2D奇异离散系统的内部稳定性

On the Internal Stability of 2D Singular Discrete Systems

针对二维奇异线性定常离散系统的一般模型 (简称 2 -DSGM) ,提出内部稳定的概念 ,该定义是对 2 -D正则线性常系数离散状态模型 (简称 2 -DGM )内部稳定性的一个推广。探讨了内部稳定与稳定性检验多项式间的关系 ,给出系统内部稳定的充要条件是稳定性检验多项式不等于零 (当 0 <｜z1｜≤ 1 ,0 <｜z2 ｜≤1时 )。举例说明稳定性检验法。此检验法也表明 ,同 2 -D正则系统一样 ,2

This paper proposed a new definition of internal stability for singular two dimensional linear discrete state space general models(2D SGM).This definition generalized the concept of internal stability for regular 2D GM. The relationship between the internal stability and stability test polynomial is discussed. It is given that a sufficient and necessary condition of internal stability of the system under consideration is that stability test polynomial isn't equal to zero when 0<｜z 1｜≤1,0<｜z 2｜≤1  An example is given to explain the stability test method. This test method also shows that the roots of stability test polynomial for 2D SGM can also be used to test internal stability of a known system just like 2D GM.