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．     

不确定多重状态时滞离散系统的LMI鲁棒稳定条件

研究了具有多重状态时滞的凸多面体不确定离散系统的鲁棒稳定性分析问题．基于参数依赖的李亚普诺夫稳定性和线性矩阵不等式推导出使得时滞鲁棒稳定系统鲁棒稳定的充分条件．应用此条件，通过测试一组线性矩阵不等式的可解性即可达到判定系统的鲁棒稳定性的目的．因为使用了参数依赖的李亚普诺夫稳定性思想，此鲁棒稳定条件比基于二次稳定概念的稳定条件的保守性更小．算例验证了结果．     

一类含未建模动态的奇异时滞系统的鲁棒镇定问题

利用线性矩阵不等式的方法，研究了一类同时含有参数摄动和未建模动态的线性奇异时滞系统的鲁棒镇定问题.得到了系统可鲁棒镇定的一个充分条件，用线性矩阵不等式的方法，将控制器的求解问题转化为受限线性矩阵不等式的求解问题，并给出了受限线性矩阵不等式的具体解法．最后举例说明了所提出方法的正确性．     

一类分布式时滞LPV系统的鲁棒H∞滤波

研究一类同时具有分布式和离散型时滞的线性参数变化系统的鲁棒H∞滤波问题．基于参数线性矩阵不等式方法，推导了滤波误差系统渐近稳定和具有H∞扰动衰减水平γ的时滞相关充分条件．同时应用投影定理，通过引入附加矩阵变量，解除了系统矩阵与依赖于参数的Lyapunov函数矩阵之间的耦合，使所得到的条件更适合于滤波器的综合．推导了系统鲁棒H∞滤波器存在的充分条件，并将滤波器的设计转化为一组线性矩阵不等式的求解．数值实例证明了所提出设计方案的可行性．     

线性不确定广义时滞系统的鲁棒无源滤波器设计

研究一类线性不确定广义时滞系统的鲁棒无源滤波器设计问题．系统中所含的不确定性假设是未知且范数有界的．利用线性矩阵不等式方法和Lyapunov函数方法相结合，给出了广义滤波增广系统时滞独立的鲁棒无源滤波器的存在条件．设计目标是对所有的不确定性，滤波增广系统是正则、稳定、无脉冲的，且满足所提的无源滤波性能指标．所提的滤波器设计问题可转化为标准的线性矩阵不等式的求解问题，并可推广到多时滞情况．数值例子验证了设计方法的可行性．     

T-S 模糊时滞模型的时滞相关稳定性分析和镇定

研究一类用T—S模糊模型描述的非线性不确定时滞系统的时滞相关鲁棒镇定问题．基于线性矩阵不等式的可行解，首先给出利用T—S模糊模型描述的非线性时滞系统时滞相关稳定性准则；然后给出了经状态反馈鲁棒镇定设计的新方法．所设计的控制器能确保闭环系统渐近稳定．     

不确定时滞双线性广义系统的鲁棒耗散控制

针对带有耗散不确定性的时滞双线性广义系统的鲁棒耗散控制问题,首先将耗散不确定性引入双线性广义系统,利用线性矩阵不等式方法给出系统鲁棒稳定且严格耗散的充分条件;然后利用线性矩阵不等式的解,构造出闭环系统鲁棒耗散的状态反馈控制器;最后通过数值算例验证了所得结论的可行性.     

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.     

一类线性时滞系统鲁棒控制器的设计

针对一类同时存在状态和控制滞后的线性不确定，时滞系统的鲁棒镇定问题进行了研究，其中系统的不确定项参数时变未知但范数有界、且滞后项也是时变的。对此，基于Lyapunov泛函，利用线性矩阵不等式给出了系统可由状态反馈鲁棒镇定的充分条件，并且利用线性矩阵不等式的解构造了使得系统鲁棒稳定的无记忆状态反馈控制律，所得结果是依赖时滞大小的，且与时滞的导数有关，从而相对减弱了控制器设计的保守性，最后通过一个例子说明了方法的有效性。     

非线性不确定随机多重时滞系统的鲁棒H_∞控制

研究一类非线性不确定随机多重时滞系统的鲁棒 H∞ 控制问题。运用线性矩阵不等式方法 ,导出了满足系统随机鲁棒稳定的充分条件 ,提出实现系统在一定概率意义下干扰衰减鲁棒镇定的鲁棒无记忆控制器设计方法     

具有时滞的不确定鲁里叶控制系统的绝对鲁棒稳定性

讨论了具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定性问题,应用Bellman-Gronwell不等式和Lyapunov泛函方法研究了不确定鲁里叶控制系统的鲁棒绝对稳定性并给出了系统的滞相关稳定和时滞无关稳定的充分判据,运用这些条件可以直接估计具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定界和时滞界。     

Lurie滞后反馈控制系统绝对稳定的鲁棒扰动界

本文应用Lyapunov方法讨论了具有时滞反馈的 Lurie控制系统的鲁棒绝对稳定性,给出了具有一个和多个滞后反馈的Lurie控制系统的绝对 鲁棒稳定的充分条件．用本文的结论可直接计算具有时滞反馈的Lurie控制系统绝对稳定的 鲁棒扰动上界．文末给出了应用本文结论的例子．     

Robust absolute stability of Lurie interval control systems

This paper considers robust absolute stability of Lurie control systems. Particular attention is given to the systems with parameters having uncertain, but bounded values. Such so‐called Lurie interval control systems have wide applications in practice. In this paper, a number of sufficient and necessary conditions are derived by using the theories of Hurwitz matrix, M matrix and partial variable absolute stability. Moreover, several algebraic sufficient and necessary conditions are provided for the robust absolute stability of Lurie interval control systems. These algebraic conditions are easy to be verified and convenient to be used in applications. Three mathematical examples and a practical engineering problem are presented to show the applicability of theoretical results. Numerical simulation results are also given to verify the analytical predictions. Copyright © 2007 John Wiley & Sons, Ltd.     

An algebraic approach to the robust stability analysis and robust stabilization of uncertain singular systems

This paper considers the problems of robust stability analysis and robust stabilization for uncertain singular systems with norm-bounded time-varying uncertainties. The robust stability problem is solved via the notion of generalized quadratic stability which guarantees that the uncertain singular system is stable, regular and impulse free simultaneously for all admissible uncertainties, while the robust stabilization problem is solved via the notion of generalized quadratic stabilizability. An algebraic approach is adopted in the paper. Our main results are extensions of some existing results on uncertain regular systems for singular systems.     

有结构摄动非线性系统的鲁棒绝对稳定性

考虑非线性闭环系统的鲁棒绝对稳定性,系统的线性部分受结构摄动以区间传递函数表 示,而其非线性(不确定)反馈函数在一个扇区内.将鲁棒性分析的现代结果与经典的圆判据 相结合,给出检验上述系统鲁棒绝对稳定性的方法.这个方法只用到16个特别选出的传递函 数的奈氏曲线.这个数目不随系统的线性部分的阶次增高而加大,在某些特别情况下却可能 更小.于是,将原问题的计算复杂性降到了一个非常低的水平.     

On absolute stability of Lur''''e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur'e form to guarantee the absolute stability of Lur'e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs), If those LMIs are feasible, free parameters in the Lyapunov function,such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems.A numerical example is provided to demonstrate the effectiveness of the proposed method.     

On absolute stability of Lur＇e control systems with multiple non-linearities using linear matrix inequalities

Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur‘e form to guarantee the absolute stability of Lur‘e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function, such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyaptmov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems. A numerical example is provided to demonstrate the effectiveness of the proposed method.     

Modified Mikhailov plots for robust absolute stability with non-parametric perturbations and uncertain nonlinearity

This paper generalizes the classical Mikhailov stability result for testing robust absolute stability of linear systems with both non-parametric perturbations and uncertain nonlinearity. Three types of non-parametric perturbations are considered: additive, multiplicative and stable-factor perturbations. Modified Mikhailov plots are developed for simultaneously testing the stability of the ‘nominal’ system and computing the maximum robust absolute stability margin.     

带有非线性不确定参数的线性系统的鲁棒稳定性和鲁棒镇定问题

研究带有非线性不确定参数的线性系统的鲁棒稳定性和鲁棒镇定问题。讨论一种有很强实际应用背景并允许带有二次不确定参数的模型,研究该系统的鲁棒稳定性和鲁棒镇定问题。以ＬＭＩ的形式给出了判据,并举例证明了该方法的优越性。     

Robust nonlinear feedback control for uncertain linear systems with nonquadratic performance criteria

In this paper we develop a unified framework to address the problem of optimal nonlinear robust control for linear uncertain systems. Specifically, we transform a given robust control problem into an optimal control problem by properly modifying the cost functional to account for the system uncertainty. As a consequence, the resulting solution to the modified optimal control problem guarantees robust stability and performance for a class of nonlinear uncertain systems. The overall framework generalizes the classical Hamilton–Jacobi–Bellman conditions to address the design of robust nonlinear optimal controllers for uncertain linear systems. © 1998 Elsevier Science B.V.