We introduce the concept of sos-convex Lyapunov functions for stability analysis of discrete time switched systems. These are polynomial Lyapunov functions that have an algebraic certificate of convexity, and can be efficiently found by semidefinite programming. We show that sos-convex Lyapunov functions are universal (i.e., necessary and sufficient) for stability analysis of switched linear sy...

In this paper we begin by assuming that an observer with a corresponding quadratic-type Lyapunov function has been designed for a given nonlinear system. We then consider the problem that arises when the output of that nonlinear system is not directly available; instead, it acts as an input to a second, linear system from which a partialstate measurement is in turn available. We develop an obse...

In this paper we develop an optimality-based framework for designing controllers for discrete-time nonlinear cascade systems. Specifically, using a nonlinear-nonquadratic optimal control framework we develop a family of globally stabilizing backstepping-type controllers parameterized by the cost functional that is minimized. Furthermore, it is shown that the control Lyapunov function guaranteei...

This paper is devoted to adaptive tracking control for a class of uncertain MIMO switched nonlinear systems. A novel systematic recursive algorithm is proposed to design adaptive update laws and an adaptive controller by multiple Lyapunov functions method combining with backstepping recursive technique. And then, by means of stability theory about the switched systems and the average dwell time...

The paper investigates the structure of the reachable set of linear switched systems. The structure of the reachable set is determined using techniques from classical nonlinear systems theory, namely, the theory of orbits developed by H. Sussman and the realization theory for nonlinear systems developed by B. Jakubczyk.

In this paper, the problems of stability analysis and H∞ controller design of a class of switched nonlinear systems are investigated. In a classical way, the modeling of the systems is approached by switched fuzzy systems, and both fast switching and slow switching are considered there. In particular, for slow switching scheme, a new mode-dependent average dwell time switching is proposed for t...

This paper investigates the problem of fault tolerant control of a class of uncertain switched nonlinear systems with time delay under asynchronous switching. The systems under consideration suffer from delayed switchings of the controller. First, a fault tolerant controller is proposed to guarantee exponentially stability of the switched systems with time delay. The dwell time approach is util...

This paper discusses the preservation of some stochastic orders between two interdependent series and parallel systems when the survival and distribution functions of all components switch to the exponentiated model. For the series systems, the likelihood ratio, hazard rate, usual, aging faster, aging intensity, convex transform, star, superadditive and dispersive orderings, and for the paralle...

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This paper develops hybrid control strategies for stabilizing a class of nonlinear systems. Common Lyapunov functions and switched Lyapunov functions are used to establish easily verifiable criteria for the stabilizability of weakly nonlinear systems under switched and impulsive control. Three types of controller switching rules are studied: time-dependent (synchronous), statedependent (asynchr...