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

Guoying Miao, Matthew Peet, Keqin Gu

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)6513-6518
Number of pages6
JournalIFAC-PapersOnLine
Volume50
Issue number1
DOIs
StatePublished - Jul 1 2017

Keywords

  • linear operator
  • Lyapunov-Krasovskii functional
  • sum-of-squares
  • time delay

ASJC Scopus subject areas

  • Control and Systems Engineering

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