Observer-based finite-time H∞H∞ control for discrete singular stochastic systems

In this work, the observer-based finite-time H∞H∞ control problem is studied for a class of discrete-time Markovian jump singular systems with time-varying norm-bounded disturbance. The main purpose of this paper is to design an observer and a state feedback controller ensuring that the resulting closed-loop error system is singular finite-time bounded via observer-based state feedback and satisfies a prescribed H∞H∞ performance level in a finite-time interval. By using the descriptor system approach presented by Fridman and Shaked, sufficient criteria on singular H∞H∞ finite-time stabilization via observer-based state feedback are derived in terms of linear matrix inequalities. A simulation example is also given to demonstrate the validity of the developed results.