, Volume 12, Issue 3, pp 375-390

On the existence and uniqueness of solutions for implicit linear systems on finite interval

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Abstract

In the present paper we study the problem of the existence and uniqueness of solutions of implicit systems considered on a finite interval of time. We consider two kinds of existence problems: input-acceptance and input-acceptance when the boundary conditions of a corresponding trajectory are set to zero, and two kinds of uniqueness problems: output uniqueness and output uniqueness when the boundary conditions of the corresponding trajectory are unknown. Geometric conditions for all of these notions are given, and the duality of these notions is studied.

This research was supported by NSF Grant ECS-8805932.