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Robust Stability and Stability Radius for Variational Control Systems

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  • Bogdan Sasu

Abstract

We consider an integral variational control system on a Banach space X and we study the connections between its uniform exponential stability and the (I(ℝ+, X), O(ℝ+, X)) stability, where I and O are Banach function spaces. We identify the viable classes of input spaces and output spaces related to the exponential stability of systems and provide optimization techniques with respect to the input space. We analyze the robustness of exponential stability in the presence of structured perturbations. We deduce general estimations for the lower bound of the stability radius of a variational control system in terms of input‐output operators acting on translation‐invariant spaces. We apply the main results at the study of the exponential stability of nonautonomous systems and analyze in the nonautonomous case the robustness of this asymptotic property.

Suggested Citation

  • Bogdan Sasu, 2008. "Robust Stability and Stability Radius for Variational Control Systems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2008(1).
    • Handle: RePEc:wly:jnlaaa:v:2008:y:2008:i:1:n:381791
    DOI: 10.1155/2008/381791
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    References listed on IDEAS

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    1. Adina Luminiţa Sasu, 2006. "Exponential dichotomy for evolution families on the real line," Abstract and Applied Analysis, Hindawi, vol. 2006, pages 1-16, April.
    2. Adina Luminiţa Sasu, 2006. "Exponential dichotomy for evolution families on the real line," Abstract and Applied Analysis, John Wiley & Sons, vol. 2006(1).
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    Cited by:

    1. M. De la Sen, 2009. "On the Characterization of Hankel and Toeplitz Operators Describing Switched Linear Dynamic Systems with Point Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    2. Adina Luminiţa Sasu & Bogdan Sasu, 2011. "Translation Invariant Spaces and Asymptotic Properties of Variational Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).

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