Hybridization for Stability Analysis of Switched Linear Systems (original) (raw)

Local analysis of hybrid systems on polyhedral sets with state-dependent switching

International Journal of Applied Mathematics and Computer Science, 2014

This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.

A review of stability results for switched and hybrid systems

2001

Abstract--Hybrid and switched dynamic systems are of major research interest nowadays due to their use as models in many applications in computer science and systems control. One of the major problems in hybrid and switched dynamic systems is establishing their key property of stability, which also is important in controller design. Stability may prove also critical for real-time systems, embedded systems, and hybrid systems in general that arise in computer science problems where verification tests are undecidable.

Analysis of switched and hybrid systems-beyond piecewise quadratic methods

2003

Abstract This paper presents a method for stability analysis of switched and hybrid systems using polynomial and piecewise polynomial Lyapunov functions. Computation of such functions can be performed using convex optimization, based on the sum of squares decomposition of multivariate polynomials.

Stability of a Switched Linear System

2012

Hybrid systems are dynamic systems that arise out of the interaction of continuous state dynamics and discrete state dynamics. Switched systems, which are a type of hybrid system, have been given much attention by control systems research over the past decade. Problems with the controllability, observability, converseability and stabilizability of switched systems have always been discussed. In this paper, the trend in research regarding the stability of switched systems will be investigated. Then the variety of methods that have been discovered by researchers for stabilizing switched linear systems with arbitrary switching will be discussed in detail.