Guaranteed Cost Robust Control for Finite-Time Boundedness of LTI Systems using Output Feedback

A problem of designing dynamic output feedback robust controller for LTI systems is considered. The reduced order controller design aims to guarantee a minimum bound in terms of disturbance attenuation performance. For a finite-time interval, the designed min-max controller attenuates the effect of worst case external disturbances and bounds the system trajectories to a predefined set, over all possible initial conditions. Sufficient conditions for the existence of such controller are formulated using differential matrix inequalities and the upper bound on the cost function can be minimized using the proposed algorithm.