Optimal disturbance attenuation for discrete-time switched and Markovian jump linear systems

J. I.Woong Lee, Geir E. Dullerud

Research output: Contribution to journalArticlepeer-review

Abstract

An exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete-time domain via the union of an increasing family of linear matrix inequality conditions. Associated with each Markovian jump linear system is a switched linear system, so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbance attenuation for Markovian jump linear systems as well. The results lead to semidefinite programming - based controller synthesis techniques, from which optimal finite-path-dependent linear dynamic output feedback controllers arise naturally. In particular, under the notion of path-by-path optimal disturbance attenuation, finite-path-dependent controllers can outperform the usual modedependent ones.

Original languageEnglish (US)
Pages (from-to)1329-1358
Number of pages30
JournalSIAM Journal on Control and Optimization
Volume45
Issue number4
DOIs
StatePublished - 2006

Keywords

  • Discrete linear inclusions
  • Dynamic output feedback
  • H control
  • Linear matrix inequalities
  • Linear time-varying systems
  • Semidefinite programming

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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