This paper is concerned with the solution of Linear Time Varying [LTV] control systems. The concept of a solution for LTV systems is defined on the basis of finding the fundamental matrix corresponding to LTV control systems. There are some numerical methods such as Euler method and Taylor method for obtaining approximate solution of LTV system [LTVs], each of them has some limitations. In the recent years, other kinds of constructive approaches for the solution of LTVs are presented limited to the particular cases of it. In this paper, we introduced a new approach that we call it AVK approach to obtain a global optimal approximation of the fundamental matrix of LTVs, by introducing a problem in calculus of variations corresponding to our LTVs problem. A global optimal approximate solution (general solution of LTV systems) by using linear programming is considered.

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