A study on new right/left inverses of nonsquare polynomial matrices

Bańka, S. and Dworak, P. (2006). Efficient algorithm for designing multipurpose control systems for invertible and right-invertible MIMO LTI plants, Bulletin of the Polish Academy of Sciences: Technical Sciences54(4): 429-436.Search in Google Scholar

Bańka, S. and Dworak, P. (2007). On decoupling of LTI MIMO systems with guaranteed stability, Measurement Automation and Monitoring53(6): 46-51.Search in Google Scholar

Ben-Israel, A. and Greville, T.N.E. (2003). Generalized Inverses, Theory and Applications, 2nd Edn., Springer-Verlag, New York, NY.Search in Google Scholar

Bernardini, R. and Rinaldo, R. (2006). Oversampled filter banks from extended perfect reconstruction filter banks, IEEE Transactions on Signal Processing54(7): 2625-2635, DOI: 10.1109/TSP.2006.874811.10.1109/TSP.2006.874811Search in Google Scholar

Boche, H. and Pohl, V. (2006). MIMO-ISI channel equalization—Which price we have to pay for causality, Proceedings of the 14th European Signal Processing Conference (EUSIPCO'2006), Florence, Italy, (on CD-ROM).Search in Google Scholar

Bose, N.K. and Mitra, S.K. (1978). Generalized inverse of polynomial matrices, IEEE Transactions on Automatic Control23(3): 491-493.10.1109/TAC.1978.1101751Search in Google Scholar

Callier, F.M. and Kraffer, F. (2005). Proper feedback compensators for a strictly proper plant by polynomial equations, International Journal of Applied Mathematics and Computer Science15(4): 493-507.Search in Google Scholar

Castella, M. and Pesquet, J.-C. (2004). An iterative blind source separation method for convolutive mixtures of images, in C.G. Puntonet and A. Prieto (Eds.), Independent Component Analysis and Blind Signal Separation, Lecture Notes in Computer Science, Vol. 3195, Springer-Verlag, Heidelberg/ Berlin, pp. 922-929.10.1007/978-3-540-30110-3_116Search in Google Scholar

Chen, J. and Hara, S. (2001). Tracking performance with finite input energy, in S.O.R. Moheimani (Ed.), Perspectives in Robust Control, Lecture Notes in Control and Information Sciences, Vol. 268, Springer-Verlag, Heidelberg/Berlin, Chapter 4, pp. 41-55.10.1007/BFb0110613Search in Google Scholar

Davison, E. (1983). Some properties of minimum phase systems and ‘squared-down’ systems, IEEE Transactions on Automatic Control28(2): 221-222.10.1109/TAC.1983.1103197Search in Google Scholar

Desoer, C.A. and Schulman, J.D. (1974). Zeros and poles of matrix transfer functions and their dynamical interpretation, IEEE Transactions on Circuits and Systems21(1): 3-8.10.1109/TCS.1974.1083805Search in Google Scholar

Edelmayer, A., Bokor, J., Szabó, Z. and Szigeti, F. (2004). Input reconstruction by means of system inversion: A geometric approach to fault detection and isolation in nonlinear systems, International Journal of Applied Mathematics and Computer Science14(2): 189-199.Search in Google Scholar

Ferreira, P.M.G. (1988). Some results on system equivalence, International Journal of Control48(5): 2033-2042, DOI: 10.1080/00207178808906303.10.1080/00207178808906303Search in Google Scholar

Fornasini, E. and Pinto, R. (2004). Matrix fraction descriptions in convolutional coding, Linear Algebra and Its Applications392: 119-158, DOI: 10.1016/j.laa.2004.06.007.10.1016/j.laa.2004.06.007Search in Google Scholar

Forney, Jr.,G.D. (1991). Algebraic structure of convolutional codes, and algebraic system theory, in A.C. Antoulas (Ed.), Mathematical System Theory: The Influence of R.E. Kalman, Springer-Verlag, Heidelberg/Berlin, pp. 527-557.10.1007/978-3-662-08546-2_31Search in Google Scholar

Gan, L. and Ling, C. (2008). Computation of the para-pseudoinverse for oversampled filter banks: Forward and backward Greville formulas, IEEE Transactions on Signal Processing56(12): 5851-5860, DOI: 10.1109/TSP.2008.2005086.10.1109/TSP.2008.2005086Search in Google Scholar

Gluesing-Luerssen, H., Rosenthal, J. and Smarandache, R. (2006). Strongly-MDS convolutional codes, IEEE Transactions on Information Theory52(2): 584-598, DOI: 10.1109/TIT.2005.862100.10.1109/TIT.2005.862100Search in Google Scholar

Guo, Y. and Levy, B.C. (2004). Design of FIR precoders and equalizers for broadband MIMO wireless channels with power constraints, EURASIP Journal on Wireless Communications and Networking2004(2): 344-356, DOI: 10.1155/S1687147204406185.10.1155/S1687147204406185Search in Google Scholar

Harikumar, G. and Bresler, Y. (1999a). Exact image deconvolution from multiple FIR blurs, IEEE Transactions on Image Processing8(6): 846-862, DOI: 10.1109/83.766861.10.1109/83.76686118267497Search in Google Scholar

Harikumar, G. and Bresler, Y. (1999b). Perfect blind restoration of images blurred by multiple filters: Theory and efficient algorithms, IEEE Transactions on Image Processing8(2): 202-219, DOI: 10.1109/83.743855.10.1109/83.74385518267468Search in Google Scholar

Hautus, M.L.J. and Heymann, M. (1983). Linear feedback decoupling—Transfer function analysis, IEEE Transactions on Automatic Control28(8): 823-832.10.1109/TAC.1983.1103320Search in Google Scholar

Henrion, D. (1998). Reliable Algorithms for Polynomial Matrices, Ph.D. thesis, Institute of Information Theory and Automation, Czech Academy of Sciences, Prague.Search in Google Scholar

Hunek, W.P. (2008). Towards robust minimum variance control of nonsquare LTI MIMO systems, Archives of Control Sciences18(1): 59-71.Search in Google Scholar

Hunek, W.P. (2009a). A new general class of MVC-related inverses of nonsquare polynomial matrices based on the Smith factorization, Proceedings of the 14th IEEE IFAC International Conference on Methods and Models in Automation and Robotics (MMAR'2009), Miedzyzdroje, Poland, (on CD-ROM).10.3182/20090819-3-PL-3002.00065Search in Google Scholar

Hunek, W.P. (2009b). Towards robust pole-free designs of minimum variance control for LTI MIMO systems, in S. Pennacchio (Ed.), Recent Advances in Control Systems, Robotics and Automation, 3rd Edn., International Society for Advanced Research, Palermo, pp. 168-174.Search in Google Scholar

Hunek, W.P. and Latawiec, K.J. (2009). Minimum variance control of discrete-time and continuous-time LTI MIMO systems—A new unified framework, Control and Cybernetics38(3): 609-624.Search in Google Scholar

Hunek, W.P., Latawiec, K.J., Łukaniszyn, M. and Gawdzik, A. (2010). Constrained minimum variance control of nonsquare LTI MIMO systems, 15th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR'2010), Miedzyzdroje, Poland, pp. 365-370.Search in Google Scholar

Hunek, W.P., Latawiec, K.J. and Stanisławski, R. (2007). New results in control zeros vs. transmission zeros for LTI MIMO systems, Proceedings of the 13th IEEE IFAC International Conference on Methods and Models in Automation and Robotics (MMAR'2007), Szczecin, Poland, pp. 149-153.Search in Google Scholar

Inouye, Y. and Tanebe, K. (2000). Super-exponential algorithms for multichannel blind deconvolution, IEEE Transactions on Signal Processing48(3): 881-888, DOI: 10.1109/78.824685.10.1109/78.824685Search in Google Scholar

Johannesson, R., Wan, Z.-X. and Wittenmark, E. (1998). Some structural properties of convolutional codes over rings, IEEE Transactions on Information Theory44(2): 839-845, DOI: 10.1109/18.661532.10.1109/18.661532Search in Google Scholar

Johannesson, R. and Zigangirov, K.S. (1999). Fundamentals of Convolutional Coding, IEEE Press, New York, NY.10.1109/9780470544693Search in Google Scholar

Kaczorek, T. (2005). Extension of the Cayley-Hamilton theorem for right and left inverses of polynomial matrices and rational matrices, Electrical Review81(11): 66-71.Search in Google Scholar

Kaczorek, T., Dzieliński, A., Dąbrowski, W. and Łopatka, R. (2009). Fundamentals of Control Theory, 3rd Edn., Wydawnictwa Naukowo-Techniczne, Warsaw, (in Polish).Search in Google Scholar

Kaczorek, T. and Łopatka, R. (2000). Existence and computation of the set of positive solutions to polynomial matrix equations, International Journal of Applied Mathematics and Computer Science10(2): 309-320.Search in Google Scholar

Kailath, T. (1980). Linear Systems, Prentice Hall, Englewood Cliffs, NJ.Search in Google Scholar

Karampetakis, N.P. and Tzekis, P. (2001). On the computation of the generalized inverse of a polynomial matrix, IMA Journal of Mathematical Control and Information18(1): 83-97, DOI: 10.1093/imamci/18.1.83.10.1093/imamci/18.1.83Search in Google Scholar

Kim, S. and Park, Y. (2004). A direct design method of inverse filters for multichannel 3D sound rendering, Journal of Sound and Vibration278(4-5): 1196-1204, DOI: 10.1016/j.jsv.2003.12.014.10.1016/j.jsv.2003.12.014Search in Google Scholar

Kon'kova, T.Y. and Kublanovskaya, V.N. (1996). Inversion of polynomial and rational matrices, Journal of Mathematical Sciences79(3): 1093-1100, DOI: 10.1007/BF02366129.10.1007/BF02366129Search in Google Scholar

Kwan, M.W. and Kok, C.W. (2006). Iterative joint optimization of minimal transmit redundancy FIR zero-forcing precoder-equalizer system for MIMO-ISI channel, IEEE Transactions on Signal Processing54(1): 204-213, DOI: 10.1109/TSP.2005.861059.10.1109/TSP.2005.861059Search in Google Scholar

Latawiec, K.J. (1998). Contributions to Advanced Control and Estimation for Linear Discrete-Time MIMO Systems, Opole University of Technology Press, Opole.Search in Google Scholar

Latawiec, K.J. (2004). The Power of Inverse Systems in Linear and Nonlinear Modeling and Control, Opole University of Technology Press, Opole.Search in Google Scholar

Latawiec, K.J. (2005). Control zeros and maximum-accuracy/maximum-speed control of LTI MIMO discrete-time systems, Control and Cybernetics34(2): 453-475.Search in Google Scholar

Latawiec, K.J., Bańka, S. and Tokarzewski, J. (2000). Control zeros and nonminimum phase LTIMIMO systems, Annual Reviews in Control24(1): 105-112. DOI: 10.1016/S1367-5788(00)90021-X.10.1016/S1367-5788(00)90021-XSearch in Google Scholar

Latawiec, K.J., Hunek, W.P. and Łukaniszyn, M. (2004). A new type of control zeros for LTI MIMO systems, Proceedings of the 10th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR'2004), Miedzyzdroje, Poland, pp. 251-256.Search in Google Scholar

Latawiec, K.J., Hunek, W.P. and Łukaniszyn, M. (2005). New optimal solvers of MVC-related linear matrix polynomial equations, Proceedings of the 11th IEEE International Conference on Methods and Models in Automation and Robotics (MMAR'2005), Miedzyzdroje, Poland, pp. 333-338.Search in Google Scholar

Law, K.L., Fossum, R.M. and Do, M.N. (2009). Generic invertibility of multidimensional FIR filter banks and MIMO systems, IEEE Transactions on Signal Processing57(11): 4282-4291, DOI: 10.1109/TSP.2009.2025826.10.1109/TSP.2009.2025826Search in Google Scholar

Lin, S. and Costello, D.J. (2004). Error Control Coding, 2nd Edn., Prentice Hall, Upper Saddle River, NJ.Search in Google Scholar

Lu, P., Li, S., Zou, Y. and Luo, X. (2005). Blind recognition of punctured convolutional codes, Science in China, Series F: Information Sciences48(4): 484-498, DOI: 10.1360/03yf0480.10.1360/03yf0480Search in Google Scholar

Moon, T.K. (2005). Error Correction Coding: Mathematical Methods and Algorithms, John Wiley & Sons, Hoboken, NJ.10.1002/0471739219Search in Google Scholar

Quadrat, A. (2004). On a general structure of the stabilizing controllers based on stable range, SIAM Journal on Control and Optimization42(6): 2264-2285, DOI: 10.1137/S0363012902408277.10.1137/S0363012902408277Search in Google Scholar

Quevedo, D.E., Bölcskei, H. and Goodwin, G.C. (2009). Quantization of filter bank frame expansions through moving horizon optimization, IEEE Transactions on Signal Processing57(2): 503-515, DOI: 10.1109/TSP.2008.2008259.10.1109/TSP.2008.2008259Search in Google Scholar

Sontag, E.D. (1980). On generalized inverses of polynomial and other matrices, IEEE Transactions on Automatic Control25(3): 514-517.10.1109/TAC.1980.1102377Search in Google Scholar

Stanimirović, P.S. (2003). A finite algorithm for generalized inverses of polynomial and rational matrices, Applied Mathematics and Computation, 144(2-3): 199-214, DOI: 10.1016/S0096-3003(02)00401-0.10.1016/S0096-3003(02)00401-0Search in Google Scholar

Stanimirović, P.S. and Petković, M.D. (2006). Computing generalized inverse of polynomial matrices by interpolation, Applied Mathematics and Computation172(1): 508-523, DOI: 10.1016/j.amc.2005.02.031.10.1016/j.amc.2005.02.031Search in Google Scholar

Tidestav, C., Sternad, M. and Ahlen, A. (1999). Reuse within a cell-interference rejection or multiuser detection?, IEEE Transactions on Communications47(10): 1511-1522, DOI: 10.1109/26.795820.10.1109/26.795820Search in Google Scholar

Tokarzewski, J. (2002). Zeros in Linear Systems: A Geometric Approach, Warsaw University of Technology Press, Warsaw.Search in Google Scholar

Tokarzewski, J. (2004). A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy, International Journal of Applied Mathematics and Computer Science14(2): 149-159.Search in Google Scholar

Trentelman, H.L., Stoorvogel, A.A. and Hautus, M. (2001). Control Theory for Linear Systems, Communications and Control Engineering, Springer-Verlag, New York, NY.10.1007/978-1-4471-0339-4Search in Google Scholar

Tuncer, T.E. (2004). Deconvolution and preequalization with best delay LS inverse filters, Signal Processing84(11): 2207-2219, DOI: 10.1016/j.sigpro.2004.06.023.10.1016/j.sigpro.2004.06.023Search in Google Scholar

Vaidyanathan, P. P. and Chen, T. (1995). Role of anticausal inverses in multirate filter-banks—Part I: System-theoretic fundamentals, IEEE Transactions on Signal Processing43(5): 1090-1102, DOI: 10.1109/78.382395.10.1109/78.382395Search in Google Scholar

Vardulakis, A.I.G. (1991). Linear Multivariable Control: Algebraic Analysis and Synthesis Methods, 1st Edn., John Wiley & Sons, Chichester.Search in Google Scholar

Varga, A. (2001). Computing generalized inverse systems using matrix pencil methods, International Journal of Applied Mathematics and Computer Science11(5): 1055-1068.Search in Google Scholar

Vologiannidis, S. and Karampetakis, N.P. (2004). Inverses of multivariable polynomial matrices by discrete Fourier transforms, Multidimensional Systems and Signal Processing15(4): 341-361, DOI: 10.1023/B:MULT.0000037345.60574.d4.10.1023/B:MULT.0000037345.60574.d4Search in Google Scholar

Wahls, S. and Boche, H. (2007). Stable and causal LTI-precoders and equalizers for MIMO-ISI channels with optimal robustness properties, Proceedings of the International ITG/IEEE Workshop on Smart Antennas (WSA'2007), Vienna, Austria, (on CD-ROM).Search in Google Scholar

Wahls, S., Boche, H. and Pohl, V. (2009). Zero-forcing precoding for frequency selective MIMO channels with H∞ criterion and causality constraint, Signal Processing89(9): 1754-1761, DOI: 10.1016/j.sigpro.2009.03.010.10.1016/j.sigpro.2009.03.010Search in Google Scholar

Williams, T. and Antsaklis, P.J. (1996). Decoupling, in W.S. Levine (Ed.), The Control Handbook, Electrical Engineering Handbook, CRC Press/IEEE Press, Boca Raton, FL, Chapter 50, pp. 745-804.Search in Google Scholar

Xia, X.-G., Su, W. and Liu, H. (2001). Filterbank precoders for blind equalization: Polynomial ambiguity resistant precoders (PARP), IEEE Transactions on Circuits and Systems—I: Fundamental Theory and Applications48(2): 193-209, DOI: 10.1109/81.904884.10.1109/81.904884Search in Google Scholar

Zhang, L. and Makur, A. (2009). Multidimensional perfect reconstruction filter banks: An approach of algebraic geometry, Multidimensional Systems and Signal Processing20(1): 3-24, DOI: 10.1007/s11045-008-0060-5.10.1007/s11045-008-0060-5Search in Google Scholar

Zhang, S.Y. (1989). Generalized proper inverse of polynomial matrices and the existence of infinite decoupling zeros, IEEE Transaction on Automatic Control34(7): 743-745, DOI: 10.1109/9.29403.10.1109/9.29403Search in Google Scholar