Canonical Discontinuous Planar Piecewise Linear Systems

Planar Bimodal Piecewise Linear Systems

Arbitrary Number of Limit Cycles for Planar Discontinuous Piecewise Linear Differential Systems with Two Zones

For any given positive integer n we show the existence of a class of discontinuous piecewise linear differential systems with two zones in the plane having exactly n hyperbolic limit cycles. Moreover, all the points on the separation boundary between the two zones are of sewing type, except the origin which is the only equilibrium point.

Piecewise Constant Controlled Linear Fuzzy Systems

Limit cycles of Discontinuous Piecewise Linear differential Systems

We study the bifurcation of limit cycles from the periodic orbits of a 2−dimensional (respectively 4−dimensional) linear center in R perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (respectively 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This uppe...

Null controllability of planar bimodal piecewise linear systems

This article investigates the null controllability of planar bimodal piecewise linear systems, which consist of two second order LTI systems separated by a line crossing through the origin. It is interesting to note that even when both subsystems are controllable in the classical sense, the whole piecewise linear system may be not null controllable. On the other hand, a piecewise linear system ...