Positive real control for discrete-time singular systems with affine parameter dependence

This paper presents a less conservative and numerically tractable solution to the static state feedback positive real control problem for affinely parameter dependent discrete-time singular systems. Relied on the use of auxiliary matrices and a positive scalar decision variable, a novel necessary and sufficient condition of positive realness is first derived in terms of a strict matrix inequality for linear time-invariant discrete-time singular systems. This characterization leads to a numerically efficient and reliable way for the controller design synthesis. Then, the results are further expanded to parameter dependent singular systems whose coefficient matrices are affine functions of a time-invariant uncertain parameter vector. Both robust analysis and robust controller synthesis are addressed. Numerical examples are included to illustrate the effectiveness of the present results. (C) 2014 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.