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

This paper is concerned with the problem of robust finite‐time H∞ 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∞ finite‐time boundedness, and finite‐time H∞ state feedback stabilization, respectively. Then, a robust finite‐time H∞ state feedback controller is designed, which, for all admissible uncertainties, guarantees the H∞ 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.