Finite-time H∞ static output control of Markov jump systems with an auxiliary approach

This paper considers the finite‐time ${\mathcal{H}}_{\infty }$ static output feedback control of Markov jump systems. With the help of introducing two new variables related to the original system state and output, sufficient conditions for the closed‐loop system to be stochastic finite‐time boundedness with the prescribed ${\mathcal{H}}_{\infty }$ performance level are proposed in terms of linear matrix inequalities (LMIs). Meanwhile, the static output control gains are solved explicitly by the proposed conditions. It is shown that the proposed method is less or at least the same conservative than the existing result. Lastly, a numerical example is given to demonstrate the effectiveness of the proposed method.