On solution, stability and transformation of linear time-varying systems

This paper presents some explicit results on solution, stability, and transformation of a fairly broad class of linear time-varying systems. It is shown that for this special class of linear time-varying systems, the solution can be represented as a product of two matrix exponential functions and the system stability can be determined directly from eigenvalues of two constant matrices. Furthermore, the system can be reduced to a linear time-invariant system by successive applications of an algebraic transformation and a t↔τ transformation. The generalized results given here contain several previously reported results as special cases.