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Stability theory for hybrid dynamical systems. (English) Zbl 0905.93024
Dynamical systems of the hybrid type are viewed as dynamical systems on so-called time-spaces. A time-space is a metric space that is completely ordered, has a minimal element and its metric is additive. Such systems are embedded into dynamical systems defined on \(\mathbb{R}_+\) as the time axis. A stability theory is formulated. Applications are given for nonlinear systems with sampled data and for systems with impulse effects.

MSC:
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93D20 Asymptotic stability in control theory
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
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