H controller design for a class of switched linear discrete-time system with polytopic uncertainties

Weiming Xiang, Jian Xiao

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


In this article, a new parameter-dependent stability criterion for switched linear discrete-time systems with polytopic uncertainties is provided to correct an error occurring in previous work, and the parameter-dependent idea is extended to ℓ2 gain analysis problem. Particularly, a less conservative result is proposed by introducing additional slack matrices. Furthermore, the H control problem is investigated. Due to the online calculation characteristic of parameter-dependent controller, a controller structure with less computation cost is of interest. Aside from the controller with the same form as in some existing results involving matrix multiplication and inversion operators, another simple structure of controller formulated by a convex combination of a set of matrices is proposed, which can reduce the online computation cost significantly. A numerical example and results of simulation performed on the model of two-mass-spring mechanical system are provided to illustrate the theoretical findings within this article.

Original languageEnglish (US)
Pages (from-to)1311-1322
Number of pages12
JournalProceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering
Issue number10
StatePublished - Nov 1 2012
Externally publishedYes


  • ℓ gain
  • H control
  • Stability
  • Switched systems
  • Time-varying polytopic uncertainties

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering


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