H∞ Control for Markov Jump Systems with Nonlinear Noise Intensity Function and Uncertain Transition Rates

The problem of robust H∞ control is investigated for Markov jump systems with nonlinear noise intensity function and uncertain transition rates. A robust H∞ performance criterion is developed for the given systems for the first time. Based on the developed performance criterion, the desired H∞ state-feedback controller is also designed, which guarantees the robust H∞ performance of the closed-loop system. All the conditions are in terms of linear matrix inequalities (LMIs), and hence they can be readily solved by any LMI solver. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed methods