Abstract:
The nonlinear impulsive control system with trajectories of bounded variation is considered. The notions of strong and weak $V$-invariance of a closed set relative to the impulsive control system are introduced. These notions are adapted to the system nonautonomy in the so-called “fast” time, in which the impulsive dynamics occurs. Invariance criteria in the form of the proximal Hamilton–Jacobi equalities were proved.
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