A polytopic approach to switched linear systems

Switched linear systems are present in a wide range of engineering applications. Even though they have been systematically addressed in the past, stability conditions are usually conservative and often valid for special cases only. In this paper we propose a novel approach using polytopic systems theory, which allows us to treat general switched linear systems by LMI tools. We propose an alternative proof for the well-known common quadratic Lyapunov stability condition. This proof is then extended to less restrictive stability conditions.