On parameterized Lyapunov and control Lyapunov functions for discrete-time systems

M. Lazar, R.H. Gielen

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

5 Citations (Scopus)

Abstract

his paper deals with the existence and synthesis of parameterized-(control) Lyapunov functions (p-(C)LFs) for discrete-time nonlinear systems that are possibly subject to constraints. A p-LF is obtained by associating a finite set of parameters to a standard LF. A set-valued map, which generates admissible sets of parameters, is defined such that the corresponding p-LF enjoys standard Lyapunov properties. It is demonstrated that the so-obtained p-LFs offer non-conservative stability analysis conditions, even when Lyapunov functions with a particular structure, such as quadratic forms, are considered. Furthermore, possible methods for synthesizing p-CLFs for discrete-time nonlinear systems are discussed. These methods make use of the receding horizon principle and require solving on-line a low-complexity convex optimization problem.
Original languageEnglish
Title of host publicationProceedings of the 49th IEEE Conference on Decision and Control [CDC] , 15-17 December 2010, Atlanta
Place of PublicationAtlanta, GA
PublisherInstitute of Electrical and Electronics Engineers
Pages3264-
ISBN (Print)978-1-4244-7745-6
DOIs
Publication statusPublished - 2010
Event49th IEEE Conference on Decision and Control (CDC 2010) - Atlanta, United States
Duration: 15 Dec 201017 Dec 2010
Conference number: 49

Conference

Conference49th IEEE Conference on Decision and Control (CDC 2010)
Abbreviated titleCDC 2010
CountryUnited States
CityAtlanta
Period15/12/1017/12/10

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