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Absolute stability and the Lagrange–Dirichlet theorem with monotone multivalued mappings. (English) Zbl 1157.93455
Summary: This note presents an extension of the absolute stability problem and of the Lagrange–Dirichlet theorem, when the nonlinearities entering the model are considered within the class of monotone multivalued mappings (consequently including operators with piecewise-linear graphs that may represent physical effects like Coulomb friction, dead-zones, saturations, elasto-plasticity, and unilateral constraints).

MSC:
93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory
70F25 Nonholonomic systems related to the dynamics of a system of particles
70K20 Stability for nonlinear problems in mechanics
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