Optimal input-output stabilization of infinite-dimensional discrete time-invariant linear systems by output injection

Mark R Opmeer, O J Staffans

Research output: Contribution to journalArticle

6 Citations (Scopus)
132 Downloads (Pure)

Abstract

We study the optimal input-output stabilization of discrete time-invariant linear systems in Hilbert spaces by output injection. We show that a necessary and sufficient condition for this problem to be solvable is that the transfer function has a left factorization over H-infinity. Another equivalent condition is that the filter Riccati equation (of an arbitrary realization) has a solution (in general, unbounded and even nondensely defined). We further show that after renorming the state space in terms of the inverse of the smallest solution of the filter Riccati equation, the closed-loop system is not only input-output stable but also strongly internally *-stable.
Original languageEnglish
Pages (from-to)5084-5107
Number of pages24
JournalSIAM Journal on Control and Optimization
Volume48
Issue number8
Early online date18 Oct 2010
DOIs
Publication statusPublished - 2010

Keywords

  • infinite-dimensional system
  • input-output stabilization
  • linear quadratic optimal control
  • Riccati equation
  • left factorization
  • output injection

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