Unified stability criteria for slowly time-varying and switched linear systems

Xiaobin Gao, Daniel Liberzon, Ji Liu, Tamer Başar

Research output: Contribution to journalArticle


This paper presents a unified approach to formulating stability conditions for slowly time-varying linear systems and switched linear systems. The concept of total variation is generalized to the case of matrix-valued functions. Using this generalized concept, a result extending existing stability conditions for slowly time-varying linear systems is derived. As special cases of this result, two sets of stability conditions are derived for switched linear systems, which match known results in the literature. A numerical example is included to further illustrate the application of the main result.

Original languageEnglish (US)
Pages (from-to)110-120
Number of pages11
StatePublished - Oct 2018



  • Linear systems
  • Slowly time-varying systems
  • Stability
  • Switched systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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