标题： 不可观测的平面双模态线性系统：最小万有形变、能控性和稳定性 显示英文标题

标题： Unobservable Planar Bimodal Linear Systems: Miniversal Deformations, Controllability and Stabilization

摘要： 我们考虑由两个线性动力学分别作用于给定超平面两侧的双模态线性系统集合，并假设在分离超平面处连续。 集中于不可观测的平面系统，我们得到了能控性的简单显式刻画。 此外，我们利用这些系统依赖于两个状态变量的规范形式，以显式获得最小万有变形，说明分岔图，并证明不可观测的能控系统是可稳定化的。 本文预印本提交至IJBC杂志进行审阅 \copyright 2011年 版权所有 © 世界科学出版公司 http://www.worldscinet.com/ijbc/ 显示英文摘要

摘要： We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple explicit characterization of controllability. Moreover, we apply the canonical forms of these systems depending on two state variables to obtain explicitly miniversal deformations, to illustrate bifurcation diagrams and to prove that the unobservable controllable systems are stabilizable. Preprint of an article submitted for consideration in IJBC \copyright 2011 copyright World Scientific Publishing Company http://www.worldscinet.com/ijbc/