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

M. Lazar; R.H. Gielen

doi:10.1109/CDC.2010.5716952

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

M. Lazar, R.H. Gielen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-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 language	English
Title of host publication	Proceedings of the 49th IEEE Conference on Decision and Control [CDC] , 15-17 December 2010, Atlanta
Place of Publication	Atlanta, GA
Publisher	Institute of Electrical and Electronics Engineers
Pages	3264-
ISBN (Print)	978-1-4244-7745-6
DOIs	https://doi.org/10.1109/CDC.2010.5716952
Publication status	Published - 2010
Event	49th IEEE Conference on Decision and Control (CDC 2010) - Atlanta, United States Duration: 15 Dec 2010 → 17 Dec 2010 Conference number: 49

Conference

Conference	49th IEEE Conference on Decision and Control (CDC 2010)
Abbreviated title	CDC 2010
Country	United States
City	Atlanta
Period	15/12/10 → 17/12/10

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title = "On parameterized Lyapunov and control Lyapunov functions for discrete-time systems",

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.",

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Lazar, M & Gielen, RH 2010, On parameterized Lyapunov and control Lyapunov functions for discrete-time systems. in Proceedings of the 49th IEEE Conference on Decision and Control [CDC] , 15-17 December 2010, Atlanta. Institute of Electrical and Electronics Engineers, Atlanta, GA, pp. 3264-, 49th IEEE Conference on Decision and Control (CDC 2010), Atlanta, United States, 15/12/10. https://doi.org/10.1109/CDC.2010.5716952

On parameterized Lyapunov and control Lyapunov functions for discrete-time systems. / Lazar, M.; Gielen, R.H.

Proceedings of the 49th IEEE Conference on Decision and Control [CDC] , 15-17 December 2010, Atlanta. Atlanta, GA : Institute of Electrical and Electronics Engineers, 2010. p. 3264-.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AB - 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.

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