Positive Observers and Dynamic Output-Feedback Controllers for Interval Positive Linear Systems

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 55; no. 10; pp. 3209 - 3222
• Main Authors: Zhan Shu, Lam, J., Huijun Gao, Baozhu Du, Ligang Wu
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2008; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Control system synthesis; Control systems; Controllers; Dynamic output-feedback; Dynamical systems; Dynamics; Error correction; interval systems; Linear matrix inequalities; linear matrix inequalities (LMIs); Linear systems; Mathematical analysis; Matrices; Matrix decomposition; Matrix methods; Observers; Optimization algorithms; positive observers; positive systems; Signal design; Signal synthesis; Studies; Sufficient conditions; uncertain systems; Uncertainty; positive observers; interval systems; linear matrix inequalities; uncertain systems; Dynamic output-feedback
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2008.924116

This paper is concerned with the design of observers and dynamic output-feedback controllers for positive linear systems with interval uncertainties. The continuous-time case and the discrete-time case are both treated in a unified linear matrix inequality (LMI) framework. Necessary and sufficient conditions for the existence of positive observers with general structure are established, and the desired observer matrices can be constructed easily through the solutions of LMIs. An optimization algorithm to the error dynamics is also given. Furthermore, the problem of positive stabilization by dynamic output-feedback controllers is investigated. It is revealed that an unstable positive system cannot be positively stabilized by a certain dynamic output-feedback controller without taking the positivity of the error signals into account. When the positivity of the error signals is considered, an LMI-based synthesis approach is provided to design the stabilizing controllers. Unlike other conditions which may require structural decomposition of positive matrices, all proposed conditions in this paper are expressed in terms of the system matrices, and can be verified easily by effective algorithms. Two illustrative examples are provided to show the effectiveness and applicability of the theoretical results.