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

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	On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes
其他题名	On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes
	Chen Hanfu
	2003
发表期刊	应用数学学报：英文版
ISSN	0168-9673
卷号	19.0 期号:004 页码:573-580
摘要	For the multidimensional ARMA system A(z)yk = C(z)ωk it is shown that stability (det A(z)≠0,Angz :\|z\|≤ 1) of A(z) is equivalent to the trajectory boundedness in the mean square sense (MSS) nlimsup ,lim sup n→∞ 1/n ∑ k=1^n‖yk‖^2<∞ a.s.,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.
其他摘要	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) lim sup/n→∞ ‖y_k‖~2 < ∞ a.s., 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.
关键词	稳定性均方指向 ARMA系统 MSS 自适应控制
收录类别	CSCD
语种	中文
CSCD记录号	CSCD:1269441
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/54156
专题	中国科学院数学与系统科学研究院
作者单位	中国科学院数学与系统科学研究院
推荐引用方式 GB/T 7714	Chen Hanfu. On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes[J]. 应用数学学报：英文版,2003,19.0(004):573-580.
APA	Chen Hanfu.(2003).On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes.应用数学学报：英文版,19.0(004),573-580.
MLA	Chen Hanfu."On Stability and Trajectory Boundedness in Mean-square Sense for ARMA Processes".应用数学学报：英文版 19.0.004(2003):573-580.