H∞ And H2 Control Design For Polytopic Continuous-time Markov Jump Linear Systems With Uncertain Transition Rates

This paper investigates the problems of H∞ and H2 state feedback control design for continuous-time Markov jump linear systems. The matrices of each operation mode are supposed to be uncertain, belonging to a polytope, and the transition rate matrix is considered partly known. By appropriately modeling all the uncertain parameters in terms of a multi-simplex domain, new design conditions are proposed, whose main advantage with respect to the existing ones is to allow the use of polynomially parameter-dependent Lyapunov matrices to certify the mean square closed-loop stability. Synthesis conditions are derived in terms of matrix inequalities with a scalar parameter. The conditions, which become LMIs for fixed values of the scalar, can cope with H∞ and H2 state feedback control in both mode-independent and mode-dependent cases. Using polynomial Lyapunov matrices of larger degrees and performing a search for the scalar parameter, less conservative results in terms of guaranteed costs can be obtained through LMI relaxations. 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