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On a Class of Linear Systems with Random Coefficients
Author(s) -
Gopalsamy K.
Publication year - 1976
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19760561103
Subject(s) - mathematics , mean square , perturbation (astronomy) , stability theory , class (philosophy) , mathematical analysis , stability (learning theory) , linear differential equation , differential equation , linear system , square (algebra) , nonlinear system , physics , computer science , quantum mechanics , geometry , machine learning , artificial intelligence
Mean‐square stability of randomly perturbed linear systems is considered. Instead of considering partial differential equations, abstract differential equations are studied. Using the perturbation theory of a semi‐group of operators, sufficient conditions on the perturbing random coefficient are obtained so that the mean‐square deviation of the perturbed system response from that of the unperturbed will remain small. A probability bound is obtained for the perturbed system to be asymptotically stable.