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Logarithmic matrix norms in motion stability problems

✍ Scribed by O.A. Peregudova

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
354 KB
Volume
72
Category
Article
ISSN
0021-8928

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✦ Synopsis

The problem of the stability of the motions of mechanical systems, described by non-linear nonautonomous systems of ordinary differential equations, is considered. Using the logarithmic matrix norm method, and constructing a reference system, the sufficient conditions for the asymptotic and exponential stability of unperturbed motion and for the stabilization of progammed motions of such systems are obtained. The problem of the asymptotic stability of a non-conservative system with two degrees of freedom is solved, taking for parametric disturbances into account. Examples of the solution of the problem of stabilizing programmed motions -for an inverted double pendulum and for a two-link manipulator on a stationary base -are considered.

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