Closed form ℒ₂/ℋ₂-optimising of zeros for model reduction of linear continuous time systems

References

• Antoulas , AC . 1986 . On Recursiveness and Related Topics in Linear Systems . IEEE Transactions on Automatic Control , AC-31 : 1121 – 1135 .
   Google Scholar
• Antoulas , AC . 2005a . Approximation of Large-Scale Dynamical Systems , Philadelphia : SIAM .
   Google Scholar
• Antoulas , AC . 2005b . An Overview of Approximation Methods for Large-scale Dynamical Systems . Annual Reviews in Control , 29 : 181 – 190 .
   Web of Science ®Google Scholar
• Antoulas , AC and Willems , JC . 1993 . A Behavioural Approach to Linear Exact Modelling . Annual Reviews in Control , AC-38 : 1776 – 1802 .
   Google Scholar
• Atkinson , K . 1989 . An Introduction to Numerical Analysis , 2nd , New York : John Wiley & Sons .
   Google Scholar
• Bryson , AE and Carrier , A . 1990 . Second-order Algorithm for Optimal Model Order Reduction . Journal of Guidance, Control, and Dynamics , 13 : 887 – 892 .
   Web of Science ®Google Scholar
• Chahlaouio , Y and Dooren , PV . 2002 . “ A Collection of Benchmark Examples for Model Reduction of Linear Time Invariant Dynamical Systems ” . In http://www.slicot.com.
   Google Scholar
• Datta , BN . 2004 . Numerical Methods for Linear Control Systems , San Diego, CA : Elsevier Academic Press .
   Google Scholar
• Enns , D . 1984a . “ Model Reduction for Control System Design ” . In PhD thesis , Stanford, CA : Department of Aeronautics and Astronautics .
   Google Scholar
• Enns , D . 1984b . Model Reduction with Balanced Realisation: An Error Bound and a Frequency Weighted Generalisation . Proceedings of the Conference on Decision and Control . 1984b , Las Vegas, Nevada.
   Google Scholar
• Gajic , Z and Lelic , M . 2001 . Improvement of System Order Reduction via Balancing using the Method of Singular Perturbations . Automatica , 37 : 1859 – 1865 .
   Web of Science ®Google Scholar
• Glover , K . 1984 . All Optimal Hankel-norm Approximation of Linear Multivariable Systems and Their ℒ∞ Error Bounds . International Journal of Control , 39 : 1115 – 1193 .
   Web of Science ®Google Scholar
• Golub , GH and Loan , CFV . 1996 . Matrix Computations , 3rd , Baltimore, MA : The Johns Hopkins University Press .
   Google Scholar
• Hauksdóttir , AS . 1996 . Analytic Expressions of Transfer Function and Choice of Numerator Coefficients (Zeros) . IEEE Transactions on Automatic Control , 41 : 1482 – 1488 .
   Web of Science ®Google Scholar
• Hauksdóttir , AS . 2000 . Optimal Zeros for Model Reduction of Continuous-time Systems . Proceedings of the 2000 American Control Conference . 2000 , Chicago, Illinois. pp. 1889 – 1893 .
   Google Scholar
• Hauksdóttir , AS . 2004 . Optimal Zero Locations of Continuous-time Systems with Distinct Poles Tracking Reference Step Responses . Dynamics of Continuous, Discrete, and Impulsive Systems, Series B: Applications and Algorithms , 11 : 353 – 361 .
   Google Scholar
• Hauksdóttir , AS , Herjólfsson , G and Sigurðsson , Sþ . 2007 . Optimizing Zero Tracking and Disturbance Rejecting Controllers–The Generalized PID Controller . Proceedings of the 2007 American Control Conference . 2007 , New York City. pp. 5790 – 5795 .
   Google Scholar
• Herjólfsson , G and Hauksdóttir , AS . 2003 . Direct Computation of Optimal PID Controllers . Proceedings of the 42nd IEEE Conference on Decision and Control . 2003 , Maui, Hawaii. pp. 1120 – 1125 .
   Google Scholar
• Herjólfsson , G , Ævarsson , B , Hauksdóttir , AS and Sigurðsson , Sþ . 2006 . Closed Form Expressions of Linear Continuous- and Discrete-time Filter Responses . NORSIG 2006, 7th Nordic Signal Processing Symposium . 2006 , Reykjavík, Iceland.
   Google Scholar
• Hyland , D and Bernstein , D . 1985 . The Optimal Projection Equations for Model Reduction and the Relationships Among the Methods of Wilson, Skelton, and Moore . IEEE Transactions on Automatic Control , AC-30 : 1201 – 1211 .
   Web of Science ®Google Scholar
• Kokotovic , PV , O'Malley , RE and Sannuti , P . 1976 . Singular Perturbations and Order Reduction in Control Theory–an Overview . Automatica , 112 : 123 – 132 .
   Google Scholar
• Liu , Y and Anderson , BDO . 1989 . Singular Perturbation Approximation of Balanced Systems . International Journal of Control , 50 : 1379 – 1405 .
   Web of Science ®Google Scholar
• Meier , L and Luenberger , DG . 1967 . Approximation of Linear Constant Systems . IEEE Transactions on Automatic Control , 12 : 585 – 587 .
   Web of Science ®Google Scholar
• Moore , BC . 1981 . Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction . IEEE Transactions on Automatic Control , 26 : 17 – 32 .
   Web of Science ®Google Scholar
• Pernebo , L and Silverman , LM . 1982 . Model Reduction via Balanced State Space Representation . IEEE Transactions on Automatic Control , 27 : 382 – 387 .
   Web of Science ®Google Scholar
• Spanos , JT , Milman , MH and Mingori , DL . 1992 . A New Algorithm for L 2 Optimal Model Reduction . Automatica , 28 : 897 – 909 .
   Web of Science ®Google Scholar
• Wilson , DA . 1970 . Optimum Solution of Model Reduction Problem . Proceedings of the IEE , 117 : 1161 – 1165 .
   Web of Science ®Google Scholar
• Wilson , DA and Mishra , RN . 1979 . Design of Low-order Estimation Using Reduced Models . International Journal of Control , 29 : 447 – 456 .
   Web of Science ®Google Scholar
• Yan , W and Lam , J . 1996 . L 2 Optimal Model Reduction . Proceedings of the 35th IEEE Conference on Decision and Control . 1996 , Kobe, Japan. pp. 4276 – 4281 .
   Google Scholar