Positive Real Control for Uncertain Singular Time-Delay Systems via Output Feedback Controllers

Abstract

This paper deals with the problem of positive real control for continuous singular systems with time delays and norm-bounded parameter uncertainties. The problem we address here is the design of an output feedback controller such that the resulting closed-loop system is regular, impulse-free and stable, while the closed-loop transfer function from the disturbance to the controlled output is extended strictly positive real for all admissible uncertainties. A sufficient condition for the solvability of this problem is obtained and a linear matrix inequality approach is developed. In addition, an explicit expression for the construction of a desired output feedback controller is given. An illustrative example is provided to demonstrate the effectiveness and applicability of the proposed approach.