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This article presents the inverse of the kernel operator associated with thecomplete quadratic Lyapunov-Krasovskii functional for coupleddifferential-functional equations when the kernel operator is separable.Similar to the case of time-delay systems of retarded type, the inverseoperator is instrumental in control synthesis. Unlike the power seriesexpansion approach used in the previous literature, a direct algebraic methodis used here. It is shown that the domain of definition of the infinitesimalgenerator is an invariant subspace of the inverse operator if it is aninvariant subspace of the kernel operator. The process of control synthesisusing the inverse operator is described, and a numerical example is presentedusing the sum-of-square formulation.

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