Positive real control for descriptor systems with uncertainties in the derivative matrix via a proportional plus derivative feedback

摘要

This article deals with the problem of normalisation and positive real control synthesis for a class of descriptor systems with uncertainties in the derivative matrix. Attention is focused on the design of a proportional plus derivative (PD) state feedback, which guarantees that the closed-loop system is quadratically normal and quadratically stable (QNQS) and the closed-loop transfer function is extended strictly positive real (ESPR). We first present a new linear matrix inequality (LMI) characterisation of positive realness for normal descriptor systems. This new characterisation provides a kind of decoupling among the Lyapunov matrix, the system matrix and the derivative matrix. Based on this, a necessary and sufficient condition for the desired PD controllers is given and a PD controller is constructed by solving LMIs. Finally, a numerical example is given to demonstrate that the proposed method is effective.