A sum-of-squares approach to the analysis of Zeno stability in polynomial hybrid systems

Chaitanya Murti, Matthew Peet

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

3 Citations (Scopus)

Abstract

Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finite-time asymptotic stability, and corresponding Lyapunov theorems have been developed. In this paper, we propose a method to construct Lyapunov functions to prove Zeno stability of compact sets in cyclic hybrid systems with parametric uncertainties in the vector fields, domains and guard sets, and reset maps utilizing sum-of-squares programming. This technique can easily be applied to cyclic hybrid systems without parametric uncertainties as well. Examples illustrating the use of the proposed technique are also provided.

Original languageEnglish (US)
Title of host publication2013 European Control Conference, ECC 2013
Pages1657-1662
Number of pages6
StatePublished - 2013
Event2013 12th European Control Conference, ECC 2013 - Zurich, Switzerland
Duration: Jul 17 2013Jul 19 2013

Other

Other2013 12th European Control Conference, ECC 2013
CountrySwitzerland
CityZurich
Period7/17/137/19/13

Fingerprint

Hybrid systems
Polynomials
Lyapunov functions
Asymptotic stability
Dynamical systems
Uncertainty

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Murti, C., & Peet, M. (2013). A sum-of-squares approach to the analysis of Zeno stability in polynomial hybrid systems. In 2013 European Control Conference, ECC 2013 (pp. 1657-1662). [6669823]

A sum-of-squares approach to the analysis of Zeno stability in polynomial hybrid systems. / Murti, Chaitanya; Peet, Matthew.

2013 European Control Conference, ECC 2013. 2013. p. 1657-1662 6669823.

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

Murti, C & Peet, M 2013, A sum-of-squares approach to the analysis of Zeno stability in polynomial hybrid systems. in 2013 European Control Conference, ECC 2013., 6669823, pp. 1657-1662, 2013 12th European Control Conference, ECC 2013, Zurich, Switzerland, 7/17/13.
Murti C, Peet M. A sum-of-squares approach to the analysis of Zeno stability in polynomial hybrid systems. In 2013 European Control Conference, ECC 2013. 2013. p. 1657-1662. 6669823
Murti, Chaitanya ; Peet, Matthew. / A sum-of-squares approach to the analysis of Zeno stability in polynomial hybrid systems. 2013 European Control Conference, ECC 2013. 2013. pp. 1657-1662
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