Taming Heterogeneity and Complexity of Embedded Control

Achieving Stability in Non-holonomic Systems by Means of Switched Control Laws

Daniele Casagrande¹—Alessandro Astolfi^2,3—Thomas Parisini¹

¹ Dipartimento di Elettronica, Elettrotecnica ed Informatica Università degli Studi di Trieste via A. Valerio, 10 - 34127 Trieste - ITALY

{dcasagrande,parisini}@units.it

² Department of Electrical and Electronic Engineering, Imperial College Exhibition Road, London SW7 2BT - UK

[e-mail]

³ Dipartimento di Informatica, Sistemi e Produzione Università degli Studi di Roma “Tor Vergata” via del Politecnico, 1 - 00133 Rome - ITALY

[e-mail]

ABSTRACT. This paper deals with the stability problem for non-holonomic systems and describes a sufficient condition for the existence of a time-varying switching control scheme which globally asymptotically stabilizes the zero equilibrium. The sufficient condition is based on a new concept of Lyapunov function for hybrid systems which is used in the demonstration of a stability theorem. The new idea is also put in relation with known theoretical tools such as multiple Lyapunov functions and common Lyapunov functions. Finally, a simple example of a non-holonomic system is taken into account, for which the existence of a stabilizing switching control law is proven. The results of some simulations are also reported in order to evaluate qulitatively the effectiveness the method.

KEYWORDS: Non-holonomic systems, hybrid systems, Lyapunov stability

1. Introduction

Recently, hybrid systems have ...