Delay-dependent adaptive variable structure control for matched uncertain Markovian jump systems

The delay-dependent adaptive variable structure control problem for a class of uncertain time-delay Markov jump hybrid systems is considered. Under the assumption of matched system uncertainties, the sufficient conditions are proposed to guarantee exponentially stable in the mean square of reduced-order sliding mode system in terms of delay-dependent matrix inequalities. Under the assumption of matched unknown upper bound system uncertainties, an adaptive variable structure control law are proposed. The control method guarantees that the trajectory of system arrives at the sliding surface in finite time interval and is kept here thereafter.