Diagonal stability of stochastic systems subject to nonlinear disturbances and diagonal H 2 norms

A known result in the stability theory of stochastic systems with nonlinear Lipschitz-bounded noise intensity states that the robust stability radius of such a stochastic system is equal to the inverse of the H 2 norm of its ‘noise-to-output’ transfer function. This paper extends this result to the...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 47; no. 7; pp. 1427 - 1434
Main Authors Langbort, C., Ugrinovskii, V.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2011
Subjects
Diagonal stability
Stability radius
Stochastic systems
Stochastic systems
Diagonal stability
Stability radius
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Summary:A known result in the stability theory of stochastic systems with nonlinear Lipschitz-bounded noise intensity states that the robust stability radius of such a stochastic system is equal to the inverse of the H 2 norm of its ‘noise-to-output’ transfer function. This paper extends this result to the case where one is interested in the diagonal stability of the system under consideration. This problem arises naturally when studying large-scale interconnected systems subject to random perturbations, as one is often interested in using diagonal or block-diagonal Lyapunov functions for such plants. The main result of the paper is the characterization of the diagonal stochastic stability radius, which is similar to the mentioned result for non-diagonal stability.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2011.02.019