Development of a solvable class of linear time varying systems

There have been various solution methods including Laplace transform developed for Time Invariant Linear Systems (TILS). However, there isn't a general analytical solution method for Time Varying Linear Systems (TVLS). To solve these systems, we should find suitable transfer matrices to transform TVLS into TILS so that analytical solution becomes possible. In this study, we have added a new class to knownsolution classes (A1 Class,Ah Class,HG Class) to transform TVLS into TILS and the proposed solution class is presented.The solvability conditions for the linear system is reviewed and the relation between solvability conditions and the eigenvalues are given. Transformation method of the new class of linear systems is derived and supported by some examples. Keywords: Time varying linear system, Solvable linear system