奇异时滞系统的时滞依赖稳定性判据

讨论了奇异时滞系统的稳定性问题. 首先, 在几个最新的结果之间建立了等价性, 并给出了一个简化的稳定性判据. 然后, 通过使用时滞分解的方法, 得到了一个新的稳定性判据. 它比现有结果具有更少的保守性. 最后, 给出了一个数值例子, 表明了新判据是有效的且保守性较小.     

具有时滞和的连续系统的时滞相关稳定性

针对一类状态向量中含有时滞和的连续系统,研究其时滞相关稳定性问题.通过构造新的Lyapunov函数,获得了保证系统稳定、基于线性矩阵不等式的时滞相关充分条件,该条件不需要对原系统进行模型变换.数值算例表明,所得到的结论较已往文献具有较小的保守性.     

不确定多时变时滞网络控制系统的时滞相关稳定性

讨论了具有不确定性和多时变时滞的网络控制系统(NCSs)的时滞相关稳定性. 针对一类多输入多输出(MIMO)的NCSs, 在考虑网络时滞和不确定性的情况下, 建立了该系统的数学模型. 利用Lyapunov稳定性理论和线性矩阵不等式(LMI)方法, 提出了新的基于LMI形式的时滞相关稳定条件. 该方法克服了已有方法的保守性且结果更具有一般性. 最后给出实例表明该方法与现有文献结果相比, 具有较小的保守性和更好的有效性.     

带有非线性扰动的时变时滞系统的稳定性准则

研究了带有非线性扰动的时变时滞系统的稳定性问题.基于时滞分割方法,提出了保守性更小的系统稳定性分析准则.利用一个自由参数将时滞区间分割为2个子区间,进而构造了含有时滞分割点状态信息和3重积分项的Lyapunov-Krasovskii泛函,并采用自由矩阵积分不等式界定泛函导数中的交叉项.基于Lyapunov稳定性定理,得到了以线性矩阵不等式描述的时滞相关型稳定性准则.数值算例表明该稳定性准则能够得到更大的时滞上界,与已有结果相比具有更小的保守性.     

同时含有状态和输入时滞系统的滑模控制

研究同时舍状态和输入时滞的系统交结构控制问题，基于LMI，给出了存在滑动模态的时滞相关的充分条件，利用LMI的解，得到了两种不同的滑动模态和控制器的设计方法，所提出的方法简单量行，具有较小的保守性，可进一步推广到多时滞和不确定时滞系统。     

具有时滞的Lurie型控制系统绝对稳定的时滞相关准则

研究了具有时滞的Lurie型控制系统的绝对稳定性,利用矩阵不等式的方法出了系统绝对稳定的时滞相关准则,与现有的结果相比,具有较小的保守性。     

时滞系统的鲁棒稳定性分析

研究时滞系统的时滞独立稳定性和时滞相关稳定性问题。基于Ｂａｒｂａｌｅｔ引理,得到了一类检验线性时滞系统稳定性的简单条件。进一步研究了一类含非线性不确定性时滞系统的鲁棒稳定性问题。数值例子表明,所得到的结果比已有结果的保守性小。     

中立型变时滞系统的鲁棒稳定性

考虑不确定中立型变时滞系统的鲁棒稳定性问题. 首先, 引入新的变量来代替系统的不确定性; 然后, 通过构造一般形式的Lyapunov-Krasovskii泛函、使用积分不等式并引入自由矩阵, 得到了基于线性矩阵不等式的系统稳定性判据. 该结论与中立型时滞, 离散时滞及其导数均相关, 具有较小的保守性. 最后, 通过仿真算例说明了所得到的结论在保守性上优于现存的结果以及中立型时滞, 离散时滞及其导数三者之间的关系.     

时变时滞离散广义Markov 跳变系统的鲁棒稳定性

研究一类具有区间时变时滞的离散不确定广义Markov跳变系统的时滞相关鲁棒稳定性问题.通过将Jensen不等式与一个新的定界不等式相结合,得到了一个新的稳定性判据,该判据中仅含有Lyapunov变量,具有较小的计算负担.进而,基于凸组合方法得到了另一个新的稳定性判据,该判据引入了一些自由矩阵变量,具有较小的保守性.数值算例表明了所提出方法的有效性.     

不确定线性多时变时滞系统的时滞相关鲁棒控制

提出一种积分不等式新方法，讨论不确定线性多时变时滞系统的鲁棒稳定性以及鲁棒稳定化问题，首先利用Park不等式建立了基于二次型项的积分不等式，利用这一不等式获得了系统基于LMI的时滞相关、时滞导数相关鲁棒稳定条件；然后利用这一条件给出了时滞状态反馈控制器的一种新的设计方法，数值例子说明了所得结论具有较小的保守性。     

基于高分辨率遥感数据的长城自动提取实验研究

长城是中华民族的象征,是人类历史上最伟大的建筑工程之一。基于高分辨率遥感数据“SPOT-5”和DEM数据,首先运用微分几何方法提取高亮度线性地物信息,然后根据长城特殊的地形地貌特征,运用GIS水文学方法提取出山脊线,并在山脊线周围做一个几米的缓冲区,将高亮度线性地物信息和山脊线缓冲区进行叠加分析,比较准确地提取出了长城信息,并进行提取精度的评估。     

Convergent Ritz approximations of the set of stabilizing controllers

A necessary and sufficient condition for linear exponential sums to be dense in is derived. Under this condition a Ritz approximation converges, which has been proposed to solve linear control problems. State-space representations of orthonormal basis functions for multivariable systems are given.     

The Eigenvalue Problem for the 2D Laplacian in ℋ-Matrix Arithmetic and Application to the Heat and Wave Equation

A class of matrices (-matrices) has recently been introduced by Hackbusch for approximating large and fully populated matrices arising from FEM and BEM applications. These matrices are data-sparse and allow approximate matrix operations of almost linear complexity. In the present paper, we choose a special class of -matrices that provides a good approximation to the inverse of the discrete 2D Laplacian. For these 2D -matrices we study the blockwise recursive schemes for block triangular linear systems of equations and the Cholesky and LDL^T factorization in an approximate arithmetic of almost linear complexity. Using the LDL^T factorization we compute eigenpairs of the discrete 2D Laplacian in -matrix arithmetic by means of a so-called simultaneous iteration for computing invariant subspaces of non-Hermitian matrices due to Stewart. We apply the -matrix techniques to approximate the solutions of the high-frequency 2D wave equation for smooth initial data and the 2D heat equation for arbitrary initial data by spectral decomposition of the discrete 2D Laplacian in, up to logarithmic factors, optimal complexity.     

Gain Scheduled Output Feedback Control Based on LTI Controller Interpolation that Preserves LPV H ∞ Performance

A new approach to the design of a gain scheduled output feedback controller based on linear time-invariant (LTI) controller interpolation that preserves H performance without a varying-parameter rate feedback is proposed. After the controller design is translated into parameterized linear matrix inequalities about parameter matrices based on a parameter-dependent Lyapunov function, the sufficient condition is given for the partition of the varying-parameter set based on the concept of H performance covering. The varying-parameter set is thus partitioned into sufficiently small subsets. After the constant matrices are found for each of the subsets, the required continuous parameter matrices are obtained by using interpolation. The proposed controller overcomes the drawback that the gain scheduled controller may not be found by using the existing gain scheduled linear parameter varying (LPV) controller synthesis. Moreover, the varying-parameter rate feedback is eliminated and the conservatism of the controller design is reduced by means of limiting the upper bound of the varying-parameter rate. Simulation and experiment results prove the effectiveness of the proposed controller.     

Algorithms to Separate $\{0,\frac{1}{2}\}$ -Chvátal-Gomory Cuts

Chvátal-Gomory cuts are among the most well-known classes of cutting planes for general integer linear programs (ILPs). In case the constraint multipliers are either 0 or , such cuts are known as -cuts. It has been proven by Caprara and Fischetti (Math. Program. 74:221–235, 1996) that separation of -cuts is -hard. In this paper, we study ways to separate -cuts effectively in practice. We propose a range of preprocessing rules to reduce the size of the separation problem. The core of the preprocessing builds a Gaussian elimination-like procedure. To separate the most violated -cut, we formulate the (reduced) problem as integer linear program. Some simple heuristic separation routines complete the algorithmic framework. Computational experiments on benchmark instances show that the combination of preprocessing with exact and/or heuristic separation is a very vital idea to generate strong generic cutting planes for integer linear programs and to reduce the overall computation times of state-of-the-art ILP-solvers.     

Solution of Systems of Linear Algebraic Equations with Two-Dimensional λ-Matrices

A finite-difference approach to the solution of systems of linear algebraic equations with two-dimensional -matrices of a special form is considered. Recursive relations are obtained for computing the elements of an arbitrary row of the matrix of a given system, and formulas are proposed for determination of solutions of the system.     

Uncertain jumping systems with strong and weak functional delays

This paper provides complete results on the stability behavior of a class of uncertain dynamical systems with jumping parameters and functional time-delays. The jumping parameters are modeled as a continuous-time, discrete-state Markov process. The parametric uncertainties are norm-bounded appearing in all system matrices and the delay factor depends on the mode of operation. Notions of weak and strong stochastic stability for the jumping system are developed depending on the available information using a prescribed -performance. Memoryless and delayed-state feedback are considered to guarantee the closed-loop stability. All the results are cast into linear matrix inequalities format. A numerical example is given to illustrate the developed results.     

Design and analysis of two-wire focusing actuator for small-sized ODD with linear VCM type’s actuator

Recent advancements in mobile devices have fueled a requirement for information storage systems with characteristics such as subminiature size, low cost, and minimum power consumption. Small optical disk drives could provide a good solution, because their storage media is cheaper than those of hard disk drives or flash memories. In this study, we design and analysis a linear voice coil motor (VCM) types actuator for the coarse and fine tracking motions and a two-wire spring types actuator for a fine focusing motion in order to apply them to small-sized optical disk drives of high data capacity. And, we make the mathematical model of a two-wire spring types actuator and find proper conditions to suppress the tilt motion of the lens holder for various focusing offset positions without sacrificing the sensitivity. Based on them, we design and modify the magnetic circuit and the structural part. Finally, we verify that the designed actuator had the proper dynamic characteristics and that it could be used in small optical disk drives by simulations and experiments.     

<Emphasis Type="Italic">D</Emphasis>-decomposition technique state-of-the-art

It is a survey of recent extensions and new applications for the classical D-decomposition technique. We investigate the structure of the parameter space decomposition into root invariant regions for single-input single-output systems linear depending on the parameters. The D-decomposition for uncertain polynomials is considered as well as the problem of describing all stabilizing controllers of the certain structure (for instance, PID-controllers) that satisfy given H _∞-criterion. It is shown that the D-decomposition technique can be naturally linked with M-Δ framework (a general scheme for analysis of uncertain systems) and it is applicable for describing feasible sets for linear matrix inequalities. The problem of robust synthesis for linear systems can be also treated via D-decomposition technique.     

Finite Computation of the ℓ1 Estimator from Huber’s M-Estimator in Linear Regression

We review and extend previous work on the approximation of the linear ₁ estimator by the Huber M-estimator based on the algorithms proposed by Clark and Osborne [7], and Madsen and Nielsen [12]. Although the Madsen-Nielsen algorithm is a promising one, it is guaranteed to terminate finitely under certain assumptions. We describe a variant of the Madsen-Nielsen algorithm to compute the ₁ estimator from the Huber M-estimator in a finite number of steps without any restrictive steps nor assumptions. Summary computational results are given.