Robust Finite-Time H ∞ Control for Nonlinear Markovian Jump Systems with Time Delay under Partially Known Transition Probabilities

Abstract

This paper is concerned with the problem of robust finite-time $H_{\infty }$ control for a class of nonlinear Markovian jump systems with time delay under partially known transition probabilities. Firstly, for the nominal nonlinear Markovian jump systems, sufficient conditions are proposed to ensure finite-time boundedness, $H_{\infty }$ finite-time boundedness, and finite-time $H_{\infty }$ state feedback stabilization, respectively. Then, a robust finite-time $H_{\infty }$ state feedback controller is designed, which, for all admissible uncertainties, guarantees the $H_{\infty }$ finite-time boundedness of the corresponding closed-loop system. All the conditions are presented in terms of strict linear matrix inequalities. Finally a numerical example is provided to demonstrate the effectiveness of all the results.