Inversion of Separable Kernel Operators in Coupled Differential-Functional Equations and Application to Controller Synthesis

• DOI: 10.48550/arxiv.1703.10253
• Publication Date: 2017-01-01
• Authors: Guoying Miao; Matthew M. Peet; Keqin Gu
• Keywords: Positive-definite kernel; Kernel (algebra); Operator (biology)

This article presents the inverse of kernel operator associated with complete quadratic Lyapunov-Krasovskii functional for coupled differential-functional equations when is separable. Similar to case time-delay systems retarded type, instrumental in control synthesis. Unlike power series expansion approach used previous literature, a direct algebraic method here. It shown that domain definition infinitesimal generator an invariant subspace if it operator. The process synthesis using described, and numerical example presented sum-of-square formulation.