Structural Stability of Planar Bimodal Linear Systems

Structural Stability of Planar Bimodal Linear Systems

Structural stability ensures that the qualitative behavior of a system is preserved under small perturbations. We study it for planar bimodal linear dynamical systems, that is, systems consisting of two linear dynamics acting on each side of a given hyperplane and assuming continuity along the separating hyperplane. We describe which one of these systems is structurally stable when (real) spira...

Planar Bimodal Piecewise Linear Systems

Differentiable Families of Stabilizers for Planar Bimodal Linear Control Systems

We consider bimodal linear control systems consisting of two subsystems acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. For a differentiable family of controllable planar ones, we construct a differentiable family of feedbacks which pointwise stabilizes both subsystems.

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 ...

Structural stability of linear random dynamical systems

In this paper structural stability of discrete-time linear random dynam-ical systems is studied. A random dynamical system is called structurally stable with respect to a random norm if it is topologically conjugate to any random dynamical system which is suuciently close to it in this norm. We prove that a discrete-time linear random dynamical system is structurally stable with respect to its ...