Quadratic Performance Analysis of Switched Affine Time-Varying Systems

Wenzhi Li, Chi Huang, Guisheng Zhai

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We analyze quadratic performance for switched systems which are composed of a finite set of affine time-varying subsystems, where both subsystem matrices and affine vectors are switched, and no single subsystem has desired quadratic performance. The quadratic performance indexes we deal with include stability, tracking and L2 gain. We show that if a linear convex combination of subsystem matrices is uniformly Hurwitz and another convex combination of affine vectors is zero, then we can design a state-dependent switching law (state feedback) and an output-dependent switching law (output feedback) such that the entire switched affine system is quadratically stable at the origin. In the case where the convex combination of affine vectors is nonzero, we show that the tracking control problem can be posed and solved using a similar switching strategy. Finally, we consider the L2gain analysis problem for the switched affine time-varying systems under state feedback.

Original languageEnglish
Pages (from-to)429-440
Number of pages12
JournalInternational Journal of Applied Mathematics and Computer Science
Issue number3
Publication statusPublished - 2018 Sept 1


  • L2 gain
  • differential LMIs
  • observers
  • quadratic stabilization
  • switched affine systems
  • switching law
  • time-varying systems
  • tracking

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Engineering (miscellaneous)
  • Applied Mathematics


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