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This paper considers interval time-varying delay systems with delayed estimation of the delay. This case is often encountered in the Networked Control Systems (NCS) field. Based on Lyapunov-Krasovskii functional methods and linear matrix inequality (LMI) techniques, a switching state feedback controller is designed to guarantee the exponential stability. The controller switches according to the measured...
In this paper, we consider the model reference adaptive control (MRAC) problem of switched linear systems in which the parameters and switching time instants are all unknown. We apply the output feedback variable structure (VS) based adaptive controller to switched linear systems with general relative degrees and show error convergence and signal boundedness properties by multiple Lyapunov functions...
In this paper we study the characterization of asymptotic stability for discrete-time switched linear systems. We first translate the system dynamics into a symbolic setting under the framework of symbolic topology. Then by using the ergodic measure theory, a lower bound estimate of Hausdorff dimension of the set of asymptotically stable sequences is obtained. We show that the Hausdorff dimension...
This paper studies the stabilisation of switched discrete-time linear control systems under arbitrary switching. A sufficient condition for the uniform global exponential stability (UGES) of such systems is the existence of a common quadratic Lyapunov function (CQLF) for the component subsystems. The existence of such CQLF can be ensured using Lie-algebraic techniques by the existence of a nonsingular...
This paper addresses the computation of the L2-induced gain for a class of switched systems. The main contribution of the paper is to completely characterize the induced gain of the switched system through a system of differential inequalities on a common storage function, one for each system being switched. The motivation for computing the induced gain of a switched system is the application of robust...
Optimal switched law, which is for the linear impulsive switched system, is discussed in this paper. First, we show that if the constraint condition of the matrix pencil is satisfied, we could obtain the asymptotically stable range of the linear impulsive switched system. For a stable linear impulsive switched system, different switched laws determine different convergence process. Then the method...
A bumpless transfer method for discrete-time switched linear systems is presented. It is based on an additional controller which is activated at the switching time for reducing the control discontinuities. Dwell time conditions to guarantee the stability of the closed-loop system are provided. Simulation tests on the Eisenhuttenstadt hot strip mill of ArcelorMittal are shown.
This paper develops semistability and uniform semistability analysis results for switched linear systems. Semistability is the property whereby the solutions of a dynamical system converge to Lyapunov stable equilibrium points determined by the system initial conditions. Since solutions to switched systems are a function of the system initial conditions as well as the switching signals, uniformity...
This paper investigates the problem of Hinfin filtering for discrete-time switched linear systems under arbitrary switching laws. New LMI-based conditions for the solvability of the problem are given via switched quadratic Lyapunov functions. By Finsler's lemma, two sets of slack variables with special structure are introduced to provide extra degrees of freedom in optimizing the guaranteed Hinfin...
This paper considers the problem of finding a common linear copositive Lyapunov function for a set of second order systems. Based on mathematical programming, we give a new proof of the result in (O. Mason, 2004). Then we extend this result to a finite number of systems, and a common linear copositive Lyapunov function is obtained.
This paper deals with a problem of controller adaptation for a system known to be in a certain set of linear time-invariant systems. It is assumed that there exists a set of linear stabilizing controllers. A method for calculating a minimum switching time between controllers commonly known as dwell time such that stability of the closed loop linear time-varying system is guaranteed is given in this...
This paper has considers the stability problem of stochastic and discrete-time switched systems with arbitrary switching. Several stability conditions based on Lyapunov theory are presented. In particular, a linear matrix inequality condition is derived for linear switched systems.
This paper presents a MATLAB toolbox that computes stabilizing state feedback controllers for a class of switched systems where the system dynamics switch interchangeably between several subsystems. The subsystems considered here are restricted to second order linear systems. The toolbox finds controllers that stabilize the system under arbitrary switching, where this is ensured by first determining...
In (D. Cheng et. al, 2004),(D. Cheng et. al, 2005), it is proved that for a given controllable pair (A, B) with A isin Ropfn times n, B isin Ropfn times m, and any lambda > 0, a gain matrix K can be designed so that pare(A + BK)t par les MlambdaLe-lambdat where M and L are constants independent of A. Here we show that M and L can be chosen much smaller than that proposed in (D. Cheng et. al, 2004),(D...
Geometric properties of null controllable region of discrete-time switched linear systems with input saturation are studied. We show that the null controllable region is not convex in general and is centrally symmetric. Under certain conditions, it can be well approximated by a nondecreasing region sequence. It is also shown that the null controllable region is contained in the Minkowski sum of null...
In this paper, we consider stability analysis and design for switched systems consisting of linear descriptor systems that have the same descriptor matrix. When all descriptor systems are stable, we show that if the descriptor matrix and all the subsystem matrices are commutative pairwise, then the switched system is stable under arbitrary switching. This is an extension of the existing well known...
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