Guaranteed Cost Robust Output Feedback Control for Finite-time Boundedness of Uncertain Linear Systems

A problem of designing reduced order robust dynamic output feedback controller for uncertain linear systems is considered. The controller design aims to guarantee an upper bound on the considered disturbance attenuation performance of the system. For all admissible uncertainties and the worst case of external disturbances, the designed controller ensures finite-time boundedness of system trajectories, while minimizing the upper bound of the considered objective function. Sufficient conditions for the existence of such an output feedback controller are derived in terms of differential matrix inequalities. An iterative algorithm is proposed to synthesize the desired controller.