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

M. Lazar, R.H. Gielen

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
4 Downloads (Pure)


This 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 are discussed. These methods require solving on-line a low-complexity convex optimization problem.
Original languageEnglish
Pages (from-to)157-171
JournalNonlinear Dynamics and Systems Theory
Issue number2
Publication statusPublished - 2013


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