A new stability preservation property is proved for the least-squares Padé order reduction method when applied to discrete-time systems. It is shown that the property depends on which free reduced model parameter is chosen to be unity. Clarification is also given on how the system is actually approximated using this method. An example illustrates the enhanced appeal of the method as a result of the stability preservation property.
OwensD. H.ChotaiA.On the use of reduced order models and simulation data in control systems design. IMA J. Math. Control Inform., 1993, 10, 83–95.
2.
AguirreL. A.Robust reference models for delayed systems. Proc. Instn Mech. Engrs, Part I, Journal of Systems and Control Engineering, 1994, 208 (I3), 197–199.
3.
JamshidiM.Large-Scale Systems: Modelling and Control, 1983 (North-Holland, Amsterdam).
4.
ShamashY.Order reduction of linear systems by Padé approximation methods. PhD thesis, Imperial College, University of London, 1973.
5.
ChenC. F.ShiehL. S.A novel approach to linear model simplification. Int. J. Control, 1968, 8, 561–570.
6.
BultheelA.Van BarelM.Padé techniques for model reduction in linear system theory: A survey. J. Comput. Appl. Math., 1986, 14, 401–438.
7.
ShojiF. F.AbeK.TakedaH.Model reduction for a class of linear dynamic systems. J. Franklin Inst., 1985, 319, 549–558.
8.
LucasT. N.BeatI. F.Model reduction by least-squares moment matching. Electron. Lett., 1990, 26, 1213–1215.
SmithI. D.LucasT. N.A unifying theory of least-squares Padé model reduction methods. Proc. Instn Mech. Engrs, Part I, Journal of Systems and Control Engineering, 1996, 210 (I2), 95–102.
LalondeR. J.HartleyT. T.De Abreu-GarciaJ. A.Least squares model reduction. J. Franklin Inst., 1992, 329, 215–240.
17.
YahagiY.On the simplification of transfer functions of linear dynamical systems. Trans. ASME, J. Dynamic System, Measmt and Control, 1980, 102, 7–12.
18.
LalondeR. J.The calculation of reduced order linear models from input/output data of high order nonlinear systems. PhD thesis, University of Akron, Ohio, 1992.
19.
LucasT. N.Optimal discrete model reduction by multipoint Padé approximation. J. Franklin Inst., 1993, 330, 855–867.
