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On the uniqueness of solutions to a class of discontinuous dynamical systems

Nonlinear Analysis: Real World Applications, 11(3), 1402–1412 (2010) .

Full text: http://dx.doi.org/10.1016/j.nonrwa.2009.02.024

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Abstract

The study of uniqueness of solutions of discontinuous dynamical systems has an important implication: multiple solutions to the initial value problem could not be found in real dynamical systems; also the (attracting or repulsive) sliding mode is inherently linked to the uniqueness of solutions. In this paper a strengthened Lipschitz-like condition for differential inclusions and a geometrical approach for the uniqueness of solutions for a class of Filippov dynamical systems are introduced as tools for uniqueness. Several theoretical and practical examples are discussed.

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