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An LMI approach for H2 dynamic output feedback control of discrete-time Markov systems with uncertain probabilities

This paper is concerned with the problem of H2 dynamic output feedback control for discrete-time Markov jump linear systems (MJLS) whose transition probability matrix is affected by uncertainties. A two step procedure based on linear matrix inequality (LMI) conditions is used to solve the problem. In the first step, a stabilizing parameter-dependent state feedback gain is computed. The gain, not implementable, is used as an input in the second step, where sufficient LMI conditions provide an H2 guaranteed cost dynamic output feedback controller for the MJLS. Reduced order and mode-independent controllers can be readily obtained from the conditions, due to the fact that the matrices of the controller realization are constructed only in terms of decision variables. As illustrated by an example, less conservative controllers with more accurate estimates of the H2 norm bound can be obtained through the proposed methodology. Moreover, lower H2 bounds can be guaranteed at the price of searching for a scalar parameter and increasing the degrees of the polynomial decision variables involved in the optimization process.