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Title: On stability of relaxive systems described by polynomials with time-variant coefficients
Authors: Mandic, Danilo P.
Chambers, Jonathon
Keywords: Contraction mapping
Convergence
Fixed-point iteration
Global asymptotic stability
Linear systems
Relaxation
Issue Date: 2000
Publisher: © IEEE
Citation: MANDIC, D.P. and CHAMBERS, J.A., 2000. On stability of relaxive systems described by polynomials with time-variant coefficients. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47(10), pp. 1534 - 1537
Abstract: The problem of global asymptotic stability (GAS) of a time-variant m-th order difference equation y(n)=aT(n)y(n-1)=a1(n)y(n-1)+···+am(n)y(n-m) for ||a(n)||1<1 was addressed, whereas the case ||a(n)||1=1 has been left as an open question. Here, we impose the condition of convexity on the set C0 of the initial values y(n)=[y(n-1),...,y(n-m)]T εRm and on the set AεRm of all allowable values of a(n)=[a1(n),...,am(n)]T, and derive the results from [1] for ai≥0, i=1,...,n, as a pure consequence of convexity of the sets C0 and A. Based upon convexity and the fixed-point iteration (FPI) technique, further GAS results for both ||a(n)||i<1, and ||a(n)||1=1 are derived. The issues of convergence in norm, and geometric convergence are tackled.
Description: This article was published in the journal IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, [© IEEE] and is also available at: http://ieeexplore.ieee.org/. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Version: Published
DOI: 10.1109/81.886985
URI: https://dspace.lboro.ac.uk/2134/5791
ISSN: 1057-7122
Appears in Collections:Published Articles (Mechanical, Electrical and Manufacturing Engineering)

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