A new class of reducible linear time-varying systems and its relation to the optimal control problem. Issue 2 (2016) - Kalenova, V.I.; Morozov, V.M.
Abstract: The previously described classes of linear time-varying systems that can be reduced to time-invariant systems are enumerated, and new constructively reducible first- and second-order systems are introduced. A theorem regarding the effective necessary and sufficient conditions for reducibility is formulated and proved for second-order linear time-varying systems. For first-order linear time-varying systems of the new class, a comparison is made with the systems of equations that appear when the optimal control problem with a quadratic quality criterion is solved.