Taming Heterogeneity and Complexity of Embedded Control

Stabilizability of Affine Switching Systems:A Kalman-like Approach

Elena De Santis, Maria D. Di Benedetto and Giordano Pola

Department of Electrical Engineering and Computer Science,

Center of Excellence DEWS,

University of L’Aquila,

Poggio di Roio, L’Aquila 67040, Italy

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ABSTRACT. In this paper, we focus on a particular subclass of hybrid systems, the class of affine switching systems. We propose hybrid state space decompositions, based on hybrid invariant subspaces, which reduce the computational effort required for checking the structural property of asymptotic stabilizability.

KEYWORDS: hybrid systems, stabilizability, Kalman decomposition

1. Introduction

In this paper, we focus on affine switching systems [De 04a], a subclass of hybrid systems, where the continuous dynamics and the reset functions are affine and the transitions depend only on an event that acts as a discrete disturbance. The continuous dynamics are given by an affine dynamical control system (whose dynamical matrices depend on the current discrete state) and therefore an input function can be designed for controlling purposes.

Stability issues of hybrid systems have been extensively investigated in the last years (see e.g. [BRA 98], [YE 98], [LIB 03], [SUN 05] and references therein). However checking stabilizability of switching systems is not an easy task in general (see e.g. [LIB 03]) and a complete characterization of stabilizability ...