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.