Balanced truncation of perturbative representations of nonlinear systems

The paper presents a novel approach for a balanced truncation style of model reduction of a perturbative representation of a nonlinear system. Empirical controllability and observability gramians for nonlinear systems are employed to define a projection matrix. However, the projection matrix is applied to the perturbative representation of the system rather than directly to the exact nonlinear system. This is to achieve the required increase in efficiency desired of a reduced-order model. Application of the new method is illustrated through a sample test-system. The technique will be compared to the standard approach for reducing a perturbative representation of a nonlinear system

A parametric macromodelling technique

With the ever growing complexity of high-frequency systems in the electronic industry, formation of reduced-order models or compact macromodels of these systems is paramount. In this contribution, a Fourier series expansion technique is extended to form a modeling strategy to approximate the frequency-domain behaviour of a system based on several design variables. In particular, it is intended to provide a tool for the designer to identify the effect of manufacturer tolerances and process fluctuations or irregularities on system behaviour

Model reduction of weakly nonlinear systems

In general, model reduction techniques fall into two categories — moment —matching and Krylov techniques and balancing techniques. The present contribution is concerned with the former. The present contribution proposes the use of a perturbative representation as an alternative to the bilinear representation [4]. While for weakly nonlinear systems, either approximation is satisfactory, it will be seen that the perturbative method has several advantages over the bilinear representation. In this contribution, an improved reduction method is proposed. Illustrative examples are chosen, and the errors obtained from the different reduction strategies will be compared

An Exactly Solvable Case for a Thin Elastic Rod

We present a new exact solution for the twist of an asymmetric thin elastic rods. The shape of such rods is described by the static Kirchhoff equations. In the case of constant curvatire and torsion the twist of the asymmetric rod represents a soliton lattice.Comment: 6 pages, title changed, revised versio

Compact models for wireless systems

For the design and analysis of wireless systems, complex simulations are required and performed. Model order reduction techniques enable greater efficiencies to be achieved and concomitantly, a reduction in memory-resource usage. However, maintaining a certain level of accuracy is paramount. In this contribution, two techniques are combined to enable the formation of a compact model of a high-order system, structure or component. The first is a Krylov subspace method which reduces the original model to a moderate size and the second is a Fourier series expansion method that enables speed and ease of determination of the time-domain responses of the system to arbitrary inputs

Generalised Fourier Transform and Perturbations to Soliton Equations

A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions` of the spectral problem, associated to the soliton equation. The Inverse Scattering Transform for the corresponding hierarchy of soliton equations can be viewed as a GFT where the expansions of the solutions have generalised Fourier coefficients given by the scattering data. The GFT provides a natural setting for the analysis of small perturbations to an integrable equation: starting from a purely soliton solution one can `modify` the soliton parameters such as to incorporate the changes caused by the perturbation. As illustrative examples the perturbed equations of the KdV hierarchy, in particular the Ostrovsky equation, followed by the perturbation theory for the Camassa- Holm hierarchy are presented.Comment: 20 pages, no figures, to appear in: Discrete and Continuous Dynamical Systems

Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras

The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1] for systems with finite number of degrees of freedom is generalized to infinite-dimensional Hamiltonian systems. The construction method is illustrated on the explicit nontrivial example of RHF of ATFT related to the exceptional algebras E_6 and E_7. The involutions of the local integrals of motion are proved by means of the classical R-matrix approach.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA

Causal and stable reduced-order model for linear high-frequency systems

With the ever-growing complexity of high-frequency systems in the electronic industry, formation of reduced-order models of these systems is paramount. In this reported work, two different techniques are combined to generate a stable and causal representation of the system. In particular, balanced truncation is combined with a Fourier series expansion approach. The efficacy of the proposed combined method is shown with an example