Robust finite-time \(H_\infty\) control for nonlinear Markovian jump systems with time delay under partially known transition probabilities (Q1725322)

Summary: 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.