H∞ control for Markovian jump systems with partially unknown transition rates via an adaptive method

This paper investigates the problem of the H∞H∞ control for a class of continuous-time Markovian jump systems with partially unknown transition rates. An adaptive H∞H∞ performance index is defined to describe the disturbance attenuation performance of Markovian jump systems. By combining the linear matrix inequality (LMI) approach for designing H∞H∞ controllers and the adaptive method for estimating the unknown terms, a new method for designing the H∞H∞ controllers is proposed, where an estimation of the transition rate matrix is given and the controller parameter matrices are dependent on the known transition rates and the estimations of the unknown terms. The sufficient conditions for the existence of the adaptive state feedback controller and the adaptive dynamic output feedback controller are proposed and the estimations of the unknown transition rates are obtained from the adaptive laws. It is shown that the proposed adaptive controllers provide better performance than the traditional fixed gain controllers. A practical example is provided to illustrate the effectiveness and advantage of the proposed method.