Sliding mode control of singularly perturbed Markovian jump delayed systems with nonlinearity

This paper is concerned with sliding mode control (SMC) of a class of time-delay nonlinear singularly perturbed Markovian jump systems. Firstly, a switching surface function is designed, and a delay-dependent condition is derived in terms of E-independent linear matrix inequality, which guarantees that the resulting sliding mode dynamics is mean-square exponentially stable. Then an algorithm is given to estimate the stability bound. Moreover, an adaptive SMC law is synthesized to drive the system trajectories onto the designed switching surface in a finite time. Finally, a numerical example is presented to show the effectiveness of proposed method. Copyright (c) 2012 John Wiley & Sons, Ltd.