| Popis: |
This paper deals with the stability problem for the planar linear switched system x'(t)=u(t)A1 x(t)+(1−u(t))A2 x(t) , x=(x1, x2) in R^2 where the real matrices A1, A2 in R^2 are Hurwitz and for t>0 u(t) in {0, 1} is a measurable function. We give a Hurwitz like characterization of globally uniformly asymptotically stable planar switched systems. Another contribution of this paper is a practical version of the main result in [NS] using real algebraic geometry tools. This new approach give a Hurwitz like characterization of switched systems which share a same strict or large common quadratic Lyapunov function and simplify the main result in [BBM]. |
