Using polynomial semi-separable kernels to construct infinite-dimensional Lyapunov functions

Abstract-- In this paper, we introduce the class of semiseparable kernel functions for use in constructing Lyapunov functions for distributed-parameter systems such as delaydifferential and partial-differential equations. We then consider the subset of semi-separable kernel functions defined by polynomials. We show that the set of such kernels which define positive integral operators can be parameterized by positive semidefinite matrices. We also show that, unlike for the class of separable kernels, semi-separable kernels defined by polynomials correspond to integral operators which map to dense subspaces of L2. This means that for a system, the existence of a Lyapunov function defined by a Gaussian-type kernel function implies the existence of a Lyapunov function defined by a polynomial semi-separable kernel function.

• Type: Conference
• Year: 2008
• Where: CDC
• Authors: Matthew M. Peet, Antonis Papachristodoulou
• Keywords: CDC 2008, Control Systems, Kernel Function, Lyapunov Function, Semi-separable Kernel