Observer-based finite-time H∞H∞ control of discrete-time Markovian jump systems

This paper investigates the observer-based finite-time H∞H∞ control problem for one family of discrete-time Markovian jump systems with time-varying norm-bounded disturbance. Firstly, the concepts of stochastic finite-time boundedness and stochastic H∞H∞ finite-time stabilization via observer-based state feedback are given. Then, under the assumption that the state vector is not available for feedback, an observer-based state feedback controller is designed to ensure stochastic finite-time stabilization or stochastic H∞H∞ finite-time stabilization via observer-based state feedback of the resulting closed-loop error discrete-time Markovian jump system. Sufficient criteria on the stochastic finite-time stabilization and stochastic H∞H∞ finite-time stabilization via observer-based state feedback are given in form of linear matrix inequalities with a fixed parameter, respectively. Finally, simulation examples are presented to illustrate the validity of the developed techniques.