Finite-Time H∞ Optimize Controller Design for Singular Positive Markovian Jump Delay Systems With Saturation Constraint

In this article, the finite-time $H_{\infty }$ control problem for singular positive Markovian jump systems with time-varying delay and saturation constraint was studied. Firstly, considering the discontinuities caused by the mode-dependent singular matrix and Markov jump switching behavior, a state feedback controller is designed to guarantee the positivity and mean-square locally finite-time $H_{\infty }$ stability of the considered system. Secondly, the maximum finite-time domain of attraction of the considered system subject to input saturation is estimated. Finally, to show the effectiveness of our control strategy, the simulation results are given.