State-space approach to discrete-time H∞ control

P. A. Iglesias, K. Glover

Research output: Contribution to journalArticlepeer-review


State-space solutions to a discrete-time H∞, problem are given. For a given number α > 0 we give a characterization of all controllers such that the H∞ norm of the closed-loop transfer function is less than α. The approach taken is based on the solution of two Riccati equations using the stable deflating subspace of a symplectic pencil. This ensures that no unnecessary assumptions on the 'A' matrix on the realization of the transfer function are needed. While the results are the direct analogues of those in the continuous time, the state-space derivation is considerably more difficult.

Original languageEnglish (US)
Pages (from-to)1031-1073
Number of pages43
JournalInternational Journal of Control
Issue number5
StatePublished - Nov 1991
Externally publishedYes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications


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