Stabilization of switched systems with polytopic uncertainties via composite quadratic functions

This paper studied the stabilization of switched linear systems with polytopic uncertainties by employing the methods of nonsmooth analysis and the composite quadratic Lyapunov functions. Above all, the minimum quadratic functions and the directional derivatives along the vertex directions of subsystems are applied to construct the new switching law. Then, some sufficient conditions for stabilization of switched linear systems are established considering the sliding modes and the directional derivatives along sliding modes. Finally, numerical examples are given to demonstrate the effectiveness of the synthesis results.