On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes

作     者：Han-Fu ChenAcademy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China 

作者机构：Academy of Mathematics and Systems Science Chinese Academy of Sciences 北京 100080 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2003年第19卷第4期

页      面：573-580页

核心收录：

学科分类：08[工学] 080101[工学-一般力学与力学基础] 0801[工学-力学（可授工学、理学学位）] 

基　　金：Supported by the National Natural Science Foundation of China (No.60074003) by the Ministry of Science and Technology of China 

主　　题：ARMA stability boundedness in MSS equivalence 

摘      要：For the multidimensional ARMA system A(z)y k = C(z)w k it is shown that stability (det A(z) = 0, z : |z| 1) of A(z) is equivalent to the trajectory boundedness in the mean square sense (MSS) which, as a rule, is a consequence of a successful stochastic adaptive control leading the closed-loop of an ARMAX system to a steady state ARMA system. In comparison with existing results the stability condition imposed on C(z) is no longer needed. The only structural requirement on the system is that det A(z) and det C(z) have no unstable common factor.