Stability and H∞ control of discrete-time switched systems via one-step ahead Lyapunov function approach

Abstract

This study concerns the problems of stability and H∞ control for a class of discrete-time switched systems by introducing a one-step ahead Lyapunov function (LF) approach. The one-step ahead LF is a function of future states. The design objectives are to reduce the conservatism of the stability criterion developed for arbitrarily switched systems and further get a better disturbance attenuation capability. The distinguishing feature is that the one-step ahead LF has no structural constraint, such as, diagonal structure, and the resulting analysis and synthesis criteria can cover the non-monotonic method considering two samples variation, i.e. Vk2+ 2 − Vk2 + Vk1+ 1 − Vk1 < 0 or Vk + 2 − Vk < 0 as a special case. The obtained results can be easily extended to the multi-step ahead case. Numerical examples are included to demonstrate the effectiveness of the developed method.