Stabilization of discrete-time switched linear systems: Lyapunov-Metzler inequalities versus S-procedure characterizations

A. Kundu, J. Daafouz, W.P.M.H. Heemels

Research output: Contribution to journalConference articleAcademicpeer-review

Abstract

In this paper we study connections between Lyapunov-Metzler inequalities and S-procedure characterizations in the context of stabilizing discrete-time switched linear systems using min-switching strategies. We propose two generalized versions of S-procedure characterization along the lines of the generalized versions of Lyapunov-Metzler inequalities recently proposed in the literature. It is shown that the existence of a solution to the generalized version(s) of Lyapunov-Metzler inequalities is equivalent to the existence of a solution to the generalized version(s) of S-procedure characterization with a restricted choice of the scalar quantities involved in the latter. This recovers some of our earlier works on the classical Lyapunov-Metzler inequalities as a special case. We also highlight and discuss an open question of whether the generalized versions of S-procedure characterization are strictly less conservative than the generalized versions of Lyapunov-Metzler inequalities, which in turn are equivalent to periodic stabilizability as was recently shown.

Original languageEnglish
Pages (from-to)3412-3417
Number of pages6
JournalIFAC-PapersOnLine
Volume50
Issue number1
DOIs
Publication statusPublished - 1 Jul 2017

Keywords

  • Discrete-time switched linear systems
  • Lyapunov-Metzler inequalities
  • matrix inequalities
  • min-switching strategy
  • S-procedure characterizations
  • stabilizability

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