Design of Robust Output Feedback Controllers for Discrete-Time Systems with Polynomial Uncertainties

This paper addresses the robust dynamic output feedback (DOF) problem for linear parameter-varying (LPV) discrete-time systems with polynomial dependence of uncertainties. For this purpose, the robust control problem is formulated via linear matrix inequalities (LMI) using Lyapunov's theory for a stability proof. Two relaxation methods are required to solve the robust LMI problem. The first is necessary to expand the Lyapunov stability condition to the structured linear control (SLC) problem for DOF controllers. The second type of relaxation is based on the theorem of Ehlich and Zeller and is required to include the polynomial dependence of uncertainties in the LMI design. These two relaxation methods yield an iterative LMI optimization approach. In this paper, we consider the specific example of a robust I-PD controller with a predefined decay rate that satisfies
$H$
∞
conditions for a polynomial parameter-dependent uncertain system.