Global stabilization of linear periodically time-varying switched systems via matrix inequalities

In this paper, we address the stabilization problem for linear periodically time-varying switched systems. Using discretization technique, we derive new conditions for the global stabilizability in terms of the solution of matrix inequalities. An algorithm for finding stabilizing controller and switching strategy is presented.

Periodic signal extraction of GNSS height time series based on adaptive singular spectrum analysis

Singular spectrum analysis is widely used in geodetic time series analysis.However,when extracting time-varying periodic signals from a large number of Global Navigation Satellite System(GNSS)time series,the selection of appropriate embedding window size and principal components makes this method cumbersome and inefficient.To improve the efficiency and accuracy of singular spectrum analysis,this paper proposes an adaptive singular spectrum analysis method by combining spectrum analysis with a new trace matrix.The running time and correlation analysis indicate that the proposed method can adaptively set the embedding window size to extract the time-varying periodic signals from GNSS time series,and the extraction efficiency of a single time series is six times that of singular spectrum analysis.The method is also accurate and more suitable for time-varying periodic signal analysis of global GNSS sites.

Wave localization in randomly disordered periodic layered piezoelectric structures

Considering the mechnoelectrical coupling, the localization of SH-waves in disordered periodic layered piezoelectric structures is studied. The waves propagating in directions normal and tangential to the layers are considered. The transfer matrices between two consecutive unit cells are obtained according to the continuity conditions. The expressions of localization factor and localization length in the disordered periodic structures are presented. For the disordered periodic piezoelectric structures, the numerical results of localization factor and localization length are presented and discussed. It can be seen from the results that the frequency passbands and stopbands appear for the ordered periodic structures and the wave localization phenomenon occurs in the disordered periodic ones, and the larger the coefficient of variation is, the greater the degree of wave localization is. The widths of stopbands in the ordered periodic structures are very narrow when the properties of the consecutive piezoelectric materials are similar and the intervals of stopbands become broader when a certain material parameter has large changes. For the wave propagating in the direction normal to the layers the localization length has less dependence on the frequency, but for the wave propagating in the direction tangential to the layers the localization length is strongly dependent on the frequency.

Wave propagation control in periodic track structure through local resonance mechanism

Excessive vibration and noise radiation of the track structure can be caused by the operation of high speed trains.Though the track structure is characterized by obvious periodic properties and band gaps,the bandwidth is narrow and the elastic wave attenuation capability within the band gap is weak.In order to effectively control the vibration and noise of track structure,the local resonance mechanism is introduced to broaden the band gap and realize wave propagation control.The locally resonant units are attached periodically on the rail,forming a new locally resonant phononic crystal structure.Then the tuning of the elastic wave band gaps of track structure is discussed,and the formation mechanism of the band gap is explicated.The research results show that a new wide and adjustable locally resonant band gap is formed after the resonant units are introduced.The phenomenon of coupling and transition can be observed between the new locally resonant band gap and the original band gap of the periodic track structure with the band gap width reaching the maximum at the coupling position.The broader band gap can be applied for vibration and noise reduction in high speed railway track structure.

Band gap analysis of periodic structures based on cell experimental frequency response functions(FRFs)

An approach is proposed to estimate the transfer function of the periodic structure, which is known as an absorber due to its repetitive cells leading to the band gap phenomenon. The band gap is a frequency range in which vibration will be inhibited. A transfer function is usually performed to gain band gap. Previous scholars regard estimation of the transfer function as a forward problem assuming known cell mass and stiffness matrices. However, the estimation of band gap for irregular or complicated cells is hardly accurate because it is difficult to model the cell exactly. Therefore, we treat the estimation as an inverse problem by employing modal identification and curve fitting. A transfer matrix is then established by parameters identitled through modal analysis. Both simulations and experiments have been performed. Some interesting conclusions about the relationship between modal parameters and band gap have been achieved.

Existence and Stability Property of Almost Periodic Solutions in Discrete Almost Periodic Systems

In this paper, we consider an almost periodic system which includes a system of the type , where k is a positive integer, aij are almost periodic in n and satisfy aij(n)≥0 for i≠j,? for 1≤j≤m. In the special case where aij(n) are constant functions, above system is a mathematical model of gas dynamics and was treated by T. Carleman and R. D. Jenks for differential systems. In the main theorem, we show that if the m X m matrix (aij(n)) is irreducible, then there exists a positive almost periodic solution which is unique and has some stability. Moreover, we can see that this result gives R. D. Jenks’ result for differential model in the case where aij(n) are constant functions. In Section 3, we consider the linear system with variable cofficients . Even in nonlinear problems, this linear system plays an important role, as their variational equations, and it is requested to determine the uniform asymptotically stability of the zero solution from the information about A(n). In order to obtain the existence of almost periodic solutions of both linear and nonlinear almost periodic discrete systems: above linear system and? for 1≤i≤m, respectively, we shall consider between certain stability properties, which are referred to as uniformly asymptotically stable, and the diagonal dominance matrix condition.

Stability of Nonlinear Feedback Shift Registers with Periodic Input

The stability of Non-Linear Feedback Shift Registers(NFSRs)plays an important role in the cryptographic security.Due to the complexity of nonlinear systems and the lack of efficient algebraic tools,the theorems related to the stability of NFSRs are still not well-developed.In this paper,we view the NFSR with periodic inputs as a Boolean control network.Based on the mathematical tool of semi-tensor product(STP),the Boolean network can be mapped into an algebraic form.Through these basic theories,we analyze the state space of non-autonomous NFSRs,and discuss the stability of an NFSR with periodic inputs of limited length or unlimited length.The simulation results are provided to prove the efficiency of the model.Based on these works,we can provide a method to analyze the stability of the NFSR with periodic input,including limited length and unlimited length.By this,we can efficiently reduce the computational complexity,and its efficiency is demonstrated by applying the theorem in simulations dealing with the stability of a non-autonomous NFSR.

A METHOD OF CALCULATING PRESSURE DISTRIBUTION OF PERIODIC PULSATION FLUID TRANSPORTED IN PIPING NETWORK

The pressure pulsation induced by the pumped periodic pulsation fluid is the main factor of causing fluid resonance and stimulating pipelines vibrations and noise. In order to reduce the faults caused by the vibrations of pipelines, two aspects have been researched: one is to develop high quality filters, weaken and restrain the crest of pulsation pressure; the other is to design structural parameters of the piping network and eliminate the fluid resonance. Both need calculating the pressure pulsations of different structural parameters and frequencies, and knowing the amplitude frequency. In this paper the stiffness matrix technique is used for treating the coupling of subsystems of pipelines and calculating the pressure distribution of the piping network and it is tested by simulation and experiments.

WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODIC PIEZOELECTRIC RODS

在周期、混乱的周期的压电的杆的波浪繁殖在这篇论文被学习。在二个连续单位房间之间的转移矩阵根据连续性条件被获得。压电的材料的机电的联合被考虑。根据矩阵特征值的理论，在周期的结构的频率乐队被学习。而且，由在两个介绍混乱尺寸更少长度和压电的陶艺的有弹性的常数，在混乱周期的结构的波浪本地化被使用矩阵特征值方法和 Lyapunov 代表方法也学习。调节了周期的结构，这被发现让频率通带和站乐队和本地化现象能发生在错误调子周期的结构。由于压电的效果，而且，为不能通过结构宣传的波浪的频率区域稍微随压电的常数的增加被增加。

Robust Stabilization for Linear Time-varying Uncertain Periodic Descriptor Systems

这个问题赶出为线性变化时间的不明确的周期的描述符系统的稳定被重游。为线性变化时间的不明确的周期的描述符系统基于柔韧的稳定性的概念，为柔韧的稳定性的一个必要、足够的条件被提出。柔韧的稳定问题也被学习，相应必要、足够的条件用双系统的符号被给。获得的矩阵不平等条件能被转变到与一些免费矩阵的介绍的线性矩阵不平等一，它使分析和设计过程简单、可靠。

ELASTIC WAVE LOCALIZATION IN TWO-DIMENSIONAL PHONONIC CRYSTALS WITH ONE-DIMENSIONAL QUASI-PERIODICITY AND RANDOM DISORDER

The band structures of both in-plane and anti-plane elastic waves propagating in two-dimensional ordered and disordered （in one direction） phononic crystals are studied in this paper. The localization of wave propagation due to random disorder is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the quasi-periodicity as the deviation from the periodicity in a special way, two kinds of quasi phononic crystal that has quasi-periodicity （Fibonacci sequence） in one direction and translational symmetry in the other direction are considered and the band structures are characterized by using localization factors. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional perfect, randomly disordered and quasi-periodic phononic crystals. Band structures of the phononic crystals can be tuned by different random disorder or changing quasi-periodic parameters. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.

ASYMPTOTIC HOMOGENIZATION IN A PARABOLIC SEMILINEAR PROBLEM WITH PERIODIC COEFFICIENTS AND INTEGRABLE INITIAL DATA

In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.

Analysis and control of a class of uncertain linear periodic discrete-time systems

Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.

Exponential stability and periodic solution for fuzzy BAM Neural networks with time varying delays

In this paper, a class of fuzzy BAM neural networks with time varying delays is discussed. By using the properties of M-matrix, Linear Matrix Inequality（LMI） approach and general Lyapunov-Krasovskii functional, some new sufficient conditions are derived to ensure the existence of periodic solutions and the global exponential stability of the fuzzy BAM neural networks with time varying delays. These results have important significance in the design of global exponential stable BAM networks with delays. Moreover, an example is given to illustrate that the conditions of the results in the paper are feasible.

Phase diagram,correlations,and quantum critical point in the periodic Anderson model

Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matriX embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin-spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin-spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.

Imaging a periodic moving/state-changed object with Hadamard-based computational ghost imaging

We propose a method for imaging a periodic moving/state-changed object based on computational ghost imaging with Hadamard speckle patterns and a slow bucket detector, named as PO-HCGI. In the scheme, speckle patterns are produced from a part of each row of a Hadamard matrix. Then, in each cycle, multiple speckle patterns are projected onto the periodic moving/state-changed object, and a bucket detector with a slow sampling rate records the total intensities reflected from the object as one measurement. With a series of measurements, the frames of the moving/state-changed object can be obtained directly by the second-order correlation function based on the Hadamard matrix and the corresponding bucket detector measurement results. The experimental and simulation results demonstrate the validity of the PO-HCGI. To the best of our knowledge, PO-HCGI is the first scheme that can image a fast periodic moving/state-changed object by computational ghost imaging with a slow bucket detector.

Analysis of the Mode of the Periodically Time-varying Vibration Systems

By Liapunov reducibility theorem, the periodically time-varying vibration system can be transformed to a linear time-invariant system. Based on the dynamic characteristics of the linear time-invariant system, the mode of the periodically time-varying vibration system has been discussed. The paper defines the mode and analyzes its characteristics. It can be found that the mode of the periodically time-varying system is periodically time-varing but has such characteristics as orthogonality. Finally, a method is given to solve the mode. By solving the eigenvalues and the eigenvectors of the state transition matrix in one period, the periodically time-varying mode can be obtained.

Stability analysis of networked control systems with time-varying sampling periods

In this paper, we present an interval model of networked control systems with time-varying sampling periods and time-varying network-induced delays and discuss the problem of stability of networked control systems using Lyapunov stability theory. A sufficient stability condition is obtained by solving a set of linear matrix inequalities. In the end, the illustrative example demonstrates the correctness and effectiveness of the proposed approach.

H_∞ Controller Design for Networked Control Systems via Active-varying Sampling Period Method

这份报纸学习由使用一个活跃变化的采样时期方法与两导致网络的时间延期和包退学学生为联网的控制系统(NCS ) 设计 H 控制器的问题，在采样时期在一个有限集合切换的地方。一个新奇线性基于评价的方法被建议补偿包退学学生，和 H 控制器设计被使用多客观的优化方法论也介绍。模拟结果说明活跃变化的采样时期方法和线性基于评价的包退学学生赔偿的有效性。

液晶填充一维阶梯型Double-period结构局域模的调控特性

利用传输矩阵法研究了向列相液晶填充一维阶梯型Double-period第4代准周期结构局域模的电场方向、外界温度调控特性。通过改变电场方向和外界温度,研究该结构透射谱的调控特性。结果表明：温度一定时,液晶的有效折射率都随着夹角θ的增大而逐渐减小,局域模波长随夹角θ的增大而发生蓝移;当夹角θ接近54°时,向列相液晶的有效折射率与温度呈现近正比线性关系;夹角θ小于54°时,向列相液晶的有效折射率随温度升高而逐渐减小,局域模波长随外界温度（300~378.15K）的升高而发生蓝移;夹角θ大于54°时,随温度升高,向列相液晶的有效折射率先减小后增大,局域模波长先发生蓝移再发生红移。无论是外界温度升高还是电场方向夹角的增大,局域模的调控量始终是减小的,且局域模的调控量与液晶有效折射率差值成正比线性关系。