Publications

1997

• On ℓ2 memoryless control of time-delay systems
  
  • Ionescu Vlad
  • Niculescu Silviu-Iulian
  • Woerdeman Hugo J.
  , 1997, 5, pp.4414-4419. This paper focuses on the design of ℓ2 memoryless controllers for a class of uncertain linear systems described by differential equations with delayed state and disturbances. We give sufficient conditions for the design of a memoryless state feedback control law which guarantees the delay-independent closed-loop stability with an ℓ2 norm bound constraint on disturbance attenuation. These conditions are derived in terms of algebraic properties of an adequate matrix pencil via a Lyapunov-Krasovskii functional based approach. The criteria proposed here are less conservative than earlier ones proposed in the literature.
• Constrained robust guaranteed cost control for uncertain linear time-delay systems
  
  • Trofino Alexandre
  • Li Huaizhong
  • Dugard Luc
  • Dion Jean-Michel
  • Niculescu Silviu-Iulian
  , 1997, 2, pp.1615-1620. This paper is concerned with constrained robust guaranteed cost control for uncertain linear time-delay systems using a linear matrix inequality (LMI) approach. Provided with necessary conditions, the problem considered is to design a static state feedback controller for a class of linear uncertain time-delay systems such that the following three goals are achieved simultaneously 1). The closed-loop systems with this controller are robustly stable; 2). A given quadratic performance index for the systems is guaranteed to be below a known upper bound; and 3). The control input is norm-bounded. We show that the solvability of the addressed problem is implied by the feasibility of some linear matrix inequalities.
• Delay-dependent closed-loop stability of linear systems with input delay An LMI approach
  
  • Niculescu Silviu-Iulian
  • Fu My
  • Li Huaizhong
  , 1997. This paper focuses on the problem of computing a control law which maximizes (in a sub-optimal sense) the delay of the closed-loop system for a class of linear systems with delayed input. The delay is assumed to be a continuous bounded time-varying function. The analysis is given using two different approaches a Razumikhin based method and a frequency-filtering based method.
• A decomposition of the electric field. Application to the Darwin model
  
  • Ciarlet Patrick
  • Sonnendrücker Eric
  Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, 1997, 7 (8), pp.1085-1120. In many cases, the numerical resolution of Maxwell's equations is very expensive in terms of computational cost. The Darwin model, an approximation of Maxwell's equations obtained by neglecting the divergence free part of the displacement current, can be used to compute the solution more economically. However, this model requires the electric field to be decomposed into two parts for which no straightforward boundary conditions can be derived. In this paper, we consider the case of a computational domain which is not simply connected. With the help of a functional framework, a decomposition of the fields is derived. It is then used to characterize mathematically the solutions of the Darwin model on such a domain. (10.1142/S0218202597000542)
  DOI : 10.1142/S0218202597000542
• Systèmes à retard. Aspects qualitatifs sur la stabilité et la stabilisation
  
  • Niculescu Silviu-Iulian
  , 1997, pp.245 pages.
• Robust stability analysis for time-delay systems using the integral quadratic constraint approach
  
  • Fu Minyue
  • Li Huaizhong
  • Niculescu Silviu-Iulian
  , 1997, pp.3643-3647. Given a time-delay system, we are interested in finding new robust stability conditions for the system. We apply the integral quadratic constraint approach to obtain two results which allow us to test the robust stability using the linear matrix inequality technique. Both results give an estimate of the maximum time-delay which preserves robust stability. The first result is simpler to apply while the second one gives a less conservative robust stability condition.
• Robust stabilization of uncertain linear systems with input delay
  
  • Li Huaizhong
  • Niculescu Silviu-Iulian
  • Dugard Luc
  • Dion Jean-Michel
  , 1997, pp.3654-3659. This paper is concerned with robust stability and robust stabilization problems of uncertain linear systems with delayed state and delayed input respectively. The admissible uncertainty of the systems considered in this paper appears in quadratic constrained forms which take the wellknown norm-bounded time-varying uncertainty as a special case. Delay-dependent results for the two addressed problems are derived using Razumikhin stability theorem and further algorithms are proposed which enable us to find suboptimal upper bounds for both cases and the controller gain matrix for the stabilization case using linear matrix inequalities (LMIs) technique.
• Delay-independent stability of linear neutral systems A Riccati equation approach
  
  • Verriest E.I.
  • Niculescu Silviu-Iulian
  , 1997, pp.3632-3636. This note focuses on the problem of asymptotic stability of a class of linear neutral systems described by differential equations with delayed state. The delay is assumed unknown, but constant. Sufficient conditions for delayindependent asymptotic stability are given in terms of the existence of symmetric and positive definite solutions of a continuous Riccati algebraic matrix equation coupled with a discrete Lyapunov equation. The approach adopted here is based on a Lyapunov-Krasovskii functional technique.
• Delay-interval stability and hyperbolicity of linear time-delay systems A matrix pencil approach
  
  • Niculescu Silviu-Iulian
  , 1997, pp.3759-3764. This paper focuses on the problems of asymptotic stability and hyperbolicitv for a class of linear systems described by delay differential equations with commensurable delays. Delay-interval necessary and sufficient conditions are given in terms of eigenvalues distribution with respect to the unit circle of two constant and regular matrix pencils one associated to finite time-delays and the other one associated to infinite delay. The so-called "delay-independent" and "delay-dependent" cases are also considered. Furthermore, a second order example from the literature is completely treated.
• On tracking control of rigid manipulators with unilateral constraints
  
  • Brogliato Bernard
  • Niculescu Silviu-Iulian
  • Monteiro-Marques M.
  , 1997, pp.3481-3486. In this note we consider the problem of feedback control of n-dof (degree-of-freedom) rigid manipulators subject to a scalar unilateral constraint f(X) 0 (X ∈ Rn is the vector of generalized coordinates). The stability analysis relies on a stability concept that incorporates the hybrid dynamical feature of the overall system. It is shown that stability of the closed-loop system can be obtained. It is pointed out that showing asymptotic stability certainly requires more advanced stability tools.
• Robust guaranteed cost control of uncertain linear time-delay systems with mixed state and input delays
  
  • Li Huaizhong
  • Niculescu Silviu-Iulian
  • Dugard Luc
  • Dion Jean-Michel
  , 1997. This paper is concerned with robust guaranteed cost control for uncertain linear time-delay systems with state delay, input delay and quadratically constrained uncertainty using a linear matrix inequality (LMI) approach. The quadratically constrained uncertainty described in this paper is general in nature and takes some well-known uncertainty descriptions as special cases. We only consider the memoryless static state feedback in this paper. We show that feasibility of some LMIs guarantees the solvability of the corresponding robust guaranteed cost control problem.
• Elementary approximation of exponentials of Lie polynomials
  
  • Jean Frédéric
  • Koseleff Pierre-Vincent
  , 1997, 1255, pp.174-188. (10.1007/3-540-63163-1_14)
  DOI : 10.1007/3-540-63163-1_14
• Finite element convergence for the Darwin model to Maxwell's equations
  
  • Ciarlet Patrick
  • Zou Jun
  ESAIM: Mathematical Modelling and Numerical Analysis, Société de Mathématiques Appliquées et Industrielles (SMAI) / EDP, 1997, 31 (2), pp.213-250.
• Une caractérisation de l'orthogonal de $\Delta (H^2(\Omega)\cap H^1_0(\Omega))$ dans $L^2(\Omega)$
  
  • Assous Franck
  • Ciarlet Patrick
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 1997, 325 (6), pp.605-610. Dans le cas d'un domaine polyédrique non convexe à frontière lipschitzienne, nous donnons une caractérisation de l'orthogonal, dans L2(Ω), de l'image par le laplacien de H2(Ω) ∩ H01(Ω). Ceci permettra par la suite de décomposer la solution des équations de Maxwell en la somme d'un terme régulier et d'un terme singulier. (10.1016/S0764-4442(97)84769-6)
  DOI : 10.1016/S0764-4442(97)84769-6
• A guided mode in the range of the radiation modes for a rib waveguide
  
  • Bonnet-Ben Dhia Anne-Sophie
  • Mahé Fabrice
  Journal of Optics, Institute of Physics (IOP), 1997, 28 (1), pp.41-43. The stratified cladding of integrated optical waveguides is dispersive, which induces quite original phenomena. We present an example of a dielectric waveguide for which there exists a guided mode which propagates faster than some waves in the stratified cladding. Such a guide presents a specific symmetry and the key point is a separate study of the symmetrical and antisymmetrical modes. (10.1088/0150-536X/28/1/008)
  DOI : 10.1088/0150-536X/28/1/008
• Résolution d'un cas test de contrôle optimal pour un système gouverné par l'équation des ondes à l'aide d'une méthode de décomposition de domaine
  
  • Benamou Jean-David
  , 1997. On utilise une méthode de décomposition de domaine pour résoudre un problème de contrôle optimal pour l'équation des ondes. La décomposition choisie (un sous-domaine par maille de discrétisation) permet d'utiliser facilement la technique de synthèse quadratique.
• On delay-independent stability criteria A matrix-pencil approach
  
  • Niculescu Silviu-Iulian
  • Ionescu Vlad
  IMA Journal of Mathematical Control and Information, Oxford University Press (OUP), 1997, 14 (3), pp.299-306. This paper focuses on the problem of asymptotic stability of a linear system described by delay-differential equations. Sufficient delay-independent stability conditions are derived in terms of some algebraic properties of an adequate matrix pencil via a Lyapunov-Krasovskii functional-based approach. The criteria proposed here are less conservative than similar ones proposed in the literature. The result is also extended to the case when a memoryless control input is considered. (10.1093/imamci/14.3.299)
  DOI : 10.1093/imamci/14.3.299
• Error Estimates for a Numerical Scheme for Ferromagnetic Problems
  
  • Monk Peter
  • Vacus Olivier
  , 1997. We propose a finite element method for approximating the non-linear equations describing the electromagnetic field in a ferromagnetic material. Using energy arguments, we prove an optimal convergence rate for the method assuming a sufficiently smooth electromagnetic field. We also verify that the finite element solution satisfies various conservation conditions appropriate to the continuous problem. Finally, we provide some numerical examples.
• On Transitions to Stationary States in a Maxwell-Landau-Lifchitz-Gilbert System
  
  • Joly Patrick
  • Komech Alexander
  • Vacus Olivier
  , 1997. In this paper we consider Maxwell's equations together with a dissipative non-linear magnetic law, the Landau-Lifchitz-Gilbert equation, and we study long time asymptotics of solutions in the 1D case in an infinite domain of propagation. We prove long-time convergence to zero of the electroma- gnetic field in a Fréchet topology defined by local energy seminorms: this corresponds to the local decay of energy. We then introduce that the set of stationary states for the Landau-Lifchitz-Gilbert equation and prove that it corresponds to the attractor set for the distribution of magnetizationwhose presence is one of the characteristics of ferromagnetic media.
• Stability of linear systems with delayed state An LMI approach
  
  • Niculescu Silviu-Iulian
  • Dion Jean-Michel
  • Dugard Luc
  • Li Huaizhong
  Journal Européen des Systèmes Automatisés, Lavoisier, 1997, 31 (6), pp.955-969. This paper focuses on the problem of asymptotic stability of a class of time-delay systems described by linear delayed state equations involving several constant (or time-varying), but unknown delays. A sufficient delays-dependent stability condition of the considered system is given using a Lyapunov-Razumikhin function approach, Futhermore, by transforming the stability problem into a linear matrix inequality optimisation problem, the approach adopted here allows the computation of a suboptimal largest ellipsoidal stability region in the delays parameter space such that the asymptotic stability of the time-delay system is ensured.
• Multivalued Solution and Viscosity Solutions of the Eikonal Equation
  
  • Benamou Jean-David
  , 1997. Some contributions to the study and computation of the multivalued solution of the Eikonal equation
• On the optimality of the median cut spectral bisection graph partitioning method
  
  • Chan Tony F.
  • Ciarlet Patrick
  • Szeto W. K.
  SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 1997, 18 (3), pp.943-948. Recursive spectral bisection (RSB) is a heuristic technique for finding a minimum cut graph bisection. To use this method the second eigenvector of the Laplacian of the graph is computed and from it a bisection is obtained. The most common method is to use the median of the components of the second eigenvector to induce a bisection. We prove here that this median cut method is optimal in the sense that the partition vector induced by it is the closest partition vector, in any ls norm, for $s\ge1$, to the second eigenvector. Moreover, we prove that the same result also holds for any m-partition, that is, a partition into m and (n-m)$ vertices, when using the mth largest or smallest components of the second eigenvector. Copyright © 1997 Society for Industrial and Applied Mathematics (10.1137/S1064827594262649)
  DOI : 10.1137/S1064827594262649
• A qualitative analysis of a simplified model for the non linear membrane-mallet interaction
  
  • Joly Patrick
  • Rhaouti Leila
  , 1997. In this paper, we are interested in a mathematical analysis of a simplified 1D mechanical model for the interaction between a mallet and an elastic membrane. First, using elementary mathematical techniques, we study quite precisely the case where the mallet is in interaction with a rigid body. This analysis allows us to understand the influence of physical parameters on the mallet behavior. Then, we show how the results of this study can be extended to the case where the mallet is in interaction with a membrane.