Journal of Mathematical Analysis and Applications zyxw 239, 7-19 (1999) Article ID jmaa. 1999.6455,available online at http://www.idealibrary.com on zy I DE hL3 Stability and Positive Realness of Time-Delay Systems Magdi S. Mahmoud Electrical and Computer Engineering Dept., Kuwait Unirwsily, P. 0. zy Box 5969, Safat-I30 60, Kuwait E-mail: magdi@eng.kuniv.edu.kw and Lihua Xie School zyxwvuts of Electrical and Electronic Engineering, Nanyang Technological Unir ersity, NanyangAr enue, Singapore 63979S, Singapore Submitted by C. T. Leondes Received May 7, 1998 In this paper, a class of linear time invariant systems with state delay is considered. A state-space characterization of the conditions for positive realness of the time-delay system is provided which extends existing positive real results for systems without delay. The developed results are expressed in terms of linear matrices or algebraic Riccati inequalities. o 1999 Academic Press 1. INTRODUCTION Time delays arise in connection with system measurements or due to physical properties of flow such as hydraulic systems and rolling mills. Other sources of delay often occur in the transmission of information between different parts of dynamical systems including chemical process- ing systems, communication systems, and power systems. Considerable research has been done for more than three decades on various aspects of dynamical systems with delay factors in the state variables and/or control inputs [l, 21. In recent years, output-feedback control schemes have been developed for the stabilization of a wide class of time-delay systems; see [3-61 and references cited therein. On another front of research, positive real theory has played a major role in stability and systems theory [7, 81. The primary motivation for designing strict positive real controllers is application to positive real plants. When a strict positive real system is 7 0022-247)3/99 $30.00 Copyright 0 1999 hy Academic Press All rights of reproduction in any form reserved.