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

This paper considers the H∞H∞ control problem for a class of singular Markovian jump systems, where the operation mode of a controller has a disordering phenomenon. Because of the operation modes in system matrices and control gains having a disagreement, an augmented Markov chain is introduced, and the corresponding controller is related to the new operation mode. Instead of designing a controller of new operation mode directly, a kind of H∞H∞ controller referring to the original operation mode is developed, which is composed of controllers depending on the new operation modes and satisfies a minimum variance approximation. Based on the developed methods, a special case of mode-independent control is studied. All the proposed conditions are given in terms of linear matrix inequalities. A numerical example is used to demonstrate the effectiveness of the proposed methods.