Control-rate Constrained Output Feedback Design for LPV Systems subject to Bounded Disturbances

Abstract

This paper addresses the output feedback control design for Linear Parameter-Varying discrete-time systems subject to persistent disturbances while guaranteeing the fulfillment of state, control, and control variation constraints. The constrained control system is described in the extended state space composed of the system’s state and control variables, in which the control variations act as the control inputs. By leveraging the Robust Positive Invariance property, we propose a new set of algebraic conditions that are then used to build up a bilinear optimization problem that jointly computes an external set of admissible initial conditions, an internal set where the system’s trajectories will be ultimately bounded, and the necessary control gains to guarantee regional closed-loop stability. Furthermore, examples are provided to showcase the technique’s capabilities.