广义不确定周期时变系统的鲁棒稳定性分析

研究广义不确定周期时变系统的鲁棒稳定性问题.基于广义周期时变系统Lyapunov不等式,提出了广义不确定周期时变系统鲁棒稳定的概念,采用矩阵不等式(LMI)方法,得到了该类系统鲁棒稳定的充分必要条件;然后,进一步研究了在状态反馈控制下保证闭环系统鲁棒稳定的条件,给出了一族状态反馈鲁棒稳定器的设计方法;最后,引入了广义周期时变系统二次稳定的概念,并讨论了二次稳定性与鲁棒稳定性之间的关系.     

一类线性时变不确定周期奇异系统的鲁棒镇定

讨论了一类线性时变不确定周期广义系统的鲁棒镇定问题．基于线性时变不确定周期广义系统的鲁棒稳定的概念, 提出鲁棒稳定的充分必要条件, 并基于对偶系统的等价性得到鲁棒镇定的充分必要条件. 通过引入自由矩阵, 所得结果表示为线性矩阵不等式, 验证过程更简单、可靠.     

广义不确定系统鲁棒稳定性及鲁棒镇定的矩阵不等式方法

考虑广义不确定系统的鲁棒稳定性及鲁棒镇定问题.提出了广义不确定系统'广义二 次稳定'及'广义二次可镇定'的概念,利用矩阵不等式,分别得到了所考虑广义不确定系统广义 二次稳定及广义二次可镇定的充要条件,而且,使广义不确定系统鲁棒镇定的状态反馈控制律 的设计可通过求解一给定的矩阵不等式而得到.     

时变不确定广义系统的鲁棒无源控制

研究了除E外其余系数矩阵均含有范数有界时变不确定性的广义系统的鲁棒无源控制器设计问题.利用线性矩阵不等式方法,首先给出自治系统广义二次稳定且无源的充分条件;然后给出状态反馈鲁棒无源控制器的存在条件并用线性矩阵不等式的解构造了相应的控制器;随后以矩阵不等式的形式得到了动态输出反馈鲁棒无源控制器的存在条件,同时利用矩阵不等式的解给出相应控制器的设计方法;最后举例说明了所提出方法的可行性.     

一类不确定非线性广义时滞系统的H∞控制

针对一类具有非线性控制输入的参数不确定广义时滞系统,研究了该类广义系统的鲁棒H∞控制问题.利用Lyapunov泛函方法和线性矩阵不等式工具,无需对广义系统进行转化,得到了闭环系统鲁棒渐近稳定且具有H∞范数界的充分条件;将其转化为不带参数不确定矩阵的线性矩阵不等式,基于相应的线性矩阵不等式可行解,给出了该类广义系统的H∞控制律的构造方法.数值例子表明了该方法的有效性和可行性.     

不确定广义时滞系统的鲁棒稳定方法研究

研究一类带有时滞不确定广义系统的鲁棒渐近稳定问题．利用Lyapunov稳定性定理和线性矩阵不等式工具，得到了广义系统正则、鲁棒渐近稳定的时滞相关充分条件．为了降低所得结果的保守性，避免了采用系统模型变换和利用矩阵不等式方法．进一步，建立一个具有线性矩阵不等式约束的凸优化问题，利用Matlab软件中的LMI工具箱求解，得到保证广义系统鲁棒渐近稳定的最大可允许时滞上界．仿真示例表明了该方法的有效性．     

传感器失效不确定时滞系统指数稳定可靠控制

针对一类含有时变时滞的不确定参数线性系统,研究了在传感器发生故障情况下系统指数稳定鲁棒可靠控制器设计问题。系统中的参数不确定性满足广义匹配条件,时变时滞及其变化率有界,并假设故障传感器元件的输出为零。经过适当的状态变换,将原系统的指数稳定鲁棒可靠控制问题转化为另一个等价系统的鲁棒可靠控制问题。根据Lyapunov稳定性理论,得到了系统存在指数稳定鲁棒可靠控制器应满足的一个矩阵不等式。为了便于数值求解,将该矩阵不等式转化为线性矩阵不等式（LMI）,并给出了可靠控制器的设计方法和步骤。利用该文方法设计的指数稳定鲁棒可靠控制器能够使得时滞系统对于任意允许的不确定性以及传感器失效都具有指定衰减度的渐近稳定性。数值算例说明了所提出设计方法的有效性。     

不确定时滞广义双线性系统的鲁棒镇定

针对不确定参数是时变但满足匹配条件的时滞广义双线性系统的鲁棒控制问题进行了研究,设计状态反馈鲁棒控制器,使得所有满足条件的不确定时滞广义双线性系统鲁棒稳定.基于Lyapunov稳定性理论,采用线性矩阵不等式方法,提出了不确定时滞广义双线性系统鲁棒镇定的充分条件,并给出了使得闭环系统鲁棒镇定的状态反馈控制器设计方法.定理解决了介于非线性和线性之间的不确定时滞广义双线性系统的有关理论.仿真实例说明了定理的有效性和合理性.     

线性广义系统的鲁棒严格耗散控制

利用线性矩阵不等式(LMI)方法,给出线性广义系统容许且严格耗散的充分必要条件,由此得到状态反馈和动态输出反馈严格耗散控制器的存在条件及设计方法.考虑除E外所有系数矩阵均具有范数有界时变不确定性的广义系统的鲁棒严格耗散控制问题,给出了系统广义二次稳定且严格耗散的充分条件,以及状态反馈和动态输出反馈鲁棒严格耗散控制器的存在条件及构造方法.     

一类带有时滞的不确定广义系统的切换渐近稳定性

研究了一类带有时滞的切换不确定广义系统的鲁棒渐近稳定问题. 利用Lyapunov稳定性定理和线性矩阵不等式(Linear matrix inequality, LMI)工具, 采用多Lyapunov函数技术, 在设定的切换律下, 得到切换不确定广义时滞系统鲁棒渐近稳定的时滞相关充分条件. 进一步, 建立了一个具有线性矩阵不等式约束的凸优化问题, 利用Matlab软件中的LMI工具箱求解, 得到保证切换广义系统鲁棒渐近稳定的最大可允许时滞上界. 最后示例表明了该方法的有效性.     

Biquadratic stability of uncertain linear systems

Deals with the problem of stability analysis for linear systems with uncertain real, possibly time-varying, parameters. A robust stability approach based on a Lyapunov function which depends quadratically on the uncertain parameters as well as in the system state is proposed. This robust stability approach, referred to as biquadratic stability, is suited to deal with uncertain real parameters with magnitude and rate of change which are confined to a given convex region. A linear matrix inequality based sufficient condition for biquadratic stability is developed. The proposed robust stability analysis method includes quadratic stability and affine quadratic stability as particular cases     

Less conservative robust stability criteria for uncertain discrete stochastic singular systems with time-varying delay

The problem of robust stabilisation for uncertain discrete singular systems with time-varying delay is discussed in this article. First, a new delay-distribution-dependent Lyapunov function is established. Then, sufficient conditions are proposed for guaranteeing that the uncertain discrete singular system with time-varying delay has the properties of regularity, causality and stability. Finally, a suitable robust state feedback controller is designed by linear matrix inequality. Numerical examples illustrate that the results derived from the proposed method are less conservative than the existing ones.     

Robust stability and stabilization of discrete singular systems with interval time-varying delay and linear fractional uncertainty

The robust stability and robust stabilization problems for discrete singular systems with interval time-varying delay and linear fractional uncertainty are discussed. A new delay-dependent criterion is established for the nominal discrete singular delay systems to be regular, causal and stable by employing the linear matrix inequality (LMI) approach. It is shown that the newly proposed criterion can provide less conservative results than some existing ones. Then, with this criterion, the problems of robust stability and robust stabilization for uncertain discrete singular delay systems are solved, and the delay-dependent LMI conditions are obtained. Finally, numerical examples are given to illustrate the e?ectiveness of the proposed approach.     

Robust stability and stabilization of discrete singular systems: an equivalent characterization

This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively. With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.     

Delay dependent robust stability of singular systems with additive time-varying delays

This paper considers the problem of delay-dependent robust stability for uncertain singular systems with additive time-varying delays. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties. The results are expressed in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.     

Robust stability and stabilization for singular systems with statedelay and parameter uncertainty

Considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay. The parametric uncertainty is assumed to be norm bounded. The purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular, impulse free, and stable for all admissible uncertainties, while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed-loop system is robustly stable. These problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization, respectively. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived. A strict linear matrix inequality (LMI) design approach is developed. An explicit expression for the desired robust state feedback control law is also given. Finally, a numerical example is provided to demonstrate the application of the proposed method     

New Robust Stability Criteria for Lur’e Systems with Time-varying Delays and Sector-bounded Nonlinearities

This paper deals with a robust stability problem for uncertain Lur’e systems with time-varying delays and sector-bounded nonlinearities. An improved delay-dependent robust stability criterion is proposed via a modified Lyapunov-Krasovskii functional (LKF) approach. Firstly, a modified LKF consisting of delay-dependent matrices and double-integral items under two delay subintervals is constructed, thereby making full use of the delay and its derivative information. Secondly, the stability criteria can be expressed as convex linear matrix inequality (LMI) via the properties of quadratic function application. Thirdly, to further reduce the conservatism of stability criteria, the quadratic generalized free-weighting matrix inequality (QGFMI) is used. Finally, some numerical examples, including the Lur’e system and the general linear time-delayed system, are presented to show the improvement of the proposed approach.

     

Robust stability analysis of singular linear system with delay and parameter uncertainty

1Introduction It is well known that the existence of a delay in adynamical system may induce instability or poorperformances in various systems suchas electric,pneumatic,and hydraulic networks,chemical processes,longtransmission lines,etc.For a survey of time_delay systems,the reader can refer to a recent overview paper[1].Control of singular systems has been extensively studied inthe past years due to the fact that singular systems betterdescribe physical systems than regular ones.Agreat numb…     

不确定离散奇异时滞系统的鲁棒稳定性

针对一类具有区间时变时滞和线性分式参数不确定性的离散奇异系统, 研究鲁棒稳定性问题。基于Lyapunov稳定性理论, 应用线性矩阵不等式方法, 给出不确定离散奇异时滞系统的新的时滞相关型稳定性准则。所给准则相比于已有一些结果, 包含较少的矩阵变量, 且具有较小的保守性。数值实例表明所得结果的有效性。