A new solvable class linear time varying system

In this thesis, a new definition of classification has been done, with regard to the time- varying linear systems can be solved and the solution method for the new proposed class has been described. There isn't a general analytical method of solution in time-varying linear systems and being solvable of these systems is related to their being able to turn into time-invariant systems, applying certain transformations. In the studies conducted to date, in general, it has been shown that two groups of the time-varying linear systems are solvable, in addition to this, some special systems that can be transformed into these groups, although not belonging to one of the these to groups, have been introduced. Determination of the system's being solvable is directly related to the structure of the system's eigenvalue and also, in this study, on the basis of eigenvalues, a new solvable group has been identified.