A sampling approach to constructing Lyapunov functions for nonlinear continuous–time systems

R.V. Bobiti, M. Lazar

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

2 Citations (Scopus)

Abstract

The problem of constructing a Lyapunov function for continuous-time nonlinear dynamical systems is tackled in this paper via a sampling-based approach. The main idea of the sampling-based method is to verify a Lyapunov-type inequality for a finite number of points (known state vectors) in the state-space and then to extend the validity of the Lyapunov inequality to a neighborhood around these points. In this way, the validity of a Lyapunov function candidate can be certified for a region of interest in the state-space in a systematic way. A candidate Lyapunov function is computed for each sample point using a recent converse Lyapunov theorem for continuous-time nonlinear systems. For certifying the candidate Lyapunov function on a neighborhood of the sampling point we propose both a deterministic and a probabilistic approach. The deterministic approach provides a formal guarantee at the cost of verifying a more conservative Lyapunov inequality, which is not valid in a neighborhood of the origin. The probabilistic approach verifies the original Lyapunov inequality and provides a probabilistic guarantee in terms of a reliability estimate. An example from the literature illustrates the proposed sampling-based approach.
Original languageEnglish
Title of host publication55th IEEE Conference on Decision and Control, 12-14 December 2016, Las Vegas, Nevada
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages2170-2175
Number of pages6
ISBN (Electronic)978-1-5090-1837-6
ISBN (Print)978-1-5090-1838-3
DOIs
Publication statusPublished - 2016

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