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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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