To the problem of studying of linear time-invariant systems / V. I. Kalenova, V. M. Morozov, P. M. Sobolevskii. //Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2009. № 1. P. 51-61 [Moscow Univ. Mech. Bulletin. Vol. 64, N 1, 2009. P. 14-24].
Some linear time-varying systems that can be solved in closed form and are of practical importance in the problems of mechanics are considered. Several properties of the linear time-varying systems whose matrices belong to different classes simultaneously are studied. The stability analysis is performed using a nontraditional method of matrix decomposition. A number of mechanical problems are discussed to illustrate the efficiency of the proposed method.