Balanced identification and model reduction of a separable denominator 2-D system

An identification and model reduction algorithm for linear discrete time invariant (LTDI) 2-D systems is proposed. A causal recursive separable denominator (CRSD) model structure is used. This allows for the 2-D system to be modeled as two independent 1-D systems. The system is then identified by extending the 1-D system identification Kung's algorithm. Reduced order models are obtained by singular value decomposition (SVD) of the 2-D impulse response data. These are shown to converge to a balanced realization.

[1]  Guoxiang Gu,et al.  2-D model reduction by quasi-balanced truncation and singular perturbation , 1994 .

[2]  Sun-Yuan Kung,et al.  A new identification and model reduction algorithm via singular value decomposition , 1978 .

[3]  Bart De Moor,et al.  N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems , 1994, Autom..

[4]  H. Zeiger,et al.  Approximate linear realizations of given dimension via Ho's algorithm , 1974 .

[5]  Andreas Antoniou,et al.  A weighted balanced approximation for 2-D discrete systems and its application to model reduction , 1995 .

[6]  M. Morf,et al.  New results in 2-D systems theory, part II: 2-D state-space models—Realization and the notions of controllability, observability, and minimality , 1977, Proceedings of the IEEE.

[7]  R. Roesser.  A discrete state-space model for linear image processing , 1975 .

[8]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

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

[10]  G. E. Colling,et al.  New Results in 2-D Systems Theory, Part II: 2-D State-Space Models-Realization and the Notions of Controllability, Observability, and Minimality , 1977 .

[11]  Victor Sreeram,et al.  Identification and model reduction of 2-D systems via the extended impulse response Gramians , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[12]  V. Sreeram,et al.  Identification/reduction to a balanced realization via the extended impulse response gramian , 1995, IEEE Trans. Autom. Control..

[13]  Victor Sreeram,et al.  Identification and model reduction of 2-D systems via the extended impulse response Gramians , 1998, Autom..

[14]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

[15]  Leonard M. Silverman,et al.  Approximation of 2-D separable in denominator filters , 1983 .