Observer‐based H∞ control for Markovian jump systems with time‐varying delays and incomplete transition rates

Summary This paper addresses the observer‐based H∞ control of Markovian jump systems with interval time‐varying delays and incomplete transition rates. To reduce the conservatism of proposed results, a modified Lyapunov‐Krasovskii functional is constructed, where an improved delay partitioning method is used by partitioning the delay interval into multiple segments with a geometric sequence. Moreover, the Jensen‐based integral inequality and the reciprocally convex technique are used to tackle the time‐varying delays. Some less conservative stochastic stability criteria are derived in the framework of linear matrix inequalities. Then, the observer‐based H∞ controller is designed. Finally, three numerical examples are given to demonstrate the merit and effectiveness of the proposed method.