Output Reachable Set Estimation for Switched Linear Systems and Its Application in Safety Verification

Weiming Xiang, Hoang Dung Tran, Taylor T. Johnson

Research output: Contribution to journalArticlepeer-review

50 Scopus citations


This paper addresses the output reachable set estimation problem for continuous-time switched linear systems consisting of Hurwtiz stable subsystems. Based on a common Lyapunov function approach, the output reachable set is estimated by a union of bounding ellipsoids. Then, multiple Lyapunov functions with time-scheduled structure are employed to estimate the output reachable set for switched systems under dwell-time constraint. Furthermore, the safety verification problem of uncertain switched systems is investigated based on the result of output reachable set estimation. First, a sufficient condition ensuring the existence of an approximate bisimulation relation between two switched linear systems with a prescribed precision is proposed. Then, the safety verification for an uncertain switched system can be performed through an alternative safety verification for a switched system with exact parameters. Numerical examples are provided to illustrate our results.

Original languageEnglish (US)
Article number7894251
Pages (from-to)5380-5387
Number of pages8
JournalIEEE Transactions on Automatic Control
Issue number10
StatePublished - Oct 2017
Externally publishedYes


  • Reachable set estimation
  • safety verification
  • switched system
  • uncertain system

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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