Stabilization and H{infty} control of two-dimensional Markovian jump systems

This paper extends the results obtained for one-dimensionalMarkovian jump systems, to investigate the problems of stochasticstabilization and H_{SRC="http://imamci.oxfordjournals.org/math/infin.gif" ALT="{infty}" BORDER="0">} control of two-dimensional (2D) systemswith Markovian jump parameters. The mathematical model of 2Djump systems is established upon the well-known Roesser model,and sufficient conditions are obtained for the existence ofdesired controllers in terms of linear matrix inequalities,which can be readily solved by available numerical software.These obtained results are further extended to more generalcases whose system matrices also contain parameter uncertaintiesrepresented by either polytopic or norm-bounded approaches.A numerical example is provided to show the applicability ofthe proposed theories.     

Properties of the weighted logarithmic matrix norms

Mingzhu Liu^{SRC="http://imamci.oxfordjournals.org/math/Dagger.gif" ALT="{ddagger}" BORDER="0">} Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China ^{SRC="http://imamci.oxfordjournals.org/math/dagger.gif" ALT="{dagger}" BORDER="0">} Email: ghu{at}hit.edu.cn, ghuca{at}yahoo.ca^{SRC="http://imamci.oxfordjournals.org/math/Dagger.gif" ALT="{ddagger}" BORDER="0">} Email: mzliu{at}hit.edu.cn Received on January 31, 2006; Accepted on December 9, 2006 In this paper, we are concerned with the properties of the weightedlogarithmic matrix norms. A relation between the elliptic logarithmicmatrix norm and the weighted logarithmic matrix norm is given.Based on Lyapunov equations, two weighted logarithmic matrixnorms are constructed which are less than 1-logarithmic matrixnorm and SRC="http://imamci.oxfordjournals.org/math/infin.gif" ALT="{infty}" BORDER="0">-logarithmic matrix norm, respectively. Then, an iterativescheme is presented to obtain the logarithmically SRC="http://imamci.oxfordjournals.org/math/epsi.gif" ALT="{epsilon}" BORDER="0">-efficientmatrix norm. Numerical examples are given to illustrate theresults.     

Locally uniformly rotund renorming and fragmentability

In this paper we characterize those Banach spaces E that admita locally uniformly rotund renorming by means of a linear topologicalcondition that is a particular case of the notion, introducedby J. E. Jayne, I. Namioka and C. A. Rogers, called countablecover by sets of small local diameter. This allows us to developa Decomposition Method and a Transfer Technique to obtain locallyuniformly rotund renormings. 1991 Mathematics Subject Classification:46B20.     

Simultaneous output feedback stabilization of time-delay systems

^** Email: magdi_mahmoud{at}cic-cairo.com^*** Email: hnounou{at}uaeu.ac.ae This paper develops new results to the problem of simultaneousfeedback stabilization using static output feedback (SOF) controlfor a finite collection of linear dynamical systems with unknownstate delay. We establish tractable synthesis conditions fornominal SOF controllers and subsequently extend the resultsto resilient SOF to cope with possible additive controller gainperturbations. In both cases, the design of SOF controllersis based on guaranteed cost and SRC="http://imamci.oxfordjournals.org/math/hamilt.gif" ALT="H" BORDER="0">_{SRC="http://imamci.oxfordjournals.org/math/infin.gif" ALT="{infty}" BORDER="0">} approaches. Previous relatedresults are recovered and all the developed results are convenientlycast in the format of linear matrix inequalities. A numericalexample is presented.     

Robust H{infty} control of uncertain systems with time-varying state and control input delays

In this paper, a new method for robust H_{SRC="http://imamci.oxfordjournals.org/math/infin.gif" ALT="{infty}" BORDER="0">} controller of uncertainsystems with time-varying state and control input delays isproposed. A sufficient condition, which is dependent on themaximum value of the time derivative of time-varying delay,is also presented for the existence of H_{SRC="http://imamci.oxfordjournals.org/math/infin.gif" ALT="{infty}" BORDER="0">} controller. The proposedcontroller not only stabilizes closed-loop uncertain systemsbut also guarantees a prescribed H_{SRC="http://imamci.oxfordjournals.org/math/infin.gif" ALT="{infty}" BORDER="0">} norm bound of the closed-looptransfer matrix from the disturbance to controlled output. Furthermore,we propose a new robust stability criterion to decide the allowedmaximum bound of plant uncertainty which still can be stabilizedby proposed robust controller. An example given illustratesthe availability of the proposed design method.     

Algorithms for the computation of the pseudospectral radius and the numerical radius of a matrix

^** Email: mengi{at}cs.nyu.edu^*** Email: overton{at}cs.nyu.edu Two useful measures of the robust stability of the discrete-timedynamical system x_k+1 = Ax_k are the SRC="http://imajna.oxfordjournals.org/math/epsi.gif" ALT="{epsilon}" BORDER="0">-pseudospectral radius andthe numerical radius of A. The SRC="http://imajna.oxfordjournals.org/math/epsi.gif" ALT="{epsilon}" BORDER="0">-pseudospectral radius of A isthe largest of the moduli of the points in the SRC="http://imajna.oxfordjournals.org/math/epsi.gif" ALT="{epsilon}" BORDER="0">-pseudospectrumof A, while the numerical radius is the largest of the moduliof the points in the field of values. We present globally convergentalgorithms for computing the SRC="http://imajna.oxfordjournals.org/math/epsi.gif" ALT="{epsilon}" BORDER="0">-pseudospectral radius and thenumerical radius. For the former algorithm, we discuss conditionsunder which it is quadratically convergent and provide a detailedaccuracy analysis giving conditions under which the algorithmis backward stable. The algorithms are inspired by methods ofByers, Boyd–Balakrishnan, He–Watson and Burke–Lewis–Overtonfor related problems and depend on computing eigenvalues ofsymplectic pencils and Hamiltonian matrices.     

L、T、十形截面型钢混凝土异形柱滞回性能对比分析

为了研究截面形状对型钢混凝土(SRC)异形柱滞回性能的影响,完成了4个L形、6个T形和2个+形截面SRC异形柱构件的低周反复荷载实验,并获取了此类构件的破坏形态和滞回曲线。在此基础上,对比分析了截面类型对SRC异形柱在耗能能力、变形性能及地震损伤等方面的影响。研究结果表明:型钢混凝土异形柱的破坏形态与剪跨比有关,剪跨比大的试件易发生弯曲型破坏,而小剪跨比的试件易发生剪切型破坏;L形柱的滞回环捏拢程度最大,其次为T形柱,最后为+形柱;+形柱和L形柱的相对受剪承载能力和耗能能力均比T形柱大;T形柱的变形能力要优于L形柱;型钢混凝土异形柱构件的相对损伤累积程度与柱肢数有关,其主要表现为随着柱肢数的增多,异形柱的损伤发展水平加快。     

一种新的快速衰落信道相干时间估计方法

快速衰落信道(FFD)是浅海中常见的畸变信道模型之一,通常用信道相干时间来描述其多普勒扩展程度。分段副本相关器(SRC)是FFD信道的最佳似然比检测器,但当信道相干时间未知时,其性能因失配受到较大影响。针对此种情况,提出了多重假设SRC,该方法能简单有效地估计FFD信道相干时间并解决SRC的失配问题。