The Mixed Robust H∞/FTS Control Problem Analysis and State Feedback Control

In this paper we deal with the mixed H-infinity/finite-time stability control problem. More specifically, given an open loop uncertain linear system, we provide a necessary and sufficient condition for quadratic input-output finite-time stability with an H-infinity bound. Exploiting this result we also give a sufficient condition to solve the related synthesis problem via state-feedback. The property of quadratic input-output finite-time stability with an H-infinity bound implies that the system under consideration satisfies an H-infinity performance bound between the disturbance input and the controlled output and, at the same time, is input-output finite-time stable for all admissible uncertainties. This condition requires the solution of a feasibility problem constrained by a pair of differential linear matrix inequalities (LMIs) coupled with a time-varying LMI. The proposed technique is illustrated by means of both a numerical and a physical example.