$ \mathcal{H}_{\infty} $ control for fuzzy markovian jump systems based on sampled-data control method
Xingyue Liang, Jianwei Xia, Guoliang Chen, Huasheng Zhang, Zhen Wang · Discrete and Continuous Dynamical Systems - S · 2020
This paper investigates the problems of $ \mathcal{H}_{\infty} $ performance analysis and sampled-data control about fuzzy Markovian jump systems. Firstly, in order to make full use of the information of both intervals $ x(t_{k}) $ to $ x(t) $ and $ x(t) $ to $ x(t_{k+1}) $, we construct the mode-dependent Lyapunov function, which consists of a two-sided closed-loop function. Built on the above Lyapunov function, the stochastically stable conditions with less conservative are given by using linear matrices inequalities (LMIs). Then, a state feedback controller is presented for the studied systems. At last, an example is offered to illustrate the efficiency of our main results.