Inversion of Separable Kernel Operators in Coupled Differential-Functional Equations and Application to Controller Synthesis
Provides a new tool for control synthesis in systems described by coupled differential-functional equations, but the approach is incremental as it extends existing inversion techniques to a broader class of systems.
This paper presents a direct algebraic method for inverting separable kernel operators in coupled differential-functional equations, enabling controller synthesis. The method avoids power series expansions and is validated with a numerical example using sum-of-squares formulation.
This article presents the inverse of the kernel operator associated with the complete quadratic Lyapunov-Krasovskii functional for coupled differential-functional equations when the kernel operator is separable. Similar to the case of time-delay systems of retarded type, the inverse operator is instrumental in control synthesis. Unlike the power series expansion approach used in the previous literature, a direct algebraic method is used here. It is shown that the domain of definition of the infinitesimal generator is an invariant subspace of the inverse operator if it is an invariant subspace of the kernel operator. The process of control synthesis using the inverse operator is described, and a numerical example is presented using the sum-of-square formulation.