Positiveness and Observer-Based Finite-Time Control for a Class of Markov Jump Systems with Some Complex Environment Parameters

الملخص EN

An observer-based finite-time L2-L∞ 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 L2-L∞ 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.