Positive realness and absolute stability problem of descriptor systems

Chunyu Yang, Qingling Zhang, Yanping Lin, Linna Zhou

Research output: Journal article publicationJournal articleAcademic researchpeer-review

47 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1142-1149
Number of pages8
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number5
Publication statusPublished - 1 May 2007
Externally publishedYes


  • Absolute stability
  • Descriptor systems
  • Linear matrix inequality (LMI)
  • Positive realness

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


Dive into the research topics of 'Positive realness and absolute stability problem of descriptor systems'. Together they form a unique fingerprint.

Cite this