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

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. V k + 2 2 − V k 2 + V k + 1 1 − V k 1 < 0 or V k + 2 − V k < 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.