On the decidability of stability of hybrid systems

Pavithra Prabhakar, Mahesh Viswanathan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A rectangular switched hybrid system with polyhedral invariants and guards, is a hybrid automaton in which every continuous variable is constrained to have rectangular flows in each control mode, all invariants and guards are described by convex polyhedral sets, and the continuous variables are not reset during mode changes. We investigate the problem of checking if a given rectangular switched hybrid system is stable around the equilibrium point 0. We consider both Lyapunov stability and asymptotic stability. We show that checking (both Lyapunov and asymptotic) stability of planar rectangular switched hybrid systems is decidable, where by planar we mean hybrid systems with at most 2 continuous variables. We show that the stability problem is unde-cidable for systems in 5 dimensions, i.e., with 5 continuous variables.

Original languageEnglish (US)
Title of host publicationHSCC 2013 - Proceedings of the 16th International Conference on Hybrid Systems
Subtitle of host publicationComputation and Control, Part of CPSWeek 2013
Pages53-62
Number of pages10
DOIs
StatePublished - Dec 1 2012
Event16th International Conference on Hybrid Systems: Computation and Control, HSCC 2013 - Part of CPSWeek 2013 - Philadelphia, PA, United States
Duration: Apr 8 2013Apr 11 2013

Publication series

NameHSCC 2013 - Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control, Part of CPSWeek 2013
Volume1

Other

Other16th International Conference on Hybrid Systems: Computation and Control, HSCC 2013 - Part of CPSWeek 2013
CountryUnited States
CityPhiladelphia, PA
Period4/8/134/11/13

Keywords

  • Decidability
  • Stability
  • Verification

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Control and Systems Engineering

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    Prabhakar, P., & Viswanathan, M. (2012). On the decidability of stability of hybrid systems. In HSCC 2013 - Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control, Part of CPSWeek 2013 (pp. 53-62). (HSCC 2013 - Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control, Part of CPSWeek 2013; Vol. 1). https://doi.org/10.1145/2461328.2461339