不确定时滞系统的区间时滞相关鲁棒镇定

研究了时间滞后满足区间变化的线性连续系统鲁棒镇定问题。采用Lyapunov-Krasovskii稳定性分析方法,给出了区间时滞依赖系统的状态反馈设计稳定解。进一步研究参数化不确定性情况下,区间时滞依赖系统的鲁棒稳定性判据和鲁棒状态反馈控制器设计方法。最后,通过仿真算例比较,验证了此方法的有效性。     

不确定线性时滞系统时滞相关状态反馈鲁棒镇定

利用Lyapunov-Krasovskii泛函方法,基于积分不等式,讨论了不确定线性时变时滞系统时滞相关状态反馈鲁棒镇定问题。采用线性化处理技术将非线性矩阵不等式（nonlinear matrix inequality, NLMI）转化为线性矩阵不等式（linear matrix inequality, LMI）,获得的鲁棒镇定准则只有一个易于选择的待定参数,避免了参数选择不当带来的保守性,数值例子说明本文方法的有效性。     

区间时滞相关不确定奇异系统的鲁棒稳定性和镇定性

研究区间时滞相关的不确定时变时滞奇异系统的鲁棒稳定性和镇定性问题,不确定参数假设是范数有界的。充分利用时滞的下界信息构造Lyapunov函数,用严格的矩阵不等式给出系统对所有的容许不确定满足正则、无脉冲、稳定的新判据。基于这个判据,设计状态反馈控制器使得系统鲁棒稳定。数值例子说明所得结果具有更小的保守性。     

具有时滞的区间大系统的鲁棒稳定性

应用Lyapunov函数方法讨论了具有时滞的区间大系统的鲁棒稳定性,给出了该系统鲁棒稳定的充分条件,同时还讨论了一类不确定时滞大系统的鲁棒稳定性,最后给出了结果的示例并与前人的结果进行了比较。     

凸多面体不确定随机时滞系统的非脆弱鲁棒镇定

针对具有凸多面体不确定性的随机时滞系统,讨论了非脆弱鲁棒指数镇定问题,其中非脆弱控制器中的不确定性采用的是凸多面体不确定描述。基于Lyapunov直接法,采用了与参数相关的Lyapunov krasovskii泛函,并结合自由权矩阵方法, 使得Lyapunov矩阵与系统矩阵分离,从而获得了系统的完全基于线性矩阵不等式的时滞相关非脆弱鲁棒镇定的充分条件。最后,用例子说明了结果的有效性。     

跳变时滞随机系统的鲁棒保性能控制

研究了马尔可夫跳变参数时滞随机系统的鲁棒保性能控制问题。通过构造一个Lyapunov函数,并应用Ito微分公式沿系统对其求微分,再利用线性矩阵不等式(LMI)的性质和广义Ito公式,给出了此类系统保性能控制律存在的充分条件,估计了其保性能值,同时,控制器的设计归结为一族LMI的求解问题。最后,数值算例说明了方法的有效性。     

不确定中立型系统的改进的时滞依赖的鲁棒镇定

研究了具有时不变不确定性的中立型系统的鲁棒镇定/稳定问题。给出了新的镇定/稳定法则。利用改进的Lyapunov泛函,得到了这类系统基于线性矩阵不等式的保守性较低的镇定/稳定条件。最后,用几个例子证明了本文所得到的结果要比现存的结果得到了提高。     

基于LMIs方法-不确定性随机分布型时滞Markov跳变系统的鲁棒镇定

研究了一类具有不确定性Markov跳变参数的线性分布型时滞系统.考虑了具不确定性、Markov跳变参数、及分布型时滞系统的鲁棒均方稳定性问题.设计了系统的鲁棒状态反馈镇定控制器.采用了Grownwall Bellman不等式,基于线性矩阵不等式(LMIs)方法,给出了鲁棒稳定性的LMI时滞依赖的代数判据,从而降低了判据的保守性.同时得到了相应的离散时滞情形下的结果.     

两类不确定奇异时滞系统鲁棒稳定的相关型判据

研究了不确定奇异时滞系统的鲁棒稳定性问题。首先以线性矩阵不等式的形式给出了奇异时滞系统正则,无脉冲模且零解渐近稳定的一种新的时滞相关型判据。通过引入新的参数避免了利用不等式处理交叉项,从而使该判据具有较小的保守性。最后,利用研究结果,给出了两类不确定奇异时滞系统新的时滞相关型鲁棒稳定性判据。     

参数不确定系统鲁棒镇定控制器设计的鲁棒可靠性方法

用区间变量描述系统参数的不确定性,从可靠性角度研究不确定系统的稳定鲁棒性设计问题。基于二次稳定性准则,提出了参数不确定系统鲁棒镇定控制器设计的鲁棒可靠性新方法。依据该法设计的控制系统可满足稳定性意义上的鲁棒可靠性要求,并给出保证系统稳定性所要求的基本参数的最大鲁棒界限。所给公式完全基于线性矩阵不等式(LMI)方法,求解方便。适用于不确定参数的摄动范围准确已知和未知等情况。对实际算例的设计和模拟结果与现有结果的比较研究表明了在传统的控制器设计中,保守性的增加并不意味着可靠性的增加。从而也说明了所提方法是实用、有效和可行的。     

Robust stability for stochastic interval delayed Hopfield neural networks

A type of stochastic interval delayed Hopfield neural networks as du(t) = [-AIu(t) WIf(t,u(t)) WIτf7τ(uτ(t)] dt σ(t, u(t), uτ(t)) dw(t) on t≥0 with initiated value u(s) = ζ(s) on - τ≤s≤0 has been studied. By using the Razumikhin theorem and Lyapunov functions, some sufficient conditions of their globally asymptotic robust stability and global exponential stability on such systems have been given. All the results obtained are generalizations of some recent ones reported in the literature for uncertain neural networks with constant delays or their certain cases.     

Robust stabilization for multi-input polytopic nonlinear systems

This paper deals with the problem of the stabilization for multi-input polytopic nonlinear systems. Based on the robust control Lyapunov function, a sufficient condition for the existence of time-invariant, continuous, asymptotically stabilizing state feedback controller is derived. It is shown that the obtained sufficient condition is also necessary if there exists a state feedback controller such that the closed-loop system has a robust Lyapunov function for all possible uncertainties. Moreover, a universal formula for constructing stabilizing controller is proposed and the existence of the corresponding Lyapunov function is proven. Particularly, a Lyapunov function is constructed for the polytopic nonlinear system in canonical form. Finally, the feasibility of the proposed control law is verified by a numerical example.     

区间系统鲁棒绝对稳定性分析

针对区间型Lurie间接控制系统和直接控制系统,提出了鲁棒绝对稳定性分析的新方法。该方法通过引入区间矩阵的一种新的描述方法,利用李亚普诺夫(Lyapunov)稳定性理论分别给出了间接控制系统和直接控制系统的鲁棒绝对稳定性的新的判别方法。所得判据以线性矩阵不等式的形式进行描述,保守性小,计算方便。分别就间接控制系统和直接控制系统,给出了算例以说明方法的有效性。     

Robust exponential stability of switched interval interconnected systems with unbounded delay

In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, by using vector Lyapunov methods and M-matrix theory, the integrodifferential inequalities with unbounded delay were constructed. By the stability analysis of the integrodifferential inequalities, the sufficient conditions to ensure the robust exponential stability of the interval interconnected systems were obtained. By using average dwell time approach, conditions for guaranteeing the robust exponential stability of the switched delay interval interconnected systems were derived. Finally, two numerical examples were given to illustrate the correction and effectiveness of the proposed theory.     

高阶随机非线性系统状态反馈镇定

针对一类高阶下三角随机非线性系统,提出一种新的镇定方案,采用增加一个幂积分的工具构建了一个全局稳定的光滑状态反馈控制律。通过反馈占有设计方法和Young不等式处理随机系统的非线性项,取消了对随机非线性系统反馈线性化和控制输入呈线性的要求,基于Lyapunov方法,证明了闭环系统依概率全局渐近稳定。最后,仿真实例说明了算法的可行性。     

大型不确定前馈型系统的分散鲁棒镇定

研究了大型不确定前馈型系统的鲁棒分散镇定问题。因为系统具有前馈型结构,采用自下而上的迭代分析方法,同时注意运用互联非线性系统有界性和稳定性判据。将设计任务转化为镇定底层子系统和其他子系统的标称部分,并可以明确构造简单的饱和控制律。该方法利用系统的结构特性,不太依赖李雅普诺夫函数,也不需要通常的LMI技巧。仿真说明该方法的有效性。     

Robust stability test for 2-D continuous-discrete systems with interval parameters

It is revealed that the dynamic stability of 2-D recursive continuous-discrete systems with interval parameters involves the problem of robust Hurwitz-Schur stability of bivariate polynomials family. It is proved that the Hurwitz-Schur stability of the denominator polynomials of the systems is necessary and sufficient for the asymptotic stability of the 2-D hybrid systems. The 2-D hybrid transformation, i. e. 2-D Laplace-Z transformation, has been proposed to solve the stability analysis of the 2-D continuous-discrete systems, to get the 2-D hybrid transfer functions of the systems. The edge test for the Hurwitz-Schur stability of interval bivariate polynomials is introduced. The Hurwitz-Schur stability of the interval family of 2-D polynomials can be guaranteed by the stability of its finite edge polynomials of the family. An algorithm about the stability test of edge polynomials is given.     

Robust dissipative control for time-delay stochastic jump systems

A robust dissipative control problem for a class of It?-type stochastic systems is discussed with Markovian jumping parameters and time-varying delay. A memoryless state feedback dissipative controller is developed based on Lyapunov-Krasovskii functional approach such that the closed-loop system is robustly stochastically stable and weakly delay-dependent (RSSWDD) and strictly (Q, S, R)-dissipative. The sufficient condition on the existence of state feedback dissipative controller is presented by linear matrix inequality (LMI). And the desired controller can be concluded as solving a set of LMI. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.