Transformation of 2D Roesser into Causal Recursive Separable Denominator Model and Decomposition into 1D Systems

A transformation for the 2D system is proposed to transform the original 2D systems into causal recursive separable denominator systems. 2D causal recursive separable denominator systems with minimal rank-decomposition can be written into two 1D systems for ease in the analysis and model order reduction.

[1]  Numerical solution of the two-dimensional Lyapunov equations and application in order reduction of recursive digital filters , 1993, Proceedings of IEEE Pacific Rim Conference on Communications Computers and Signal Processing.

[2]  Jacek Gondzio,et al.  A Preconditioner for A Primal-Dual Newton Conjugate Gradient Method for Compressed Sensing Problems , 2014, SIAM J. Sci. Comput..

[3]  Leiba Rodman,et al.  Algebraic Riccati equations , 1995 .

[4]  Mohamed Chaabane,et al.  Stability and Stabilization of 2D Singular Systems: A Strict LMI Approach , 2019, Circuits Syst. Signal Process..

[5]  Ioannis K. Dassios,et al.  Optimal Solutions for Non-consistent Singular Linear Systems of Fractional Nabla Difference Equations , 2014, Circuits, Systems, and Signal Processing.

[6]  Masayuki Kawamata,et al.  On controllability, observability, and minimality of 2-D separable denominator systems: A new approach based on the reduced-dimensional decomposition , 1987 .

[7]  Zhengrong Xiang,et al.  Robust state feedback $$H_\infty $$H∞ control for uncertain 2-D continuous state delayed systems in the Roesser model , 2016, Multidimens. Syst. Signal Process..

[8]  Tadeusz Kaczorek,et al.  Singular multidimensional linear discrete systems , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[9]  Zhiping Lin,et al.  Non-fragile H2 and H∞ filter designs for polytopic two-dimensional systems in Roesser model , 2010, Multidimens. Syst. Signal Process..

[10]  Muhammad Imran,et al.  Stability Preserving Model Reduction Technique and Error Bounds Using Frequency-Limited Gramians for Discrete-Time Systems , 2014, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Johannes R. Sveinsson,et al.  Separately balanced realization and model reduction of 2-D separable-denominator transfer functions from input - output data , 1987 .

[12]  Victor Sreeram,et al.  Model Reduction Via Limited Frequency Interval Gramians , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  Zhengrong Xiang,et al.  Stability analysis of two-dimensional switched non-linear continuous-time systems , 2016 .

[14]  N. Bose.  Multidimensional systems theory and applications , 1995 .

[15]  Decomposition of the Roesser model and new conditions for local controllability and local observability , 1989 .

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

[17]  T. Kaczorek.  Decomposition of 2-D linear systems into 1-D systems in the frequency domain , 1989 .

[18]  Jing Wang,et al.  Frequency-Weighted Model Reduction Method with Error Bounds for 2-D Separable Denominator Discrete Systems , 2005, Proceedings of the 2005 IEEE International Symposium on, Mediterrean Conference on Control and Automation Intelligent Control, 2005..

[19]  Masayuki Kawamata,et al.  Decomposition of 2-D separable-denominator systems: Existence, uniqueness, and applications , 1987 .

[20]  D. Enns.  Model reduction with balanced realizations: An error bound and a frequency weighted generalization , 1984, The 23rd IEEE Conference on Decision and Control.

[21]  Donald D. Givone,et al.  Minimization of Multidimensional Linear Iterative Circuits , 1973, IEEE Transactions on Computers.

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

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

[24]  Kamal Premaratne,et al.  An algorithm for model reduction of 2-D discrete time systems , 1990 .

[25]  Ahmed S. Elwakil,et al.  Guest Editorial: Fractional-Order Circuits and Systems: Theory, Design, and Applications , 2016, Circuits Syst. Signal Process..

[26]  Muhammad Imran,et al.  Frequency Limited Model Reduction Techniques With Error Bounds , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[27]  Huijun Gao,et al.  Robust H∞ Filtering for 2-D Systems with Intermittent Measurements , 2009, Circuits Syst. Signal Process..

[28]  Chao Wu,et al.  Realization of 2D FIR filters using generalized polyphase structure combined with singular-value decomposition , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[29]  Tarun Kumar Rawat,et al.  Optimal Design of 2D FIR Filters with Quadrantally Symmetric Properties Using Fractional Derivative Constraints , 2016, Circuits Syst. Signal Process..

[30]  Zhengrong Xiang,et al.  State Feedback $$L_1$$L1-Gain Control of Positive 2-D Continuous Switched Delayed Systems Via State-Dependent Switching , 2016, Circuits Syst. Signal Process..

[31]  Dali Wang,et al.  Model reduction of discrete linear systems via frequency-domain balanced structure , 2000 .

[32]  Zhengrong Xiang,et al.  H∞ control of a class of 2-D continuous switched delayed systems via state-dependent switching , 2016, Int. J. Syst. Sci..

[33]  Joos Vandewalle,et al.  Separation of 2-D nonsingular MIMO digital filters into a cascade of 1-D filters , 1988, IEEE Trans. Acoust. Speech Signal Process..

[34]  Ioannis K. Dassios,et al.  On Non-homogeneous Generalized Linear Discrete Time Systems , 2012, Circuits, Systems, and Signal Processing.