Positiveness and observer-based finite-time control for a class of Markov jump systems with some complex environment parameters (Q1723043)

Summary: An observer-based finite-time \(L_2\)-\(L_\infty\) control law is devised for a class of positive Markov jump systems in a complex environment. The complex environment parameters include bounded uncertainties, unknown nonlinearities, and external disturbances. The objective is to devise an appropriate observer-based control law that makes the corresponding augment error dynamic Markov jump systems be positive and finite-time stabilizable and satisfy the given \(L_2\)-\(L_\infty\) disturbance attenuation index. A sufficient condition is initially established on the existence of the observer-based finite-time controller by using proper stochastic Lyapunov-Krasovskii functional. The design criteria are presented by means of linear matrix inequalities. Finally, the feasibility and validity of the main results can be illustrated through a numerical example.