含有非线性扰动的时滞随机微分系统的鲁棒均方稳定性

研究一类含有非线性扰动的多时变时滞随机微分系统在有记忆状态的反馈控制器下的鲁棒均方稳定性问题.通过构造Lyapunov-Krasovskii泛函,运用Ito公式,引入适当的自由权矩阵,利用积分不等式和分析技巧,基于线性不等式(LMI)方法和Schur补定理,获得含该系统的鲁棒均方渐近稳定和鲁棒均方指数稳定,并给出了相应反馈控制器设计.所得结果与时滞和随机干扰相关,丰富了已有的结果.     

不确定变时滞模糊随机系统鲁棒稳定性

本文研究了不确定T-S模糊随机时滞系统的时滞相关鲁棒稳定性问题,这里的不确定性是范数有界的.通过构造新的Lyapunov泛函和矩阵不等式引理,利用具有时滞的非线性随机系统的Lypaunov稳定性理论和自由权矩阵方法,导出了使系统鲁棒均方指数稳定的时滞相关线性矩阵不等式(LMI)条件.该判据具有较低的保守性,适用时滞变化率大于1的情形.最后通过数值例子验证了所得结果的有效性.     

不确定多重时滞中立系统的时滞相关鲁棒H∞控制

本文利用一个新的积分不等式方法讨论了一类不确定多重时滞中立系统的时滞相关鲁棒H∞控制器设计问题.该中立系统的状态项、控制项、微分项、外部干扰输入项均含有时滞.首先,利用Lyapunov稳定性理论,推导出系统鲁棒可镇定的充分条件.在此基础上,进一步给出了鲁棒H∞控制器存在的充分条件.不需要对原系统进行模型变换,仿真算例说明了定理的可行性.     

中立型灰色随机分布时滞系统的指数鲁棒稳定性

为了得到一类中立型灰色随机分布时滞系统的指数鲁棒稳定性,本文利用Lyapunov-Krasovskii泛函法、灰矩阵的连续矩阵覆盖的分解技术和Ito公式,分别得到了以非线性矩阵不等式和线性矩阵不等式(LMI)表示的该系统指数鲁棒稳定的时滞依赖性判据。对非线性矩阵不等式判据,我们给出了一般性算法,解决了非线性矩阵不等式判据不便于实际应用的问题。数值例子表明,本文所给判据是有效的,且系统的指数稳定性和时滞,随着绝对灰度矩阵的谱范数的增大而减小。     

考虑执行器响应时滞的磁流变悬架H2/H∞鲁棒控制研究

针对磁流变阻尼器响应时滞对半主动悬架系统控制效果和稳定性造成的不良影响,设计了一种时滞H₂/H_∞鲁棒控制器对执行器输入的定常时滞进行鲁棒控制,推导了控制器反馈控制增益和系统临界时滞;开展了磁流变阻尼器力学试验并对Bingham模型实现参数识别;基于MotoTron平台完成了驱动电流PI控制参数整定,使阻尼器响应时滞降低到临界时滞以内。仿真结果表明：C级随机路面下,所设计的时滞H₂/H_∞鲁棒控制器相比被动悬架和不考虑时滞的鲁棒控制器,车身加速度和悬架动挠度分别降低了24.52%、9.79%、11.26%和7.19%,乘坐舒适性得到明显改善,轮胎动载荷相比鲁棒控制优化了3.21%,兼顾了行驶安全性。为进一步验证时滞H₂/H_∞鲁棒控制器实际工作性能,设计了悬架ECU,开展了单轮悬架台架试验。试验结果表明：时滞H₂/H_∞鲁棒控制器能保证时滞输入系统的控制性能和稳定性。     

结构不确定线性时滞系统的无记忆鲁棒镇定

针对状态和控制均存在时滞的一类结构不确定线性时滞系统，讨论了鲁棒镇定问题，当不确定性参数满足有界性条件时，提出了一种无记忆线性状态反馈控制控制，可保证闭环系统具有二次稳定性。     

含非线性扰动的混合变时滞中立系统鲁棒稳定性新判据

中立型时滞系统在工程实际中有着广泛应用背景.本文研究了一类含非线性扰动的混合变时滞中立型系统地鲁棒稳定性问题.基于直接Lyapunov泛函方法,通过构造一类新的包含时滞区间上下界的三重积分项Lyapunov-Krasovskii泛函,并结合积分不等式方法、自由权矩阵技术和凸组合处理方法,建立了一种新的线性矩阵不等式形式的离散时滞和中立时滞均相关的鲁棒稳定性判据.最后,通过数值算例验证了新判据的有效性和优越性,和一些已有文献相比,本文提出的判据具有更低的保守性.     

一类具有范数有界不确定性的非线性时滞系统的控制

本文研究了一类具有范数有界不确定性的非线性时滞系统的鲁棒稳定性及其控制问题,结合Lyapunov稳定性定理、线性矩阵不等式及自由权矩阵,给出了系统的状态反馈鲁棒二次稳定的充分条件以及控制器的设计,并建立了一个具有线性矩阵不等式约束的凸优化问题,得到不确定时滞系统的最优状态反馈控制律.仿真示例说明了该方法的可行性.     

一类中立型时滞系统新的鲁棒稳定性准则

本文考虑了一类具有时变时滞和非线性扰动的中立型系统的鲁棒稳定性问题.基于Lyapunov稳定性理论和自由权矩阵方法,得到保证系统鲁棒渐近稳定的新的充分条件.所得结果同时依赖于离散时滞和中立时滞,并用LMIs表示.由于对Lyapunov泛函导数采用了无保守的估计,因此所得结果具有较小的保守性,能够给出时变时滞较大的允许时...     

切换区间系统的鲁棒指数稳定

研究一类连续切换区间系统的鲁棒指数稳定及其扰动衰减性能估计。利用平均驻留时间方法和线性矩阵不等式（LMIs）方法,得出了连续切换区间系统鲁棒指数稳定且满足扰动衰减度的充分条件。同时设计了系统的线性无记忆状态反馈控制器,所得结果均以LMIs的形式给出,求解方便。最后通过仿真实例验证了结果的有效性。     

具有多滞后时变区间Lurie间接控制系统的指数稳定性

本文讨论了具有多滞后时变区间Lurie间接控制系统的指数稳定性问题.通过引入多时滞时变区间控制系统的指数稳定性的概念,采用矩阵测度和时滞微分不等式,对具有多个滞后的时变区间Lurie间接控制系统的指数稳定性做了研究,并给出了此系统指数稳定性的若干充分条件.最后给出数值例子说明了本文结论的有效性.     

Mean-square stability of linear stochastic dynamical systems under parametric wide-band excitations

A new simplified condition is developed for determining the exponential meansquare stability margins of linear stochastic dynamical systems. It is well-known that under parametric wide-band noise disturbances, the governing equations of motion of such a system can be approximated by linear Itô stochastic differential equations (SDE). A necessary and sufficient condition for exponential mean square stability of the resulting ltô SDE is that the real parts of all the eigenvalues of the matrix describing the system of second-order moments are negative. Equivalently, the Routh-Hurwitz procedure provides conditions for stability in the form of several inequalities. In this study, it is shown that a necessary condition for the system configuration to correspond to a point on the stability boundary is that the determinant of the matrix describing the system of secondorder moments be zero. This condition is a single algebraic expression allowing for the straightforward calculation of all candidate stability boundaries. In addition, the topological properties of the stability domain are presented and shown to be useful in identifying stability boundaries and stability domains from the developed single stability boundary condition. This simplified condition provides significant advantages in the analytical and numerical estimation of the stability border and stability region of dynamical systems. The usefulness and superiority of the new condition is demonstrated by applications to example dynamical systems, including a long-span bridge model subjected to turbulent wind.     

基于忆阻器的随机神经网络的稳定性

与传统的神经网络相比，基于忆阻器的神经网络能够更好地反映突触的强度可变的这一特性，从而更好地模拟人脑的神经系统。在 Filippov 解的框架下，通过构造恰当的 Lyapunov 泛函，利用 It$\hat{\rm o}$ 微分公式、微分包含和集值映射理论，研究了一类基于忆阻器的随机神经网络的动力学行为，获得了确保该系统均方指数稳定的充分判别条件。最后，通过给出两个数值仿真的例子验证了结论的有效性。     

Stability of two-time scale linear stochastic hybrid systems

The problem of exponential mean-square stability of two-time scale, linear stochastic hybrid systems has been studied in this paper. To obtain the sufficient conditions of stability, two basic approaches of stability analysis: for one-time hybrid systems with a Markovian switching rule as well as switching rule and singularly perturbed nonhybrid systems, were combined. The Lyapunov techniques were used in both approaches.     

Necessary and sufficient conditions for exponential stability of a family of generalized Liénard differential equations

A class of generalized Liénard differential equations determined by prescribed bilateral bounds for the nonlinear terms is considered. Necessary and sufficient conditions for exponential stability of the system expressed in the indicated bounds are found. The results are compared with known sufficient stability conditions obtained via the Lyapunov function method.     

Improved robust exponential stability for Takagi–Sugeno fuzzy uncertain systems with time-varying delays

This paper concerns managing the robust exponential stability problem of uncertain Takagi–Sugeno fuzzy systems with time-varying delay by employing a further improved integral inequality matrix approach. Based on the linear matrix inequality (LMI) approach, delay-dependent robust exponential stability criteria have been developed. By taking the relationship among the time-varying delay, its upper bound and their difference into account, some less conservative LMI-based delay-dependent robust exponential stability criteria are obtained without ignoring any useful terms in the derivative of Lyapunov–Krasovskii functionals. Maximum allowable upper bound for time-varying delays is determined. Numerical examples are provided to show that the obtained results significantly improve the allowed upper bounds of delay size over some methods existing in the literature.     

有界窄带激励柴油机轴系扭振系统主参数共振

研究柴油机轴系扭振强非线性系统在有界窄带激励下的主参数共振响应和稳定性问题。应用改进多尺度法得到在有界窄带随机激励下柴油机轴系扭振系统的幅频响应方程,导出系统的Ito随机微分方程。通过矩法得到系统随机均方响应的近似表达式,分析各个参数对柴油机轴系扭振系统主参数共振均方值的影响。结果表明,主参数共振稳态解稳定的充分必要条件与系统二阶矩稳定的充分必要条件是一样的;随着阻尼值的增大,系统主参数共振振幅的均方值减小;随着曲轴扭转刚度的减小,系统主参数共振的均方响应曲线的斜率增大;随着随机扰动强度的增大,系统时间响应曲线和相图变化微小。     

Robust pole‐assignment for dynamic systems with uncertain parameters

Abstract

In this paper, by using discrete‐type Lyapunov stability criterion, new sufficient conditions for robust pole‐assignment of uncertain systems in a specified disk are presented. The norm bound on linear time‐invariant perturbations is obtained. The relationship between the allowable bound and the eigenvalues of the nominal system matrix is discussed. A design method for robust pole‐assignment is proposed. Examples are given to demonstrate the use of the proposed techniques.     

Stable numerical integration of dynamical systems subject to equality state-space constraints

Numerical simulation of constrained dynamical systems is known to exhibit stability problems even when the unconstrained system can be simulated in a stable manner. We show that not the constraints themselves, but the transformation of the continuous set of equations to a discrete set of equations is the true source of the stability problem. A new theory is presented that allows for stable numerical integration of constrained dynamical systems. The derived numerical methods are robust with respect to errors in the initial conditions and stable with respect to errors made during the integration process. As a consequence, perturbations in the initial conditions are allowed. The new theory is extended to the case of constrained mechanical systems. Some numerical results obtained when implementing the numerical method here developed are shown.