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Algebraic Stability Criteria and Symbolic Derivation of Stability Conditions for Feedback Control Systems

Dongming Wang 1, 2
2 PolSys - Polynomial Systems
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : This article provides algebraic settings of the stability criteria of Nyquist and Popov and the circle criterion for closed-loop linear control systems with linear or nonlinear feedback whose transfer functions are rational ones with integer coefficients. The proposed settings make use of algebraic methods of parametric curve implicitisation, real root isolation, symbolic integration and quantifier elimination and allow one to derive exact stability conditions for feedback control systems with symbolic computation. An example is presented to illustrate the algebraic approach and its effectiveness. Some numerical stability results obtained previously are confirmed.
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https://hal.inria.fr/hal-00779248
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Submitted on : Monday, January 21, 2013 - 9:32:11 PM
Last modification on : Friday, January 21, 2022 - 3:22:06 AM

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Dongming Wang. Algebraic Stability Criteria and Symbolic Derivation of Stability Conditions for Feedback Control Systems. International Journal of Control, Taylor & Francis, 2012, 85 (10), pp.1414-1421. ⟨10.1080/00207179.2012.686633⟩. ⟨hal-00779248⟩

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