A design scheme of variable structure -infinity control for uncertain singular Markov switched systems based on linear matrix inequality method

A H ∞ variable structure control is presented for singular Markov switched system with mismatched norm-bounded uncertainties and mismatched norm-bounded external disturbances. A sufficient condition guaranteeing the existence of linear switching surface is given based on the linear matrix inequality method (LMIs). It is shown that the sliding mode dynamic on the switching surface is regular, impulse-free and stochastically stable and satisfies H ∞ performance. A variable structure controller is designed to guarantee that the system trajectory is convergent to the linear switching surface. Final numerical example is solved to show the effectiveness and validity of the theoretical results.