Quadratic stabilizability of switched linear systems with polytopic uncertainties

Guisheng Zhai, Hai Lin, Panos J. Antsaklis

Research output: Contribution to journalArticlepeer-review

251 Citations (Scopus)


In this paper, we consider quadratic stabilizability via state feedback for both continuous-time and discrete-time switched linear systems that are composed of polytopic uncertain subsystems. By state feedback, we mean that the switchings among subsystems are dependent on system states. For continuous-time switched linear systems, we show that if there exists a common positive definite matrix for stability of all convex combinations of the extreme points which belong to different subsystem matrices, then the switched system is quadratically stabilizable via state feedback. For discrete-time switched linear systems, we derive a quadratic stabilizability condition expressed as matrix inequalities with respect to a family of non-negative scalars and a common positive definite matrix. For both continuous-time and discrete-time switched systems, we propose the switching rules by using the obtained common positive definite matrix.

Original languageEnglish
Pages (from-to)747-753
Number of pages7
JournalInternational Journal of Control
Issue number7
Publication statusPublished - 2003 May 10
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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