Many physical systems are hybrid in the sense that they have continuous behaviors and discrete phenomena. In control system with multiple models, switching strategy and stability of the closed-loop system under switching are very important issues. In this paper, a novel adaptive control scheme based on multiple parameter models is proposed to cope with a change in parameters. Switching strategy...

The aim of this work is to present an entropy-like Lyapunov function based dynamic feedback design technique for quasi-polynomial and Lotka-Volterra systems. It is shown, that the dynamic feedback design problem is equivalent to the feasibility of a bilinear matrix inequality. The problem is also formulated as a control Lyapunov function based feedback design when the Lyapunov function paramete...

This paper develops a novel method to deal with the stability problem of sampled-data systems. The multiple Lyapunov function method used in switched systems is extended to sampled-data systems and a multiple Lyapunov functional method is developed for nonlinear sampled-data systems. An application is presented where two different Lyapunov functionals are constructed in order to determine the s...

In previous works, the authors introduced a framework for software analysis, which is based on optimization of Lyapunov invariants. These invariants prove critical software properties such as absence of overflow and termination in finite time. In this paper, graph models of software are introduced and the software analysis framework is further developed and extended on graph models. A distribut...

The paper deals with the stability properties of linear discrete-time switched systems with polytopic sets of modes. The most classical and viable way of studying the uniform asymptotic stability of such a system is to check for the existence of a quadratic Lyapunov function. It is known from the literature that letting the Lyapunov function depend on the time-varying switching parameter improv...

In this paper, we present an automatable decompositional method for the computation of Lyapunov functions for hybrid systems with complex discrete state spaces. We use graph-based reasoning to decompose hybrid automata into subgraphs, for which we then solve semidefinite optimization problems to obtain local Lyapunov functions. These local computations are made in a way that ensures that the fa...

In this paper we will extend the input-to-state stability (ISS) framework to continuous-time discontinuous dynamical systems adopting Filippov’s solution concept and using non-smooth ISS Lyapunov functions. The main motivation for adopting non-smooth ISS Lyapunov functions is that “multiple Lyapunov functions” are commonly used in the stability theory for hybrid systems. We will show that the e...

We show that for any positive integer d, there are families of switched linear systems— in fixed dimension and defined by two matrices only—that are stable under arbitrary switching but do not admit (i) a polynomial Lyapunov function of degree ≤ d, or (ii) a polytopic Lyapunov function with ≤ d facets, or (iii) a piecewise quadratic Lyapunov function with ≤ d pieces. This implies that there can...

For both discrete-time and continuous-time linear multi-variable control systems, we introduce a concept of control Lyapunov modes associated with a control Lyapunov function in a quadratic form. We prove that the number of unstable control Lyapunov modes is at most equal to the number of input of the system.