Robust observer-based mixed H2/H∞ control design for uncertain linear discrete-time systems

This paper is concerned with the robust observer-based mixed H₂/H_∞ control design for a class of uncertain linear discrete-time systems. A new sufficient condition for the existence of an observer-based controller is given in the term of linear matrix inequality, which can lead to a less conservative result. The sufficient condition for the existence of an observer-based mixed H₂/H_∞ controller is then derived, and a convex optimization method is presented to get the desired observer-based controller with the minimized H₂/H_∞ performances. Numerical examples are given to indicate the novelty and effectiveness of the proposed approach.