不可观测平面双峰线性系：微小变形、能控性与镇定
Unobservable Planar Bimodal Linear Systems: Miniversal Deformations, Controllability and Stabilization
摘要：
我们考虑一组双峰线性系，由两个线性动力学作用在一个给定的超平面的每一边，假设连续沿分离超平面。针对不可观测的平面的，我们得到了一个简单的显式表征的可控性。此外，我们应用依赖于两个状态变量的这些系统的标准型，以获得显式的极小化变形，说明分歧图，并证明不可观测的可控系统是稳定的。提交IJBC审议的文章的预印本©2011版权所有世界科学出版公司http://www.worldscinet.com/ijbc/
英文摘要：
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 ©2011 copyright World Scientific Publishing Company http://www.worldscinet.com/ijbc/
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