Comments on "Determination of matrix transfer function in the form of matrix fraction from input-output observations"

-Furuta and Paquet have proposed an algorithm for determining coefficients of an input-output relation from input-output observations. The purpose of this note is to point out that these coefficients can be obtaiined by a simpler algorithm which requires less computation and that there are other algorithms for minimal realization from these coefficients.     

Numerical computation of a coprime factorization of a transfer function matrix

A new algorithm is presented for computing a coprime factorization of a transfer function matrix. The method is based on reformulating the problem as a problem of constructing a minimal basis of the right nullspace of a matrix pencil λB - A. Due to the special structure and rank properties of the pencil obtained after transforming λB - A to generalized Schur form, the original problem can be easily solved in a numerically reliable way.     

A note on transmission zeros of a transfer function matrix

A new proof is provided to show that the numerator polynomials of the Smith-McMillan form of a rational transfer function matrix are the same as the invariant factors of a mapsI-A_{t}, with Ata map determined from the system state equations.     

Conditions for a feedback transfer function matrix to be proper

Given rational matrixhat{G}(s)and a constant matrixK, necessary and sufficient conditions are given for the ration matrixhat{H}(s) = hat{G}(s) [I + Khat{G}(s)]^{-1}to be proper.     

Determination of the transfer matrix of multidimensional-singular systems

A computationally simple algorithm for determining the transfer function of multidimensional singular systems, described by a state-space model based on the Givone-Roesser state space setting, is proposed. The method uses the discrete Fourier transform and can be readily implemented on a digital computer. An example is given to illustrate the simplicity and the efficiency of the algorithm.     

On the calculation of the transfer function matrix

Given the state space realization{A,B,C}of a linear time-invariant multivariable dynamic system, a computational algorithm for calculating elements of the corresponding transfer function matrix is presented. The algorithm neither requires cofactor calculation, nor applies any state transformation. The only requirement is calculation of the coefficients of characteristic equations of given matrices. Also, the Fortran subroutine based on the presented algorithm is included.     

Shaping of the output response in a class of linear multivariablesystems

A state feedback controller is designed to regulate, as desired, the output response of minimum-phase linear multivariable square plants with CB having full rank (B: input matrix and C : output matrix). Properties of the controller are given and an example is worked out for illustration     

A new algorithm for the minimal balanced realization of a transfer function matrix

A new algorithm is proposed here to obtain a minimal balanced realization directly from the transfer function matrix (TFM). This method which employs the singular-value decomposition (SVD) of an infinite block-Hankel matrix requires neither an initial minimal realization nor the solution of a Lyapunov matrix equation. The formulation is solely in terms of the coefficients of the transfer function matrix.     

Improved quantitative measures of robustness for multivariablesystems

Asymptotically stable linear systems subject to unstructured time varying perturbations are considered. Allowable perturbation bounds are obtained such that the perturbed systems remain stable. These bounds are derived iteratively by means of adjusting a sequence of Lyapunov matrices. In comparison with existing methods, less conservative quantitative measures of robustness are obtained     

New algorithm for minimal balanced realization of transfer function matrix

A simple method for calculating the gramians of any stable realization using algebraic computation is described. This allows the development of a new algorithm to obtain a minimal balanced realization. The algorithm presented is shown to be computationally simpler and more efficient than previous methods and is illustrated by an example.     

An eigenspace and residual approach to transfer function matrix synthesis

Based on results from eigenspace and residual assignment a closed-form parameterization of all transfer function matrices obtainable by state feedback is given.     

Hysteresis switching adaptive control of linear multivariablesystems

This paper presents a model reference adaptive control scheme for deterministic continuous-time multivariable systems represented by square, strictly proper, minimum-phase transfer function matrices. A typical requirement of existing algorithms is to assume that the zero structure at infinity and the high-frequency gain matrix are fully (or at least partially) known. It is well known that these requirements may be very restrictive, since, in general, both the zero structure at infinity and the high-frequency gain matrix depend on plant parameters. In this paper we show that these restrictive assumptions may be considerably weakened using Morse et al.'s hysteresis switching control strategy (1992). The strategy entails running a finite number of parameter estimators in parallel and using a switching algorithm to select between candidate estimators based on their associated prediction errors. Hysteresis in the switching algorithm precludes switching arbitrarily rapidly between estimators, and all switching ceases within a finite time. The results represent a significant step forward in understanding the minimal amount of prior knowledge necessary to design a stabilizing controller for a linear multivariable system     

The computation of a transfer function matrix from the given state equations for time-delays systems

An algorithm is established to compute the transfer function matrix from the state equations for linear multivariable system with constant noncommensurable delays. The proposed algorithm requires operations with constant matrices only and is suitable for computer programming. An example illustrating the proposed algorithm is given.     

An algorithm for pole assignment in high order multivariablesystems

An efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions. A given multiinput system is first transformed to an upper block Hessenberg form by means of orthogonal state coordinate transformations. The state feedback problem is then reformulated in terms of the Sylvester equation. The transformed system matrices, along with certain assumed block forms for unknown matrices, enable the Sylvester equation to be decomposed and solved effectively. A distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast. Computational aspects of the algorithm are discussed and numerical examples are provided     

Recursive parameter estimation of transfer function matrix models via Simpson's integrating rules

Recursive formulae for repeated integration of a continuous-time function with uniformly sampled data using Simpson's 1/3 and 3/8 integrating rules are derived. Combined with the recursive algorithm of the least-squares solution, a method for recursive parameter estimation of transfer function matrix models in multiple-input-multiple-output systems is proposed. It is demonstrated that the use of the popular integrating rules for parameter estimation can be as effective as sophisticated methods that use orthogonal functions and the associated operational properties reported in the literature. The proposed algorithm is suitable for on-line applications and computer programming. Three numerical examples are included to illustrate the applicability of the proposed method.     

A self-tuning decoupling controller for a class of multivariablesystems and global convergence analysis

A simple multivariable self-tuning controller is presented which decouples a class of multivariable systems and specifically handles multivariable systems with a different delay associated with each output. The global convergence of this adaptive control algorithm is established. It is shown that the system input-output vectors are always sample-mean-square bounded and the conditional mean-square-generalized tracking error achieves its global minimum, even for nonminimum phase systems, for an appropriate cost function