Sliding modes in infinite-dimensional dynamic systems with impulse control

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.