Abstract
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 language | English |
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Pages (from-to) | 157-171 |
Journal | Nonlinear Dynamics and Systems Theory |
Volume | 13 |
Issue number | 2 |
Publication status | Published - 2013 |