental passification is achieved by the design of a state-dependent switching law and a set of state feedback controllers. Finally, we show that once the incremental passivity for switched nonlinear systems is assured, the output regulation problem is solved by the design of global nonlinear regulator controllers comprising two components: the steady-state control and the linear output feedback stabilising controllers, even though the problem for none of subsystems is solvable. Two examples are presented to illustrate the effectiveness of the proposed approach.     

Exponential dissipativity analysis of discrete‐time switched memristive neural networks with actuator saturation via quasi‐time‐dependent control

The dissipativity of discrete‐time switched memristive neural networks with actuator saturation is considered in this paper. By constructing a quasi‐time‐dependent Lyapunov function, sufficient conditions are obtained to guarantee the exponential stability and exponential dissipativity for the closed‐loop system with mode‐dependent average dwell time switching. Furthermore, the exponential H_∞ performance of discrete‐time switched memristive neural networks is also analyzed, while the quasi‐time‐dependent controller and observer gains of the desired exponential dissipative and H_∞ performance can be calculated from linear matrix inequalities. Finally, the effectiveness of theoretical results is illustrated through the numerical examples.     

Determining Dissipativity of Switched Nonlinear Systems Using Linearization

Local strict QSR‐dissipativity of a switched nonlinear system is studied using the linearization technique in this paper. We obtain local strict QSR‐dissipativity of a switched system even if each subsystem is not locally strictly QSR dissipative by designing a switching law. The derived dissipative sufficient condition is characterized by a modified Lyapunov‐Metzler inequality that can be simplified as an LMI by assuming specific forms. Two special forms of local strict QSR‐dissipativity, local input state strict passivity and local L₂‐gain, are considered. When the approximate errors of a switched affine system satisfy certain conditions, local strict passivity can be drawn from its linearization. Finally, a numerical example is given to illustrate how to apply the proposed method to achieve passivity of switched nonlinear systems.     

Delay‐dependent dissipativity analysis and synthesis of switched delay systems

In this paper, we study the problem of dissipative analysis for a class of switched systems with time‐varying delays. Sufficient conditions for dissipativity are developed for a class of switching signals with average dwell time. These conditions express delay‐dependent exponential stability and are provided in terms of linear matrix inequalities (LMIs). It is shown that the derived results encompass some available results on ??_∞ approach and arbitrary switching case. Numerical examples are given to illustrate the developed results. Copyright © 2010 John Wiley & Sons, Ltd.     

Observer‐Based Reliable Control for Discrete‐Time Switched Linear Systems with Faulty Actuators

This paper deals with the issue of reliable control for discrete‐time switched linear systems with faulty actuators by utilizing a multiple Lyapunov functions method and estimate state‐dependent switching technique. A solvability condition for the reliable control problem is given in terms of matrix inequality with an extra matrix variable. This condition allows the reliable control problem for each individual subsystem to be unsolvable. For each subsystem of such a switched system, we design an observer and an observer‐based controller. A switching rule depending on the observer state is designed which, together with the controllers, can guarantee the stability of the closed‐loop switched system for all admissible actuator failures. The observers, controllers, and switching law are explicitly computed by solving linear matrix inequalities (LMIs). The proposed design method is illustrated by two numerical examples.     

Dissipative control for nonlinear Markovian jump systems with mixed time‐delays: The discrete‐time case

This article is concerned with the dissipative control problem for discrete‐time nonlinear Markovian jump systems subject to both discrete and distributed time‐delays. The purpose is to design a state feedback controller that is capable of guaranteeing the required closed‐loop stability and dissipativity performances simultaneously. By resorting to Lyapunov functional methodology and completing square technique, sufficient conditions are established for the existence of the desired state feedback controller in terms of certain Hamilton‐Jacobi inequalities (HJIs). Within the provided framework, the required controller parameters can be obtained by solving the corresponding HJIs. Finally, two numerical simulation examples are presented to demonstrate the correctness and effectiveness of the developed control paradigm.     

Incremental passivity and output tracking of switched nonlinear systems

This article studies incremental passivity and the output tracking problem for switched nonlinear systems. The concept of incremental passivity for switched systems is given using the proposed weak-storage functions. Furthermore, conditions for a switched nonlinear system to be incrementally passive are obtained without the requirement of the incremental passivity conditions for subsystems. It is shown that once the incremental passivity is assured, the output tracking problem for switched systems is solvable via the designed controllers, even though the problem for none of subsystems is solvable.     

至少有一个增长无源的子系统切换非线性系统的输出跟踪控制

本文利用平均驻留时间方法解决至少有一个增长无源的子系统的切换非线性系统的输出跟踪问题.对于给定的无源率,设计子系统控制器使得平均驻留时间变小.所得到的平均驻留时间依赖于增长无源子系统的增长指数小时间范数可观性.最后,通过数值例子验证所提出方法的有效性.     

Dissipativity and dissipative control for positive switched systems: A multiple linear copositive storage function method

In this article, the problems of dissipativity analysis and dissipative control are investigated for positive switched linear systems in both continuous and discrete‐time domains. We aim at solving the problems via employing a multiple linear copositive storage function scheme. The solvability of the problems for individual subsystem is only on their active regions. Switching laws and a set of feedback controllers are jointly devised such that the associated closed‐loop switched systems are not only positive but also dissipative, which is from the exogenous input to the output. Asymptotic stability is derived if all subsystems are zero‐state detectable. Moreover, sufficient conditions guaranteeing dissipativity with positivity constraint are presented, which can be easily examined on the grounds of linear programming approach. Finally, an example is offered, illustrating that the proposed control strategy is successful.     

State‐dependent switching law design with guaranteed dwell time for switched nonlinear systems

In this article, without the help of predesigned dwell time constraints, a new state‐dependent switching law with guaranteed dwell time for switched nonlinear systems is studied. Some sufficient conditions for asymptotic stability of switched nonlinear systems are derived. Also, all the abovementioned conditions can be transformed to a set of sum of squares (SOS) constraints, which can be checked by using the bilinear SOS methodology. Meanwhile, an improved path following method is provided to solve a bilinear SOS problem. Finally, three simulation examples are given to demonstrate the effectiveness of the obtained results.     

On the Exponential Stability of Moving Horizon Observer for Globally N‐Detectable Nonlinear Systems

A moving horizon observer is analyzed for nonlinear discrete‐time systems. Exponential stability relies on a global detectability assumption that utilizes the concept of incremental input‐to‐state‐stability.     

Stabilization of Discrete‐time Switched Systems with State Constraints Based on Mode‐Dependent Average Dwell Time

This paper considers the stabilization problem for a class of switched systems with state constraints based on mode‐dependent average dwell time (MDADT) in discrete‐time context. An improved average dwell time method is proposed, which is less conservative than the common average dwell time method. The sufficient conditions and stabilizing state feedback controllers for stabilization of discrete‐time switched systems with state constraints under MDADT switching are derived. Finally, the simulation results show that the approach designed by this paper is effective.     

Input‐to‐state stability of impulsive switched nonlinear time‐delay systems with two asynchronous switching phenomena

This summary addresses the input‐to‐state stability (ISS) and integral ISS (iISS) problems of impulsive switched nonlinear time‐delay systems (ISNTDSs) under two asynchronous switching effects. In our investigated systems, impulsive instants and switching instants do not necessarily coincide with each other. Meanwhile, systems switching signals are not simultaneous with the corresponding controllers switching signals, which will induce instability seriously, and cause many difficulties and challenges. By utilizing methods of Lyapunov‐Krasovskii and Lyapunov‐Razumikhin, mode‐dependent average dwell time approach, and mode‐dependent average impulsive interval technique, some stability criteria are presented for ISNTDSs under two asynchronous switching effects. Our proposed results improve the related existing results on the same topic by removing some restrictive conditions and cover some existing results as special cases. Finally, some simulation examples are presented to illustrate the effectiveness and advantages of our results.     

Stability and l2‐gain of discrete‐time switched systems with unstable modes

This paper addresses stability and l₂‐gain for discrete‐time switched systems with unstable modes based on slow/fast mode‐dependent average dwell time (MDADT) switching strategies. Firstly, by employing a class of multiple discontinuous Lyapunov functions (MDLFs) and developing a kind of alternative switching signals, the sufficient conditions on stability are established for the system without external disturbances under a slow/fast MDADT switching scheme with a tighter bounds on the dwell time. Furthermore, by defining indicator functions and exploring the features of slow/fast MDADT switching, the weighted l₂‐gain conditions are achieved for the system with external disturbances. Particularly, the criteria of stability and l₂‐gain are also established for the corresponding discrete‐time switched linear systems with unstable modes via the MDLFs method and the slow/fast MDADT switching strategy. Finally, two numerical examples are presented to illustrate the advantages of the proposed methods.     

Stability analysis and control synthesis of switched impulsive systems

In this paper, we investigate the stability analysis problem of switched impulsive nonlinear systems and several stabilization problems of switched discrete‐time linear systems are studied. First, sufficient conditions ensuring globally uniformly asymptotically stability of switched nonlinear impulsive system under arbitrary and DDT (dynamical dwell time which defines the length of the time interval between two successive switchings) switching are derived, respectively. In the DDT switching case, we first consider the switched system composed by stable subsystems, then we extend the results to the case where not all subsystems are stable. The stabilizations of switched discrete‐time linear system under arbitrary switching, DDT switching and asynchronous switching are investigated respectively. Based on the stability analysis results, the control synthesis consists of controller design for each subsystem and state impulsive jumping generators design at switching instant. With the aid of the state impulsive jumping generators at switching instant, the ‘energy’ produced by switching can be minimized, which leads to less conservative results. Several numerical examples are given to illustrate the proposed results within this paper. Copyright © 2011 John Wiley & Sons, Ltd.     

Unified mode‐dependent average dwell time stability criteria for discrete‐time switched systems

In this article, a unified mode‐dependent average dwell time (MDADT) stability result is investigated, which could be applied to switched systems with an arbitrary combination of stable and unstable subsystems. Combined with MDADT analysis method, we classified subsystems into two categories: switching stable subsystems and switching unstable subsystems. State divergence caused by switching unstable subsystems could be compensated by activating switching stable subsystems for a sufficiently long time. Based on the above considerations, a new globally exponentially stability condition was proposed for discrete‐time switched linear systems. Under the premise of not resolving the LMIs, the MDADT boundary of the new stability condition is allowed to be readjusted according to the actual switching signal. Furthermore, the new stability result is a generalization of the previous one, which is more suitable for the case of more unstable subsystems. Some simulation results are given to show the advantages of the theoretic results obtained.     

Fixed‐time state estimation for a class of switched nonlinear time‐varying systems

This paper deals with the state estimation problem of a class of nonlinear time‐varying systems with switched dynamics. Based on the concept of fixed‐time stability, an observer is designed to reconstruct the continuous state of switched nonlinear time‐varying systems with state jumps, satisfying the minimal dwell‐time condition. Using the past input and output values of the studied system, some sufficient conditions are provided to estimate the state before the next switching. Some numerical results illustrate the effectiveness of the proposed scheme.