Observer-based l2–l∞l2–l∞ control for discrete-time nonhomogeneous Markov jump Lur׳e systems with sensor saturations

•The observer-based l2–l∞l2–l∞ controller is designed for a class of Markov jump Lur׳e systems subject to sensor saturations.•Sensor saturations are decomposed into a linear term and a nonlinear term satisfying a sector condition.•Lyapunov function contains three quadratic functions of the estimation error,observer states and nonlinearities.•The explicit expressions of desired gain matrices for the designed observer and controller are obtained.

This paper addresses the observer-based l2–l∞l2–l∞ control problem for a class of nonhomogeneous Markov jump Lur׳e systems subject to sensor saturations in discrete-time domain. The time-varying characteristic of transition probabilities is considered as a polytope description. The saturations occurred in the sensor outputs are handled by a decomposition approach. By constructing a stochastic multiple Lyapunov function, sufficient conditions for the existence of an observer-based controller with nonlinear feedback terms are derived, such that the closed-loop systems are stochastically stable and satisfy a given l2–l∞l2–l∞ performance index. A linear matrix inequality approach is presented for designing such an observer-based l2–l∞l2–l∞ controller. Finally, a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results.