MATLAB LMI工具在鲁棒稳定性分析中的应用

针对一类普遍存在的不确定时滞系统，基于线性矩阵不等式(LMI)的描述进行系统的稳定性分析，得到了用一个线性矩阵不等式系统的可行性表示的鲁棒稳定性滞后依赖型条件。介绍了如何利用MATLAB软件中的LMI工具箱进行分析与设计，据此计算出最大的允许时滞界。针对此类系统的鲁棒稳定性分析给出了数值算例。     

时滞独立的网络控制系统H∞控制器设计

介绍了网络控制系统中的时滞独立系统.利用Lyapunov稳定性定理和线性矩阵不等式(LMI)工具给出了H∞控制器存在的时滞独立网络控制系统的充分条件.通过求解一个具有线性矩阵不等式的凸优化问题,得出γ最小的H∞控制率.仿真实验结果显示,整个系统对干扰信号有较好的抑制作用.     

汽轮机/调速器系统的时滞无关分散控制器的设计

针对具有非线性关联作用和时变时滞的一类关联电力大系统,对其进行分散反馈控制。首先把非线性函数变化成子系统状态变量的二次有界不等式形式,然后基于Lyapunov稳定性理论,利用矩阵的Schur补定理及线性矩阵不等式方法,通过构造适当的Lyapunov泛函,得到了使电力系统渐近稳定的时滞无关的充分条件,并作为特例,给出了常...     

基于磁流变减振器的半主动悬架时滞变结构控制

针对控制输入通道中存在的时滞对磁流变半主动悬架系统控制品质的影响,建立含时滞的1/4汽车磁流变半主动悬架模型。从磁流变半主动悬架系统的时滞微分方程出发,根据滑模变结构控制理论设计出磁流变半主动悬架系统时滞依赖滑模控制器。通过理论推导,利用线性矩阵不等式(Linear matrix inequality,LMI)处理方法把系统时滞稳定的条件转化为LMI可行性分析,保证系统稳定的最大临界时滞求取转化成LMI中的广义特征值最小化问题。Matlab/Simulink仿真及道路模拟振动台上实车试验结果表明,在系统临界时滞范围内,时滞依赖滑模控制器能从根本上保证系统的稳定性,削弱时滞对系统控制效果的影响,有效地改善汽车的乘坐舒适性。     

具有参数摄动的时滞系统鲁棒控制

本文给出了具有参数摄动的时滞自治系统二次稳定充分条件，该条件为－Ｒｉｃｃａｔｉ不等式。进而将具有参数摄动的时滞系统鲁棒控制问题等效为Ｈ∞标准设计问题。     

基于多项式判别理论时滞半主动悬架稳定性研究

基于多项式判别理论研究车辆时滞半主动悬架系统失稳机理，得出了悬架系统的失稳条件及其失稳临界时滞，为半主动悬架系统时滞控制研究提供了依据。应用数值仿真的方法分析时滞对悬架系统稳定性的影响，并在自行研制的1：1物理模型半主动悬架试验系统上进行了台架试验。结果表明，基于多项式理论研究时滞半主动悬架稳定性的方法简单，得出的稳定性条件可靠，为半主动悬架及其控制系统设计和分析奠定了基础。     

广域测量时变时滞电力系统鲁棒稳定性的新判据

针对某一增广的Lyapunov-Krasovskii函数,利用二阶Bessel-Legendre不等式和改进的逆凸不等式方法导出了稳定性判据,并在求导过程中对改进的广义Lyapunov-Krasovskii函数的积分项进行分段处理,避免缩放性误差。通过单机无穷大系统进行实例仿真,得出系统时滞稳定裕度的计算结果,由此实现了对这一方法有效性与可行性的成功验证。     

含时滞天棚阻尼半主动悬架建模及稳定性分析

为研究时滞对天棚阻尼半主动悬架动态特性及稳定性的影响,建立含时滞的二自由度半主动悬架模型,运用稳定性判据对该悬架系统进行时滞稳定性分析,提出悬架失稳临界时滞及其稳定裕度求取的分析理论及其计算方法;利用数值解法求出悬架系统临界时滞,得到不同基值阻尼和天棚阻尼增益下悬架系统失稳的临界时滞量及全(非全)时滞稳定域;通过建立含时滞半主动悬架系统仿真模型,分析得到时滞对悬架系统动特性及稳定性的影响规律。     

一类非线性时滞系统的迭代学习控制设计

为了研究时滞对非线性系统的迭代学习控制收敛性的影响,采用了λ范数和一系列不等式技术,通过建立精确的数学模型,分析了在PD学习律下的Hopfield非线性神经网络系统。在全局Lipschi-tz连续条件下,研究了确保系统跟踪误差收敛的充分条件。理论推导证明时滞对这类非线性系统的迭代学习控制系统的收敛性没有显著的影响,仿真结果表明,迭代学习控制可以实现对非线性时滞系统的精确轨迹跟踪。     

一类时滞线性系统的变结构振动控制

应用自适应性和鲁棒性良好的变结构控制理论，研究时滞影响下机械和结构的振动问题，给出控制律的等速趋近律设计方法和系统稳定性与时滞量无关的判据，排除时滞带给系统稳定性分析的困扰。算例结果表明，所提出的变结构控制方法能有效地减小时滞振动系统的峰值响应，系统保持稳定。     

Robust absolute stability criteria for uncertain Lurie interval time-varying delay systems of neutral type

This study investigates the delay-dependent robust absolute stability analysis for uncertain Lurie systems with interval time-varying delays of neutral type. First, we divide the whole delay interval into two segmentations with an unequal width and checking the variation of the Lyapunov–Krasovskii functional (LKF) for each subinterval of delay, much less conservative delay-dependent absolute and robust stability criteria are derived. Second, a new delay-dependent robust stability condition for uncertain Lurie neutral systems with interval time-varying delays, which expressed in terms of quadratic forms of linear matrix inequalities (LMIs), and has been derived by constructing the LKF from the delayed decomposition approach (DDA) and integral inequality approach (IIA). Finally, three numerical examples are given to show the effectiveness of the proposed stability criteria.     

Passivity-based sliding mode control for a polytopic stochastic differential inclusion system

Passivity-based sliding mode control for a polytopic stochastic differential inclusion (PSDI) system is considered. A control law is designed such that the reachability of sliding motion is guaranteed. Moreover, sufficient conditions for mean square asymptotic stability and passivity of sliding mode dynamics are obtained by linear matrix inequalities (LMIs). Finally, two examples are given to illustrate the effectiveness of the proposed method.     

Stability analysis for discrete-time switched systems with unstable subsystems by a mode-dependent average dwell time approach

This paper mainly intends to present new stability results of a discrete-time switched system with unstable subsystems. By adopting multiple Lyapunov functions? (MLFs?) method, new and less conservative stability conditions are derived in terms of a set of numerical feasible linear matrix inequalities (LMIs) with mode-dependent average dwell time (MDADT) techniques. Different from previous literatures, unstable subsystems are considered under two situations in this paper. It is shown that the discrete-time switched system can achieve exponential stability under a slow switching scheme and even in the presence of fast switching of unstable subsystems. Finally a numerical example is given to demonstrate the effectiveness of the proposed method.     

Stability analysis of neutral type neural networks with mixed time-varying delays using triple-integral and delay-partitioning methods

This paper investigates the asymptotical stability problem for a class of neutral type neural networks with mixed time-varying delays. The system not only has time-varying discrete delay, but also distributed delay, which has never been discussed in the previous literature. Firstly, improved stability criteria are derived by employing the more general delay partitioning approach and generalizing the famous Jensen inequality. Secondly, by constructing a newly augmented Lyapunov–Krasovskii functionals, some less conservative stability criteria are established in terms of linear matrix inequalities (LMIs). Finally, four numerical examples are given to illustrate the effectiveness and the advantage of the proposed main results.     

Event-triggered control design of linear networked systems with quantizations

This paper is concerned with the control design problem of event-triggered networked systems with both state and control input quantizations. Firstly, an innovative delay system model is proposed that describes the network conditions, state and control input quantizations, and event-triggering mechanism in a unified framework. Secondly, based on this model, the criteria for the asymptotical stability analysis and control synthesis of event-triggered networked control systems are established in terms of linear matrix inequalities (LMIs). Simulation results are given to illustrate the effectiveness of the proposed method.     

Mixed H2/Hinfinity output-feedback control of second-order neutral systems with time-varying state and input delays

A mixed H2/Hinfinity output-feedback control design methodology is presented in this paper for second-order neutral linear systems with time-varying state and input delays. Delay-dependent sufficient conditions for the design of a desired control are given in terms of linear matrix inequalities (LMIs). A controller, which guarantees asymptotic stability and a mixed H2/Hinfinity performance for the closed-loop system of the second-order neutral linear system, is then developed directly instead of coupling the model to a first-order neutral system. A Lyapunov-Krasovskii method underlies the LMI-based mixed H2/Hinfinity output-feedback control design using some free weighting matrices. The simulation results illustrate the effectiveness of the proposed methodology.     

Improved delay-dependent stability analysis for neural networks with time-varying delays

In this paper, the problem of delay-dependent asymptotic stability analysis for neural networks with time-varying delays is considered. A new class of Lyapunov functional is proposed by considering the information of neuron activation functions adequately. By using the delay-partitioning method and the reciprocally convex technique, some less conservative stability criteria are obtained in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are given to illustrate the effectiveness of the derived method.     

Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system

A robust fuzzy control method for fractional order hydro-turbine governing system (FOHGS) in the presence of random disturbances is investigated in this paper. Firstly, the mathematical model of FOHGS is introduced, and based on Takagi-Sugeno (T-S) fuzzy rules, the generalized T-S fuzzy model of FOHGS is presented. Secondly, based on fractional order Lyapunov stability theory, a novel T-S fuzzy control method is designed for the stability control of FOHGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed fractional order T-S fuzzy control scheme works well compared with the existing method.     

Sampled-data-based vibration control for structural systems with finite-time state constraint and sensor outage

The problem of sampled-data-based vibration control for structural systems with finite-time state constraint and sensor outage is investigated in this paper. The objective of designing controllers is to guarantee the stability and anti-disturbance performance of the closed-loop systems while some sensor outages happen. Firstly, based on matrix transformation, the state-space model of structural systems with sensor outages and uncertainties appearing in the mass, damping and stiffness matrices is established. Secondly, by considering most of those earthquakes or strong winds happen in a very short time, and it is often the peak values make the structures damaged, the finite-time stability analysis method is introduced to constrain the state responses in a given time interval, and the H-infinity stability is adopted in the controller design to make sure that the closed-loop system has a prescribed level of disturbance attenuation performance during the whole control process. Furthermore, all stabilization conditions are expressed in the forms of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using the LMI Toolbox. Finally, numerical examples are given to demonstrate the effectiveness of the proposed theorems.