Representation of motion of controlled dynamic systems with unilateiral constrafints

A long-standing problem of deriving a system representation that admits unique extensibility of motion beyond accumulation point for systems with Zeno-type behavior subject to continuous control signal is solved. This representation is shown to be given by a pair (limit system, prelimit system) where the former supports a family of extensions beyond accumulation point and the latter selects a particular extension through limit procedure. The smooth sliding mode is shown to represent a motion beyond the right accumulation points. Examples demonstrating the difficulties that arise in the cases of discontinuous and/or feedback control are given