H∞ control of singular Markovian jump systems with operation modes disordering in controller

This paper considers the H-infinity control problem for a class of singular Markovian jump systems, where the operation mode of controller has disordering phenomenon. Because of operation modes in system matrices and control gains having a disagreement, an augment Markov chain is introduced, and the corresponding controller is related to the new operation mode. In stead of designing a controller with new operation mode directly, a kind of H-infinity controller related to the original operation mode is developed by using non-fragile control method, which is composed of controllers depending on the new operation modes and satisfies a minimum variance approximation. All the proposed conditions are given in terms of linear matrix inequalities. A numerical example is used to demonstrate the effectiveness of the proposed method.