On convexity of the Probabilistic Design Problem for quadratic stabilizability

    Research output: Contribution to journalArticle

    8 Citations (Scopus)

    Abstract

    This paper concentrates on a risk-adjusted version of the well known quadratic stabilization problem for uncertain linear systems. For a wide class of probability density functions and state equation structures for the uncertain parameters, the main result of this paper is as follows: With nominally determined quadratic Lyapunov function V(x) = xTPx, the set of controller gains Kε guaranteeing quadratic Lyapunov instability risk level 0≤ε≤1 or less is convex. Hence, this so-called Probabilistic Design Problem reduces to a convex program. One of the ramifications of this result involves the issue of high-gain control. It is demonstrated that for small values of the risk probability ε, the controller gains which are required can be much smaller than their counterpart obtained via classical robustness theory.

    Original languageEnglish (US)
    Pages (from-to)430-434
    Number of pages5
    JournalProceedings of the American Control Conference
    Volume1
    StatePublished - 1999

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    Controllers
    Gain control
    Lyapunov functions
    Probability density function
    Linear systems
    Stabilization

    All Science Journal Classification (ASJC) codes

    • Control and Systems Engineering

    Cite this

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    title = "On convexity of the Probabilistic Design Problem for quadratic stabilizability",
    abstract = "This paper concentrates on a risk-adjusted version of the well known quadratic stabilization problem for uncertain linear systems. For a wide class of probability density functions and state equation structures for the uncertain parameters, the main result of this paper is as follows: With nominally determined quadratic Lyapunov function V(x) = xTPx, the set of controller gains Kε guaranteeing quadratic Lyapunov instability risk level 0≤ε≤1 or less is convex. Hence, this so-called Probabilistic Design Problem reduces to a convex program. One of the ramifications of this result involves the issue of high-gain control. It is demonstrated that for small values of the risk probability ε, the controller gains which are required can be much smaller than their counterpart obtained via classical robustness theory.",
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    On convexity of the Probabilistic Design Problem for quadratic stabilizability. / Barmish, B. R.; Lagoa, Constantino Manuel.

    In: Proceedings of the American Control Conference, Vol. 1, 1999, p. 430-434.

    Research output: Contribution to journalArticle

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    AB - This paper concentrates on a risk-adjusted version of the well known quadratic stabilization problem for uncertain linear systems. For a wide class of probability density functions and state equation structures for the uncertain parameters, the main result of this paper is as follows: With nominally determined quadratic Lyapunov function V(x) = xTPx, the set of controller gains Kε guaranteeing quadratic Lyapunov instability risk level 0≤ε≤1 or less is convex. Hence, this so-called Probabilistic Design Problem reduces to a convex program. One of the ramifications of this result involves the issue of high-gain control. It is demonstrated that for small values of the risk probability ε, the controller gains which are required can be much smaller than their counterpart obtained via classical robustness theory.

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