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Discontinuity-induced limit cycles in a general planar piecewise linear system of saddle–focus type
Nonlinear Analysis: Hybrid Systems, 2019The aim of this paper is to deal with the problem of limit cycles for a general planar piecewise linear differential system of saddle–focus type. By using the Lienard-like canonical form with five parameters and dividing the total parameter space into ...
Jiafu Wang +2 more
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Piecewise-linear system reliability estimates
, 2020C. Menun, G. Tarján
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Bifurcations in a piecewise linear system
Physics Letters A, 1986Abstract We study two bifurcations which, because of the piecewise linear nature of the system under consideration, occur at the same parameter value. The three orbits created in this compound bifurcation are the principal periodic orbits of a homoclinic bifurcation seen in the system.
Daniel P. George
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Singular perturbation in piecewise-linear systems
IEEE Transactions on Automatic Control, 1988This note analyzes piecewise-linear systems which are singularly perturbed. A technique is developed that allows decoupling of such systems into fast and slow subsystems for analysis and design. The results of a numerical example are included to demonstrate this technique.
Heck, B. S., Haddad, A. H.
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Linear conjugacy of n-dimensional piecewise linear systems
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1994Summary: A proof is given that \(n\)-dimensional systems characterized by a piecewise linear continuous vector field with odd symmetry and three linear regions are linearly conjugate if their sets of eigenvalues are identical. For this the eigenvalues in the inner region are assumed to be pairwise distinct.
Feldmann, Ute, Schwarz, Wolfgang
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Controllability of piecewise linear systems
Systems & Control Letters, 1986The paper gives a necessary and sufficient condition for the local controllability of a discontinuous linear control system. The set of discontinuities is a hyperplane S. The system is defined by two different linear time-independent equations on the two closed halfspaces defined by S.
Veliov, Vladimir M. +1 more
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