Observer-Based Finite-Time Fuzzy H∞ Control for Markovian Jump Systems with Time-Delay and Multiplicative Noises

In this article, the observer-based finite-time H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\infty$$\end{document} control (OFTHC) issue is considered for a category of nonlinear discrete-time Markovian jump systems (DMJSs) with multiplicative noises and time-delay. The nonlinear object is described via linear Takagi Sugeno (T–S) fuzzy model (TSFM). State feedback is an effective method to realize system control, which requires all states to be measurable. In the presence of the system state is not fully measurable, an observer-based state feedback controller (OSFC) represented by TSFM is designed via the parallel distributed compensation (PDC) method. By applying Lyapunov functional and linear matrix inequality (LMI) methods, sufficient criteria are given, which guarantee the resulting closed-loop systems (CLSs) finite-time boundedness (FTB) with a specified H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\infty$$\end{document} attenuation level. Finally, numerical simulations are employed to prove the feasibility of the developed techniques.