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A general transfer function representation for a class of hyperbolic distributed parameter systems

Krzysztof Bartecki (2013)

International Journal of Applied Mathematics and Computer Science

Results of transfer function analysis for a class of distributed parameter systems described by dissipative hyperbolic partial differential equations defined on a one-dimensional spatial domain are presented. For the case of two boundary inputs, the closed-form expressions for the individual elements of the 2×2 transfer function matrix are derived both in the exponential and in the hyperbolic form, based on the decoupled canonical representation of the system. Some important properties of the transfer...

A new Nyquist-based technique for tuning robust decentralized controllers

Alena Kozáková, Vojtech Veselý, Jakub Osuský (2009)

Kybernetika

An original Nyquist-based frequency domain robust decentralized controller (DC) design technique for robust stability and guaranteed nominal performance is proposed, applicable for continuous-time uncertain systems described by a set of transfer function matrices. To provide nominal performance, interactions are included in individual design using one selected characteristic locus of the interaction matrix, used to reshape frequency responses of decoupled subsystems; such modified subsystems are...

Approximation of a linear dynamic process model using the frequency approach and a non-quadratic measure of the model error

Krzysztof B. Janiszowski (2014)

International Journal of Applied Mathematics and Computer Science

The paper presents a novel approach to approximation of a linear transfer function model, based on dynamic properties represented by a frequency response, e.g., determined as a result of discrete-time identification. The approximation is derived for minimization of a non-quadratic performance index. This index can be determined as an exponent or absolute norm of an error. Two algorithms for determination of the approximation coefficients are considered, a batch processing one and a recursive scheme,...

Comparison of the stability boundary and the frequency response stability condition in learning and repetitive control

Szathys Songschon, Richard Longman (2003)

International Journal of Applied Mathematics and Computer Science

In iterative learning control (ILC) and in repetitive control (RC) one is interested in convergence to zero tracking error as the repetitions of the command or the periods in the command progress. A condition based on steady state frequency response modeling is often used, but it does not represent the true stability boundary for convergence. In this paper we show how this useful condition differs from the true stability boundary in ILC and RC, and show that in applications of RC the distinction...

Derivation of effective transfer function models by input, output variables selection

Nicos Karcanias, Konstantinos G. Vafiadis (2002)

Kybernetika

Transfer function models used for early stages of design are large dimension models containing all possible physical inputs, outputs. Such models may be badly conditioned and possibly degenerate. The problem considered here is the selection of maximal cardinality subsets of the physical input, output sets, such as the resulting model is nondegenerate and satisfies additional properties such as controllability and observability and avoids the existence of high order infinite zeros. This problem is...

Exponential stability and transfer functions of processes governed by symmetric hyperbolic systems

Cheng-Zhong Xu, Gauthier Sallet (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system is...

Exponential Stability and Transfer Functions of Processes Governed by Symmetric Hyperbolic Systems

Cheng-Zhong Xu, Gauthier Sallet (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we study the frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent theory of well-posed infinite-dimensional linear systems, we prove that the system...

Global synchronization of chaotic Lur’e systems via replacing variables control

Xiaofeng Wu, Yi Zhao, Muhong Wang (2008)

Kybernetika

Finding sufficient criteria for synchronization of master-slave chaotic systems by replacing variables control has been an open problem in the field of chaos control. This paper presents some recent works on the subject, with emphasis on chaos synchronization of both identical and parametrically mismatched Lur’e systems by replacing variables control. The synchronization schemes are formally constructed and two classes of sufficient criteria for global synchronization, linear matrix inequality criterion...

New coprime polynomial fraction representation of transfer function matrix

Yelena M. Smagina (2001)

Kybernetika

A new form of the coprime polynomial fraction C ( s ) F ( s ) - 1 of a transfer function matrix G ( s ) is presented where the polynomial matrices C ( s ) and F ( s ) have the form of a matrix (or generalized matrix) polynomials with the structure defined directly by the controllability characteristics of a state- space model and Markov matrices H B , H A B , ...

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