Abstract
The notion of superstability of linear control systems was introduced. Superstability which is a sufficient condition for stability was formulated in terms of linear constraints on the entries of a matrix or the coefficients of a characteristic polynomial. In the first part of the paper, the properties of superstable systems were studied. The norms of solutions were proved to decrease exponentially monotonically in the absence of perturbations, and the solutions were proved to be uniformly bounded in the presence of bounded perturbations. A generalization to nonlinear and time varying systems was discussed. Spectral properties of superstable systems were studied. For interval matrices, a complete solution was given to the problem of robust superstability.
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Polyak, B.T., Shcherbakov, P.S. Superstable Linear Control Systems. I. Analysis. Automation and Remote Control 63, 1239–1254 (2002). https://doi.org/10.1023/A:1019823208592
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DOI: https://doi.org/10.1023/A:1019823208592