Analysis of switched and hybrid systems-beyond piecewise quadratic methods (original) (raw)

Robust stability analysis of nonlinear hybrid systems

2009

Abstract We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems.

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.

Stabilizing Supervisory Control of Hybrid Systems Based on Piecewise Linear Lyapunov Functions 1

2000

In this paper, the stability of discrete-time piecewise linear hybrid systems is in- vestigated using piecewise linear Lyapunov functions. In particular, we consider switched discrete-time linear systems and we identify classes of switching sequences that result in stable trajectories. Given a switched linear system, we present a systematic methodology for computing switching laws that guarantee stability based on the matrices of the system. In the proposed approach, we assume that each individual subsystem is stable and admits a piece- wise linear Lyapunov function. Based on these Lyapunov functions, we compose "global" Lyapunov functions that guarantee stability of the switched linear system. A large class of stabilizing switching sequences for switched linear systems is characterized by computing conic partitions of the state space.