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Stability of Switched Feedback Time‐Varying Dynamic Systems Based on the Properties of the Gap Metric for Operators

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  • M. De la Sen

Abstract

The stabilization of dynamic switched control systems is focused on and based on an operator‐based formulation. It is assumed that the controlled object and the controller are described by sequences of closed operator pairs (L,C) on a Hilbert space H of the input and output spaces and it is related to the existence of the inverse of the resulting input‐output operator being admissible and bounded. The technical mechanism addressed to get the results is the appropriate use of the fact that closed operators being sufficiently close to bounded operators, in terms of the gap metric, are also bounded. That philosophy is followed for the operators describing the input‐output relations in switched feedback control systems so as to guarantee the closed‐loop stabilization.

Suggested Citation

  • M. De la Sen, 2012. "Stability of Switched Feedback Time‐Varying Dynamic Systems Based on the Properties of the Gap Metric for Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:612198
    DOI: 10.1155/2012/612198
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    References listed on IDEAS

    as
    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, Hindawi, vol. 2009, pages 1-34, August.
    2. 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).
    3. Jianting Zhou & Qiankun Song & Jianxi Yang, 2009. "Stochastic Passivity of Uncertain Neural Networks with Time-Varying Delays," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-16, January.
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