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Stability regions of nonlinear dynamical systems: A constructive methodology. (English) Zbl 0689.93046
Summary: A constructive methodology for estimating stability regions of nonlinear dynamical systems is developed. The constructive methodology starts with a given Lyapunov function (either a global Lyapunov function or a local Lyapunov function) and yields a sequence of Lyapunov functions which are then used to estimate the stability region. The resulting sequence of estimated stability regions is shown to be a strictly monotonic increasing sequence and yet each of them remains inside the entire stability region. The significance of this methodology includes: 1) its ability to significantly reduce the conservativeness in estimating the stability regions; 2) its computational efficiency; 3) its adaptability; and 4) its sound theoretical basis. Furthermore, the methodology is applicable to estimate the stability regions of general nonlinear dynamical systems.

93D05Lyapunov and other classical stabilities of control systems
93C10Nonlinear control systems
34D20Stability of ODE
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