Transfer Matrices Of Systems Research Articles

Steady-state analysis of a rotor mounted on nonlinear bearings by the transfer matrix method

The steady-state responses of subharmonic, superharmonic and synchronous vibrations of a flexible rotor supported by bearings of power nonlinearity (i.e. the bearing force satisfies a power law of the deflection) are studied. The transfer matrix method is applied to formulate the transfer matrices of nonlinear rotor-bearing systems with MDOF (multi-degree of freedom) and in conjunction with the harmonic balance method to obtain the steady-state responses. Two examples of rotor-bearing systems with cubic nonlinearity spring characteristics are given to investigate the effects of nonlinearity on frequency response and the whirling orbits.

New random matrix theory of scattering in mesoscopic systems.

A previously unnoticed group structure for the transfer matrices of mesoscopic systems is identified. From the invariant measure for this group and a maximum entropy ansatz we derive the Laguerre ensemble of random matrices. A comparison with the Hofstadter model shows that the Laguerre ensemble provides a quantitative description of scattering in mesoscopic systems under applied magnetic fields.

THE CORNER TRANSFER MATRIX OF SOME FREE-FERMION SYSTEMS AND MEIXNER’S POLYNOMIALS

Corner transfer matrices of some free-fermion vertex systems on a finite lattice, are exactly diagonalised in the Hamiltonian limit with the help of a special class of orthogonal polynomials: the Meixner polynomials. We present the derivation, discuss the asymptotic behavior for a large lattice and compare the results with numerical computation.

Necessary and sufficient conditions for strictly positive real matrices

In this paper we present some useful properties of strictly positive real transfer matrices for both continuous and discrete-time linear time-invariant systems in the frequency and state space domains. Some of these properties follow from known results and are presented for the sake of completeness. The new results obtained are mainly for discrete-time systems and include the discretetime version of the Lefschetz-Kalman-Yakubovich lemma for transfer matrices.

On the existence of approximately coprime factorizations for retarded systems

This note establishes a result linking algebraically coprime factorizations of transfer matrices of delay systems to approximately coprime factorizations in the sense of distributions. The latter have been employed by the second author in the study of function-space controllability for such systems.

Hessenberg-triangular reduction and transfer function matrices of singular systems

The author is concerned with the computation of transfer function matrices of liner multivariable systems described by their generalized state-space equations. An algorithm is outlined that may be considered a generalization of an existing technique for computation of transfer matrices of systems described by standard state-space equation. The propose algorithm can be used for evaluating transfer function matrices of nonsingular as well as singular generalized systems, and performs satisfactorily when implemented with finite-precision arithmetic. Several examples are included to demonstrate the performance of the proposed algorithm. >

State-space realization of multiple-frequency-scale transfer matrices

The class of linear, time-variant, singularly perturbed systems is considered in which all poles are O(1) or O(1/ epsilon ) as epsilon to O, with coefficient matrices that are analytic functions of epsilon . It has been shown previously that transfer matrices of systems in the above class are two-frequency-scale. This means that such transfer matrices behave as dynamical systems in two separate frequency ranges. It is shown that any two-frequency-scale transfer matrix can be realized in state-space form as a system in the above-mentioned class of singularly perturbed systems. The result is generalized to N frequency scales.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the factorization of rational matrices depending on a parameter

In 1961 Youla published his paper “On the factorization of rational matrices”. He proved that any proper rational para-Hermitian matrix that is positive definite on the imaginary axis can be factorized as the product of a proper rational matrix, stable with respect to the closed right half plane, and its adjoint. In this paper it is proved that for any positive definite, nonstrictly proper matrix this factorization can be given depending analytically on the original matrix, in a sufficiently small neighbourhood. This result is applied to the problem of metrizing the space of transfer matrices of linear systems, in accordance with Vidyasagar's graph topology.

A computer-based method to analyze electrostatic, surface-ionization ion-source configurations

This article describes a computer-based method to analyze the optics of axially symmetrical, electrostatic, surface-ionization, ion-source configurations. The method can be applied with a personal computer. It employs matrix formulation, which simplifies the solution of a complex system, called the optical stack, by multiplying the transfer matrices of the simpler component systems. The method computes the source efficiency and the beam losses caused by collimation at points upstream, and it plots the luminosity and divergence profiles. One simulates focusing by changing the values for the voltages applied to the electrodes and noting the effect on the luminosity profiles. When the theory is applied to the design of a source that was tested in 1960, it agrees satisfactorily with the experiment and provides new insights.

Properties of acoustic and electromagnetic transmission coefficients and transfer matrices of multilayered plates

With the aid of certain symmetry properties of the elementary transfer matrices of acoustic and electromagnetic field vectors in single layers of absorbing materials, we derive the transformation properties of the system transfer matrices of bonded stacks of absorbing layers under the operation of reversal of the direction of incident radiation. While writing the energy transmission coefficients in such a way that the system transfer matrices appear explicitly, we apply their transformation properties to show that under certain circumstances these coefficients are invariant with respect to front and back surface illumination.

The calculation of transfer matrices of linear systems with continuous and sampled‐data signals by signal flow graphs

AbstractThe paper presents a method based on the concept of signal flow graphs which is suitable for the determination of transfer matrices of linear systems excited by continuous or by continuous and sampled‐data signals. the method is valid in case of several excitations and responses.

On the stability of linear composite systems with delays

It is shown that the stability of composite feedback control systems with delays both in the state and the input can be checked from the stabilities of the individual isolated subsystems, if the composite system matrix has a certain new structure called the GKK-structure; and if the numerators and denominators of the determinants of the overall system transfer matrix and of the isolated system transfer matrices contain some term of a certain expansion called the principal term. The GKK-structure includes diagonal dominance, the Hadamard (M-matrix) structure, and normality as special cases.

On Matrix Fraction Representations for Linear Systems over Commutative Rings

This paper deals with the problem of existence of polynomial matrix fraction representations for transfer matrices of linear systems over rings as well as the related realization theory. These representations are then used in establishing new results for various classes of systems including split systems. The relevance of these results to the regulation of various “nonclassical” classes of linear systems (for example, delay-differential systems, two-dimensional systems, etc.) is also discussed.

Spectral properties of certain composition operators arising in statistical mechanics

By applying the theory of linear positive operators in a Banach space we derive spectral properties of certain composition operators in the Banach spaceA∞(Ω) of holomorphic functions over some domain Ω⊂ℂ. Examples of such operators are provided by the so called generalized transfer matrices of classical one-dimensional lattice systems.

Dynamic analysis of a class of mixed lumped-distributed parameter systems via numerical techniques

The modeling via transfer matrices of mixed lumped-distributed parameter systems with feedback control is discussed and novel methods of obtaining information on the controlled system's dynamic response via numerical methods is presented. These methods utilize numerical searches in the complex plane for the roots of the transcendental characteristic equation to determine the closed loop system eigenvalues. The fast Fourier transform (FFT) algorithm is utilized but in the inverse fashion (from frequency domain to time domain). The information obtained is identical to that contained in a model in modal coordinates, and can be used to construct such a model. An interactive computer program to do the required calculation is described, as well as its application to a manipulator arm design problem.

Geometric interpretation of complex vectors arising in the frequency-domain analysis of multivariable systems

It is shown that an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -dimensional vector whose components are complex numbers can be visualized as a plane ellipse in geometric <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -space. The length and direction of a complex vector are interpreted in terms of the ellipse axes thus giving a deeper insight into the eigenstructure of system transfer matrices. The system characteristic ellipse is introduced and its application to the measurement of characteristic loci is discussed.

Resonance in Pressurized Piping Systems

A new approach, based on the transfer matrix method used in the theory of vibrations, is presented to study the steady-oscillatory flows, and to determine the resonating characteristics of pressure conduits. By linearizing the friction loss term, considering the system as distributed, and assuming the discharge and pressure head fluctuations as sinusoidal, field matrices for simple pipelines and for parallel systems are derived. Point matrices for orifices, and for oscillating valves having sinusoidal valve movement are obtained by linearizing the gate equation. Point transfer matrices for branch systems with the side branch having different boundary conditions are also developed. A procedure is outlined to determine the resonant frequencies of system types commonly used in waterpower development and water supply schemes. A number of examples are solved.