In view of the particular interest in the problem of reduced-order modeling in recent years, some considerations not sufficiently investigated in current literature are pointed out and a comprehensive set of references is given.

A note on the derivation and use of reduced-order models

Based on Chuang's continued fraction method of model reduction, an algorithm for obtaining the reduced order model of linear time-invariant system from its state-space model directly, without requiring to determine the corresponding transfer function, has been suggested The algorithm can also be used for determining the transfer function from the state-space model

http://ieeexplore.ieee.org/iel5/9/24179/01102437.pdf

On Chuang's continued fraction method of model reduction

The approximation of discrete-time multivariable high-order linear systems is considered. Reduced order models are derived by a generalized minimal partial realization algorithm. The derived models approximate the system in the Pade sense and the presented method overcomes some serious limitations of former multivariable reduction methods. The set of all different models of minimal order that approximate a mixed sequence of Markov and time moment matrices of a given length is characterized by the common structural properties of these, models. A maximal set of free parameters for the above set of all models is determined. These parameters can assign values independently and can be used to satisfy further desired specifications. A procedure is presented to solve the problem of possible instability of Pade approximated models of a stable system. Stable models maybe chosen among the models of the same minimal order that differently emphasize the approximation of the steady state and the transient responses. When applicable, the free parameters can also be adjusted to yield stable models. Finally, a complementary systematic method is presented by which unstable models can be replaced by a stable model of the same order and with the same singular values that approximate, in the Pade sense, the magnitude of the high-order system.

http://ieeexplore.ieee.org/iel5/31/23555/01085514.pdf

Discrete multivariable system approximations by minimal Pade-type stable models

A new combined time and frequency domain method for the model reduction of discrete systems in z-transfer function is presented. First, the z-transfer functions are transformed into the w-domain by the bilinear transformation, z = (1+w)/(1−w). Then, four model reduction methods—Routh approximation, Hurwitz polynomial approxima- tion, stability equation, and retaining dominant poles—are used respectively to reduce the order of the denominator polynomials in the w-domain. Least squares estimate is then used to find the optimal coefficients in the numerator polynomials of the reduced models so that the unit step response errors are reduced to a minimum. The advantages of the proposed method are that both frequency domain and time domain characteristics of the original systems can be preserved in the reduced models, and the reduced models are always stable provided the original models are stable.

A combined time and frequency domain method for model reduction of discrete systems

An algorithm for directly obtaining the canonical state-space model corresponding to the Cauer third form of continued fraction expansion (CFE) from a given general state-space model is presented. The algorithm can be used to determine the transfer function of linear time-invariant system from its state-space model as well as to obtain the reduced order models..Two new similarity matrices, one transforms a state-space equation from a general form to a Cauer third CFE canonical form, and the other transforms a state-space model in phase-variable form to a state-space model in a Cauer third CFE canonical form, are derived. Using these matrices an approximate relationship between the original state vector and the state-vector of reduced model obtained by the method of Cauer third CFE is established

On Cauer third continued fraction expansion method for the simplification of large system dynamics

An algorithm for determining the Stieltjes continued-fraction expansion of driving-point function from its Taylor-series expansion has been suggested. This algorithm can be used to determine the elements of lossy ladder networks with advantage when the driving point function is represented in time domain by state variables.

Determining elements of lossy ladder networks

Shamashs's method for determining the numerator a transfer function between a particular output and input of a multivariable system has been modified by the use of a continued fraction to effect a saving in computational effort.

Computing the zeros of systems

Correspondence Comment on the paper “ simplification of z-transfer functions by continued fractions ”

Q-matrix technique can be used for the transformation of rational functions. An algorithm for determining the entries of Q-matrix has been suggested. This algorithm is more useful than the existing one.

On Transformation of Rational Functions

New algorithms for determining the elements of band-pass and band-elimination lossless networks with and without resistive termination from the given driving-point immittance functions are suggested. These algorithms require less computation than the existing ones.

J. S. Bajwa

Papers

Determining elements of lossy ladder networks

Computing the zeros of systems

Correspondence Comment on the paper “ simplification of z-transfer functions by continued fractions ”

On Transformation of Rational Functions

Determination of Elements of Band-pass and Band-elimination Networks