Abstract
The present paper supplements and formulates in a more rigorous form, the statement of the problem on stability of processes over a specified time interval, which was given in /1, 2/. The refinement concerns the case in which the specified time interval is finite, and we find that an imposition of stronger constraints on the region of limiting deviations becomes necessary. As far as the character of the constraints imposed on the perturbations of the parameters of the process is concerned, the proposed formulation and the initial formulation are both related to /3/. We use the fact that a linear differential system can be transformed into a diagonal one, as the basis for establishing the necessary and sufficient conditions of stability of a linear process, and for obtaining certain conditions of stability and instability of a nonlinear process in the linear approximation. We show how transformation of a linear system to a “nearly” diagonal system can be utilized for the same purpose.
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