Abstract
This study focuses on the characterization of the forward invariance property in hybrid dynamical systems, considering state-dependent conditions for both differential and difference inclusions. The first step is to establish necessary and sufficient conditions for (controlled) forward invariance, using cones and set inclusions. For linear hybrid systems, an explicit characterization of the invariance property of polyhedral sets is given in terms of linear matrix inequalities. The result is illustrated by a practical example involving a bouncing ball.
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