Finite-dimensional characterizations of H control for linear systems with delays in input and output

Kenko Uchida*, K. Ikeda, T. Azuma, A. Kojima

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    12 Citations (Scopus)


    We formulate H control problems for linear systems with delays in input and output, and discuss possibility of finite-dimensional characterizations of solutions. In the case when delay exists in control input and controlled output, first, we derive an output feedback H control formula of the central solution type, which is given by using solutions of finite- and infinite-dimensional Riccati matrix inequalities. Second, we show that, if the controlled output is chosen such that it satisfies the 'prediction condition', the solution to the infinite-dimensional Riccati inequality can be calculated by solving a finite-dimensional Riccati inequality. We provide a system theoretic interpretation for the prediction condition, and show that, if the prediction condition is satisfied, there is an equivalent H control problem for finite-dimensional linear systems with no delay. Finally, the equivalence result is extended to the case when delay exists also in measurement output.

    Original languageEnglish
    Pages (from-to)833-843
    Number of pages11
    JournalInternational Journal of Robust and Nonlinear Control
    Issue number9
    Publication statusPublished - 2003 Jul 30


    • Finite-dimensional characterization
    • H control
    • Input delay
    • Linear time-delay system
    • Output delay
    • Prediction condition

    ASJC Scopus subject areas

    • Control and Systems Engineering
    • Electrical and Electronic Engineering
    • Applied Mathematics


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