Guaranteed cost controllers under pole placement constraints for uncertain linear systems: an LMI approach

This paper deals with the problem of synthesizing dynamic output feedback controller minimizing the upper bound of quadratic cost under pole placement constraint for a polytopic uncertain linear plant. First, the mathematical model of polytopic uncertain linear plant with dynamic output feedback controller is given. Next, the necessary and sufficient condition for assigning all poles of closed-loop system in a preassigned region and the sufficient condition for guaranteeing an upper bound of cost are described as bilinear matrix inequalities. These are reduced to linear matrix inequalities. The problem of finding controller which achieves two objectives can be reduced to a convex optimization problem (COP) and, furthermore, to a convex feasibility problem using the solution of the COP. The controller is numerically obtained by using a software package. Finally, an example is provided to illustrate the methodology