Computing transfer function zeros of a state space system

References

• AXELBY , G. S. , LAUB , A. J. , and DAVISON , E. J. , 1978 , Further discussion on the calculation of transmission zeros. Automatica , 14 , 403 – 405 .
   Web of Science ®Google Scholar
• BENGTSSON , G. , 1973 , A theory for control of linear multi variable systems. , Report 7341, Division of Automatic Control, Lund Institute of Technology, Lund , Sweden .
   Google Scholar
• DAVISON , E. J. , and WANG , S. H. , 1974 , Properties and calculations of transmission zeros of linear multi variable systems. Automatica , 10 , 643 – 658 .
   Web of Science ®Google Scholar
• DUFF , I. S. , and REID , J. K. , 1978 a, An implementation of Tarjan's algorithm for the block triangularization of a matrix. ACM Transactions on Mathematical Software , 4 , 137 – 147 ; 1978 b, ALGORITHM 529 permutations to block triangular form IFI). Ibid., 4, 189-192.
   Google Scholar
• EMAMI–NAEINI , A. , and VAN DOOREN , P. , 1982 a, Computation of zeros of linear multivariable systems. Automatica , 18 , 415 – 430 ; 1982 b, On computation of transmission zeros and transfer functions. Proceedings I.E.E.E. Conference on Control, Orlando , Florida , pp. 51-52.
   Google Scholar
• GARBOW , B. S. , BOYLE , J. M. , DONGARRA , J. J. , and MOLER , C. B. , 1977 , Matrix Eigensystem Routines-EISPACK Guide Extension , ( Berlin : Springer-Verlag ).
   Google Scholar
• HARARY , F. , 1959 , A graph theoretic method for the complete reduction of a matrix with a view toward finding its eigenvalues. Journal of Mathematics and Physics , 38 , 104 – 111 .
   Google Scholar
• KALMAN , R. E. , 1963 , Mathematical description of linear dynamical systems. SIAM Journal on Control , 1 , 153 .
   Google Scholar
• KAUFMAN , I. , 1973 , On poles and zeros of linear systems. I. E. E. E. Transactions on Circuit Theory , 20 , 93 – 101 .
   Google Scholar
• KOUVARITAKIS , B. , and MACFARLANE , A. G. J. , 1976 , Geometric approach to the analysis and synthesis of system zeros. Parts 1 and 2. International Journal of Control , 23 , 149 .
   Web of Science ®Google Scholar
• LEFSCHETZ , S. , 1965 , Stability of nonlinear control systems , ( New York : Academic Press ), pp. 132 – 133 .
   Google Scholar
• MARTIN , R. S. , and WILKINSON , J. H. , 1968 , Similarity reduction of a general matrix to Hessenberg form. Numerical Mathematics , 12 , 349 – 368 ; 1969, Handbook for Automatic Computation, Vol. II, Linear Algebra, edited by J. H. Wilkinson and C. Reinsch ( New York : Springer-Verlag ).
   Google Scholar
• MOLER , C. B. , and STEWART , G. W. , 1973 , An algorithm for generalized matrix eigenvalue problems. SIAM Journal on Numerical Analysis , 10 , 241 – 256 .
   Web of Science ®Google Scholar
• PARLETT , B. N. , and REINSCH , c. , 1969 a, Balancing a matrix for calculation of eigenvalues and eigenvectors. Numerical Mathematics , 13 , 293 – 304 ; 1969b, Handbook for Automatic Computation, Vol. II, Linear Algebra, edited by J. H. Wilkinson and C. Reinsch ( New York : Springer-Verlag ).
   Google Scholar
• PATEL , R. V. , 1976 , On computing the invariant zeros of multivariable systems. International Journal of Control , 24 , 145 – 146 .
   Web of Science ®Google Scholar
• PATEL , R. V. , SINSWAT , V. , and FALLSIDE , F. , 1977 , A method for computing the zeros of transfer functions in linear systems. International Journal of Systems Science , 8 , 241 – 249 .
   Web of Science ®Google Scholar
• SANDBERG , I. W. , and So , H. c. , 1969 , A two-sets-of-eigenvalues approach to the computer analysis of linear systems. I. E. E. E. Transactions Circuit Theory , 16 , 509 – 517 .
   Google Scholar
• SMITH , B. T. , BOYLE , J. M. , DONGARRA , J. J. , GARBOW , B. S. , IKEBE , Y. , KLEMA , V. c. , and MOLER , C. B. , 1976 , Matrix Eigensystem Routines-EISPACK Guide , second edition ( Berlin : Springer-Verlag ).
   Google Scholar