Stability of Linear Time-Varying Systems

Only few explicit solutions exist for time varying systems, namely: The A1 class, the Ah class and the commutative class, and transparent stability results for these three classes are obtained. In this paper, we present a practical criterion of stability which can be defined directly from the matrix A(t). This method is based on Gronwall’s theorem and shows that a linear time varying system can be stabilised by increasing the damping of the constant nominal of the matrix A(t).