Search results for "Equality."

Numerical Approximation of Elliptic Variational Problems

2003

This chapter is dedicated to the study of Elliptic Variational Inequalities (EVI). Different forms of such an EVI are considered. The Ritz—Galerkin discretization method is introduced, and methods to approximate the solution of an EVI are presented. The finite dimensional subspaces are built by use of the Finite Element Method. The discretized problems are solved using variants of the Successive OverRelaxation (SOR) method. The algorithms are tested on a typical example. The way to develop computer programs is carefully analysed.

model reduction for continuous-time Markovian jump systems with incomplete statistics of mode information

2013

This paper investigates the problem of model reduction for a class of continuous-time Markovian jump linear systems with incomplete statistics of mode information, which simultaneously considers the exactly known, partially unknown and uncertain transition rates. By fully utilising the properties of transition rate matrices, together with the convexification of uncertain domains, a new sufficient condition for performance analysis is first derived, and then two approaches, namely, the convex linearisation approach and the iterative approach, are developed to solve the model reduction problem. It is shown that the desired reduced-order models can be obtained by solving a set of strict linear…

Notice of Violation of IEEE Publication Principles: Robust Observer Design for Unknown Inputs Takagi–Sugeno Models

2013

This paper deals with the observer design for Takagi-Sugeno (T-S) fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system. Sufficient conditions to design an unknown input T-S observer are given in linear matrix inequality (LMI) terms. Both continuous-time and discrete-time cases are studied. Relaxations are introduced by using intermediate variables. Extension to the case of unmeasured decision variables is also given. A numerical example is given to illustrate the effectiveness of the given results.

A variational inequality approach to the problem of the design of the optimal covering of an obstacle

2005

Relaxed Stability and Performance LMI Conditions for Takagi-Sugeno Fuzzy Systems With Polynomial Constraints on Membership Function Shapes

2008

Most linear matrix inequality (LMI) fuzzy control results in literature are valid for any membership function, i.e., independent of the actual membership shape. Hence, they are conservative (with respect to other nonlinear control approaches) when specific knowledge of the shapes is available. This paper presents relaxed LMI conditions for fuzzy control that incorporate such shape information in the form of polynomial constraints, generalizing previous works by the authors. Interesting particular cases are overlap (product) bounds and ellipsoidal regions. Numerical examples illustrate the achieved improvements, as well as the possibilities of solving some multiobjective problems. The result…

Efficient Pruning LMI Conditions for Branch-and-Prune Rank and Chirality-Constrained Estimation of the Dual Absolute Quadric

2014

International audience; We present a new globally optimal algorithm for self- calibrating a moving camera with constant parameters. Our method aims at estimating the Dual Absolute Quadric (DAQ) under the rank-3 and, optionally, camera centers chirality constraints. We employ the Branch-and-Prune paradigm and explore the space of only 5 parameters. Pruning in our method relies on solving Linear Matrix Inequality (LMI) feasibility and Generalized Eigenvalue (GEV) problems that solely depend upon the entries of the DAQ. These LMI and GEV problems are used to rule out branches in the search tree in which a quadric not satisfy- ing the rank and chirality conditions on camera centers is guarantee…

A remark on the radial minimizer of the Ginzburg-Landau functional

2014

Let Omega subset of R-2 be a bounded domain with the same area as the unit disk B-1 and letE-epsilon(u, Omega) = 1/2 integral(Omega) vertical bar del u vertical bar(2) dx + 1/4 epsilon(2) integral(Omega) (vertical bar u vertical bar(2) - 1)(2) dxbe the Ginzburg-Landau functional. Denote by (u) over tilde (epsilon) the radial solution to the Euler equation associated to the problem min {E-epsilon (u, B-1) : u vertical bar(partial derivative B1) = x} and byK = {v = (v(1), v(2)) is an element of H-1 (Omega; R-2) : integral(Omega) v(1) dx = integral(Omega) v(2) dx = 0,integral(Omega) vertical bar v vertical bar(2) dx >= integral(B1) vertical bar(u) over tilde vertical bar(2) dx}.In this note…

Loomis-Whitney inequalities in Heisenberg groups

2021

This note concerns Loomis-Whitney inequalities in Heisenberg groups $\mathbb{H}^n$: $$|K| \lesssim \prod_{j=1}^{2n}|\pi_j(K)|^{\frac{n+1}{n(2n+1)}}, \qquad K \subset \mathbb{H}^n.$$ Here $\pi_{j}$, $j=1,\ldots,2n$, are the vertical Heisenberg projections to the hyperplanes $\{x_j=0\}$, respectively, and $|\cdot|$ refers to a natural Haar measure on either $\mathbb{H}^n$, or one of the hyperplanes. The Loomis-Whitney inequality in the first Heisenberg group $\mathbb{H}^1$ is a direct consequence of known $L^p$ improving properties of the standard Radon transform in $\mathbb{R}^2$. In this note, we show how the Loomis-Whitney inequalities in higher dimensional Heisenberg groups can be deduced…

Semianalyticity of isoperimetric profiles

2009

It is shown that, in dimensions $<8$, isoperimetric profiles of compact real analytic Riemannian manifolds are semi-analytic.

Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds

2012

Abstract We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres. To cite this article: R. Grimaldi et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).