346
Views
46
CrossRef citations to date
0
Altmetric
Original Articles

Stability and stabilisation of linear multidimensional discrete systems in the frequency domain

, &
Pages 1969-1989 | Received 09 Feb 2013, Accepted 07 Jul 2013, Published online: 15 Oct 2013

References

  • Anantharam , V . 1985 . On stabilization and the existence of coprime factorizations . IEEE Transactions on Automatic Control , 30 : 1030 – 1031 . doi: 10.1109/TAC.1985.1103809
  • Bachelier , O. , Paszke , W. and Mehdi , D . 2008 . On the KYP lemma and the multidimensional models . Multidimensional Systems and Signal Processing , 19 : 425 – 447 . doi: 10.1007/s11045-008-0055-2
  • Basu , S . 1990 . On boundary implications of stability and positivity properties of multidimensional systems . Proceedings of the IEEE , 78 : 614 – 626 . doi: 10.1109/5.54802
  • Basu , S. 1987 . New results on stable multivariable polynomials: Part II, discrete case . IEEE Transactions on Circuits and Systems , 34 : 1257 – 1270 . doi: 10.1109/TCS.1987.1086065
  • Bisiacco , M . 1995 . New results in 2D optimal control theory . Multidimensional Systems and Signal Processing , 6 : 189 – 222 . doi: 10.1007/BF00981083
  • Bisiacco , M. , Fornasini , E. , Marchesini , G , Byrnes , C. I. and Lindquist , A. 1986 . “ Controller design for 2D systems ” . In Frequency domain and state space methods for linear systems , 99 – 113 . North-Holland : Elsevier .
  • Bistritz , Y . “ An immittance-type stability test for two-dimensional digital filters ” . In Proceedings of the 28th Annual Asilomar Conference on Signals, Systems, and Computers 918 – 922 .
  • Bistritz , Y . 1999 . Stability testing of two-dimensional discrete linear system polynomials by a two-dimensional tabular form . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 46 : 666 – 676 . doi: 10.1109/81.768823
  • Bistritz , Y . 2000 . Immittance-type tabular stability test for 2-D LSI systems based on a zero location test for 1-D complex polynomials . Circuits, Systems, and Signal Processing , 19 : 245 – 265 . doi: 10.1007/BF01204577
  • Bistritz , Y . 2002a . Stability testing of two-dimensional discrete-time systems by a scattering-type stability table and its telepolation . Multidimensional Systems and Signal Processing , 13 : 55 – 77 . doi: 10.1023/A:1013843411523
  • Bistritz , Y . 2002b . Zero location of polynomials with respect to the unit-circle unhampered by nonessential singularities . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 49 : 305 – 314 . doi: 10.1109/81.989164
  • Bistritz , Y . 2003 . Real-polynomial based immittance-type tabular stability test for two-dimensional discrete systems . Circuits, Systems, and Signal Processing , 22 : 255 – 276 . doi: 10.1007/s00034-004-7030-4
  • Bistritz , Y . 2004a . An efficient integer-preserving stability test for discrete-time systems . Circuits, Systems, and Signal Processing , 23 : 195 – 213 . doi: 10.1007/s00034-004-7016-2
  • Bistritz , Y . 2004b . Testing stability of 2-D discrete systems by a set of real 1-D stability tests . IEEE Transactions on Circuits and Systems I: Regular Papers , 51 : 1312 – 1320 . doi: 10.1109/TCSI.2004.830679
  • Bistritz , Y . 2006 . Critical stability constraints for discrete-time linear systems . IEEE Transactions on Circuits and Systems II: Express Briefs , 53 : 95 – 99 . doi: 10.1109/TCSII.2005.856032
  • Bose , N. K . 1977 . Implementation of a new stability test for two-dimensional filters . IEEE Transactions on Acoustics, Speech and Signal Processing , 25 : 117 – 120 . doi: 10.1109/TASSP.1977.1162917
  • Bose , N. K . 1982 . Applied multidimensional systems theory , New York : Van Nostrand Reinhold .
  • Bose , N. K . 1993 . Simplification of a multidimensional digital filter stability test . Journal of the Franklin Institute , 330 : 905 – 911 . doi: 10.1016/0016-0032(93)90084-8
  • Bose , N. K. and Basu , S . 1978 . Tests for polynomial zeros on a polydisc distinguished boundary . IEEE Transactions on Circuits and Systems , 25 : 684 – 693 . doi: 10.1109/TCS.1978.1084546
  • Bose , N. K. and Jury , E . 1974 . Positivity and stability tests for multidimensional filters (discrete-continuous) . IEEE Transactions on Acoustics, Speech and Signal Processing , 22 : 174 – 180 . doi: 10.1109/TASSP.1974.1162564
  • Buchberger , B . 2001 . Gröbner bases and systems theory . Multidimensional Systems and Signal Processing , 12 : 223 – 251 . doi: 10.1023/A:1011949421611
  • Byrnes , C. , Spong , M. and Tarn , T . 1984 . A several complex variables approach to feedback stabilization of linear neutral delay-differential systems . Theory of Computing Systems , 17 : 97 – 133 .
  • Charoenlarpnopparut , C. and Bose , N. K . 2001 . Gröbner bases for problem solving in multidimensional systems . Multidimensional Systems and Signal Processing , 12 : 365 – 376 . doi: 10.1023/A:1011965825246
  • Cichy , B. , Galkowski , K. and Rogers , E . 2012 . Iterative learning control for spatio-temporal dynamics using Crank-Nicholson discretization . Multidimensional Systems and Signal Processing , 23 : 185 – 208 . doi: 10.1007/s11045-010-0132-1
  • Cichy , B. , Galkowski , K. , Rogers , E. and Kummert , A . 2011 . An approach to iterative learning control for spatio-temporal dynamics using nD discrete linear systems models . Multidimensional Systems and Signal Processing , 22 : 83 – 96 . doi: 10.1007/s11045-010-0108-1
  • Curtin , E. and Saba , S . 1999 . Stability and margin of stability tests for multidimensional filters . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 46 : 806 – 809 . doi: 10.1109/81.774225
  • DeCarlo , R. , Murray , J. and Saeks , R . 1977 . Multivariable Nyquist theory . International Journal of Control , 25 : 657 – 675 . doi: 10.1080/00207177708922261
  • de Oliveira , M. “ Decomposition of a polynomial as a Sum-Of-Squares of polynomials and the S-procedure ” . In Proceedings of the 44th IEEE Conference Decision and Control (CDC) and the European Control Conference (ECC) 1654 – 1659 . Seville , , Spain 12–15 December
  • Desoer , C. , Liu , R. , Murray , J. and Saeks , R . 1980 . Feedback system design: The fractional representation approach to analysis and synthesis . IEEE Transactions on Automatic Control , 25 : 399 – 412 . doi: 10.1109/TAC.1980.1102374
  • Du , C. and Xie , L . 2002 . H control and filtering of two-dimensional systems , Springer Verlag .
  • Dumitrescu , B . 2006 . Stability test of multidimensional discrete-time systems via sum-of-squares decomposition . IEEE Transactions on Circuits and Systems I: Regular Papers , 53 : 928 – 936 . doi: 10.1109/TCSI.2005.859624
  • Dumitrescu , B . 2007 . Positivstellensatz for trigonometric polynomials and multidimensional stability tests . IEEE Transactions on Circuits and Systems II: Express Briefs , 54 : 353 – 356 . doi: 10.1109/TCSII.2006.890409
  • Dumitrescu , B . 2008 . LMI stability tests for the Fornasini-Marchesini model . IEEE Transactions on Signal Processing , 56 : 4091 – 4095 . doi: 10.1109/TSP.2008.921768
  • Dumitrescu , B. and Chang , B . 2006 . Robust Schur stability with polynomial parameters . IEEE Transactions on Circuits and Systems II: Express Briefs , 53 : 535 – 537 . doi: 10.1109/TCSII.2006.875329
  • Feng , Z. , Wu , Q. and Xu , L . 2012 . H ∞ control of linear multidimensional discrete systems . Multidimensional Systems and Signal Processing , 23 : 381 – 411 . doi: 10.1007/s11045-011-0148-1
  • Fu , P. , Chen , J. and Niculescu , S . 2006 . Generalized eigenvalue-based stability tests for 2-D linear systems: Necessary and sufficient conditions . Automatica , 42 : 1569 – 1576 . doi: 10.1016/j.automatica.2006.04.015
  • Fu , P. , Chen , J. and Niculescu , S . 2010 . Author’s reply to ‘A counterexample to generalized eigenvalue-based stability tests for 2-D linear systems: Necessary and sufficient conditions’ . Automatica , 46 : 236 – 237 . doi: 10.1016/j.automatica.2009.10.003
  • Galkowski , K. , Lam , J. , Xu , S. and Lin , Z . 2003 . LMI approach to state-feedback stabilization of multidimensional systems . International Journal of Control , 76 : 1428 – 1436 . doi: 10.1080/00207170310001599113
  • Ghamgui , M. , Yeganefar , N. , Bachelier , O. and Mehdi , D . 2013 . Robust stability of hybrid Roesser models against parametric uncertainty: A general approach . Multidimensional Systems and Signal Processing , 24 , 667–684. doi: 10.1007/s11045-012-0213-4
  • Ghamgui , M. , Yeganefar , N. , Paszke , W. , Bachelier , O. and Mehdi , D. “ S-procedure for deriving stability conditions of hybrid Roesser models ” . In Proceedings of the 7th International Workshop on Multidimensional Systems (nDS) Poitiers , , France 5–7 September
  • Goodman , D . 1977 . Some stability properties of two-dimensional linear shift-invariant digital filters . IEEE Transactions on Circuits and Systems , 24 : 201 – 208 . doi: 10.1109/TCS.1977.1084322
  • Guillernin , E . 1957 . Synthesis of passive networks , New York, NY: Wiley and Sons .
  • Guiver , J. , Bose , N. K and Bose , N. K. “ Causal and weakly causal 2-D filters with applications in stabilization ” . In Multidimensional systems theory: Progress, directions and open problems). The Netherlands: Kluwer Academic Publishers. 52 – 100 .
  • Hmamed , A. , Mesquine , F. , Tadeo , F. , Benhayoun , M. and Benzaouia , A . 2010 . Stabilization of 2D saturated systems by state feedback control . Multidimensional Systems and Signal Processing , 21 : 277 – 292 . doi: 10.1007/s11045-010-0107-2
  • Horn , R. A. and Johnson , C. R . 1990 . Matrix analysis , Cambridge: Cambridge University Press .
  • Hu , X . 1991 . 2-D filter stability-tests using polynomial array for f(z1, z2) on |z1| = 1 . IEEE Transactions on Circuits and Systems , 38 : 1092 – 1095 . doi: 10.1109/31.83882
  • Hu , X . 1995 . Stability tests of N-dimensional discrete time systems using polynomial arrays . IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing , 42 : 261 – 268 . doi: 10.1109/82.378039
  • Hu , X. and Jury , E . 1994 . On two-dimensional filter stability test . IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing , 41 : 457 – 462 .
  • Huang , T . 1972 . Stability of two-dimensional recursive filters . IEEE Transactions on Audio and Electroacoustics , 20 : 158 – 163 . doi: 10.1109/TAU.1972.1162364
  • Idczak , D. and Majewski , M . 2012 . Existence of optimal solutions of two-directionally continuous linear repetitive processes . Multidimensional Systems and Signal Processing , 23 : 155 – 162 . doi: 10.1007/s11045-010-0105-4
  • Jury , E . 1978 . Stability of multidimensional scalar and matrix polynomials . Proceedings of the IEEE , 66 : 1018 – 1047 . doi: 10.1109/PROC.1978.11079
  • Kaczorek , T . 1985 . Two-dimensional linear systems , Berlin: Springer-Verlag .
  • Kailath , T . 1986 . A theorem of I. Schur and its impact on modern signal processing . Operator Theory: Advances and Applications , 18 : 9 – 30 . doi: 10.1007/978-3-0348-5483-2
  • Kar , H. and Singh , V . 2003 . Stability of 2-D systems described by the Fornasini-Marchesini first model . IEEE Transactions on Signal Processing , 51 : 1675 – 1676 . doi: 10.1109/TSP.2003.811237
  • Kojima , C. , Rapisarda , P. and Takaba , K . 2011 . Lyapunov stability analysis of higher-order 2-D systems . Multidimensional Systems and Signal Processing , 22 : 287 – 302 . doi: 10.1007/s11045-010-0124-1
  • Kucera , V . 1979 . Discrete linear control: The polynomial equation approach , New York, NY: John Wiley & Sons, Inc .
  • Li , C. and Fadali , M. S . 1991 . Optimal control of 2-D systems . IEEE Transactions on Automatic Control , 36 : 223 – 228 . doi: 10.1109/9.67300
  • Lin , Z. 1987 . Multidimensional linear systems: Factorisation and stabilisation (Ph.D. thesis) , University of Cambridge , , U.K : Dept. of Engineering .
  • Lin , Z . 1988a . Feedback stabilization of multivariable two-dimensional linear-systems . International Journal of Control , 48 : 1301 – 1317 . doi: 10.1080/00207178808906247
  • Lin , Z . 1988b . On matrix fraction descriptions of multivariable linear n-D systems . IEEE Transactions on Circuits and Systems , 35 : 1317 – 1322 . doi: 10.1109/31.7606
  • Lin , Z . 1992 . On primitive factorizations for 3-D polynomial matrices . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 39 : 1024 – 1027 . doi: 10.1109/81.207728
  • Lin , Z . 1998 . Feedback stabilizability of MIMO nD linear systems . Multidimensional Systems and Signal Processing , : 149 – 172 . doi: 10.1023/A:1008230204251
  • Lin , Z . 1999 . Feedback stabilization of MIMO 3-D linear systems . IEEE Transactions on Automatic Control , 44 : 1950 – 1955 . doi: 10.1109/9.793738
  • Lin , Z . 2000 . Feedback stabilization of MIMO nD linear systems . IEEE Transactions on Automatic Control , 45 : 2419 – 2424 . doi: 10.1109/9.895573
  • Lin , Z , Galkowski , K. and Wood , J. “ Output feedback stabilizability and stabilization of linear nD systems ” . In Multidimensional signals, circuits and systems). London: Taylor & Francis. 59 – 76 .
  • Lin , Z. , Lam , J. , Galkowski , K. and Xu , S . 2001 . A constructive approach to stabilizability and stabilization of a class of nD systems . Multidimensional Systems and Signal Processing , 12 : 329 – 343 . doi: 10.1023/A:1011909707499
  • Lin , Z. , Xu , L. and Bose , N. K . 2008 . A tutorial on Grobner bases with applications in signals and systems . IEEE Transactions on Circuits and Systems I: Regular Papers , 55 : 445 – 461 . doi: 10.1109/TCSI.2007.914007
  • Lu , W. -S . 1992 . Two-dimensional digital filters , CRC . . New York, NY: Marcel Dekker, Inc.
  • MacFarlane , A. G.J. 1979 . Frequency response methods in control systems , New York : IEEE Reprint Series .
  • Maria , G. and Fahmy , M . 1973 . On the stability of two-dimensional digital filters . IEEE Transactions on Audio and Electroacoustics , 21 : 470 – 472 . doi: 10.1109/TAU.1973.1162511
  • Mastorakis , N. , Gonos , I. and Swamy , M . 2003 . Stability of multidimensional systems using genetic algorithms . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 50 : 962 – 965 . doi: 10.1109/TCSI.2003.813968
  • Mori , K . 2002a . Parameterization of stabilizing controllers over commutative rings with application to multidimensional systems . IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 49 : 743 – 752 . doi: 10.1109/TCSI.2002.1010030
  • Mori , K . 2002b . Parameterization of stabilizing controllers with either right-or left-coprime factorization . IEEE Transactions on Automatic Control , 47 : 1763 – 1767 . doi: 10.1109/TAC.2002.803556
  • Mori , K . 2009 . Parameterization of all strictly causal stabilizing controllers . IEEE Transactions on Automatic Control , 54 : 2211 – 2215 . doi: 10.1109/TAC.2009.2026847
  • Mori , K . 2012 . Parameterisation of stabilising controllers with precompensators . IET Control Theory and Applications , 6 : 297 – 304 . doi: 10.1049/iet-cta.2010.0693
  • Mori , K. and Abe , K . 2001 . Feedback stabilization over commutative rings: Further study of the coordinate-free approach . SIAM Journal on Control and Optimization , 39 : 1952 – 1973 . doi: 10.1137/S0363012998336625
  • Oberst , U . 2006 . Stability and stabilization of multidimensional input/output systems . SIAM Journal on Control and Optimization , 45 : 1467 – 1507 . doi: 10.1137/050639004
  • Oberst , U. , Scheicher , M , Park , H. and Regensburger , G. 2007 . “ A survey of (BIBO) stability and (proper) stabilization of multidimensional input/output systems ” . In Gröbner bases in control theory and signal processing , 151 – 190 . Berlin: Walter de Gruyter .
  • Park , H. and Regensburger , G. 2007 . Gröbner bases in control theory and signal processing , Berlin: Walter de Gruyter .
  • Paszke , W. , Galkowski , K. and Rogers , E . “ Repetitive process based iterative learning control design using frequency domain analysis ” . In Proceedings of the IEEE Conference on Control Applications (CCA) 1479 – 1484 .
  • Paszke , W. , Lam , J. , Galkowski , K. , Xu , S. and Lin , Z . 2004 . Robust stability and stabilisation of 2D discrete state-delayed systems . Systems & Control Letters , 51 : 277 – 291 . doi: 10.1016/j.sysconle.2003.09.003
  • Paszke , W. , Rapisarda , P. , Rogers , E. and Steinbuch , M . “ Dissipative stability theory for linear repetitive processes with application in iterative learning control ” . In Proceedings of Symposium on Learning Control at IEEE CDC Shangai , , China
  • Paszke , W. , Rogers , E. and Galkowski , K. “ Design of robust iterative learning control schemes in a finite frequency range ” . In Proceedings of the 7th International Workshop on Multidimensional Systems (nDS) Poitiers , , France 5–7 September
  • Paszke , W. , Rogers , E. and Galkowski , K . “ Finite frequency range control law synthesis for differential linear repetitive processes ” . In Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) 6037 – 6042 .
  • Postlethwaite , I. and MacFarlane , A. G.J . 1979 . A complex variable approach to the analysis of linear multivariable feedback systems , Berlin : Springer-Verlag .
  • Prajna , S. , Papachristodoulou , A. and Parrilo , P . 2002 . Introducing SOSTOOLS: A general purpose sum of squares programming solver . Proceedings of the 41st IEEE Conference on Decision and Control , 1 : 741 – 746 .
  • Prajna , S. , Papachristodoulou , A. , Seiler , P. and Parrilo , P . 2004 . New developments in sum of squares optimization and SOSTOOLS . Proceedings of the 2004 American Control Conference , 6 : 5606 – 5611 .
  • Quadrat , A . 2003a . On a generalization of the Youla–Kučera parametrization. Part I: The fractional ideal approach to SISO systems . Systems and Control Letters , 50 : 135 – 148 . doi: 10.1016/S0167-6911(03)00149-X
  • Quadrat , A . 2003b . The fractional representation approach to synthesis problems: An algebraic analysis viewpoint, part I: (Weakly) doubly coprime factorizations . SIAM Journal on Control and Optimization , 42 : 266 – 299 . doi: 10.1137/S0363012902417127
  • Quadrat , A . 2003c . The fractional representation approach to synthesis problems: An algebraic analysis viewpoint, Part II: Internal stabilization . SIAM Journal on Control and Optimization , 42 : 300 – 320 . doi: 10.1137/S0363012902417139
  • Quadrat , A. “ An elementary proof of the general Q-parametrization of all stabilizing controllers ” . In Proceedings of IFAC World Congress Prague
  • Quadrat , A . 2006a . A lattice approach to analysis and synthesis problems . Mathematics of Control, Signals, and Systems , 18 : 147 – 186 . doi: 10.1007/s00498-005-0159-2
  • Quadrat , A . 2006b . On a generalization of the Youla–Kučera parametrization. Part II: The lattice approach to MIMO systems . Mathematics of Control, Signals, and Systems , 18 : 199 – 235 . doi: 10.1007/s00498-005-0160-9
  • Rafajlowicz , E. and Rafajlowicz , W . 2013 . Control of linear extended nD systems with minimized sensitivity to parameter uncertainties . Multidimensional Systems and Signal Processing , 24 637–656. doi: 10.1007/s11045-013-0236-5
  • Rosenbrock , H. H . 1970 . State-space and multivariable theory , London : Nelson .
  • Serban , I. and Najim , M . 2007 . Multidimensional systems: BIBO stability test based on functional Schur coefficients . IEEE Transactions on Signal Processing , 55 : 5277 – 5285 . doi: 10.1109/TSP.2007.896070
  • Serban , I. , Stitou , Y. , Najim , M. and Turcu , F . 2005 . Multidimensional Schur coefficients and BIBO stability . Communications in Information & Systems , : 131 – 142 .
  • Serban , I. , Turcu , F. and Najim , M . 2006 . Schur coefficients in several variables . Journal of Mathematical Analysis and Applications , 320 : 293 – 302 . doi: 10.1016/j.jmaa.2005.06.068
  • Shanks , J. , Treitel , S. and Justice , J . 1972 . Stability and synthesis of two-dimensional recursive filters . IEEE Transactions on Audio and Electroacoustics , 20 : 115 – 128 . doi: 10.1109/TAU.1972.1162358
  • Strintzis , M . 1977 . Tests of stability of multidimensional filters . IEEE Transactions on Circuits and Systems , 24 : 432 – 437 . doi: 10.1109/TCS.1977.1084368
  • Sule , V . 1994 . Feedback stabilization over commutative rings: The matrix case . SIAM Journal on Control and Optimization , 32 : 1675 – 1695 . doi: 10.1137/S036301299122027X
  • Swamy , M. , Roytman , L. and Plotkin , E . 1985 . On stability properties of three-and higher dimensional linear shift-invariant digital filters . IEEE Transactions on Circuits and Systems , 32 : 888 – 892 . doi: 10.1109/TCS.1985.1085812
  • Toker , O. and Ozbay , H . 1998 . On the complexity of purely complex μ computation and related problems in multidimensional systems . IEEE Transactions on Automatic Control , 43 : 409 – 414 . doi: 10.1109/9.661609
  • Vidyasagar , M. , Schneider , H. and Francis , B . 1982 . Algebraic and topological aspects of feedback stabilization . IEEE Transactions on Automatic Control , 27 : 880 – 894 . doi: 10.1109/TAC.1982.1103015
  • Willems , J. C. 1986/87 . From time series to linear system . Part I: Automatica, 22, 561-580 Part II: Automatica, 22, 675-694 Part III: Automatica, 23, 87-115 ,
  • Xu , L , Park , H. and Regensburger , G. 2007 . “ Applications of Gröbner bases in synthesis of multidimensional control systems ” . In Gröbner bases in control theory and signal processing , 215 – 234 . Berlin: Walter de Gruyter .
  • Xu , L. , Lin , Z. , Ying , J. , Saito , O. , Anazawa , Y , Blondel , V. and Megretski , A. 2004c . “ Open problems in control of linear discrete multidimensional systems ” . In Unsolved problems in mathematical systems and control theory , 212 – 220 . New Jersey, NJ: Princeton University Press . Part 6
  • Xu , L. , Saito , O. and Abe , K . 1990 . Bilateral polynomial matrix equations in two indeterminates . Multidimensional Systems and Signal Processing , : 363 – 379 . doi: 10.1007/BF01937366
  • Xu , L. , Saito , O. and Abe , K . 1994 . Output feedback stabilizability and stabilization algorithms for 2D systems . Multidimensional Systems and Signal Processing , 5 : 41 – 60 . doi: 10.1007/BF00985862
  • Xu , L. , Wu , Q. , Lin , Z. and Anazawa , Y . 2004b . A μ approach to robust stability analysis of nD discrete systems . Multidimensional Systems and Signal Processing , 15 : 277 – 239 . doi: 10.1023/B:MULT.0000028009.31571.0d
  • Xu , L. , Yamada , M. , Lin , Z. , Saito , O. and Anazawa , Y . 2004a . Further improvements on Bose’s 2D stability test . International Journal of Control Automation and Systems , : 319 – 332 .
  • Xu , L. , Ying , J. , Lin , Z. and Saito , O . 2003 . Comments on “Stability tests of N-dimensional discrete time systems using polynomial arrays” . IEEE Transactions on Circuits and Systems II-Analog and Digital Signal Processing , 50 : 666 – 669 . doi: 10.1109/TCSII.2003.816934
  • Youla , D. and Gnavi , G . 1979 . Notes on n-dimensional system theory . IEEE Transactions on Circuits and Systems , 26 : 105 – 111 . doi: 10.1109/TCS.1979.1084614
  • Youla , D. C. , Jabr , H. A. and Jr , J. J . 1976 . Modern Wiener-Hopf design of optimal controllers, Part II: The multivariable case . IEEE Transactions on Automatic Control , 21 : 319 – 338 . doi: 10.1109/TAC.1976.1101223
  • Youla , D. and Pickel , P . 1984 . The Quillen-Suslin theorem and the structure of n-dimensional elementary polynomial matrices . IEEE Transactions on Circuits and Systems , 31 : 513 – 518 . doi: 10.1109/TCS.1984.1085545

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.