Nonfragile observer‐based <i>H</i>_∞ sliding mode control for Itô stochastic systems with Markovian switching

Abstract

SUMMARY The paper is devoted to investigating sliding mode control for a class of nonlinear uncertain stochastic systems with input nonlinearity and Markovian switching. A nonfragile observer subjected to the transition rates of the modes is designed. By some specified matrices, the connections among the designed sliding surfaces corresponding to every mode are established. The state estimation‐based sliding mode control law is derived to guarantee the reachability of the sliding surface in finite time interval. The sufficient conditions on asymptotically stochastic stability of the error system and sliding mode dynamics with a given disturbance attenuation level are derived in terms of linear matrix inequalities. Finally, an example is provided to illustrate the efficiency of the proposed method. Copyright © 2013 John Wiley &amp; Sons, Ltd.