Further Improvements in High Gain Observer Design for Systems with Structured Nonlinearities

Due to their simple implementation based on a constant gain matrix, high gain observers are very common in practical applications. We consider systems whose dynamics can be decomposed into a linear and a nonlinear part, where the nonlinear part meets some Lipschitz condition. In many cases there exists a finite bound on the maximum feasible Lipschitz constant for which the error dynamics can be stabilized. Necessary and in some sense sufficient conditions for this maximum Lipschitz constant are given in [1]. These results has been improved in [2,3] by taking the structure of the linear part into account. Having a system with one single nonlinearity, the results given in [2,3] are strict. If multiple nonlinearities occur, even this approach tends to be to conservative. In this case, one could additionally take the internal structure of the nonlinearities into account which leads to a larger set of systems for which convergence of the observer error can be guaranteed. Our new approach is based on an approximation of the structured singular value [4] which yields existence conditions in terms of linear matrix inequalities (LMIs). These LMIs may as well be used for the numerical computation of the observer gain. We demonstrate the advantage of our method on an example. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

High Gain Observers Using an Approximate Observer Normal Form

If one can transform a nonlinear system into observer normal form, it is possible to design an observer with exactly linear error dynamics. Unfortunately, many systems of practical relevance violate the existence conditions of the normal form. This drawback can be circumvented by means of an approximate observer normal form. The actual computation of the associated transformation may still be very difficult. We suggest a nonlinear observer design procedure that avoids this drawback. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Remarks on Kernels

Kernel smoothing provides a simple way of finding a structure in data. Oneof the most popular settings where kernel smoothing ideas can be applied isthe simple regression model. In the context of kernel estimates of aregression function, the choice of a kernel from the different points ofview can be investigated. The aim of this paper is to present constructionsof minimum variance kernels and smooth kernels by means of the Legendrepolynomials and the Gegenbauer polynomials as well. Some of these kernelshave been introduced, e.g., in [2], [3], and [5], but here another approachby using the variational calculus is presented.     

Some Remarks on Pseudotrees

This paper provides new results on pseudotrees. First, it is shown that pseudotrees are precisely those posets for which consistent sets, directed sets, and nonempty chains coincide. Second, we show that chain-complete pseudotrees yield complete meet-semilattices. Third, we prove that pseudotrees are precisely those posets that admit a set representation by sets of appropriate chains. This latter result generalizes results needed for applications in game theory and economics.     

Some Remarks on Chung's Law

We discuss the notion of a "functional version of Chung's law of the iterated logarithm", and prove a result that incorporates both possible interpretations.     

关于拟本原p-块的一些说明

本文主要研究了拟本原p-块的性质,从而得到拟本原p-块与群中心结构的一些关系．     

极空间的注记

本文中我们提到的极空间的秩不必是有限的。得到的主要结果是，令S是一个不可约的极空间，如果p～q，p～q是S中的点，则有极空间是同构的，我们把它记作     

Some Remarks on Distributed PCHD-Systems

Port controlled Hamiltonian systems with dissipation are a well known tool for the modeling and the controller design for plants, described by nonlinear ordinary differential equations. This contribution presents a possible extension to systems, described by partial differential equations, where the state manifold and the input space of the ODE case are replaced by new geometric structures. This approach takes dissipative effects into account and shows, how distributed ports can be introduced. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Noether环的几点注记

本文利用特征模给出了Ｎｏｅｔｈｅｒ环的一些充分必要条件，并由此讨论了Ｎｏｅｔｈｅｒ环上的内射模与平坦模的一些性质     

Some Remarks on Korn Inequalities

A recent joint paper with Doina Cioranescu and Julia Orlik was concerned with the homogenization of a linearized elasticity problem with inclusions and cracks(see[Cioranescu, D., Damlamian, A. and Orlik, J., Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymptotic Analysis, 82, 2013, 201–232]). It required uniform estimates with respect to the homogenization parameter. A Korn inequality was used which involves unilateral terms on the boundaries where a nopenetration condition is imposed. In this paper, the author presents a general method to obtain many diverse Korn inequalities including the unilateral inequalities used in [Cioranescu, D., Damlamian, A. and Orlik, J., Homogenization via unfolding in periodic elasticity with contact on closed and open cracks, Asymptotic Analysis, 82, 2013, 201–232]. A preliminary version was presented in [Damlamian, A., Some unilateral Korn inequalities with application to a contact problem with inclusions, C. R. Acad. Sci. Paris, Ser. I,350, 2012, 861–865].     

Some Remarks on Orlicz-Lorentz Spaces

Spaces of Lorentz type called Orlicz-Lorentz spaces are studied. There are given necessary and sufficient conditions for the spaces to be order continuous, separable, KB-spaces and to contain isometric or isomorphic copy of l∞ or c₀. Moreover a criterion for strict convexity of these spaces is found.     

Some Remarks on Absolute Mathematics

We calculate Hochschild cohomology groups of the integers treated as an algebra over so-called field with one element. We compare our results with calculation of the topological Hochschild cohomology groups of the integers—this is the case when one considers integers as an algebra over the sphere spectrum.     

Some Remarks on Connected Coalgebras

In this paper we introduce the notions of connected, 0-connected and strictly graded coalgebra in the framework of an abelian monoidal category $ \mathcal{M} $ and we investigate the relations between these concepts. We recover several results, involving these notions, which are well known in the case when $ \mathcal{M} $ is the category of vector spaces over a field K. In particular we characterize when a 0-connected graded bialgebra is a bialgebra of type one.     

Some Remarks on Steiner Systems

The main purpose of this paper is to introduce Steiner systems obtained from the finite classical generalized hexagons of order q. We show that we can take the blocks of the Steiner systems amongst the lines and the traces of the hexagon, and we prove some facts about the automorphism groups. Also, we make a remark concerning the geometric construction of a known class (KW) of Steiner systems and we deduce some properties of the automorphism group.     

Some Remarks on Rainbow Connectivity

An edge (vertex) colored graph is rainbow‐connected if there is a rainbow path between any two vertices, i.e. a path all of whose edges (internal vertices) carry distinct colors. Rainbow edge (vertex) connectivity of a graph G is the smallest number of colors needed for a rainbow edge (vertex) coloring of G. In this article, we propose a very simple approach to studying rainbow connectivity in graphs. Using this idea, we give a unified proof of several known results, as well as some new ones.     

关于有序域的几则短记

Dubois在文[1]中举反例示明,在Artin所解决的Hilbert第17问题中所出现的系数域是个亚基米德有序域这一条件是不能减弱的(见[1]或者[7])在他所举出的反例中,隐约地使用了一些有关序与赋值相互关系的概念与事实,但都没有明显地提出或证明。这篇短文首先是阐明隐含在[1]中的一些概念和事实;其次指出他的例子还可以用来说明     

关于可信性模型的若干评注

可信性模型是经验费率厘定中最重要的方法，本文在简述可信性概念的发展简史并强调了有限扰动可信性和最精确可信性的区别后，重点剖析了最精确可信性的理论基础，且详尽地解释了导出（修正）Buehlmann单合同可信性模型的基本思路，在阶段性地展示了建立此模型基本假定的过程后，给出了风险保费与预测值的可信性估计的简明公式，现今最基础的Buehlmann-Straub可信性模型可视为由多个相互独立，且具有相同的结构函数的（修正）Buhlmann单合同模型相嵌而成，这种组嵌方式使得估计该模型的未知结构参数成为可能，本文最后概述了可信性模型的主要进展，全文的叙述是说明性的，不步及技术性证明过程，目的在于为理解可信性模型提供一个直观与清晰的思路。     

Some Remarks on Some Second-order Hyperbolic Differential Equations

We are concerned with the almost automorphic solutions to the second-order hyperbolic differential equations of type ü(s) + 2B ù(s) + Au(s) = f(s) (*), where A, B are densely defined closed linear operators acting in a Hilbert space H, and f : R |—> H is a vector-valued almost automorphic function. Using invariant subspaces, it will be shown that under appropriate assumptions, every solution to (*) is almost automorphic.