Mathematical Description of Motions on Discontinuity Boundaries
As already noted, the behaviour of system (1.7), (1.8) on discontinuity boundaries cannot be adequately described in terms of the classical theory of differential equations. To solve this problem, various special ways are usually suggested, in order to reduce the original problem to a form which yields a solution close, in a sense, to that of the original problem, and which allows the use of classical analysis techniques. Such a substitution of the problem is usually called regularization. The physical ways described in Chap. 2, Part 1 are, in essence, the ways of regularization of the problem of discontinuous dynamic system behaviour.
KeywordsManifold Covariance Hull Sliding Mode
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