Discrete-time $H_2$ and $H_\infty$ low-gain theory

Xu Wang, Antonie Arij Stoorvogel, Ali Saberi, Peddapullaiah Sannuti

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    6 Citations (Scopus)


    For stabilization of linear systems subject to input saturation, there exist four different approaches of low-gain design all of which are independently proposed in the literature, namely direct eigenstructure assignment, $H_2$ and $H_\infty$ algebraic Riccati equation (ARE) based methods, and parametric Lyapunov equation based method. It is shown in earlier work that for continuous-time linear systems, all these methods are rooted in and can be unified under two fundamental control theories, $H_2$ and $H_\infty$ theory. In this paper, we extend such a result to a discrete-time setting. Both the $H_2$ and $H_\infty$ ARE-based methods are generalized to consider systems where all input channels are not necessarily subject to saturation, and explicit design methods are developed.
    Original languageUndefined
    Pages (from-to)743-762
    Number of pages20
    JournalInternational journal of robust and nonlinear control
    Issue number7
    Publication statusPublished - 2012


    • low-grain theory
    • EWI-21694
    • H∞ optimal control
    • Constrained Control
    • METIS-289634
    • IR-79973
    • H2 optimal control

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