Viability theory
Introduction to Hybrid Dynamical Systems
Introduction to Hybrid Dynamical Systems
Qualitative Theory of Hybrid Dynamical Systems
Qualitative Theory of Hybrid Dynamical Systems
Hybrid Dynamical Systems: Controller and Sensor Switching Problems
Hybrid Dynamical Systems: Controller and Sensor Switching Problems
Viability Kernels and Capture Basins of Sets Under Differential Inclusions
SIAM Journal on Control and Optimization
The Substratum of Impulse and Hybrid Control Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Dynamical Qualitative Analysis of Evolutionary Systems
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
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Path-dependent impulse differential inclusions, and in particular, path-dependent hybrid control systems, are defined by a path-dependent differential inclusion (or path-dependent control system, or differential inclusion and control systems with memory) and a path-dependent reset map. In this paper, we characterize the viability property of a closed subset of paths under an impulse path-dependent differential inclusion using the Viability Theorems for path-dependent differential inclusions. Actually, one of the characterizations of the Characterization Theorem is valid for any general impulse evolutionary system that we shall defined in this paper.