Journal ArticleDOI
Determination of stability by linear approximation of a periodic solution of a system of differential equations with discontinuous right-hand sides
M. A. Aizerman,F. R. Gantmacher +1 more
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This article is published in Quarterly Journal of Mechanics and Applied Mathematics.The article was published on 1958-01-01. It has received 31 citations till now. The article focuses on the topics: Homogeneous differential equation & Differential equation.read more
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Exponentially stabilizing continuous-time controllers for periodic orbits of hybrid systems
TL;DR: The power of this systematic approach to robustly and exponentially stabilize periodic orbits of hybrid dynamical systems arising from bipedal walking is illustrated by finding robust and stabilizing continuous-time feedback laws for walking gaits of two underactuated 3D bipingal robots.
Journal ArticleDOI
Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems
TL;DR: In this article, it was shown that near an exponentially stable periodic orbit undergoing isolated transitions in a hybrid dynamical system, nearby executions generically contract superexponentially to a constant-dimensional subsystem.
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Model Reduction Near Periodic Orbits of Hybrid Dynamical Systems
TL;DR: In this article, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems, and the contraction occurs in finite time regardless of the stability properties of the orbit.
Journal ArticleDOI
Event--Selected Vector Field Discontinuities Yield Piecewise--Differentiable Flows
TL;DR: In this paper, the authors study a class of discontinuous vector fields brought to our attention by multilegged animal locomotion and show that the flow is locally conjugate (via a piecewise-differentiable homeomorphism) to a f...
Journal ArticleDOI
Fundamental matrix solutions of piecewise smooth differential systems
Luca Dieci,Luciano Lopez +1 more
TL;DR: The fundamental matrix solution associated to piecewise smooth differential systems of Filippov type, in which the vector field varies discontinuously as solution trajectories reach one or more surfaces, is considered.