Robust observer-based finite-time H∞ control for discrete-time singular Markovian jumping system with time delay and actuator saturation

This paper is concerned with the problem of robust observer-based finite-time H∞ control for discrete-time singular Markovian jumping system with time-varying delay and actuator saturation. By using linear matrix inequality (LMI) approach and constructing proper Lyapunov-Krasovskii functional, sufficient criteria have been obtained that ensure the system singular stochastic finite-time boundedness and singular stochastic finite-time H∞ boundedness. Then the observer and feedback controllers are designed, and with the following the results are extended to convex optimization problems so that the optimal values of attenuation level and the maximum saturation attraction domain can be calculated directly. In the end, some numerical examples are presented to show the feasibility and validity of the proposed results.