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

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 pCLFs 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.

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Mircea Lazar, Rob H. Gielen
• Keywords: CDC 2010, Control Systems, Discrete-time Nonlinear Systems, Lyapunov Functions, Standard Lyapunov Properties