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.

Hybrid Predictive Control Based on High-Order Differential State Observers and Lyapunov Functions for Switched Nonlinear Systems

In this paper, a hybrid predictive controller is proposed for a class of uncertain switched nonlinear systems based on high-order differential state observers and Lyapunov functions. The main idea is to design an output feedback bounded controller and a predictive controller for each subsystem using high-order differential state observers and Lyapunov functions, to derive a suitable switched law to stabilize the closed-loop subsystem, and to provide an explicitly characterized set of initial conditions. For the whole switched system, based on the high-order differentiator, a suitable switched law is designed to ensure the whole closed-loop’s stability. The simulation results for a chemical process show the validity of the controller proposed in this paper.

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.

Nonsmooth Control-Lyapunov Function and Stabilization of Nonlinear Switching Systems

在这份报纸，我们认为一般非线性的切换 systems.Under 是一个另外的假设，我们证明那在那里存在看情况交换在很一般的意义稳定 8vstem 的统治的一个州的空格。

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.

Quadratic Stability of Switched Nonlinear Systems in Block-triangular Form

The problem of globally quadratic stability of switched nonlinear systems in block-triangular form under arbitrary switching is addressed. Under the assumption that all block-subsystems are zero input-to-state stable, a su?cient condition for the problem to be solvable ispresented. A common Lyapunov function is constructed iteratively by using the Lyapunov functionsof block-subsystems.

Control of switched systems with actuator saturation

This paper is concerned with controller synthesis for linear switched systems with actuator saturation. Based on common Lyapunov function technique and multiple-Lyapunov function technique, two methods for designing state feedback controller are proposed respectively in terms of linear matrix inequalities for the switched systems with saturation. An approach on enlarging the attractive domain is then investigated. The application of the presented approach is illustrated finally by a numerical example.

Stability and Robust Stability of Switched Positive Linear Systems With All Modes Unstable

This paper is concerned with the stability and robust stability of switched positive linear systems(SPLSs) whose subsystems are all unstable. By means of the mode-dependent dwell time approach and a class of discretized co-positive Lyapunov functions, some stability conditions of switched positive linear systems with all modes unstable are derived in both the continuous-time and the discrete-time cases, respectively. The copositive Lyapunov functions constructed in this paper are timevarying during the dwell time and time-invariant afterwards. In addition, the above approach is extended to the switched interval positive systems. A numerical example is proposed to illustrate our approach.

Constructing Common Quadratic Lyapunov Functions for a Class of Stable Matrices

Narendra 和 Balakrishnan 建议了一个方法构造普通二次的 Lyapunov 功能(CQLF )[1 ] ，稳定的矩阵的 whena 集合是可交换的。这份报纸的目的是概括方法到非可交换、非可解决的大小写。一个修改构造算法被建议，某些条件被提供向是的矩阵保证结果 CQLF。下次，讨论的问题是一个稳定的矩阵什么时候能与 CQLF 被加到一套矩阵为扩大集合构造新 CQLF。

Admissibility analysis and control synthesis for switched linear singular systems

The problem of admissibility analysis and control synthesis of discrete-time switched linear singular (SLS) systems for arbitrary switching laws is solved.By using the switched Lyapunov function approach,some new sufficient conditions under which the SLS system is admissible for arbitrary switching laws are derived in terms of linear matrix inequalities(LMIs).Based on the admissibility results,control synthesis is then to design switched state feedback and static output feedback controllers,guaranteeing that the resulting closed-loop system is admissible.The presented results can be viewed as the extensions of previous works on switched Lyapunov function approach from the regular switched systems to singular switched cases.Examples are provided to demonstrate the reduced conservatism and effectiveness of the proposed conditions.

Global stabilization of linear periodically time-varying switched systems via matrix inequalities

In this paper, we address the stabilization problem for linear periodically time-varying switched systems. Using discretization technique, we derive new conditions for the global stabilizability in terms of the solution of matrix inequalities. An algorithm for finding stabilizing controller and switching strategy is presented.

Observer-based robust H-infinity control for uncertain switched systems

The problem of observer-based robust H-infinity control is addressed for a class of linear discrete-time switched systems with time-varying norm-bounded uncertainties by using switched Lyapunov function method. None of the individual subsystems is assumed to be robustly H-infinity solvable. A novel switched Lypunov function matrix with diagonal-block form is devised to overcome the difficulties in designing switching laws. For robust H-infinity stability analysis, two linear-matrix-inequality-based sufficient conditions are derived by only using the smallest region function strategy if some parameters are preselected. Then, the robust H-infinity control synthesis is studied using a switching state feedback and an observer-based switching dynamical output feedback. All the switching laws are simultaneously constructively designed. Finally, a simulation example is given to illustrate the validity of the results.

Stabilization of a class of discrete-time switched systems via observer-based output feedback

In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched Lya- punov function (SLF) method with Finsler’s Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation exam- ple is given to illustrate the efficiency of the result.

Stabilization of a class of switched nonlinear systems

The stabilization of a class of switched nonlinear systems is investigated in the paper. The systems con- cerned are of (generalized) switched Byrnes-Isidori canonical form, which has all switched models in (generalized) Byrnes- Isidori canonical form. First, a stability result of switched systems is obtained. Then it is used to solve the stabilization prob- lem of the switched nonlinear control systems. In addition, necessary and sufficient conditions are obtained for a switched affine nonlinear system to be feedback equivalent to (generalized) switched Byrnes-Isidori canonical systems are presented. Finally, as an application the stability of switched lorenz systems is investigated.

Global exponential stability of switched systems

This paper proposes a method for the stability analysis of deterministic switched systems.Two motivational examples are introduced (nonholonomic system and constrained pendulum).The finite collection of models consists of nonlinear models,and a switching sequence is arbitrary.It is supposed that there is no jump in the state at switching instants,and there is no Zeno behavior,i.e.,there is a finite number of switches on every bounded interval.For the analysis of deterministic switched systems,the multiple Lyapunov functions are used,and the global exponential stability is proved.The exponentially stable equilibrium of systems is relevant for practice because such systems are robust to perturbations.

Robust stability and stabilization for uncertain discrete-time switched singular systems with time-varying delays

The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities(LMIs).An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms(ignored in previous methods) when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.

H_∞ Control Based on LMIs for a Class of Time-delay Switched Systems

H 稳定性分析和有在任意的切换的法律下面的推迟的状态的交换系统的控制合成的问题被考虑。借助于 Lyapunov 功能和线性矩阵不平等工具， H 稳定性的足够的状况以线性矩阵不平等被介绍。而且，经由州的反馈的柔韧的 H 控制合成和产量反馈被学习。最后，一个数字例子被给表明建议方法的有效性。

Non-fragile hybrid guaranteed cost control for a class of uncertain switched linear systems

This paper focuses on the problem of non-fragile hybrid guaranteed cost control for a class of uncer- tain switched linear systems. The controller gain to be designed is assumed to have additive gain variations. Based on multiple-Lyapunov function technique, the design of non-fragile hybrid guaranteed cost controllers is derived to make the corresponding closed-loop system asymptotically stable for all admissible uncertainties. Furthermore, a convex optimiza- tion approach with LMIs constraints is introduced to select the optimal non-fragile guaranteed cost controllers. Finally, a simulation example illustrates the effectiveness of the proposed approach.

Stability control of multi-parameter adaptive wireless communication systems based on multi-Lyapunov function

With the occurrence of burst interference,bit error rate( BER) stability of the wireless communication system( WCS) always degrades significantly. To cope with it,a stability control algorithm is proposed,utilizing the stability theory of switched systems,which is specifically applicable for multi-parameter adaptive WCS with spectrum sensing ability,and it is capable of stabilizing BER within a reasonable range. Firstly,WCS is modeled as a switched system. Then,based on the multi-Lyapunov function,controlling rules are presented to enable the switched system to satisfy stable condition asymptotically. Finally,analysis and numerical simulation results demonstrate that the switched WCS with the proposed controlling rules is superior to conventional power-controlled WCS with or without state feedback control in terms of stability performance.

Stability and Stabilization of Block-cascading Switched Linear Systems

这篇论文的主要目的是用可约的谎言代数学在交换线性系统调查二次的稳定性和稳定的问题。首先，我们为一个给定的线性系统调查所有真实不变的 subspaces 的结构。结果然后被用来为交换模型提供一种可比较的串联形式。用普通串联形式，普通二次的 Lyapunov 功能是(QLF ) 被发现斜块的普通 QLF 探索。另外，一个串联教友派会员词根被证明。把它与稳定性结果相结合，为交换线性系统的一个类的反馈稳定的问题被解决。交换线性系统的关键词 - 二次的稳定性 - 普通二次的 Lyapunov 功能 - 可约的谎言代数学 - 中华人民共和国(号码 60343001， 60274010， 66221301 和 60334040 ) 的国家自然科学基础部分支持的串联教友派会员词根你 hong 朱收到了她的 B.Sc。在来自苏州大学的数学的部门的度，在 2002 的中国苏州。自从 2002，她是在系统科学的研究所的一个研究生学生，中国科学院。她的研究兴趣包括非线性的控制系统，交换系统。Dai-Zhan Cheng 在 1970 从清华大学毕业了，从研究生院收到了他的 M.Sc，在 1981 的中国科学院(CAS ) ，来自在 1985 的华盛顿大学的博士。自从 1990，他是有系统科学，数学的学院和系统科学(AMSS ) 的研究所的一个教授， CAS。他是 160 篇杂志论文， 6 本书和 80 篇会议论文的作者 / 合作者。他的研究兴趣为控制设计包括非线性的控制系统，交换系统， Hamiltonian 系统和数字实现。琴教授当前是控制理论， CSA，和 IEEE 家伙上的技术委员会的主席。