Robust Finite-Time Dissipative Output-Feedback Control of Linear Time-Varying Discrete-Time Uncertain Systems

This paper presents the design of a dissipativity-based output feedback control for transient performance im-provement in linear time-varying discrete-time systems. The un-certain system dynamics is described in a convex polytope, and is subjected to bounded external disturbances. The proposed reduced-order time-varying dynamic controller guarantees that the system trajectories are bounded below a specified threshold for a given finite time interval. Moreover, using the notion of QSR-dissipativity, we aim for the system to simultaneously satisfy dissipativity to external disturbances within the considered finite time interval. Sufficient difference linear matrix inequality (DLMI) conditions are derived to design output feedback finite-time dissipative controller gains, considering the augmented form of the closed-loop system-controller dynamics. The paper unifies the procedure of designing finite-time robust controllers, as performance indices such as finite-time passivity and finite
$\mathscr{L}_2$
-gain are special cases of finite-time dissipativity. Numerical simulations demonstrate the effectiveness of the proposed scheme in bounding the state trajectories within the prescribed limit, for a specified finite time interval.