Abstract
The sliding mode existence and uniqueness problem is studied for a dynamic system with vector impulse control described by an infinite-dimensional differential equation in vector distribution with discontinuous regular functions in a right-hand side. A sliding mode equation is designed to maintain a trajectory on a discontinuity surface. The existence and uniqueness conditions are obtained for a solution to a sliding mode equation. The ellipsoidal filtering problem over discrete-continuous observations is considered as an illustrative example.
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