Stability Criterion with Less LMI Variables for Linear Discrete-time Systems with Additive Time-delays

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality （LMI） variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

A simple criterion for finite time stability with application to impacted buckling of elastic columns

The existing theories of finite-time stability depend on a prescribed bound on initial disturbances and a prescribed threshold for allowable responses. It remains a challenge to identify the critical value of loading parameter for finite time instability observed in experiments without the need of specifying any prescribed threshold for al- lowable responses. Based on an energy balance analysis of a simple dynamic system, this paper proposes a general criterion for finite time stability which indicates that finite time stability of a linear dynamic system with constant coefficients during a given time interval [0, tf] is guaranteed provided the product of its maximum growth rate （determined by the maximum eigen-root pl 〉0） and the duration tf does not exceed 2, i.e., pltf 〈2. The proposed criterion （pltf=2） is applied to several problems of impacted buckling of elastic columns： （i） an elastic column impacted by a striking mass, （ii） longitudinal impact of an elastic column on a rigid wall, and （iii） an elastic column compressed at a constant speed （＂Hoff problem＂）, in which the time-varying axial force is replaced approximately by its average value over the time duration. Comparison of critical parameters predicted by the proposed criterion with available experimental and simulation data shows that the proposed criterion is in robust reasonable agreement with the known data, which suggests that the proposed simple criterion （pltf---2） can be used to estimate critical parameters for finite time stability of dynamic systems governed by linear equations with constant coefficients.

THE CRITERIONS FOR ABSOLUTE STABILITY OF DIRECT CONTROL SYSTEMS OF LURIE TYPE

In this paper, we give necessary and sufficient conditions for absolute stability of several classes of direct control systems, and discuss the absolute stability of the first canonical form of control system. The corresponding results in references [3,5,6] and [7] are improved.

Stability analysis of the projectile based on random center manifold reduction

The center manifold method has been widely used in the field of stochastic dynamics as a dimensionality reduction method.This paper studied the angular motion stability of a projectile system under random disturbances.The random bifurcation of the projectile is studied using the idea of the Routh-Hurwitz stability criterion,the center manifold reduction,and the polar coordinates transformation.Then,an approximate analytical presentation for the stationary probability density function is found from the related Fokker–Planck equation.From the results,the random dynamical system of projectile generates three different dynamical behaviors with the changes of the bifurcation parameter and the noise strength,which can be a reference for projectile design.

Simplified Method of Stability Analysis of Nonlinear Systems without Using of Lyapunov Concept

In this paper a new simplified method of stability study of dynamical nonlinear systems is proposed as an alternative to using Lyapunov’s method. Like the Lyapunov theorem, the new concept describes a sufficient condition for the systems to be globally stable. The proposed method is based on the assumption that, not only the state matrix contains information on the stability of the systems, but also the eigenvectors. So, first we will write the model of nonlinear systems in the state-space representation, then we use the eigenvectors of the state matrix as system stability indicators.

Dynamical investigation and parameter stability region analysis of a flywheel energy storage system in charging mode

In this paper, the dynamic behavior analysis of the electromechanical coupling characteristics of a flywheel energy storage system （FESS） with a permanent magnet （PM） brushless direct-current （DC） motor （BLDCM） is studied. The Hopf bifurcation theory and nonlinear methods are used to investigate the generation process and mechanism of the coupled dynamic behavior for the average current controlled FESS in the charging mode. First, the universal nonlinear dynamic model of the FESS based on the BLDCM is derived. Then, for a 0.01 kWh/1.6 kW FESS platform in the Key Laboratory of the Smart Grid at Tianjin University, the phase trajectory of the FESS from a stable state towards chaos is presented using numerical and stroboscopic methods, and all dynamic behaviors of the system in this process are captured. The characteristics of the low-frequency oscillation and the mechanism of the Hopf bifurcation are investigated based on the Routh stability criterion and nonlinear dynamic theory. It is shown that the Hopf bifurcation is directly due to the loss of control over the inductor current, which is caused by the system control parameters exceeding certain ranges. This coupling nonlinear process of the FESS affects the stability of the motor running and the efficiency of energy transfer. In this paper, we investigate into the effects of control parameter change on the stability and the stability regions of these parameters based on the averaged-model approach. Furthermore, the effect of the quantization error in the digital control system is considered to modify the stability regions of the control parameters. Finally, these theoretical results are verified through platform experiments.

Robust stability and stabilization for uncertain discrete-time switched singular systems with time-varying delays

The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities（LMIs）.An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms（ignored in previous methods） when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.

Comparison of Two Novel MRAS Based Strategies for Identifying Parameters in Permanent Magnet Synchronous Motors

Two model reference adaptive system （MRAS） estimators are developed for identifying the parameters of permanent magnet synchronous motors （PMSM） based on the Lyapunov stability theorem and the Popov stability criterion, respectively. The proposed estimators only need online measurement of currents, voltages, and rotor speed to effectively estimate stator resistance, inductance, and rotor flux-linkage simultaneously. The performance of the estimators is compared and verified through simulations and experiments, which show that the two estimators are simple, have good robustness against parameter variation, and are accurate in parameter tracking. However, the estimator based on the Popov stability criterion, which can overcome parameter variation in a practical system, is superior in terms of response speed and convergence speed since there are both proportional and integral units in the estimator, in contrast to only one integral unit in the estimator based on the Lyapunov stability theorem. In addition, the estimator based on the Popov stability criterion does not need the expertise that is required in designing a Lyapunov function.

Feedback Scheduling of Model-based Networked Control Systems with Flexible Workload

In this paper,a novel control structure called feedback scheduling of model-based networked control systems is proposed to cope with a flexible network load and resource constraints.The state update time is adjusted according to the real-time network congestion situation.State observer is used under the situation where the state of the controlled plant could not be acquired.The stability criterion of the proposed structure is proved with time-varying state update time.On the basis of the stability of the novel system structure,the compromise between the control performance and the network utilization is realized by using feedback scheduler. Examples are provided to show the advantage of the proposed control structure.

A DISCUSSION OF NON-LINEAR MECHANISM ON SUBTROPICAL ANTICYCLONE'S EXTENDING/SHRINKING OVER EAST-ASIA IN SUMMER

Based on the actual circulation structure as well as weather characters over East_Asia subtropical region in summer, by using three_dimension non_linear forced/dissipated dynamic model, the activities of subtropical anticyclone over East_Asia have been studied and discussed. The potential enstrophy criteria of system stability have been derived and also been analysed. The criterion can provide useful reference for analysing and predicting subtropical anticyclone's extending/shrinking as well as corresponding weather over East_Asia in summer.

The identification and criteria of short-term seismicity gap before a great earthquake

Based on the background of the medium term seismic gap, and the creep rate slow down after accelerated strain release, by using a method of gradually reducing the step length and the window length of scanning, the characteristics and criteria of a short term seismic gap have been studied from multi dimension space research. A new method for identifying a short term gap from 3 D axial stability collation has been advanced. Through the study of 26 earthquake examples in north and south west region of China, we found that a short term seismicity gap appeared in 9～16 months before a strong earthquake, this type of gap is different from the seismogenic gap, and will lasted 4～7 months, end at the time of 3～8 months before the mainshock . The ending is marked by the appearance of a significant earthquake in or near the gap (Sun and Cao, 1995) and of small earthquake in the gap.

Schur Complement Based Preconditioners for Twofold an

In this paper,we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point problems.One type of the preconditioners are based on the nested(or recursive)Schur complement,the other is based on an additive type Schur complement after permuting the original saddle point systems.We analyze different preconditioners incorporating the exact Schur complements.We show that some of them will lead to positively stable preconditioned systems if proper signs are selected in front of the Schur complements.These positive-stable preconditioners outperform other preconditioners if the Schur complements are further approximated inexactly.Numerical experiments for a 3-field formulation of the Biot model are provided to verify our predictions.

Stability Analysis of Multi-paralleled Grid-connected Inverters Including Distribution Parameter Characteristics of Transmission Lines

The sparse distribution characteristics of renewable energy resources can lead to there being tens of kilometers of transmission lines between a grid-connected inverter and the actual grid.Accurate analysis of the stability of such gridconnected inverter systems currently involves using a complex hyperbolic function to shaped model of the transmission line circuit.This has proved to be problematic,so,drawing upon the distribution parameter characteristics of transmission lines,this paper looks at how to use impedance-based stability criteria to assess the stability of multi-paralleled grid-connected inverters.First,the topology of multi-paralleled inverters connected to the grid via transmission lines is established,using each transmission line terminal as a grid connection point.Each grid-connected system is taken to be equivalent to a small-signal circuit model of the“current source-grid”.Euler’s formula and the Nyquist stability criterion are combined to assess the stability of the associated grid-connected current transfer functions and evaluate the stability of the grid-connected current.Finally,a simulation analysis circuit is constructed to verify whether power line intervention will cause stability problems in the grid-connected system.Overall,it is found that long-distance transmission lines are more likely to cause unstable output of the grid-connected current.It is also found that the number of grid-connected inverters,the short-circuit ratio(SCR),the distorted grid and the inverter parameters can all have a significant impact on the stability of the grid-connected current.

Stability Investigation and Improvement for DC Cascade Systems with Simplified Impedance-based Stability Criterion

In DC distributed power systems(DPSs),the complex impedance interactions possibly lead to DC bus voltage oscillation or collapse.In previous research,the stability analysis of DPSs is implemented based on mathematical analysis in control theory.The specific mechanisms of the instability of the cascade system have not been intuitively clarified.In this paper,the stability analysis of DPSs based on the traditional Nyquist criterion is simplified to the resonance analysis of the seriesconnected port impedance(Z=R+jX)of source and load converters.It reveals that the essential reason for impedance instability of a DC cascade system is that the negative damping characteristic(R<0)of the port the overall impedance amplifies the internal resonance source at reactance zero-crossing frequency.The simplified stability criterion for DC cascade systems can be concluded as:in the negative damping frequency ranges(R<0),there exists no zero-crossing point of the reactance component(i.e.,X=0).According to the proposed stability criterion,the oscillation modes of cascade systems are classified.A typical one is the internal impedance instability excited by the negative damping,and the other one is that the external disturbance amplified by negativity in a low stability margin.Thus,the impedance reshaping method for stability improvement of the system can be further specified.The validity of the simplified criterion is verified theoretically and experimentally by a positive damping reshaping method.

EVANS FUNCTIONS AND INSTABILITY OF A STANDING PULSE SOLUTION OF A NONLINEAR SYSTEM OF REACTION DIFFUSION EQUATIONS

In this paper, we consider a nonlinear system of reaction diffusion equa- tions arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients. The main purpose is to couple together linearized stability criterion （the equivalence of the nonlinear stability, the linear stability and the spectral sta- bility of the standing pulse solutions） and Evans functions to accomplish the existence and instability of standing pulse solutions of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equa- tions. The Evans functions for the standing pulse solutions are constructed explicitly.

Equivalence of stability criteria for time-delay systems

During the past few decades,there have been a number of new delay-dependent stability criteria based on linear matrix inequalities published in the literature.These criteria,to some extent,can reduce the conservativeness.In fact,some criteria are equivalence.In this paper,we aim to theoretically establish equivalence of two stability criteria.One was obtained by Sun et al.[Sun et al.In:Proceedings of IEEE Power&Energy Society General Meeting.2009,1–7]and the other was given by Xu et al.[Xu et al.IEEE Transactions on Automatic Control,2005,50(3):384–387].Also,we theoretically establish equivalence of the robust stability criterion presented by Jia et al.[Jia et al.Automation of Electric Power Systems,2010,34(3):6–11]and the one given by Xu et al.(2005).

STABILITY OF DELAY DIFFERENCE EQUATIONS IN BANACH SPACES

We derive stability criteria for delay difference equations in Banach spaces and illustrate our results by considering partial difference equations which model diffusion and reaction processes.

Theoretical and experimental investigation on novel 2D maglev servo proportional valve

This paper presents a novel two-dimensional maglev servo proportional cartridge valve(2 D maglev valve),where a contactless maglev coupling is introduced between electro-mechanical converter and valve body to realize functions of force transmission,spool position feedback and linear-rotary motion conversion.Such configuration can effectively reduce cost of both valve manufacturing and electro-mechanical converter,while still maintain features of 2 D valve such as null pilot leakage,high power-to-weight ratio and excellent anti-pollution capacity.Firstly,the characteristic equation of the valve is derived using linear theory,and the stability criterion is established for parameter determination.The influences of crucial structural parameters such as initial height of overlapping area,width of high-pressure and low-pressure holes,acting radius of magnetic force,pitch angle of maglev coupling,length of sensitive chamber and system pressure on the dynamic response are investigated based on AMESim numerical simulation.The prototype valve is then designed and manufactured and a special test rig is built.The no-load flow characteristic,load flow characteristic,leakage characteristic,amplitude and phase frequency characteristics and step response under different system pressures are measured.The experimental results are in a good agreement with the simulated analysis.As an over-damped system,the prototype valve has excellent working stability,which can reach a no-load flow rate of 105.9 L/min with hysteresis of 3.51%,amplitude bandwidth of 28.7 Hz and phase bandwidth of 42.8 Hz under 21 MPa.The research indicates that the 2 D maglev valve can be a potential solution of flow rate control valve for flight control surface system of civil aircraft with high pressure and large flow rate application.

A graphical tuning of PI~λ controllers for fractional-delay systems

This article provides a graphical parameter tuning method of PI^λ controllers for fractional-order time-delay systems. First, the complete stabilizing region of PI^λ controller in proportional-integral plane, for a fixed A, is determined in terms of a graphical stability criterion applicable to fractional-delay systems. Then, the stabilizing region is maximized analytically with respect to parameter ）, to expect the most various behaviors of the closed-loop systems. Finally, by defining appropriate functions relative to the requirements of gain and phase margins, the curves in the maximized stabilizing region satisfying the pre-specified gain and phase margins are drawn, which releases a flexible parameter tuning procedure. Numerical examples are given to illustrate the design steps.

Inverse Lyapunov Theorem for Linear Time Invariant Fractional Order Systems

This paper investigates the inverse Lyapunov theorem for linear time invariant fractional order systems.It is proved that given any stable linear time invariant fractional order system,there exists a positive definite functional with respect to the system state,and the first order time derivative of that functional is negative definite.A systematic procedure to construct such Lyapunov candidates is provided in terms of some Lyapunov functional equations.