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Stability rates for patchy vector fields

Fabio Ancona, Alberto Bressan (2004)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude...

Stability rates for patchy vector fields

Fabio Ancona, Alberto Bressan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude...

Systems of differential equations modeling non-Markov processes

Irada Dzhalladova, Miroslava Růžičková (2023)

Archivum Mathematicum

The work deals with non-Markov processes and the construction of systems of differential equations with delay that describe the probability vectors of such processes. The generating stochastic operator and properties of stochastic operators are used to construct systems that define non-Markov processes.

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