H control of linear singularly perturbed systems with small state delay

Valery Y. Glizer*, Emilia Fridman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An infinite horizon H state-feedback control problem for singularly perturbed linear systems with a small state delay is considered. An asymptotic solution of the hybrid system of Riccati-type algebraic, ordinary differential, and partial differential equations with deviating arguments, associated with this problem, is constructed. Based on this asymptotic solution, conditions for the existence of a solution of the original H problem, independent of the singular perturbation parameter, are derived. A simplified controller with parameter-independent gain matrices, solving the original problem for all sufficiently small values of this parameter, is obtained. An illustrative example is presented.

Original languageEnglish
Pages (from-to)49-85
Number of pages37
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - 1 Oct 2000


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