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

Abstract EN

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.