Insufficiencies of practical BIBO stable n-D systems

This paper is focused on analyzing the practical bounded input bounded output (BIBO) stability concept originally introduced by Agathoklis and Bruton with respect to its applicability in n-D signal processing applications. By comparing the frequency response expected on basis of the transfer function to the Fourier transform of the actually measured impulse response of exemplary systems it is shown that the concept of practical stability cannot be a general n-D stability criterion for systems, in particular for signal processing applications, if roots of the given transfer function are not guaranteed to be close to the respective n-D BIBO stability region.

[1]  Thomas S. Huang,et al.  Stability of two-dimensional recursive filters , 1972 .

[2]  Douglas R. Goodman,et al.  Some stability properties of two-dimensional linear shift-invariant digital filters , 1977 .

[3]  E. Jury.  Stability of multidimensional scalar and matrix polynomials , 1978, Proceedings of the IEEE.

[4]  N. Bose.  Applied multidimensional systems theory , 1982 .

[5]  Leonard T. Bruton,et al.  Practical-BIBO stability of n-dimensional discrete systems , 1983 .

[6]  M.N.S. Swamy,et al.  On stability properties of three- and higher dimensional linear shift-invariant digital filters , 1985 .

[7]  Li Xu,et al.  The design of practically stable nD feedback systems , 1994, Autom..

[8]  K. Abe,et al.  Design of practically stable n-dimensional feedback systems : a state-space approach , 1996 .

[9]  K. Abe,et al.  Practical internal stability of n-D discrete systems , 1996, IEEE Trans. Autom. Control..

[10]  Anton Kummert,et al.  Strong practical stability and stabilization of discrete linear repetitive processes , 2009, Multidimens. Syst. Signal Process..

[11]  Anton Kummert,et al.  On the usability of practical stable n-D systems for signal processing applications , 2009, 2009 IEEE International Symposium on Circuits and Systems.

[12]  Germain Garcia,et al.  Practical stability and stabilization of linear systems , 2009, 2009 17th Mediterranean Conference on Control and Automation.

[13]  Anton Kummert,et al.  Realization of multidimensional signal processing systems given in natural k-D state space description , 2012, Multidimens. Syst. Signal Process..