A unified approach for the H∞H_\infty-stability analysis of classical and fractional neutral systems with commensurate delays

International audienceWe examine the stability of linear integer-order and fractional-order systems with commensurate delays of neutral type in the sense of $H_\infty$-stability. The systems may have chains of poles approaching the imaginary axis. While several classes of these systems have been previously studied on a case-by-case basis, a unified method is proposed in this paper which allows to deal with all these classes at the same time. Approximation of poles of large modulus is systematically calculated based on a convex hull derived from the coefficients of the system. This convex hull also serves to establish sufficient conditions for instability and necessary and sufficient conditions for stability

Spectrum analysis of LTI continuous-time systems with constant delays: A literature overview of some recent results

In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampled-data, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles-which are most closely related to the research area-are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field. © 2013 IEEE.MSMT-7778/2014, FEDER, European Regional Development Fund; LO1303, FEDER, European Regional Development Fund; CZ.1.05/2.1.00/19.0376, FEDER, European Regional Development FundEuropean Regional Development Fund through the Project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; National Sustainability Program Project [LO1303 (MSMT-7778/2014)

A comparison of possible exponential polynomial approximations to get commensurate delays

The paper is aimed at a comparative simulation study on three prospective ideas how to approximate a general exponential polynomial by another one having all its exponents in the exp-function as integer multiples of some real number. This work is motivated by spectral properties of neutral time-delay systems (NTDS) and the contemporary state of the knowledge about the spectrum of NTDS with commensurate delays which are characterized by the latter family of exponential polynomials. The three ideas are, namely, those: Taylor series expansion, the interpolation in points given by dominant roots estimates and the special extrapolation technique presented by the authors recently. The goal is to match dominant parts of both the spectra as close as possible. However, some properties from the so called strong stability point of view can not be, in principle, preserved. The presented simulation example demonstrates the accuracy and efficiency of all the methods.Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [L01303, MSMT-7778/2014]; European Regional Development Fund [CZ.1.05/2.1.00/03.0089

A numerical method for stability windows and unstable root-locus calculation for linear fractional time-delay systems

This paper aims to provide a numerical algorithm able to locate all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by giving the asymptotic position of the chains of poles and the conditions for their stability for a small delay. When these conditions are met, the root continuity argument and some simple substitutions allow us to determine the locations where some roots cross the imaginary axis, providing therefore the complete characterization of the stability windows. The same method can be extended to provide the position of all unstable poles as a function of the delay. © 2012 Elsevier Ltd. All rights reserved

Stability windows and unstable root-loci for linear fractional time-delay systems

The main point of this paper is on the formulation of a numerical algorithm to find the location of all unstable poles, and therefore the characterization of the stability as a function of the delay, for a class of linear fractional-order neutral systems with multiple commensurate delays. We start by the asymptotic position of the chains of poles and conditions for their stability, for a small delay. When these conditions are met, we continue by means of the root continuity argument, and using a simple substitution, we can find all the locations where roots cross the imaginary axis. We can extend the method to provide the location of all unstable poles as a function of the delay. Before concluding, some examples are presented. © 2011 IFAC

Properties of Delay Systems and Diffusive Systems

In this thesis, we investigate questions about the properties of delay systems and diffusive systems as well as Hankel and weighted Hankel operators. After detailing the necessary background in Chapter 1, in Chapter 2 the focus is on the development of methods to study the stability of delay and fractional systems. This analysis is carried forward using some BIBO and H∞ stability tests. Generalisation of the Walton-Marshall method [38] enable us to move from the single and multi-delay cases to fractional delay systems. This method gives procedures for finding stability windows as the delay varies. Chapter 3 is concerned with diffusive systems. Via convenient adaptations of some tests due to Howland [19], it becomes possible to give necessary and sufficient conditions for the Hankel operator and the weighted Hankel operator to be nuclear. Also, in this Chapter we introduce more general weighted Hankel operators and discuss their boundedness. Here the reproducing kernel test plays an essential role in testing boundedness. Some fundamental examples are given to support our work. In Chapter 4 here we investigate questions regarding approximating infinitedimensional linear system by finite-dimensional ones. Moreover, we develop more research on the rate of decay of singular values of the associated Hankel operator. In Chapter 5 we mainly focus on diffusive systems defined by holomorphic distributions and measures on a half plane. In particular we look at the nuclearity (trace class) and Hilbert-Schmidt properties of such systems. Moreover, we begin further study of explicit examples of weighted Hankel operators for which we did not know whether they were bounded, those examples already introduced in Chapter 3. In Chapter 6 the boundedness of weighted Hankel corresponding to diffusive systems is analysed using the theory of Carleson measures. Chapter 7 gives some suggestions for further work

High gain and bandwidth current-mode amplifiers : study and implementation

Doutoramento em Engenharia ElectrotécnicaEsta tese aborda o problema do projecto de amplificadores com grandes produtos de ganho por largura de banda. A aplicação final considerada consistiu no projecto de amplificadores adequados à recepção de sinais ópticos em sistemas de transmissão ópticos usando o espaço livre. Neste tipo de sistemas as maiores limitações de ganho e largura de banda surgem nos circuitos de entrada. O uso de detectores ópticos com grande área fotosensível é uma necessidade comum neste tipo de sistemas. Estes detectores apresentam grandes capacidades intrínsecas, o que em conjunto com a impedância de entrada apresentada pelo amplificador estabelece sérias restrições no produto do ganho pela largura de banda. As técnicas mais tradicionais para combater este problema recorrem ao uso de amplificadores com retroacção baseados em configurações de transimpedância. Estes amplificadores apresentam baixas impedâncias de entrada devido à acção da retroacção. Contudo, os amplificadores de transimpedância também apresentam uma relação directa entre o ganho e a impedância de entrada. Logo, diminuir a impedância de entrada implica diminuir o ganho. Esta tese propõe duas técnicas novas para combater os problemas referidos. A primeira técnica tem por base uma propriedade fundamental dos amplificadores com retroacção. Em geral, todos os circuitos electrónicos têm tempos de atraso associados, os amplificadores com retroacção não são uma excepção a esta regra. Os tempos de atraso são em geral reconhecidos como elementos instabilizadores neste tipos da amplificadores. Contudo, se usados judiciosamente, este tempos de atraso podem ser explorados como uma forma da aumentar a largura de banda em amplificadores com retroacção. Com base nestas ideias, esta tese apresenta o conceito geral de reatroacção com atraso, como um método de optimização de largura de banda em amplificadores com retroacção. O segundo método baseia-se na destruição da dualidade entre ganho e impedância de entrada existente nos amplificadores de transimpedância. O conceito de adaptação activa em modo de corrente é neste sentido uma forma adequada para separar o detector óptico da entrada do amplificador. De acordo com este conceito, emprega-se um elemento de adaptação em modo de corrente para isolar o detector óptico da entrada do amplificador. Desta forma as tradicionais limitações de ganho e largura de banda podem ser tratadas em separado. Esta tese defende o uso destas técnicas no desenho de amplificadores de transimpedância para sistemas de recepção de sinais ópticos em espaço livre.This thesis addresses the problem of achieving high gain-bandwidth products in amplifiers. The adopted framework consisted on the design of a free-space optical (FSO) front end amplifier able to amplify very small optical signals over large frequency bandwidths. The major gain-bandwidth limitations in FSO front end amplifiers arise due to the input circuitry. Usually, it is necessary to have large area optical detectors in order to maximize signal reception. These detectors have large intrinsic capacitances, which together with the amplifier input impedance poses a severe restriction on the gain-bandwidth product. Traditional techniques to combat this gain-bandwidth limitation resort to feedback amplifiers consisting on transimpedance configurations. These amplifiers have small input impedances due to the feedback action. Nevertheless, transimpedance amplifiers have a direct relation between gain and input impedance. Thus reducing the input impedance usually implies reducing the gain. This thesis advances two new methods suitable to combat the above mentioned problems. The first method is based on a fundamental property of feedback amplifiers. In general, all electronic circuits have associated time delays, and feedback amplifiers are not an exception to this rule. Time delays in feedback amplifiers have been recognized as destabilizing elements. Nevertheless, when used with appropriate care, these delays can be exploited as bandwidth enhancement elements. Based on these ideas, this thesis presents the general concept of delayed feedback, as a bandwidth optimization method suitable for feedback amplifiers. The second method is based on the idea of destroying the impedance-gain duality in transimpedance amplifiers. The concept of active current matching is in this sense a suitable method to detach the optical detector from the transimpedance amplifier input. According to this concept, a current matching device (CMD) is used to convey the signal current sensed by the optical detector, to the amplifier’s input. Using this concept the traditional gainbandwidth limitations can be treated in a separate fashion. This thesis advocates the usage of these techniques for the design of transimpedance amplifiers suited for FSO receiving systems

Performance limits and robustness issues in the control of flexible link manipulators

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1992.Includes bibliographical references (leaves 179-186).by Carlos Eduardo Padilla Santos.Ph.D