Robust output feedback controller design with covariance and disc closed-loop pole constraints

This paper is concerned with the problem of robust output feedback controller design for a class of linear discrete-time systems with norm-bounded uncertainty. The objective is to design a controller such that the closed-loop poles are assigned within a specified disc and the steady regulated output covariance is guaranteed to be less than a given upper bound. Using a linear matrix inequality (LMI) approach, the existence conditions of such controllers are derived and a parametrized characterization of a set of desired controllers (if they exist) is presented in terms of the feasible solutions to a set of LMIs. A procedure is given to select a suitable output feed-back controller that minimizes the desired control effort.