Reachable set estimation for switched linear systems with dwell-time switching

Simone Baldi, Weiming Xiang

Research output: Contribution to journalArticle

Abstract

In this work we address the problem of (outer) estimation of reachable sets in switched linear systems subject to dwell-time switching. After giving some conditions that exploit the well-known properties of exponential decrease/bounded increase of the Lyapunov function (i.e. exponential decrease in between switching times and bounded increase at switching times), we overcome the need for such properties. This is done by introducing a new notion of τ-reachable set, i.e. the set that can be reached by the trajectories defined at time τ after the switch. Such extended notion of reachable set can be used to parametrize the estimate of the reachable set as a function of the distance in time from the switch. Two approaches are provided to implement such parametrization: the first approach exploits the evolution of the system in between switches via the matrix exponential of the state subsystem matrix; the second approach exploits a time-scheduled Lyapunov function. A numerical example is provided to show the effectiveness of the proposed methods and computational cost is addressed.

Original languageEnglish (US)
Pages (from-to)20-33
Number of pages14
JournalNonlinear Analysis: Hybrid Systems
Volume29
DOIs
StatePublished - Aug 1 2018

Fingerprint

Switched Linear Systems
Reachable Set
Dwell Time
Linear systems
Switches
Lyapunov functions
Switch
Lyapunov Function
Matrix Exponential
Decrease
Trajectories
Parametrization
Computational Cost
Subsystem
Costs
Trajectory
Numerical Examples
Estimate

Keywords

  • Dwell-time switching
  • Reachable set estimation
  • Switched linear systems

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Analysis
  • Computer Science Applications

Cite this

Reachable set estimation for switched linear systems with dwell-time switching. / Baldi, Simone; Xiang, Weiming.

In: Nonlinear Analysis: Hybrid Systems, Vol. 29, 01.08.2018, p. 20-33.

Research output: Contribution to journalArticle

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