Abstract
The problem of the practical stability (PS) of motion, which generalizes the well-known statement of Chetayev { λ, A, t 0, T}-stability, is considered. For linear systems, criteria for the optimal estimation of PS conditions are obtained. The new concept of directional stability is used to devise algorithms for obtaining extremal sets of stability. The problem of maximizing the PS domain is formulated. The problems of structural parametric optimization of discontinuous dynamic systems, and of maximizing the maximum function with respect to the initial data and the independent variable, are studied. The algorithms of PS and parametric optimization are used to formulate approaches to the optimal design of acceleration and focussing systems. The present paper differs from existing work on the stability of motion in a finite time interval /1, 2/ in that a numerical approach to the study PS is developed on the basis of the results obtained in /3–5/.
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