Parametrising the solutions of the generalised partial realisation problem through an atlas of coordinates

References

• Antoulas , AC . 1983 . New Results on the Algebraic Theory of Linear Systems: The Solution of the Cover Problem . Linear Algebra and its Applications , 50 : 1 – 43 .
   Web of Science ®Google Scholar
• Baragaña , I , Puerta , F , Puerta , X and Zaballa , I . 2010 . On the Geometry of the Generalised Partial Problem . Mathematics of Control, Signals and Systems , 22 : 39 – 89 .
   Web of Science ®Google Scholar
• Barreiro , A . 1995 . Recursive Techniques in State-space and Matrix Fraction Realisations for Linear Systems . Discrete-time Control System Implementation Techniques , 72 : 25 – 57 .
   Google Scholar
• Bosgra , OH . 1983 . On Parametrisations for the Minimal Partial Realisation Problem . Systems and Control Letters , 3 : 181 – 187 .
   Web of Science ®Google Scholar
• Brockett , RW . 1978 . “ The Geometry of the Partial Realisation Problem ” . In in Proceedings of the 17th IEEE Conference on Decision and Control 1048 – 1052 . San Diego, CA
   Google Scholar
• Brunovsky , P . 1970 . Classification of Linear Controllable Systems . Kybernetica (Praga) , 3 : 173 – 188 .
   Google Scholar
• Damen , AAH , Guidorzi , RP , Hajdasinski , AK and van den Hopf , PMJ . 1985 . On Multivariable Partial Realisation . International Journal of Control , 41 : 589 – 613 .
   Web of Science ®Google Scholar
• De Schutter , D . 2000 . Minimal State-space Realization in Linear System Theory: and Overview . Journal of Computational and Applied Mathematics , 121 : 331 – 354 .
   Web of Science ®Google Scholar
• Feldmann , S and Heinig , G . 1999 . Parametrization of Minimal Rank Block Hankel Matrix Extensions and Minimal Partial Realizations . Integral Equations and Operator Theory , 33 : 153 – 171 .
   Web of Science ®Google Scholar
• Gohberg , I , Kaashoek , MA and Lerer , L . 1987 . On Minimality in the Partial Realization Problem . System and Control Letters , 9 : 97 – 104 .
   Web of Science ®Google Scholar
• Gohberg , I , Kaashoek , MA and Lerer , L . 1991 . A Directional Partial Realisation Problem . System and Control Letters , 17 : 305 – 314 .
   Web of Science ®Google Scholar
• Gragg , WB and Lindquist , A . 1983 . On the Partial Realization Problem . Linear Algebra and its Applications , 50 : 277 – 319 .
   Web of Science ®Google Scholar
• Helmke , U . 1986 . Topology of the Moduli Space for Reachable Linear Dynamical Systems: The Complex Case . Mathematical Systems Theory , 19 : 155 – 187 .
   Google Scholar
• Hinrichsen , D , Manthey , W and Helmke , U . 2001 . Minimal Partial Realisation by Descriptor Systems . Linear Algebra and its Applications , 326 : 45 – 84 .
   Web of Science ®Google Scholar
• Kalman , RE . 1976 . “ Realization Theory of Linear Dynamical Systems ” . In Control Theory and Topics in Functional Analysis. II , 235 – 256 . Vienna : International Atomic Energy Agency .
   Google Scholar
• Kalman , RE . 1979 . On Partial Realisations, Transfer Functions and Canonical Forms . Acta Polytechnica Scandinavica: Mathematics and Computers Science Series , 31 : 9 – 32 .
   Google Scholar
• Kuijper , M . 1997 . An Algorithm for Constructing a Minimal Partial Realisation in the Multivariable Case . Systems and Control Letters , 31 : 225 – 233 .
   Web of Science ®Google Scholar
• Lee , JM . 2003 . Introduction to Smooth Manifolds , New York : Springer Verlag .
   Google Scholar
• Manthey , W , Helmke , U and Hinrichsen , D . 1992 . Topological Aspects of the Partial Realization Problem . Math. Control Signal Systems , 5 : 117 – 149 .
   Web of Science ®Google Scholar
• Marshall , AW and Olkin , I . 1979 . Inequalities: Theory of Majorization and its Applications , New York : Academic Press. New edition with Arnold B.C., Springer . (2011)
   Google Scholar
• Puerta , F , Puerta , X and Zaballa , I . 1992 . A Cellular Decomposition of the Manifold of Observable Conditioned Invariant Subspaces . Linear Algebra and its Applications , 351-352 : 601 – 621 .
   Web of Science ®Google Scholar
• Woerdeman , H . 1989 . Minimal Rank Completions for Block Matrices . Linear Algebra and its Applications , 121 : 105 – 122 .
   Web of Science ®Google Scholar
• Zaballa , I . 1997 . Controllability and Hermite Indices of Matrix Pairs . International Journal of Control , 68 : 61 – 86 .
   Web of Science ®Google Scholar
• Zazworsky , RM , Jensen , D and Baker , WP . 1979 . The Set of All Minimal Partial Realizations . IEEE Transactions on Automatic Control , 24 : 966 – 970 .
   Web of Science ®Google Scholar