In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems ẋ = fσ(t,x), possessing a uniformly asymptotically stable equilibrium. Let ẋ = fp(t,x), p ∈ P, be the collection of the ODEs, to which the switched system corresponds. The number of the vector fields fp on the right-hand side of the differential equation is assumed to be finite...

In this paper, discrete-time switched linear systems affected by both parameter variations and exterior disturbances are considered. The problem of synthesis of switching control laws, which assure that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence, is investigated. The method is based on set-induced Lyapunov functio...

This paper addresses the L2-gain analysis and control synthesis problem for a class of switched nonlinear systems affected by both time-varying uncertainties and external disturbances. Firstly, the L2-gain for the autonomous switched disturbed uncertain system is analyzed. Then, a switched state feedback control law is designed and the L2 -gain is analyzed for the disturbed uncertain non-autono...

This paper is dedicated to the study of robust stability analysis and control synthesis for discrete time uncertain switching systems under arbitrary switching. Polytopic uncertainties are considered. We show that Lyapunov functions that depend on the uncertain parameter and that take into account the structure of the system may be used in order to reduce the conservatism related to uncertainty...

This paper is concerned with the problem of designing switched state feedback H∞ controllers for discrete-time Takagi– Sugeno (T–S) fuzzy systems. New types of state feedback controllers, namely, switched parallel distributed compensation (PDC) controllers, are proposed, which are switched based on the values of membership functions. Switched quadratic Lyapunov functions are exploited to derive...

We study switched nonlinear differential algebraic equations (DAEs) with respect to existence and nature of solutions as well as stability. We utilize piecewise-smooth distributions introduced in earlier work for linear switched DAEs to establish a solution framework for switched nonlinear DAEs. In particular, we allow induced jumps in the solutions. To study stability, we first generalize Lyap...

In this paper we discuss the notion of universality for classes candidate common Lyapunov functions linear switched systems. On one hand, prove that a family absolutely homogeneous is universal as soon it approximates arbitrarily well every convex function C0 topology unit sphere. other several obstructions class to be universal, showing, in particular, families piecewise-polynomial continuous ...

1 Abstract—Utilizing model reference adaptive control approach and multiple Lyapunov functions method, we propose a switched adaptive controller for uncertain switched linear systems in control canonical form. These systems exist naturally in many practical applications, such as variable capacity hydraulic pump involving discrete changes that are specified by the valve position. We show that th...