An algebraic analysis approach to linear time-varying systems

^** Email: zerz{at}mathematik.uni-kl.de This paper introduces an algebraic analysis approach to lineartime-varying systems. The analysis is carried out in an ‘almosteverywhere’ setting, i.e. the considered signals are smoothexcept for a set of measure zero, and the coefficients of thelinear ordinary differential equations are supposed to be rationalor meromorphic functions. The methodology is based on a normalform for matrices over the resulting ring of differential operators,which is a non-commutative analogue of the Smith form. Thisis used to establish a duality between linear time-varying systemson the one hand and modules over the ring of differential operatorson the other. This correspondence is based on the fact thatthe signal space is an injective cogenerator when consideredas a module over this ring of differential operators.     

ROBUST STABILITY FOR DEGENERATE NEUTRAL SYSTEMS WITH MIXED TIME-VARYING DELAYS

This paper concerns the stability and robust stability criteria for degenerate neu-tral systems with mixed time-varying delays. A method based on the stability of a new operator D and the linear matrix inequalities is presented that makes it easy to calculate both the upper stability bounds and the free weighting matrices. Since the criteria take the time-varying delays and degenerate neutral systems into account, they are less conservative than previous methods. The Matlab LMI toolbox illustrates the impro...     

海面微波散射场多普勒谱特性研究

基于粗糙面电磁散射双尺度模型推导给出了海面微波散射场多普勒谱频移和谱宽的理论公式, 在该理论公式的推导过程中同时考虑了大尺度海浪的倾斜调制、遮蔽效应和曲率修正效应等因素的影响. 文中将理论公式计算结果与精确数值结果进行了比较, 并讨论了倾斜调制、遮蔽效应及曲率修正效应等因素对多普勒频移和谱宽的影响, 发现倾斜调制使水平极化散射回波多普勒频移显著增大, 从而导致水平极化回波多普勒频移比垂直极化回波多普勒频移大; 在中等入射角度区域, 遮蔽效应和曲率修正效应对多普勒谱并无显著影响, 而在掠射条件下, 遮蔽效应使得多普勒频移增大、谱宽变窄. 本研究对深入理解动态海面散射场频谱特性具有一定参考意义.     

Adaptive synchronization of Cohen-Grossberg neural networks with unknown parameters and mixed time-varying delays

In this paper, we investigate the synchronization problem of chaotic Cohen-Grossberg neural networks with unknown parameters and mixed time-varying delays. An adaptive linear feedback controller is designed to guarantee that the response system can be synchronized with a drive system by utilizing Lyapunov stability theory and parameter identification. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. These results generalize a few previous known results and remove some restrictions on amplification function and time delay. This research also demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.     

弱光反馈下正交时变光注入VCSEL的双稳特性研究

基于垂直腔面发射激光器(VCSEL)的自旋反转模型(SFM),研究了弱光反馈下正交时变光注入VCSEL的双稳特性。研究结果表明,当副激光器(S-VCSEL)受到主激光器(M-VCSEL)正交时变光注入时,弱光反馈的引入不改变正交时变光注入VCSEL的双稳宽度随光注入扫描速率增大而增大的性质;对于确定的光注入扫描速率,随着反馈强度的增大,双稳宽度将变窄;当M-VCSEL与S-VCSEL之间存在频率失谐Δν(等于νm-νs,νm、νs分别为主、副激光器自由运行时的频率)时,随着Δν从负值逐渐增加到正值,双稳宽度总体呈现先减小后增大的趋势,无反馈时在负频区域双稳环宽度呈现的较大波动在引入光反馈后可得到一定程度的抑制。     

一类不确定广义周期时变系统的鲁棒H_∞控制

本文研究了状态矩阵具不确定性广义周期时变系统的鲁棒H∞控制问题.利用线性矩阵不等式(LMI)方法,在给出不确定广义周期时变系统广义可镇定和广义二次可镇定且具有H∞性能指标概念的基础上,得到了该系统广义二次可镇定且具有H∞性能指标γ的充要条件,并给出了相应的鲁棒H∞状态反馈控制律的设计方法,推广了周期系统的鲁棒控制理论结果.最后,通过数值算例说明了设计方法的有效性.     

Constructing the field of values of decomposable and general matrices using the ZNN based path following method

This paper describes and develops a fast and accurate path following algorithm that computes the field of values boundary curve $\partial F(A)$ for every conceivable complex or real square matrix $A$. It relies on the matrix flow decomposition algorithm that finds a proper block-diagonal flow representation for the associated hermitean matrix flow ${ℱ}_A(t)=\cos (t)H+\sin (t)K$ under unitary similarity if that is possible. Here ${ℱ}_A(t)$ is the 1-parameter-varying linear combination of the real and skew part matrices $H=(A+A^{\ast })/2$ and $K=(A-A^{\ast })/(2i)$ of $A$. For indecomposable matrix flows, ${ℱ}_A(t)$ has just one block and the ZNN based field of values algorithm works with ${ℱ}_A(t)$ directly. For decomposing flows ${ℱ}_A(t)$, the algorithm decomposes the given matrix $A$ unitarily into block-diagonal form $U^{\ast }AU=\text{diag}(A_j)$ with $j>1$ diagonal blocks $A_j$ whose individual sizes add up to the size of $A$. It then computes the field of values boundaries separately for each diagonal block $A_j$ using the path following ZNN eigenvalue method. The convex hull of all sub-fields of values boundary points $\partial F(A_j)$ finally determines the field of values boundary curve correctly for decomposing matrices $A$. The algorithm removes standard restrictions for path following FoV methods that generally cannot deal with decomposing matrices $A$ due to possible eigencurve crossings of ${ℱ}_A(t)$. Tests and numerical comparisons are included. Our ZNN based method is coded for sequential and parallel computations and both versions run very accurately and fast when compared with Johnson's Francis QR eigenvalue and Bendixson rectangle based method and compute global eigenanalyses of ${ℱ}_A(t_k)$ for large discrete sets of angles $t_k\in [0,2\pi ]$ more slowly.