The Analysis of Global Input-to-state Stability for Piecewise Affine Systems with Time-delay

In this paper, global input-to-state stability （ISS） for discrete-time piecewise affine systems with time-delay are considered Piecewise quadratic ISS-Lyapunov functions are adopted. Both Lyapunov-Razumikhiu and Lyapunov-Krasovskii methods are used The theorems of Lyapunov-Razumikhin type and Lyapunov-Krasovskii type for piecewise affine systems with time-delay are shown respectively.

Electronic Structure Research on Lattice Stability of V, Nb, and Ta by Density Functional Theory

The difference of energy and electronic structure of V, Nb, and Ta in different crystalline structures were investigated by different methods in density functional theory （DFT）. Lattice constants, total energies, and densities of states of these metals were calculated using the plane-wave pseudopotential method in DFT. Results were compared with those of projector augmented wave method, CALPHAD method, and experiments. Total energy and electronic structure analyses showed that valence electrons mostly transferred from s to p or d state, changing obviously with both the crystal structure and the elemental period number from V to Ta and leading to stronger cohesion, higher cohesive energy and more stable lattice of heavier metals.

Controlling chaos in permanent magnet synchronous motor based on finite-time stability theory

This paper reports that the performance of permanent magnet synchronous motor （PMSM） degrades due to chaos when its systemic parameters fall into a certain area. To control the undesirable chaos in PMSM, a nonlinear controller, which is simple and easy to be constructed, is presented to achieve finite-time chaos control based on the finite-time stability theory. Computer simulation results show that the proposed controller is very effective. The obtained results may help to maintain the industrial servo driven system＇s security operation.

Stability analysis of shallow tunnels subjected to seepage with strength reduction theory

Based on strength reduction theory,the stability numbers of shallow tunnels were investigated within the framework of upper and lower bound theorems of limit analysis. Stability solutions taking into account of water seepage were presented and compared with those without considering seepage. The comparisons indicate that the maximum difference does not exceed 3.7%,which proves the present method credible. The results show that stability numbers of shallow tunnels considering seepage are much less than those without considering seepage,and that the difference of stability numbers between considering seepage and without considering seepage increase with increasing the depth ratio. The stability numbers decrease with increasing permeability coefficient and groundwater depth. Seepage has significant effects on the stability numbers of shallow tunnels.

Analysis on stability of strategic alliance: A game theory perspective

Strategic alliance has suffered much instabilities since its first implementation. Scholars have carried out many em- bedded, precise and comprehensive researches from both theory and empiricism. Here we try to find certain stable solutions by employing game theory, in an attempt to construct theoretical bases for strategic alliance, which people called “one of the most important organizational innovation in the end of the 20th century” (Shi, 2001), to exploit its advantages in the process of glob- alization. Finally, this article puts forward some advices for its success.

AN APPLICATION OF EXTENSION THEORY TO THE EVALUATION OF SLOPE STABILITY

The slope stability is affected by multiple factors. Thecomprehensive evaluation of the slope stability is a complicateproblem. The principles of extension theory have been used in thispaper to establish the matter-element model for the evaluation ofslope stability. The quantitative evaluated results have been giventhrough the calculation of the matter-element dependent degree.

Stability of Spatial Structure of Urban Agglomeration in China Based on Central Place Theory

This paper brings forward the concept of stability of the spatial structure of urban agglomeration(UA)based on Central Place Theory by introducing centrality index and fractal theory.Before assessment,K=4 is selected as parameter to calculate centrality index and fractal dimension(K represents the quantitive relationship between city and the counties in Central Place Theory),and then found the number of nodes,the type of spatial structure,the spatial allocation of nodes with different hierarchy affecting the stability of spatial structure.According to spatial contact direction and the level of stability,UAs in China are classified into five types.Finally,it is posed as a further question that how to use hierarchical relation K=6 and K=7 in central place system to coordinate with the assessment of stability of soatial structure is brought forward.

Input-to-State Stabilization of Nonlinear Impulsive Delayed Systems: An Observer-Based Control Approach

This paper addresses the problems of input-to-state stabilization and integral input-to-state stabilization for a class of nonlinear impulsive delayed systems subject to exogenous dis-turbances.Since the information of plant’s states,time delays,and exogenous disturbances is often hard to be obtained,the key design challenge,which we resolve,is the construction of a state observer-based controller.For this purpose,we firstly propose a corresponding observer which is independent of time delays and exogenous disturbances to reconstruct(or estimate)the plant’s states.And then based on the observations,we establish an observer-based control design for the plant to achieve the input-to-state stability(ISS)and integral-ISS(iISS)properties.With the help of the comparison principle and average impulse interval approach,some sufficient conditions are presented,and moreover,two different linear matrix inequalities(LMIs)based criteria are proposed to design the gain matrices.Finally,two numerical examples and their simulations are given to show the effectiveness of our theoretical results.

Stability condition of FAST TCP in high speed network on the basis of control theory

Considering the instability of data transferred existing in high speed network, a new method is proposed for improving the stability using control theory. Under this method, the mathematical model of such a network is established. Stability condition is derived from the mathematical model. Several simulation experiments are performed. The results show that the method can increase the stability of data transferred in terms of the congestion window, queue size, and sending rate of the source.

Forced oscillations and stability analysis of a nonlinear micro-rotating shaft incorporating a non-classical theory

In this paper,the stability and bifurcation analysis of symmetrical and asymmetrical micro-rotating shafts are investigated when the rotational speed is in the vicinity of the critical speed.With the help of Hamilton's principle,nonlinear equations of motion are derived based on non-classical theories such as the strain gradient theory.In the dynamic modeling,the geometric nonlinearities due to strains,and strain gradients are considered.The bifurcations and steady state solution are compared between the classical theory and the non-classical theories.It is observed that using a non-classical theory has considerable effect in the steady-state response and bifurcations of the system.As a result,under the classical theory,the symmetrical shaft becomes completely stable in the least damping coefficient,while the asymmetrical shaft becomes completely stable in the highest damping coefficient.Under the modified strain gradient theory,the symmetrical shaft becomes completely stable in the least total eccentricity,and under the classical theory the asymmetrical shaft becomes completely stable in the highest total eccentricity.Also,it is shown that by increasing the ratio of the radius of gyration per length scale parameter,the results of the non-classical theory approach those of the classical theory.

Effect of graph generation on slope stability analysis based on graph theory

Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.

Stability Analysis of Transfer Alignment Filter Based on theμTheory

The performance of the transfer alignment has great impact on inertial navigation systems.As the transfer alignment is generally implemented using a filter to compensate the errors,its accuracy,rapidity and anti-disturbance capability are key properties to evaluate the filtering process.In terms of the superiority in dealing with the noise,H∞filtering has been used to improve the anti-disturbance capability of the transfer alignment.However,there is still a need to incorporate system uncertainty due to various dynamic conditions.Based on the structural value theory,a robustness stability analysis method has been proposed for the transfer alignment to evaluate the impact of uncertainty on the navigation system.The mathematical derivation has been elaborated in this paper,and the simulation has been carried out to verify the effectiveness of the algorithm.

Stability Analysis of a Single-Degree-of Freedom Mechanical Model with Distinct Critical Points: I. Bifurcation Theory Approach

The buckling and post-buckling response of a single-degree-of-freedom mechanical model is re-examined in this work, within the context of nonlinear stability and bifurcation theory. This system has been reported in pioneer as well as in more recent literature to exhibit all kinds of distinct critical points. Its response is thoroughly discussed, the effect of all parameters involved is extensively examined, including imperfection sensitivity, and the results obtained lead to the important conclusion that the model is possibly associated with the butterfly singularity, a fact which will be validated by the contents of a companion paper, based on catastrophe theory.

THE RE-EXAMINATION OF THE WEAKLY NONLINEAR THEORY OF HYDRODYNAMIC STABILITY

The weakly nonlinear theory has been widely applied in the problem of hydrodynamic stability and also in other fields. However, although its application has been successful for some problems, yet, for other problems, the results obtainedhre not satisfactory, especially for problems like transition or the evolution of the vortex in the free shear flow, for which the goal of the theoretical investigation is not seeking for a steady state, but predicting an evolutional process. In this paper, we shall examine the reason for the unsuccessfulness and suggest ways for its amendment.

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

Analysis of grid-connected voltage stability of FSCWT based on bifurcation theory

This paper studies on the change mechanisms of the voltage stability caused by the grid connection of front-end speed-controlled wind turbines(FSCWT)integrating into power system.First of all,the differential algebraic equations describing the dynamic characteristics of wind turbines are illustrated.Then,under the guidance of IEEE3 node system model,the influence of the angular velocity of wind turbines,the reactive power and the active power at load bus on the voltage stability of grid-connection has been analyzed by using bifurcation theory.Finally,the method of linear-state feedback control has been applied to the original system in accordance with the bifurcation phenomenon of grid-connected voltage caused by the increase in the active power at load bus.Research shows that voltage at the grid-connected point would be changed with the fluctuation of turbines angular velocity.And increasing its reactive power can enhance voltage at the grid-connected point;problem of bifurcation at the grid-connected point can be delayed when increasing the gain k s of feedback controller within a certain range.

Stability Analysis of a SDOF Mechanical Model with Distinct Critical Points: II. Catastrophe Theory Approach

In a recent publication [1], the fully nonlinear stability analysis of a Single-Degree-of Freedom (SDOF) model with distinct critical points was dealt with on the basis of bifurcation theory, and it was demonstrated that this system is associated with the butterfly singularity. The present work is the companion one, tackling the problem via the Theory of Catastrophes. After Taylor expanding the original potential energy function and introducing Padè approximants of the trigonometric expression involved, the resulting truncated potential is a universal unfolding of the original one and an extended canonical form of the butterfly catastrophe potential energy function. Results in terms of equilibrium paths, bifurcation sets and manifold hyper-surface projections fully validate the whole analysis, being in excellent agreement with the findings obtained via bifurcation theory.

ON THE STABILITY OF DISTORTED LAMINAR FLOW(Ⅰ)—BASIC IDEAS AND THEORY

This paper suggests a hydrodynamic stability theory of distorted laminar flow, and presents a kind of distortion profile of mean velocity in parallel shear flow. With such distortion profiles, the new theory can be used to investigate the stability behaviour of parallel shear flow, and thus suggests a new possible approach to instability.

Practical φ_0-stability of stochastic differential equations and corresponding stochastic perturbation theory

The notions of practical φ0-stability were introduced for stochastic differential equations. Sufficient conditions on such practical properties were obtained by using the comparison principle and the cone-valued Lyapunov function methods. Based on an extended comparison theorem, a perturbation theory of stochastic differential systems was given.

Thermal stability and Judd-Ofelt analysis of optical properties of Er^(3+)-doped tellurite glasses

Er3＋-doped TeO2-ZnO-Na2O-B2O3-GeO2 （TZNBG） glasses were prepared by melt-quenching method. Differential scanning calorimetry （DSC） and thermal mechanical analysis （TMA） were used to calculate thermal parameters： crystallization temperature （Tx）, glass transition temperature （Tg） and thermal expansion （α）. Besides, Judd-Ofelt theory is applied to analyzing absorption spectra. Intensity parameters -λ （λ=2, 4, 6）, transition probabilities Aed, radiative lifetime τi, and branching ratios β of Er3＋ transitions were obtained. Emission cross-section σemis of 4I13/2→4I15/2 transition of Er3＋ was calculated according to the theory of McCumber. All of the parameters indicate that the thermal stability and optical properties of Er3＋-doped TZNBG glasses are improved effectively.