35 results on '"Niculescu, Silviu-Iulian"'
Search Results
2. New Features of P3δ Software. Insights and Demos
- Author
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Boussaada, Islam, Mazanti, Guilherme, Niculescu, Silviu-Iulian, Hammoumou, Ayrton, Millet, Titouan, Raj, Jayvir, Huynh, Julien, Institut Polytechnique des Sciences Avancées (IPSA), Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and ANR-11-IDEX-0003,IPS,Idex Paris-Saclay(2011)
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Control and Systems Engineering ,Optimization and Control (math.OC) ,delay ,GUI ,FOS: Mathematics ,online software ,[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] ,stability ,Mathematics - Optimization and Control ,controller design ,Python toolbox - Abstract
This paper presents the software entitled "Partial Pole Placement via Delay Action", or "P3$\delta$" for short. P3$\delta$ is a Python software with a friendly user interface for the design of parametric stabilizing feedback laws with time-delays for dynamical systems. After recalling the theoretical foundation of the so-called "Partial Pole Placement" methodology we propose as well the main features of the current version of P3$\delta$. We illustrate its use in feedback stabilization of several control systems operating under time delays., Comment: arXiv admin note: text overlap with arXiv:2107.11341
- Published
- 2022
3. Characterizing the Codimension of Zero Singularities for Time-Delay Systems: A Link with Vandermonde and Birkhoff Incidence Matrices
- Author
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Boussaada, Islam and Niculescu, Silviu-Iulian
- Published
- 2016
- Full Text
- View/download PDF
4. Sampled-data estimator for nonlinear systems with uncertainties and arbitrarily fast rate of convergence
- Author
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Mazenc, Frédéric, Malisoff, Michael, Niculescu, Silviu-Iulian, Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Baton Rouge] (LSU Mathematics), Louisiana State University (LSU), and The work of M. Malisoff was supported by US National Science Foundation Grant 1711299.
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delay ,Control and Systems Engineering ,[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering ,nonlinear systems ,stability ,Electrical and Electronic Engineering ,Estimation - Abstract
International audience; We study a class of continuous-time nonlinear systems with discrete measurements, model uncertainty, and sensor noise. We provide an estimator of the state for which the observation error enjoys a variant of the exponential input-to-state stability property with respect to the model uncertainty and sensor noise. A valuable novel feature is that the overshoot term in this stability estimate only involves a recent history of uncertainty values. Also, the rate of exponential convergence can be made arbitrarily large by reducing the supremum of the sampling intervals. Our proof uses a recently developed trajectory based approach. We illustrate our work using a model for a pendulum whose suspension point is subjected to an unknown time-varying bounded horizontal oscillation.
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- 2022
5. ANALYSIS AND DESIGN OF STRONGLY STABILIZING PID CONTROLLERS FOR TIME-DELAY SYSTEMS.
- Author
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APPELTANS, PIETER, NICULESCU, SILVIU-IULIAN, and MICHIELS, WIM
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CLOSED loop systems , *FUNCTIONAL differential equations , *PID controllers , *DYNAMICAL systems - Abstract
This paper presents the analysis of the stability properties of proportional-integralderivative (PID) controllers for dynamical systems with multiple state delays, focusing on the mathematical characterization of the potential sensitivity of stability with respect to infinitesimal parametric perturbations. These perturbations originate, for instance, from neglecting feedback delay, a finite-difference approximation of the derivative action, or neglecting fast dynamics. It is also shown that adding a low-pass filter, which might be necessary to reduce sensitivity to high-frequency noise, under certain conditions on the derivative feedback gain may destabilize the closed loop even for arbitrarily large cutoff frequencies. The analysis of these potential sensitivity problems leads us to the introduction of a "robustified" notion of stability called strong stability, inspired by the corresponding notion for neutral functional differential equations. We prove that strong stability can be achieved by adding a low-pass filter with a sufficiently large cutoff frequency to the control loop on the condition that the filter itself does not destabilize the nominal closed loop system. Throughout the paper, the theoretical results are illustrated by examples that can be analyzed analytically, including, among others, a third-order unstable system for which both proportional and derivative control action are necessary for achieving stability, while the regions in the gain parameter-space for stability and strong stability are not identical. Besides the analysis of strong stability, a computational procedure is provided for designing strongly stabilizing PID controllers. Computational case studies illustrating this design procedure complete the presentation. [ABSTRACT FROM AUTHOR]
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- 2022
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6. Stability and Stabilization Through Envelopes for Retarded and Neutral Time-Delay Systems.
- Author
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Cardeliquio, Caetano B., Fioravanti, Andre R., Bonnet, Catherine, and Niculescu, Silviu-Iulian
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LINEAR matrix inequalities ,TIME delay systems ,STATE feedback (Feedback control systems) ,SYMMETRIC matrices - Abstract
This paper deals with a new approach to develop an envelope that engulfs all poles of a time-delay system. Through linear matrix inequalities, we are able to determine envelopes for retarded and neutral time-delay systems. The envelopes proposed are not only tighter than the ones in the literature, but, with our procedure, they can also be applied to verify the stability of the system and design state-feedback controllers, which cope with design requirements regarding $\alpha$ -stability. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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7. iterative frequency-sweeping approach for stability analysis of linear systems with multiple delays.
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Li, Xu-Guang, Niculescu, Silviu-Iulian, and Çela, Arben
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LINEAR systems , *LINEAR statistical models , *SYSTEM analysis , *LINEAR differential equations , *TIME delay systems , *FREQUENCY-domain analysis - Published
- 2019
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8. Stability analysis for a class of distributed delay systems with constant coefficients by using a frequency‐sweeping approach.
- Author
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Zhang, Lu, Mao, Zhi‐Zhong, Li, Xu‐Guang, Niculescu, Silviu‐Iulian, and Çela, Arben
- Abstract
This study focuses on the stability property of a class of distributed delay systems with constant coefficients. More precisely, the authors will discuss deeper the stability analysis with respect to the delay parameter. The authors' approach will allow to give new insights in solving the so‐called complete stability problem. There are three technical issues need to be studied: First, the detection of the critical zero roots (CZRs); second, the analysis of the asymptotic behaviour of such CZRs; third, the asymptotic behaviour analysis of the critical imaginary roots (CIRs) with respect to the infinitely many critical delays. They extended their recently‐established frequency‐sweeping approach, with which these technical issues can be effectively solved. Based on these results, a procedure was proposed, with which the complete stability analysis of such systems was accomplished systematically. Moreover, the procedure represents a unified approach: Most of the steps required by the complete stability problem may be fulfilled through observing the frequency‐sweeping curves. Finally, some examples illustrate the effectiveness and advantages of the approach. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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9. An eigenvalue perturbation approach to stability analysis, Part 1 Eigenvalue series of matrix operators
- Author
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Chen, Jie, Fu, Peilin, Niculescu, Silviu-Iulian, Guan, Zhihong, City University of Hong Kong [Hong Kong] (CUHK), National University [San Diego], Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Huazhong University of Science and Technology [Wuhan] (HUST), NSF/USA [CCF-0541456, ECCS-0801874], Natural Science Foundation of China [60628301, 60834003], City University of Hong Kong [9380054], Hong Kong RGC [9041557], and CNRS/France
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eigenvalue series ,asymptotic analysis ,[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering ,matrix perturbation ,stability ,time-delay systems - Abstract
International audience; This two-part paper is concerned with stability analysis of linear systems subject to parameter variations, of which linear time-invariant delay systems are of particular interest. We seek to characterize the asymptotic behavior of the characteristic zeros of such systems. This behavior determines, for example, whether the imaginary zeros cross from one half plane into another, and hence plays a critical role in determining the stability of a system. In Part I of the paper we develop necessary mathematical tools for this study, which focuses on the eigenvalue series of holomorphic matrix operators. While of independent interest, the eigenvalue perturbation analysis has a particular bearing on stability analysis and, indeed, has the promise to provide efficient computational solutions to a class of problems relevant to control systems analysis and design, of which time-delay systems are a notable example.
- Published
- 2010
10. Stability crossing curves of SISO systems controlled by delayed output feedback
- Author
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Irinel-Constantin Morarescu, Niculescu, Silviu-Iulian, Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire des signaux et systèmes (L2S), and Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)
- Subjects
Delay ,Quasipolynomials ,SISO systems ,[INFO]Computer Science [cs] ,Stability ,Crossing curves - Abstract
International audience; This paper focuses on closed-loop stability analysis of a class of linear single- input single-output (SISO) systems subject to delayed output feedback. The considered approach makes use of some geometric arguments in frequency-domain, arguments that simplify the understanding of the delay stabilizing mechanism. More precisely, the geometry of stability crossing curves of the closed-loop system is explicitly characterized (classification, tangent and smoothness, direction of crossing) in the parameter space defined by the pair (gain, delay). Such stability crossing curves divide the corresponding parameter space into different regions, such that, within each region, the number of characteristic roots in the right-half plane is fixed. This naturally describes the regions of (gain, delay)-parameters where the system is stable. Various illustrative examples complete the presentation. Copyright © 2007 Watam Press.
- Published
- 2007
11. Stability results for a class of neutral functional differential equations. A Liapunov like analysis
- Author
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Niculescu, Silviu-Iulian, Rasvan, Vladimir, LE PIOLET, DELPHINE, Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), and Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS)
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[SPI]Engineering Sciences [physics] ,Neutral functional differential equations ,[SPI.AUTO] Engineering Sciences [physics]/Automatic ,[SPI] Engineering Sciences [physics] ,Liapunov func- tional ,Stability ,ComputingMilieux_MISCELLANEOUS ,[SPI.AUTO]Engineering Sciences [physics]/Automatic - Abstract
International audience
- Published
- 2006
12. STABILITY AND CONTROL DESIGN FOR TIME-VARYING SYSTEMS WITH TIME-VARYING DELAYS USING A TRAJECTORY-BASED APPROACH.
- Author
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MAZENC, FREDERIC, MALISOFF, MICHAEL, and NICULESCU, SILVIU-IULIAN
- Subjects
TIME-varying systems ,STABILITY theory ,TRAJECTORY measurements ,LYAPUNOV functions ,EXPONENTIAL families (Statistics) - Abstract
A recent work by Mazenc and Malisoff provides a trajectory-based approach for proving stability of time-varying systems with time-varying delays. Here, we provide several significant applications of their approach. In two results, we use a Lyapunov function for a corresponding undelayed system to provide a new method for proving stability of linear continuous-time time-varying systems with bounded time-varying delays. We allow uncertainties in the coefficient matrices of the systems. Our main results use upper bounds on an integral average involving the delay. The results establish input-to-state stability with respect to disturbances. We also provide a novel reduction model approach that ensures global exponential stabilization of linear systems with a time-varying pointwise delay in the input, which allows the delay to be discontinuous and uncertain. Finally, we provide an alternative to the reduction model method, based on a different dynamic extension. Our examples demonstrate the usefulness of our findings in several settings. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
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13. Pseudospectra and stability radii of analytic matrix functions with application to time-delay systems
- Author
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Michiels, W, Green, K, Wagenknecht, T, and Niculescu, Silviu-Iulian
- Subjects
pseudospectrum ,robustness ,delay equations ,Mathematics::Spectral Theory ,stability - Abstract
Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated.
- Published
- 2005
14. An adaptive Smith-controller for time-delay systems with relative degree n* ≤ 2
- Author
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Niculescu, Silviu-Iulian, Annaswamy, A.M., Heuristique et Diagnostic des Systèmes Complexes [Compiègne] (Heudiasyc), Université de Technologie de Compiègne (UTC)-Centre National de la Recherche Scientifique (CNRS), Department of Mechanical Engineering [Massachusetts Institute of Technology] (MIT-MECHE), Massachusetts Institute of Technology (MIT), and Université de Technologie de Compiègne
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Time-delay systems ,Strictly positive real ,Adaptive control ,Lyapunov-Krasovskii functionals ,Stability ,[SPI.AUTO]Engineering Sciences [physics]/Automatic - Abstract
This paper addresses the control of time-delay systems whose relative degree does not exceed two. An adaptive Smith controller together with an adaptive law similar to the delay-free case is proposed. By using Lyapunov-Krasovskii functionals for an appropriate model transformation of the original system, semiglobal stability of the closed-loop system and asymptotic convergence of the output error is established. Strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties. Robustness properties of the adaptive controller are briefly discussed. © 2003 Elsevier B.V. All rights reserved.
- Published
- 2003
15. Stability Analysis of Polynomially Dependent Systems by Eigenvalue Perturbation.
- Author
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Chen, Jie, Fu, Peilin, Mendez-Barrios, Cesar-Fernando, Niculescu, Silviu-Iulian, and Zhang, Hongwei
- Subjects
PERTURBATION theory ,EIGENVALUES ,LINEAR dependence (Mathematics) ,POLYNOMIALS ,STABILITY theory ,MATRIX pencils - Abstract
In this technical note we present a stability analysis approach for polynomially-dependent one-parameter systems. The approach, which appears to be conceptually appealing and computationally efficient and is referred to as an eigenvalue perturbation approach, seeks to characterize the analytical and asymptotic properties of eigenvalues of matrix-valued functions or operators. The essential problem dwells on the asymptotic behavior of the critical eigenvalues on the imaginary axis, that is, on how the imaginary eigenvalues may vary with respect to the varying parameter. This behavior determines whether the imaginary eigenvalues cross from one half plane into another, and hence plays a critical role in determining the stability of such systems. Our results reveal that the eigenvalue asymptotic behavior can be characterized by solving a simple generalized eigenvalue problem, leading to numerically efficient stability conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
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16. Tracking the Algebraic Multiplicity of Crossing Imaginary Roots for Generic Quasipolynomials: A Vandermonde-Based Approach.
- Author
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Boussaada, Islam and Niculescu, Silviu-Iulian
- Subjects
- *
VANDERMONDE matrices , *DYNAMICAL systems , *EIGENVALUES , *BIFURCATION theory , *MULTIPLICITY (Mathematics) , *DIFFERENTIAL equations , *MATRICES (Mathematics) - Abstract
A standard approach in analyzing dynamical systems consists in identifying and understanding the eigenvalues bifurcations when crossing the imaginary axis. Efficient methods for crossing imaginary roots identification exist. However, to the best of the author's knowledge, the multiplicity of such roots was not deeply investigated. In recent papers by the authors [1], [2], it is emphasized that the multiplicity of the zero spectral value can exceed the number of the coupled scalar delay-differential equations and a constructive approach Vandermonde-based allowing to an adaptive bound for such a multiplicity is provided. Namely, it is shown that the zero spectral value multiplicity depends on the system structure (number of delays and number of non zero coefficients of the associated quasipolynomial) rather than the degree of the associated quasipolynomial [3]. This technical note extends the constructive approach in investigating the multiplicity of crossing imaginary roots $j\omega$ where $\omega\neq 0$ and establishes a link with a new class of functional confluent Vandermonde matrices. A symbolic algorithm for computing the LU-factorization for such matrices is provided. As a byproduct of the proposed approach, a bound sharper than the Polya-Szegö generic bound arising from the principle argument is established. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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17. Invariance properties for a class of quasipolynomials.
- Author
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Li, Xu-Guang, Niculescu, Silviu-Iulian, Cela, Arben, Wang, Hong-Hai, and Cai, Tiao-Yang
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MATHEMATICAL symmetry , *POLYNOMIALS , *SET theory , *TIME delay systems , *THEORY of knowledge , *NEWTON diagrams , *MATHEMATICAL series - Abstract
Abstract: When a time-delay system involves multiple imaginary roots (MIRs), the stability analysis will become much more complicated than that in the case with only simple imaginary roots (SIRs). An MIR may exhibit different splitting behaviors and, to the best of the authors’ knowledge, their properties have not been fully investigated. In this paper, we focus on characterizing the invariance properties for MIRs with any multiplicity. Furthermore, the proposed methodology makes it possible to also cover some degenerate cases already encountered and discussed in the literature. In addition, we propose an easily implemented frequency-sweeping method, making it possible to derive the asymptotic behavior without invoking the Puiseux series. [Copyright &y& Elsevier]
- Published
- 2014
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18. Output feedback stabilisation of single-input single-output linear systems with I/O network-induced delays. An eigenvalue-based approach.
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Méndez-Barrios, César-Fernando, Niculescu, Silviu-Iulian, Chen, Jie, and Maya-Méndez, Mauro
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FEEDBACK control system stability , *PROBLEM solving , *LINEAR systems , *PARAMETERS (Statistics) , *DELAY lines , *CLOSED loop systems , *MATRIX pencils , *EIGENVALUES - Abstract
This work addresses the output feedback stabilisation problem for a class of linear single-input single-output systems subject to I/O network delays. More precisely, we are interested in the characterisation of the set of delay and gain parameters guaranteeing the stability of the closed-loop system. To perform such an analysis, we adopt aneigenvalue perturbationbased approach. Various illustrative numerical examples complete the presentation. [ABSTRACT FROM PUBLISHER]
- Published
- 2014
- Full Text
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19. Lyapunov–Krasovskii functionals and application to input delay compensation for linear time-invariant systems
- Author
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Mazenc, Frédéric, Niculescu, Silviu-Iulian, and Krstic, Miroslav
- Subjects
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LYAPUNOV functions , *LINEAR systems , *TIME delay systems , *DISTRIBUTED algorithms , *FUNCTIONAL analysis , *CLOSED loop systems - Abstract
Abstract: For linear systems with pointwise or distributed delay in the inputs which are stabilized through the reduction approach, we propose a new technique of construction of Lyapunov–Krasovskii functionals. These functionals allow us to establish the ISS property of the closed-loop systems relative to additive disturbances. [Copyright &y& Elsevier]
- Published
- 2012
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20. Stability of an imatinib and immune model with delays.
- Author
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Mazenc, Frédéric, Kim, Peter S., and Niculescu, Silviu-Iulian
- Subjects
IMATINIB ,DELAY differential equations ,CHRONIC myeloid leukemia ,CANCER ,IMMUNITY - Abstract
This paper focuses on the stability analysis of a delay differential system encountered in modelling immune dynamics during imatinib treatment for chronic myelogenous leukemia. A simple algorithm is proposed for the analysis of delay effects on the stability. Such an algorithm takes advantage of the particular structure of the dynamical interconnections of the model. The analysis shows that the model yields three fixed points, two of which are always unstable and one of which is sometimes stable. The stable fixed point corresponds to an equilibrium solution in which the leukemia population is kept below the cytogenetic remission level. This result implies that, during imatinib treatment, the resulting anti-leukemia immune response can serve to control the leukemia population. However, the rate of approach to the stable fixed point is very slow, indicating that the immune response is largely ineffective at driving the leukemia population towards the stable fixed point. To extend the stability analysis with respect to the delay parameter, we conduct a global non-linear analysis to demonstrate the existence of unbounded solutions. We provide sufficient conditions based on initial cell concentrations that guarantee unbounded solutions and comment on how these conditions can serve to predict whether imatinib treatment will result in a sustained remission based on a patient's initial leukemia load and initial anti-leukemia T cell concentration. [ABSTRACT FROM PUBLISHER]
- Published
- 2011
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21. Some problems in the stability of networked-control systems with periodic scheduling.
- Author
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Xu-Guang Li, Çela, Arben, Niculescu, Silviu-Iulian, and Reama, Abdellatif
- Subjects
PRODUCTION scheduling ,PRODUCTION control ,NUMERICAL analysis ,MATHEMATICAL analysis ,NONLINEAR theories - Abstract
This article addresses three stability problems related to networked-control systems (NCSs) with periodic scheduling, where control systems may have multiple samplings in a hyperperiod (a hyperperiod is a periodically repeated scheduling sequence for all tasks in an NCS). As expected, the analysis of a system with multiple samplings is much richer than the case with single sampling. For example, a system with two samplings may be stable (unstable) even if it is unstable (stable) when sampled by either sampling. In this context, it is important to understand how network-induced delays and multiple samplings affect the system's stability. In this article, three particular stability problems involving constant and/or time-varying parameters are investigated, and the corresponding stability regions are derived. Numerical examples and various discussions complete the presentation. [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
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22. CONSENSUS PROBLEMS WITH DISTRIBUTED DELAYS, WITH APPLICATION TO TRAFFIC FLOW MODELS.
- Author
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Michiels, Wim, Constantin-Irinel Morǎrescu, and Niculescu, Silviu-Iulian
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TRAFFIC flow ,LINEAR systems ,TOPOLOGICAL dynamics ,DIFFERENTIABLE dynamical systems ,LINEAR differential equations ,ANALYTICAL mechanics ,DISTRIBUTED algorithms ,DELAY differential equations ,STIFF computation (Differential equations) ,FUNCTION spaces - Abstract
This paper focuses on consensus problems for a class of linear systems with distributed delay that are encountered in modeling traffic flow dynamics. In the application problems the distributed delay, whose kernel is a ?-distribution with a gap, represents the human drivers' behavior in the average. The aim of the paper is to give a characterization of the regions in the corresponding delay parameter space, where a consensus is reached for all initial conditions. The structure and properties of the system are fully exploited, which leads to explicit and computationally tractable expressions. As a by-product a stability theory for distributed delay systems with a ?-distribution kernel is developed. Also explicit expressions for the consensus function(al) of time-delay systems with constant and distributed delays that solve a consensus problem are provided. Several illustrative examples complete the presentation. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
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23. Stability Crossing Curves of Shifted Gamma-Distributed Delay Systems.
- Author
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Morărescu, Constantin-Irinel, Niculescu, Silviu-Iulian, and Keqin Gu
- Subjects
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STABILITY (Mechanics) , *LINEAR systems , *SYSTEMS theory , *POLYNOMIALS , *TIME delay systems , *FEEDBACK control systems , *DYNAMICS - Abstract
This paper characterizes the stability crossing curves of a class of linear systems with gamma-distributed delay with a gap. First, we describe the crossing set, i.e., the set of frequencies where the characteristic roots may cross the imaginary axis as the parameters change. Then, we describe the corresponding stability crossing curves, i.e., the set of parameters such that there is at least one pair of characteristic roots on the imaginary axis. Such stability crossing curves divide the parameter space ℝ+2 defined by the mean delay and the gap into different regions. Within each such region, the number of characteristic roots on the right half complex plane is fixed. This naturally describes the regions of parameters where the system is stable. The classification of the stability crossing curves is also discussed. Some illustrative examples (Cushing equation in biology, traffic flow models in transportation systems, and control over networks of a simplified helicopter model) are also presented. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
24. CHARACTERIZATION OF DELAY-INDEPENDENT STABILITY AND DELAY INTERFERENCE PHENOMENA.
- Author
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Michiels, Wim and Niculescu, Silviu-Iulian
- Subjects
- *
DELAY lines , *DELAY differential equations , *LINEAR differential equations , *FUNCTIONAL differential equations , *DIFFERENCE equations , *LINEAR systems , *SYSTEMS theory - Abstract
The problem of the asymptotic stability independent of delays for a class of linear systems including multiple delays is addressed. Both cases where the delays are allowed to vary independently of each other and where they are restricted to a one-dimensional subspace of the delay-parameter space are considered. It the latter case it turns out that the resulting dependency between the delays (rationally independent, rationally dependent, commensurate) plays an important role. The stability conditions are expressed in terms of the spectral properties of some appropriate complex matrices. As a consequence of the stability study, a complete characterization of the delay interference phenomenon is given. Furthermore, a connection is established with the stability theory for continuous-time delay-difference equations, subjected to delay perturbations. Various illustrative examples complete the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
25. On stability crossing curves for general systems with two delays
- Author
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Gu, Keqin, Niculescu, Silviu-Iulian, and Chen, Jie
- Subjects
- *
DIFFERENTIAL equations , *CONTROL theory (Engineering) , *BESSEL functions , *MACHINE theory - Abstract
Abstract: For the general linear scalar time-delay systems of arbitrary order with two delays, this article provides a detailed study on the stability crossing curves consisting of all the delays such that the characteristic quasipolynomial has at least one imaginary zero. The crossing set, consisting of all the frequencies corresponding to all the points in the stability crossing curves, are expressed in terms of simple inequality constraints and can be easily identified from the gain response curves of the coefficient transfer functions of the delay terms. This crossing set forms a finite number of intervals of finite length. The corresponding stability crossing curves form a series of smooth curves except at the points corresponding to multiple zeros and a number of other degenerate cases. These curves may be closed curves, open ended curves, and spiral-like curves oriented horizontally, vertically, or diagonally. The category of curves are determined by which constraints are violated at the two ends of the corresponding intervals of the crossing set. The directions in which the zeros cross the imaginary axis are explicitly expressed. An algorithm may be devised to calculate the maximum delay deviation without changing the number of right half plane zeros of the characteristic quasipolynomial (and preservation of stability as a special case). [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
- View/download PDF
26. An adaptive Smith-controller for time-delay systems with relative degree <f>n*⩽2</f>
- Author
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Niculescu, Silviu-Iulian and Annaswamy, Anuradha M.
- Subjects
- *
LYAPUNOV functions , *ASYMPTOTIC expansions - Abstract
This paper addresses the control of time-delay systems whose relative degree does not exceed two. An adaptive Smith controller together with an adaptive law similar to the delay-free case is proposed. By using Lyapunov–Krasovskii functionals for an appropriate model transformation of the original system, semiglobal stability of the closed-loop system and asymptotic convergence of the output error is established. Strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties. Robustness properties of the adaptive controller are briefly discussed. [Copyright &y& Elsevier]
- Published
- 2003
- Full Text
- View/download PDF
27. On delay-dependent stability for linear neutral systems
- Author
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Ivănescu, Dan, Niculescu, Silviu-Iulian, Dugard, Luc, Dion, Jean-Michel, and Verriest, Erik I.
- Subjects
- *
LINEAR systems , *MATRIX inequalities - Abstract
This paper focuses on the problem of uniform asymptotic stability of a class of linear neutral systems. Sufficient conditions for delay-dependent stability are given in terms of the existence of solutions of some linear matrix inequalities. Furthermore, the proposed technique extends to neutral systems the results obtained for delay-difference equations using model transformations. Illustrative examples are included. [Copyright &y& Elsevier]
- Published
- 2003
- Full Text
- View/download PDF
28. On delay robustness analysis of a simple control algorithm in high-speed networks
- Author
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Niculescu, Silviu-Iulian
- Subjects
- *
TIME delay systems , *ROBUST control , *TRANSFER functions - Abstract
This paper focuses on the robustness analysis of a simple (second-order) control algorithm for data transfer in high-speed networks. The model under consideration (derived using a fluid approximation technique) can be found in Izmailov (SIAM J. Contr. Optimiz. 34 (1996) 1767). The novelty of the approach lies in characterizing the stability of the scheme in the delay-parameter space (where the delays correspond to the control-time interval, and to the round-trip time, respectively). Thus, we shall compute some delay-insensitive measures for the algorithm which give upper and lower bounds for the uncertainty in the knowledge of the round-trip times. [Copyright &y& Elsevier]
- Published
- 2002
- Full Text
- View/download PDF
29. On Computing Puiseux Series for Multiple Imaginary Characteristic Roots of LTI Systems With Commensurate Delays.
- Author
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Li, Xu-Guang, Niculescu, Silviu-Iulian, Cela, Arben, Wang, Hong-Hai, and Cai, Tiao-Yang
- Subjects
- *
QUANTUM perturbations , *TIME delay systems , *ROOT-locus method , *NEWTON diagrams , *TAYLOR'S series , *ASYMPTOTIC controllability - Abstract
Obtaining the Puiseux series of multiple imaginary (characteristic) roots (MIRs) is a fundamental issue in the stability analysis of time-delay systems. However, to the best of the authors' knowledge, this issue has not been fully investigated up to date. This note focuses on the Puiseux series expansion of MIRs of linear time-invariant systems including commensurate delays. For an MIR of any multiplicity, we propose an algorithm for defining the structure of the Puiseux series, as well as the explicit computation of the corresponding coefficients. By using the proposed method, we can find all the Puiseux series corresponding to all the root loci. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
30. Stability of Linear Neutral Time-Delay Systems: Exact Conditions via Matrix Pencil Solutions.
- Author
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Peilin Fu, Niculescu, Silviu-Iulian, and Jie Chen
- Subjects
- *
TIME delay systems , *MATRIX pencils , *MATRICES (Mathematics) , *AUTOMATIC control systems , *FEEDBACK control systems , *PROCESS control systems , *SYSTEM analysis , *STABILITY (Mechanics) , *AUTOMATION - Abstract
In this note, we study the stability properties of linear neutral delay systems. We consider systems described by both neutral differential-difference and state-space equations, and we seek to determine the delay margin of such systems, that is, the largest range of delay values for which a neutral delay system may preserve its stability. In both cases, we show that the delay margin can be found by computing the eigenvalues and generalized eigenvalues of certain constant matrices, which can be executed efficiently and with high precision. The results extend previously known work on retarded systems, and demonstrate that similar stability tests exist for neutral systems; in particular, the tests require essentially the same amount of computation required for retarded systems. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
31. Further remarks on the effect of multiple spectral values on the dynamics of time-delay systems. Application to the control of a mechanical system.
- Author
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Boussaada, Islam, Tliba, Sami, Niculescu, Silviu-Iulian, Ünal, Hakki Ulaş, and Vyhlídal, Tomáš
- Subjects
- *
TIME delay systems , *EXPONENTIAL stability , *SPECTRAL theory , *VANDERMONDE matrices , *BIRKHOFF'S theorem (Relativity) - Abstract
A question of ongoing interest for linear Time-delay systems is to determine conditions on the equation parameters that guarantee the exponential stability of solutions. In recent works a new interesting property of time-delay systems was emphasized. As a matter of fact, the multiple spectral values for time-delay systems was characterized by using a Birkhoff/Vandermonde-based approach. Then, a multiplicity induced stability criteria were exhibited for reduced order systems; scalar delay-equations and a special class of second order systems. This work, further explores such a criteria and shows their applicability to the control of a mechanical system. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
32. Inverted pendulum stabilization: Characterization of codimension-three triple zero bifurcation via multiple delayed proportional gains.
- Author
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Boussaada, Islam, Morărescu, Irinel-Constantin, and Niculescu, Silviu-Iulian
- Subjects
- *
INVERTED pendulum (Control theory) , *STABILITY theory , *BIFURCATION theory , *PROBLEM solving , *EIGENVALUES - Abstract
The paper considers the problem of stabilization of systems possessing a multiple zero eigenvalue at the origin. The controller that we propose, uses multiple delayed measurements instead of derivative terms. Doing so, we increase the performances of the closed loop in presence of system uncertainties and/or noisy measurements. The problem formulation and the analysis is presented through a classical engineering problem which is the stabilization of an inverted pendulum on a cart moving horizontally. On one hand, we perform a nonlinear analysis of the center dynamics described by a three dimensional system of ordinary differential equations with a codimension-three triple zero bifurcation. On the other hand, we present the complementary stability analysis of the corresponding linear time invariant system with two delays describing the behavior around the equilibrium. The aim of this analysis is to characterize the possible local bifurcations. Finally, the proposed control scheme is numerically illustrated and discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
33. Generalized eigenvalue-based stability tests for 2-D linear systems: Necessary and sufficient conditions
- Author
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Fu, Peilin, Chen, Jie, and Niculescu, Silviu-Iulian
- Subjects
- *
POLYNOMIALS , *MATRICES (Mathematics) , *EIGENVALUES , *ALGEBRA - Abstract
Abstract: This paper studies the stability of 2-D dynamic systems. We consider systems characterized by 2-D polynomials and 2-D state–space descriptions. For each description, we derive necessary and sufficient stability conditions, which all require only the computation of a constant matrix pencil. The stability of the underlying system can then be determined by inspecting the generalized eigenvalues of the matrix pencil. The results consequently yield 2-D stability tests that can be checked both efficiently and with high precision. Additionally, frequency-sweeping tests are also obtained which complement the matrix-pencil tests and are likely to be more advantageous analytically. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
34. Pseudospectra and stability radii for analytic matrix functions with application to time-delay systems
- Author
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Michiels, Wim, Green, Kirk, Wagenknecht, Thomas, and Niculescu, Silviu-Iulian
- Subjects
- *
FUNCTIONAL differential equations , *FUNCTIONAL analysis , *FUNCTIONAL equations , *MATRICES (Mathematics) - Abstract
Abstract: Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated. [Copyright &y& Elsevier]
- Published
- 2006
- Full Text
- View/download PDF
35. Reversals in stability of linear time-delay systems: A finer characterization.
- Author
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Li, Xu, Liu, Jian-Chang, Li, Xu-Guang, Niculescu, Silviu-Iulian, and Çela, Arben
- Subjects
- *
LINEAR systems , *TIME delay systems , *GLOBAL asymptotic stability - Abstract
In most of the numerical examples of time-delay systems proposed in the literature, the number of unstable characteristic roots remains positive before and after a multiple critical imaginary root (CIR) appears (as the delay, seen as a parameter, increases). This fact may lead to some misunderstandings: (i) A multiple CIR may at most affect the instability degree; (ii) It cannot cause any stability reversals (stability transitions from instability to stability). As far as we know, whether the appearance of a multiple CIR can induce stability is still unclear (in fact, when a CIR generates a stability reversal has not been specifically investigated). In this paper, we provide a finer analysis of stability reversals and some new insights into the classification: the link between the multiplicity of a CIR and the asymptotic behavior with the stabilizing effect. Based on these results, we present an example illustrating that a multiple CIR's asymptotic behavior is able to cause a stability reversal. To the best of the authors' knowledge, such an example is a novelty in the literature on time-delay systems. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
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