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Stability analysis of linear dynamical systems with saturation nonlinearities and a short time delay. (English) Zbl 1220.93065

Summary: A class of linear dynamical systems subject to saturation nonlinearities and a short time delay were approximated by singular perturbation dynamical systems with saturation nonlinearities based on the notion of Pade approximation. The stability region of the approximate systems was proved to be decomposed and a convex linear matrix inequality (LMI) optimization model was introduced to estimate the decomposed stability region with least degree of conservativeness.

MSC:

93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
34D15 Singular perturbations of ordinary differential equations
37F15 Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems
41A21 Padé approximation
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References:

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