Sliding mode H _∞ control of time-varying delay Markov jump with quantized output

This paper investigates the quantized sliding mode control of Markov jump systems with time-varying delay. A dynamical adjustment law is explored to quantize the system output. By constructing an observer-based integral sliding surface, a sliding mode controller is designed to take over the dynamical motion of state estimation and ensure the reachability of sliding surface. A new scaling manner is developed to build the bound between the system output and quantized error. With the help of separation strategies for controller synthesis and general transition probabilities and a lower bound theorem for nonlinear integral terms, a new synthesis method to ensure the required stability and meet the required H _∞ performance is proposed in the form of linear matrix inequalities. The validity of the proposed control method is illustrated by a numerical example.