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New criteria for exponential stability of nonlinear time-varying differential systems. (English) Zbl 1279.93091

Summary: General nonlinear time-varying differential systems are considered. An explicit criterion for exponential stability is presented. Furthermore, an explicit robust stability bound for systems subjected to nonlinear time-varying perturbations is given. In particular, it is shown that the generalized Aizerman conjecture holds for positive linear systems. Some examples are given to illustrate obtained results.

MSC:

93D20 Asymptotic stability in control theory
93D09 Robust stability
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
93C73 Perturbations in control/observation systems
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