Browsing by Author "Lucas, T. Nigel"
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Constrained suboptimal Padé model reduction
Lucas, T. Nigel (Sage Publications, 1995)An extension of a recent Pade suboptimal model reduction method is presented which ensures that the initial time response values of the reduced models coincide with those for the full system for impulse or step inputs. ... 
Continuedfraction algorithm for biased model reduction
Lucas, T. Nigel (Institution of Engineering and Technology, 198306)An algorithm is presented for linear system reduction which produces biased models such that combinations of retained time moments and Markov parameters may be varied. It is based on the Cauer continuedfraction expansions ... 
Continuedfraction expansion about two or more points: a flexible approach to linear system reduction
Lucas, T. Nigel (Elsevier, 198601)Model reduction by continuedfraction expansion about two or more points, including the general point s = a, is shown to be a real alternative to the methods which guarantee stability. Suitable choice of a is seen to ... 
Differentiation reduction method as a multipoint Pade approximant
Lucas, T. Nigel (Institution of Engineering and Technology, 198801)The differentiation method for model order reduction is shown to be a special case of multipoint Pade approximation. This link also extends to other reduction methods where reduced models are generated successively. An ... 
Discretetime leastsquares Padé order reduction: a stability preserving method
Lucas, T. Nigel; Smith, I. D. (Sage Publications, 199802)A new stability preservation property is proved for the leastsquares Padé order reduction method when applied to discretetime systems. It is shown that the property depends on which free reduced model parameter is chosen ... 
Efficient algorithm for reduction by continuedfraction expansion about s = 0 and s = a
Lucas, T. Nigel (Institution of Engineering and Technology, 198311)An algorithm is given for model reduction by continuedfraction expansion about the origin and a general point. It is seen to be more efficient than the existing method and has the advantage of also generating biased models. ... 
Enhancement of the leastsquares Padé method for discrete systems
Lucas, T. Nigel (Sage Publications, 200003)The leastsquares Padé method for discrete system order reduction is further enhanced. First, it is shown how the method may be extended to produce true leastsquares approximations between the time responses of the full ... 
Evaluation of scalar products of repeated integrals by Routh algorithm
Lucas, T. Nigel (Institution of Engineering and Technology, 198809)It is shown that evaluation of Gram matrix entries for model reduction information may be carried out by repeated use of the well known Routh algorithm. This procedure is seen to enhance both the understanding and ... 
Extension of matrix method for complete multipoint Pade approximation
Lucas, T. Nigel (Institution of Engineering and Technology, 199309)A recent multipoint Pade approximation technique for linear system reduction is extended to include expansion points at infinity. The method is then seen to be completely general, covering the cases of real, complex, ... 
Factor division: a useful algorithm in model reduction
Lucas, T. Nigel (Institution of Engineering and Technology, 198311)An alternative approach is given for linearsystem reduction by Pade approximation to allow retention of dominant modes. It avoids calculation of system time moments and the solution of Pade equations by simply dividing ... 
Finding roots by deflated polynomial approximation
Lucas, T. Nigel (Elsevier, 1990)A numerical technique is presented which evaluates the roots of polynomials with real coefficients. Features of the method include no complex arithmetic requirements, no need to guess at initial quadratic factor estimates, ... 
Finding roots of polynomials by using the Routh array
Lucas, T. Nigel (Institution of Engineering and Technology, 199608)A robust method for finding the roots of polynomials using the Routh array is given. Certain multipoint approximation properties of the array are clarified, which enable a simple criterion to be used in the rootfinding ... 
Flexible timeresponse matching in discrete model reduction
Lucas, T. Nigel (Sage Publications, 200008)A simple way to match the time responses of the full and reducedorder models at arbitrary sampling points is given for discretetime systems. It is seen to be a natural extension of the Padé methods and is particularly ... 
Frequencydomain reduction of linear systems using Schwarz approximation
Lucas, T. Nigel; Davidson, A. M. (Taylor & Francis, 1983)A frequency domain approach for reducing linear, timeinvariant systems is presented which produces stable approximations of stable systems. The method is based upon the Schwarz canonical form and is shown to have a ... 
Further discussion on impulse energy approximation
Lucas, T. Nigel (Institute of Electrical and Electronics Engineers, 198702)Recent criticisms by Rao about impulse energy approximation are answered in detail. Further ideas are put forward as to how weighted energy parameters may be used to determine the reduced models for step inputs. 
Leastsquares moment matching reduction methods
Smith, I. D.; Lucas, T. Nigel (Institution of Engineering and Technology, 199505)It is shown how the two apparently different approaches to modelling reduction by leastsquares time moment matching give identical results. This property also enables a clear understanding of how the method actually ... 
Leastsquares Pade reduction: a nonuniqueness property
Lucas, T. Nigel; Smith, I. D. (Institution of Engineering and Technology, 199509)It is shown that leastsquares Pade reduced order models are not unique for a given order. Depending on which reduced denominator coefficient is chosen to be unity. The method is seen to minimise an error index over different ... 
Linear system reduction by continuedfraction expansion about s = 0 and s = a alternately
Lucas, T. Nigel (Institution of Engineering and Technology, 198303)A method of reduction is given which uses the concept of expanding the system transfer function about the origin and about a general point. This results in good overall responses, and families of reduced models of the same ... 
Linear system reduction by continuedfraction expansion about three points
Lucas, T. Nigel (Institution of Engineering and Technology, 198401)The method of model reduction by continuedfraction expansion about s = 0 and s = a is extended to include the point s = Ã Â¿ also. This achieves more accurate transient approximations and thus highlights further the ... 
Linear system reduction by impulse energy approximation
Lucas, T. Nigel (Institute of Electrical and Electronics Engineers, 198508)A method is given for linear system reduction which is a more general form of the Routh method. The reduced models retain stability, and a fuller contribution is made to the impulse response energy of the reduced system ...