Existence and uniqueness of linear time invariant system and its application

Abstract

In this thesis, structural decomposition of linear periodic continuous time system is addressed. Decomposition of a state of a periodic system into controllable and uncontrollable parts is achieved by a continuously differentiable and periodic coordinate transformation with the same period of the system. Also, a counter-example has been examined for the conjecture. Hence we get a condition for the existence of such a coordinate transformation. This is a survey of the existing work done by I. Jikuya and I. Hodaka [4]. The main highlight of this thesis is that we have proved existence and uniqueness theorem of Linear Time Variant system and extended these results for n th order.