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Simultaneous stabilization: Universal controller synthesis

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Abstract

We consider the simultaneous stabilization problem for linear time-invariant stationary objects of arbitrary order. For such objects, we formulate numerically verifiable necessary and sufficient simultaneous stabilization conditions and show a constructive algorithm for the construction of a stabilizing controller with minimal restrictions on the structure and parameters of the stabilized objects. We give a general scheme of studying simultaneous stabilizability of a family of objects and analyze in detail a numerical algorithm for finding a stabilizing controller with applied interval analysis. To solve the problem, we use an approach based on the study of affine transformations of controller parameter spaces into the spaces of coefficients of denominators of closed-loop objects.

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    S. K. Korovin & A. S. Fursov

Authors
  1. S. K. Korovin
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  2. A. S. Fursov
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Original Russian Text © S.K. Korovin, A.S. Fursov, 2011, published in Avtomatika i Telemekhanika, 2011, No. 9, pp. 61–73.

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Korovin, S.K., Fursov, A.S. Simultaneous stabilization: Universal controller synthesis. Autom Remote Control 72, 1852–1863 (2011). https://doi.org/10.1134/S0005117911090074

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