Positive Realness and Absolute Stability Problem of Descriptor Systems

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 54; no. 5; pp. 1142 - 1149
• Main Authors: Yang, C, Zhang, Q, Lin, Y, Zhou, L
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.05.2007; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Absolute stability; Circuits; Control systems; Control theory; Criteria; descriptor systems; Equivalence; Feasibility; Frequency domain analysis; Linear matrix inequalities; linear matrix inequality (LMI); Linear systems; Lyapunov method; Nonlinearity; positive realness; Riccati equations; Stability; Stability criteria; State feedback
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2007.895516

This paper considers a class of nonlinear descriptor systems described by a linear time-invariant descriptor system with feedback-connected sector-constrained nonlinearities. First, we discuss the positive realness problem of descriptor systems and present a new version of positive real lemma. Second, we define the notion of strongly absolute stability (SAB) which is equivalent to the linear part is regular and impulsive-free and the overall feedback system is exponential stable and a SAB criteria in frequency domain is derived. Then, we address the problem of designing a state feedback controller such that the closed-loop feedback-connected system is SAB. To achieve this, we give a linear matrix inequality (LMI)-based SAB criteria, and the above problem is converted into an LMI feasibility problem. Finally, some numerical examples are given to illustrate our approach