时滞相关型离散时变时滞奇异系统的鲁棒镇定

讨论含参数不确定的离散时变时滞奇异系统的时滞相关的鲁棒状态反馈稳定化问题. 在一系列等价变换下, 阐述了其和一个不确定正常线性离散时变时滞系统的鲁棒状态反馈稳定化问题的等价关系;利用矩阵不等式方法, 给出一个对所有容许的不确定, 使得闭环系统正则、因果且稳定的时滞相关鲁棒状态反馈稳定化控制器存在的充分条件以及无记忆状态反馈控制器的一个解.     

轧机厚控系统时滞相关鲁棒容错H∞控制器设计

研究了轧机厚控系统时滞相关鲁棒容错控制问题.轧机厚控系统实际足一个线性不确定时滞系统,考虑其可能发生的执行器增益故障,利用Lyapunov-Krasovskii泛函方法和线性矩阵不等式,给出了厚控系统时滞相关鲁棒容错控制器存在的充分条件,并给出了控制器的设计方法.所获得的控制器不仅能使故障系统鲁棒稳定,并且能达到给定的...     

一类不确定离散奇异系统的鲁棒稳定化

讨论了离散奇异系统矩阵E中含时不变参数不确定的鲁棒状态反馈稳定化问题.首先,在一系列等价变换下,阐述了其和一个不确定正常线性离散系统的鲁棒状态反馈稳定化问题的等价关系;然后,利用线性矩阵不等式(LMI)方法,给出了鲁棒状态反馈稳定化控制器存在的一个充分必要条件,控制器的设计方法及控制器的一个解;最后,通过一个数值算例验证了本设计方法的有效性.     

具有输入时滞的不确定采样系统的鲁棒控制北大核心CSCD

针对具有输入时滞的结构不确定采样系统,研究了该类系统基于离散化模型的鲁棒控制器设计问题。通过将采样系统的连续的结构不确定对象离散化得到其近似模型,使具有输入时滞不确定采样系统的鲁棒控制器设计问题转换为讨论具有输入时滞的离散系统的鲁棒稳定性问题。利用Lyapunov函数的构造及解析技巧,给出了基于线性矩阵不等式(LMI)的输入时滞离散系统的鲁棒稳定性条件,并在此基础上将控制器参数化,得到了一个通过求解线性矩阵不等式(LMI)来获得采样系统鲁棒控制器的设计方法,所设计的控制器保证了系统的鲁棒稳定性,对结构摄动有着较好的鲁棒性能。最后,通过数值计算仿真验证了本文方法的可行性。     

具有输入时滞的不确定采样系统的鲁棒控制

针对具有输入时滞的结构不确定采样系统,研究了该类系统基于离散化模型的鲁棒控制器设计问题。通过将采样系统的连续的结构不确定对象离散化得到其近似模型,使具有输入时滞不确定采样系统的鲁棒控制器设计问题转换为讨论具有输入时滞的离散系统的鲁棒稳定性问题。利用Lyapunov函数的构造及解析技巧,给出了基于线性矩阵不等式(LMI)的输入时滞离散系统的鲁棒稳定性条件,并在此基础上将控制器参数化,得到了一个通过求解线性矩阵不等式(LMI)来获得采样系统鲁棒控制器的设计方法,所设计的控制器保证了系统的鲁棒稳定性,对结构摄动有着较好的鲁棒性能。最后,通过数值计算仿真验证了本文方法的可行性。     

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.     

不确定时滞系统基于观测器的鲁棒控制器设计

研究了不确定线性时滞系统的状态观测器和基于观测器的鲁棒控制器设计问题，其中不确定性是时变的，通过构造增广系统，利用线性矩阵不等式方法，获得了该不确定系统存在状态观测器和基于观测器的鲁棒控制器的充分条件，同时给出了相应的状态观测器和基于观测器的鲁棒控制器，所给示例说明了本文方法的设计步骤和有效性。     

线性不确定系统的鲁棒稳定控制器设计

对于满足匹配条件的线性不确定系统,本文根据Lyapunov稳定性原理给出一种鲁棒稳 定控制器的设计方法,这种方法可以设计鲁棒稳定控制器对于标称系统是最优的.本文还将 这种方法推广到不满足匹配条件的线性不确定系统,并给出数值例子说明了这种方法的有效 性.     

含饱和驱动的线性时滞系统的时滞相关鲁棒稳定化

讨论含饱和驱动的线性时滞系统的时滞相关鲁棒稳定化以及控制器的设计问题.借助于积分不等式,利用Lyapunov-Krasovskii泛函方法,结合S-过程,获得了基于LMI的可稳定化的时滞相关条件,同时给出了无记忆控制器的设计方法,不必对原系统进行任何模型变换.实例表明,本文方法所得结论具有较小的保守性.     

具有扰动的多时滞线性系统的鲁棒控制器

本文讨论了多时滞多扰动线性系统的鲁棒控制器设计问题，证明了在一定条件下时滞扰动系统能稳的充分条件为其标称系统二次型能稳，给出了按标称系统的给定稳定裕度设计系统鲁棒控制器的方法。     

A stabilization algorithm for a class of uncertain linear systems

This paper presents an algorithm for the stabilization of a class of uncertain linear systems. The uncertain systems under consideration are described by state equations which depend on time-varying unknown-but-bounded uncertain parameters. The construction of the stabilizing controller involves solving a certain algebraic Riccati equation. Furthermore, the solution to this Riccati equation defines a quadratic Lyapunov function which is used to establish the stability of the closed-loop system. This leads to a notion of ‘quadratic stabilizability’. It is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable.The paper also deals with a notion of ‘overbounding’ for uncertain linear systems. This procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems. Also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process.     

Robust asymptotic stabilizability of Petersen's counterexample viaa linear static controller

A stabilizing linear static controller is discovered for a linear time-varying uncertain system of Petersen. We use the concept of a sandwich cone decomposition to show that Petersen's system is stabilizable by linear static controllers. We establish the surprising result that Petersen's system is stabilizable against time-varying uncertainties on any given compact subset of the uncertainty controllability space. Our work suggests the use of “scalar-quadratic” Lyapunov functions, a special subclass of polyhedral Lyapunov functions, in establishing stability for other linear time-varying uncertain systems, and it reopens the study of the conjecture: stabilizability via nonlinear control always implies stabilizability via linear control     

不确定多通道奇异时滞系统分散H∞控制

针对不确定多通道奇异时滞大系统, 研究其分散鲁棒H_∞控制问题. 假定不确定性是时不变、范数有界. 基于奇异系统Lyapunov稳定性理论, 通过设定Lyapunov-Krasovskii矩阵为合适的块对角结构, 推导出了使不确定多通道奇异时滞大系统可鲁棒镇定, 且满足一定的扰动水平的充分条件即一组线性矩阵不等式(LMIs)有可行解. 给出了具有期望阶数的分散输出反馈H_∞控制器的设计方法.     

线性时滞不确定系统的鲁棒稳定控制

对于线性时滞不确定系统,给出一种鲁棒渐近稳定控制器的设计方法,且对匹配与不匹 配两类不确定系统进行了研究.与现有结果相比,按此方法设计的系统不但控制器增益较小, 实现方便,而且可以容许较大的系统不确定性.     

Quadratic stabilizability of uncertain linear systems: Existence of a nonlinear stabilizing control does not imply existence of a linear stabilizing control

This note is concerned with the problem of stabilizing an uncertain linear system via state feedback control. An uncertain system which admits a stabilizing state feedback control and some associated quadratic Lyapunov function is said to be quadratically stabilizable. In a number of recent papers, conditions are given under which quadratic stabilizability via nonlinear control implies quadratic stabilizability via linear control. These papers restrict the manner in which the uncertain parameters are permitted to enter structurally into the state equation in order to establish this result. This note presents an example which shows that this implication is not true for more general uncertain linear systems. To this end, we describe an uncertain linear system which is quadratically stabilizable via nonlinear control but not quadratically stabilizable via linear control.     

一类多通道不确定时滞大系统分散鲁棒H∞控制：LMI方法

研究多通道不确定时滞大系统的鲁棒分散H_∞控制问题. 假定不确定性是时不变、范数有界, 且存在于系统、时滞和输出矩阵中. 主要针对动态输出反馈控制问题. 基于Lyapunov稳定性理论, 通过设定Lyapunov矩阵为合适的块对角结构, 采用矩阵替换的方法推导出了使多通道不确定时滞大系统可鲁棒镇定, 且满足一定的扰动水平的时滞依赖充分条件即线性矩阵不等式(LMI) 有可行解, 并且给出了具有期望阶数的分散鲁棒控制器的设计方法. 数值例子说明了本文提出方法的有效性.     

Memoryless stabilization of uncertain linear systems includingtime-varying state delays

The problem of stabilizing a class of uncertain time-delay systems via memoryless linear feedback is examined. The systems under consideration are linear systems with time-varying state delays. They also contain uncertain parameters (possibly time-varying) whose values are known only to within a prescribed compact bounding set. The main contribution given is to enlarge the class of time-delay systems for which one can construct a stabilizing memoryless linear feedback controller. Within this framework, a novel notion of robust memoryless stabilizability is first introduced via the method of Lyapunov functionals. Then a sufficient condition for the stabilizability is proposed. It is shown that solvability of a parameterized Riccati equation can be used to determine whether the time-delay system satisfies the sufficient condition. If there exists a positive definite symmetric solution satisfying the Riccati equation, a suitable memoryless linear feedback law can be derived     

Nonlinear versus linear control in the robust stabilizability oflinear uncertain systems via fixed-order output feedback

This paper considers the problem of robustly stabilizing an uncertain system via fixed-order output feedback control. This problem is considered by defining a notion of robust stabilizability with a quadratic storage function. This notion is closely related to the notion of quadratic stabilizability. The main result of the paper shows that if an uncertain system is robustly stabilizable with a quadratic storage function via a nonlinear time-varying controller, then it will also be robustly stabilizable with a quadratic storage function via a linear time-invariant controller of the same order     

Delta算子时滞系统的可靠D--镇定

研究同时含有执行器故障和传感器故障的Delta算子时滞系统的鲁棒可靠D-镇定问题.利用矩阵特征值理论和线性矩阵不等式方法,给出了Delta算子时滞系统D-稳定的充分条件,进而,针对同时含有执行器故障和传感器故障的Delta算子范数有界参数不确定时滞系统,设计鲁棒可靠D-镇定状态反馈控制器,使得对于所有容许的不确定性、执行器故障和传感器故障,Delta算子闭环时滞系统的极点均落在复平面指定圆盘区域内.最后,通过数值算例验证了控制器设计方法的可行性和有效性.     

不确定性时滞系统的鲁棒镇定控制器设计——LMI 方法*

采用线性矩阵不等式方法,研究一类不确定性动态系统,这类系统具有多重时变状态时滞多重时变控制输入时滞,其不确定性满足范数有界条件。我们得到一了类不确定性时滞系统的可状态反馈镇定的充分条件。