Stability of linear switched systems with quadratic bounds and Observability of bilinear systems

Details Stability of linear switched systems with quadratic bounds and Observability of bilinear systems Stability of linear switched systems with quadratic bounds and Observability of bilinear systems

2012-01-19

arxiv.org/abs/1201.4078v1

Mathematics

Optimization and Control

Scientific paper

The aim of this paper is to give sufficient conditions for a switched linear system defined by a pair of Hurwitz matrices that share a common but not strict quadratic Lyapunov function to be GUAS. We show that this property is equivalent to the uniform observability of a bilinear system defined on a subspace whose dimension is in most cases much smaller than the dimension of the switched system. Some sufficient conditions of uniform asymptotic stability are then deduced from the equivalence theorem, and illustrated by examples.

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