Now showing items 15-34 of 47

  • Evaluation of scalar products of repeated integrals by Routh algorithm 

    Lucas, T. Nigel (Institution of Engineering and Technology, 1988-09)
    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, 1993-09)
    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, 1983-11)
    An alternative approach is given for linear-system 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, 1996-08)
    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 root-finding ...
  • Flexible time-response matching in discrete model reduction 

    Lucas, T. Nigel (Sage Publications, 2000-08)
    A simple way to match the time responses of the full- and reduced-order models at arbitrary sampling points is given for discrete-time systems. It is seen to be a natural extension of the Padé methods and is particularly ...
  • Frequency-domain reduction of linear systems using Schwarz approximation 

    Lucas, T. Nigel; Davidson, A. M. (Taylor & Francis, 1983)
    A frequency domain approach for reducing linear, time-invariant 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, 1987-02)
    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.
  • Least-squares moment matching reduction methods 

    Smith, I. D.; Lucas, T. Nigel (Institution of Engineering and Technology, 1995-05)
    It is shown how the two apparently different approaches to modelling reduction by least-squares time moment matching give identical results. This property also enables a clear understanding of how the method actually ...
  • Least-squares Pade reduction: a nonuniqueness property 

    Lucas, T. Nigel; Smith, I. D. (Institution of Engineering and Technology, 1995-09)
    It is shown that least-squares 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 continued-fraction expansion about s = 0 and s = a alternately 

    Lucas, T. Nigel (Institution of Engineering and Technology, 1983-03)
    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 continued-fraction expansion about three points 

    Lucas, T. Nigel (Institution of Engineering and Technology, 1984-01)
    The method of model reduction by continued-fraction expansion about s = 0 and s = a is extended to include the point s = à ¿ 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, 1985-08)
    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 ...
  • Linear system reduction by the modified factor division method 

    Lucas, T. Nigel (Institution of Engineering and Technology, 1986-11)
    A novel method of linear system simplification is presented based on a modified factor division approach. It is seen to be more flexible than most model reduction methods in that families of reduced models may be easily ...
  • Linear system reduction using Schwarz canonical form 

    Davidson, A. M.; Lucas, T. Nigel (Institution of Engineering and Technology, 1976-06)
    A system reduction method based on Schwarz canonical form has recently been observed to have certain moment-matching properties. By reformulating the method, these properties are proved and extended and the stability of ...
  • Linear-system reduction by continued-fraction expansion about a general point 

    Davidson, A. M.; Lucas, T. Nigel (Institution of Engineering and Technology, 1974-07)
    Capacity requirements for multiple-access demand-assigned communication systems are broken down into information, demand and assignment signalling. A simultaneous-transmission scheme for demand signalling greatly reduces ...
  • Model reduction by condensed continued-fraction method 

    Lucas, T. Nigel (Institution of Engineering and Technology, 1985-08)
    It is shown how the continued-fraction method of Chen and Shieh may be used on part of the transfer function to produce reduced-order models when its normal application is unsatisfactory. In addition, the truncation method ...
  • Model reduction by generalised least-squares method 

    Lucas, T. Nigel; Munro, A. R. (Institution of Engineering and Technology, 1991-07)
    The method of model reduction by least-squares moment matching is generalised to include Markov parameters in the process. This is seen to enhance the flexibility of the method with very little extra computational requirement. ...
  • Model reduction by least-squares moment matching 

    Lucas, T. Nigel; Beat, I. F. (Institution of Engineering and Technology, 1990-07)
    Model reduction by least-squares moment matching is shown to be very sensitive to the pole distribution of the original system. Systems with poles of modulus less than unity are seen to present numerical problems. A ...
  • Modelling an athletics track 

    Lucas, T. Nigel (Oxford University Press, 1991)
    When introducing students to mathematical modelling ideas it is often useful to have them tackle a fairly "well-defined" problem, possibly related to an outside interest, involving the use of traditional mathematical ...