基于模糊Lyapunov-Krasovskii函数的离散时滞T-S模糊模型的非二次镇定条件

研究了离散时滞T-S模糊模型基于模糊Lyapunov-Krasovskii函数的稳定性分析及控制器设计问题.首先,构造出离散型模糊Lyapunov-Krasovskii函数,此函数是系数与T-S模糊模型的模糊规则权重相对应的复合型Lyapunov-Krasovskii函数.然后,基于一系列线性矩阵不等式,得到了开环系统稳定的充分条件,进而又基于非二次PDC控制律,设计出了模糊控制器.最后,仿真实例验证了该方法的有效性和优越性.

基于模糊Lyapunov-Krasovskii函数的模糊系统的鲁棒H_∞控制

针对公共Lyapunov-krasovskii函数(LKF)方法判断离散时滞模糊系统鲁棒稳定性的保守性,构造了模糊LKF,并给出了系统鲁棒稳定的充分条件。应用并行分布补偿算法(PDC),设计了全局鲁棒稳定的模糊控制器。多个附加矩阵变量的引入,使控制器可以通过求解一系列线性矩阵不等式(LMI)获得。最后,通过一个仿真例子验证了方法的有效性。

基于模糊Lyapunov-Krasovskii函数的T-S模糊系统的H_∞控制

研究了离散时滞T-S模糊系统基于模糊Lyapunov-Krasovskii函数的H∞控制问题.通过构造离散型模糊Lyapunov-Krasovskii函数,首先给出了一个使得T-S模糊系统渐近稳定的充分条件,然后给出了相应的H∞控制器的设计方法,该设计方法保证了模糊闭环系统内部渐近稳定并满足从干扰输入到控制输出的H∞范数界约束,且具有较少的保守性.最后通过仿真实例,验证了该方法的有效性.

Non-Monotonic Lyapunov-Krasovskii Functional Approach to Stability Analysis and Stabilization of Discrete Time-Delay Systems

In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities(LMIs)to study the global asymptotic stability of state-delay systems.Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a p H neutralizing process are provided to demonstrate the efficacy of the proposed method.

A new approach to stability analysis of neural networks with time-varying delay via novel Lyapunov-Krasovskii functional

In this paper, new delay-dependent stability criteria for asymptotic stability of neural networks with time-varying delays are derived. The stability conditions are represented in terms of linear matrix inequalities （LMIs） by constructing new Lyapunov-Krasovskii functional. The proposed functional has an augmented quadratic form with states as well as the nonlinear function to consider the sector and the slope constraints. The less conservativeness of the proposed stability criteria can be guaranteed by using convex properties of the nonlinear function which satisfies the sector and slope bound. Numerical examples are presented to show the effectiveness of the proposed method.

基于Lyapunov-krasovskii泛函的线性时滞系统低保守性研究

针对带有线性的时滞系统稳定性与低保守性是该领域研究的主要问题。由此提出基于Lyapunov-krasovskii泛函的线性时滞系统低保守性研究方法。对Lyapunov-krasovskii泛函进行构造,将自由权矩阵的牛顿-莱布尼兹的公式引入到Lyapunov-krasovskii泛函分析中,对泛函导数的交叉项进行界定,基于Lyapunov的稳定性的定理,得出线性矩阵时滞相关的稳定性准则,并由数值的算例表明,该稳定性的准则能使时滞系统得到更大时滞的上界,具有较好的稳定性,与当前存在的结果相对比具有更低的保守性。

时滞切换系统指数稳定性分析:Lyapunov-Krasovskii泛函方法

考虑由两个线性时滞子系统构成的切换系统,分析其在任意切换序列作用下保持指数稳定性的条件.分别利用二次型与逐段二次型的Lyapunov-Krasovskii泛函构造方式给出了以线性矩阵不等式所表述的稳定性判据;进而通过状态变量代换结合积分不等式技巧证明了指数衰减率对于所有切换序列一致成立,即其完全取决于系统的结构特征.最后给出了一个算例.

考虑时变时滞的伺服进给系统稳定性分析

为了研究时变时滞对机床进给系统稳定性的影响,提出了一个基于Lyapunov-Krasovskii稳定性定理的判定准则。首先,结合机床的传动系统模型,分析了延迟干扰对控制系统的影响规律,建立了含时变时滞的闭环伺服进给系统模型;其次,利用积分不等式和时滞分割技术,构建了一个包含延迟项的Lyapunov-Krasovskii泛函,提出了保证时变时滞系统稳定的相关准则;最后,通过与其他方法的仿真对比,结果表明所提出的稳定性准则具有更低的保守性,并且给出了机床伺服进给系统稳定的时变时滞上界与控制参数的关系。

Input-to-State Stability of Switched Nonlinear Delay Systems Based on a Novel Lyapunov-Krasovskii Functional Method

In this paper, the input-to-state stability （ISS） analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new- criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.

New Lyapunov-Krasovskii Functional for Stability Analysis of Linear Systems with Time-Varying Delay

This paper focuses on the problem of delay-dependent stability of linear systems with time-varying delay.A new delay-product-type augmented Lyapunov-Krasovskii functional(LKF)is constructed.Based on the LKF and by employing a generalized free-matrix-based integral inequality,less conservative delay-dependent stability criteria are obtained.Finally,two well-known numerical examples are used to confirm the effectiveness and the superiority of the presented stability criteria.

Event-triggered state estimation for T-S fuzzy affine systems based on piecewise Lyapunov-Krasovskii functionals

This paper investigates the problem of event-triggered H∞state estimation for Takagi-Sugeno (T-S) fuzzy affine systems. The objective is to design an event-triggered scheme and an observer such that the resulting estimation error system is asymptotically stable with a prescribed H∞performance and at the same time unnecessary output measurement transmission can be reduced. First, an event-triggered scheme is proposed to determine whether the sampled measurements should be transmitted or not. The output measurements, which trigger the condition, are supposed to suffer a network-induced time-varying and bounded delay before arriving at the observer. Then, by adopting the input delay method, the estimation error system can be reformulated as a piecewise delay system. Based on the piecewise Lyapunov-Krasovskii functional and the Finsler's lemma, the event-triggered H∞observer design method is developed. Moreover, an algorithm is proposed to co-design the observer gains and the event-triggering parameters to guarantee that the estimation error system is asymptotically stable with a given disturbance attenuation level and the signal transmission rate is reduced as much as possible. Simulation studies are given to show the effectiveness of the proposed method.

Novel Non-monotonic Lyapunov-Krasovskii Based Stability Analysis and Stabilization of Discrete State-delay System

This paper proposes a novel less-conservative non-monotonic Lyapunov-Krasovskii stability approach for stability analysis of discrete time-delay systems.In this method,monotonically decreasing requirements of the Lyapunov-Krasovskii method are replaced with non-monotonic ones.The Lyapunov-Krasovskii functional is allowed to increase in some steps,but the overall trend should be decreasing.The model of practical systems used for stability analysis usually contain uncertainty.Therefore,firstly a non-monotonic stability condition is derived for certain discrete time-delay systems,then robust non-monotonic stability conditions are proposed for uncertain systems.Finally,a novel stabilization algorithm is derived based on the introduced non-monotonic stability condition.The Lyapunov-Krasovskii functional and the controller are obtained by solving a set of linear matrix inequalities(LMI)or iterative LMI based nonlinear minimization.The proposed theorems are first evaluated by some numerical examples,and then by simulation and implementation on the pH neutralizing process plant.

可再生能源高渗透下时滞孤岛微电网的负荷频率控制

针对孤岛微电网系统中大规模接入可再生能源导致的低惯性和开放通信网络中通信延迟对系统稳定运行造成的不可忽略的影响,该文研究变时滞影响下低惯性孤岛微电网系统的负荷频率控制问题。首先,提出一种引入虚拟惯性控制的时滞微电网分层频率控制模型;然后构造一个新的Lyapunov-Krasovskii泛函,它包括时滞乘积项和增广的s-dependent积分项。进而,选取复合松弛积分不等式、二次函数不等式和凸组合等方法与所构造泛函有效配合,得到保守性更低的稳定性判据。最后,通过不同场景的仿真分析验证所提方法在提高孤岛微电网时滞稳定裕度和系统动态性能方面具有更好的效果,并分析了时滞稳定裕度与控制器参数、非线性负载扰动之间的关系。

考虑通信时滞的采样控制系统稳定性分析

为了研究带有通信时滞的采样控制系统的稳定性问题,首先,考虑采样区间的采样特性,构造一种依赖于采样区间最值的闭环泛函,在这种泛函中,泛函相关的矩阵不需要满足正定定义,且矩阵随着采样区间最值的变化而变化;然后,利用采样控制系统的动态信息以及定积分的分部积分法,提出一些含自由矩阵的零等式;再次,结合广义自由矩阵积分不等式,推导出采样控制系统带有通信时滞和无通信时滞的2个稳定性判据;最后,通过数值和实际仿真验证采样区间最值的闭环泛函方法的可靠性。研究结果表明:基于采样区间最值的双边闭环泛函能够使采样控制系统稳定性判断更优且更有效。

离散奇异摄动系统的输出反馈Η_(∞)控制

以Lyapunov稳定性理论为依据,基于线性矩阵不等式方法,通过构造新的依赖于奇异摄动参数的Lyapunov-Krasovskii泛函,并引用新的依赖于奇异摄动参数的交叉项界定方法,对含有控制输入和干扰输入的不确定时变时滞离散奇异摄动控制系统设计了记忆输出反馈γ-次优Η_(∞)控制器,给出了线性化矩阵不等式判定定理,并用数值样例验证了设计方法的可行性和优越性.

2-D离散时滞系统的新时滞相关稳定性准则

研究了具有时变时滞的二维(two-dimensional,2-D)离散系统的时滞相关稳定性问题.所创建的Lyapunov-Krasovskii泛函(Lyapunov-Krasovskii functionals,LKFs)考虑在二次项和单项求和项中引入时滞相关矩阵,包含了更多的状态信息.同时在单项求和项中引入增广向量矩阵,并给出适用于2-D系统的多重辅助函数不等式和互凸组合不等式,用于处理LKFs差分,以便降低计算负担.然后,为具有时变时滞的2-D离散系统推导出保守性更小的稳定性准则.通过两个数值算例验证了所设计方法的有效性和优越性.

新的广义时滞系统容许性条件

针对广义时滞系统,基于李雅普诺夫第二方法和广义系统的受限等价变换,结合积分不等式技术,给出一个线性矩阵不等式(linear matrix inequality,LMI)形式的容许性条件。首先,利用广义系统的受限等价变换得出广义时滞系统是正则且无脉冲的;然后,通过选取增广型Lyapunov-Krasovskii泛函(L-K泛函)和多重积分型L-K泛函,引入松弛型L-K泛函构建新的L-K泛函,利用Jensen积分不等式和Wirtinger积分不等式对L-K泛函求导后产生的积分项进行处理,得出广义时滞系统的稳定性条件,进而得到广义时滞系统的容许性条件;最后,利用MATLAB中的LMI工具箱,通过数值算例验证所用方法的可行性和有效性。

时变时滞奇异复杂动态网络的间歇控制与同步

利用周期性间歇控制策略研究了具有时变时滞的奇异复杂动态网络的指数同步问题.通过构建Lyapunov-Krasovskii泛函,推导出驱动系统和响应系统的指数同步判据;然后运用LMI工具箱求解线性矩阵不等式,得出了控制增益矩阵.最后,利用Runge-Kutta算法求解具有时变时滞微分代数方程,并通过数值仿真验证了结论的有效性.

基于二次函数负定判据的LFC系统稳定性分析

基于改进的二次积分不等式和二次多项式不等式建立的稳定性条件,研究了基于负荷频率控制(LFC)的时滞电力系统稳定性问题。首先,搭建了包含PI参数的负荷频率时滞系统数学模型;然后,通过引入增广的Lyapunov-Krasovskii泛函,利用近年改进的二次积分不等式和二次多项式不等式的充分条件,成功导出了具有时变时滞的系统稳定性判据;最后,通过负荷频率系统模型的实例仿真,验证了所得稳定性判据优于现有的一些计算结果。

考虑时滞的自平衡车控制系统稳定性分析

研究了自平衡车控制系统的时滞相关稳定性问题。首先,应用牛顿经典力学,对自平衡车进行数学建模,给出了自平衡车瞬时力学平衡方程,并对控制电机模型进行线性化处理。在此基础上,建立了基于PID控制器并考虑传输时滞的自平衡车系统的整体状态空间模型。为了评估系统的时滞稳定裕度,基于Lyapunov-Krasovskii(L-K)泛函方法,并应用广义自由矩阵积分不等式技术,建立了系统的时滞相关稳定性判据。然后基于给出的稳定性判据,借助Matlab中的线性矩阵不等式(linear matrix inequality,LMI)工具箱,研究了速度环PID参数对自平衡车控制系统时滞稳定裕度的影响。最后,通过仿真实验验证了所提出系统稳定性判据的有效性。