H -norm and invariant manifolds of systems with state delays

Emilia Fridman*, Uri Shaked

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of finding bounds on the H -norm of systems with a finite number of point delays and distributed delay is considered. Sufficient conditions for the system to possess an H-norm which is less or equal to a prescribed bound are obtained in terms of Riccati partial differential equations (RPDE's). We show that the existence of a solution to the RPDE's is equivalent to the existence of a stable manifold of the associated Hamiltonian system. For small delays the existence of the stable manifold is equivalent to the existence of a stable manifold of the ordinary differential equations that govern the flow on the slow manifold of the Hamiltonian system. This leads to an algebraic, finite-dimensional, criterion for systems with small delays.

Original languageEnglish
Pages (from-to)157-165
Number of pages9
JournalSystems and Control Letters
Volume36
Issue number2
DOIs
StatePublished - 15 Feb 1999

Keywords

  • Invariant manifolds
  • Linear H-control
  • Singular perturbations
  • Small delay
  • Time-delay systems

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