An LMI-based variable structure control for a classof uncertain singular Markov switched systems

An H-infinifty variable structure control is presented for singular Markov switched systems with mis- matched norm-bounded uncertainties and mismatched norm-bounded external disturbances.It is shown that the sliding mode dynamics on the given switching surface is regular,impulse-free,and stochastically stable and satisfies H-infinity performance.A variable structure controller is designed to guarantee that the system trajectory converges to the linear switching surface in some finite time.Finally,a numerical example is solved to show the effectiveness and validness of the theoretical results.