线性时滞系统滞后反馈鲁棒镇定

本文研究时不变线性时滞系统的鲁棒镇定问题。通过建立时滞系统的一个渐近稳定性定理，对摄动矩阵满足匹配条件和不满足匹配条件的情况分别给出了完全鲁棒镇定控制器的设计方法与鲁棒镇定控制器的存在性充分条件和设计方法；文中尤其提出了非滞后线性系统的一种简单的滞后反馈镇定方案。文末用例子示例了本文的设计方法。     

具有状态滞后的线性不确定时滞系统鲁棒输出反馈控制

针对具有状态滞后和时变未知且有界不确定性的线性时变不确定时滞系统，研究了当状态不完全可测时的鲁棒镇定问题。利用Ｒｉｃｃａｔｉ方程方法，提出了一种基于观测器的动态输出反馈镇定控制器设计方法，并得到了不确定时滞系统可输出反馈镇定的充分条件。最后通过一数值例子来说明了所得结果的可行性。     

基于Riccati-It方程设计线性时滞系统鲁棒控制器的方法

利用Riccati-Ito型矩阵代数方程研究线性时不变系统的状态反馈镇定问题，对时滞系统给出了一种状态反馈镇定方法，这种镇定方法适应于许多时滞系统，其设计方案具有滞后无关性及对于许多系统滞后项系数任意性的完全适应性．本文第二部分研究时不变线性不确定系统的鲁棒镇定，利用Riccati-Ito型矩阵代数方程给出了这类系统鲁棒镇定控制器的设计方法．     

具有状态滞后的线性不确定时滞系统鲁棒输出反馈控制(英)

针对具有状态滞后和时变未知且有界不确定性的线性时变不确定时滞系统，研究了当状态不完全可测时的鲁棒镇定问题．利用Riccati方程方法，提出了一种基于观测器的动态输出反馈镇定控制器设计方法，并得到了不确定时滞系统可输出反馈镇定的充分条件．最后通过一数值例子来说明了所得结果的可行性．     

基于Riccati-ItXô方程设计线性时滞系统鲁棒控制器的方法*

利用Ｒｉｃｃａｔｉ－Ｉｔｏ型矩阵代数方程研究线性时不变系统的状态反馈镇定问题，对时滞系统给出了一种状态反馈镇定方法，这种镇定方法适应于许多时滞系统，其设计方案具有滞后无关性及对于许多系统滞后项系数任意性的完全适应性，本文第二部分研究对不变线性不确定系统的鲁棒镇定，利用Ｒｉｃｃａｔｉ－Ｉｔｏ型矩阵代数方程给出了这类系统鲁棒镇定控制器的设计方法。     

不确定时滞系统无记忆鲁棒镇定控制

本文研究了一类状态和控制同时存在滞后的线性时变不确定时滞系统的鲁棒镇定控制问题，针对所有容许的时变未知且有界的不确定性，得到了确保闭环系统二次稳定的充分条件。文中进一步把不确定时滞系统的二次镇定控制器设计问题等价为线性时不变系统的状态反馈标准Ｈ∞控制问题，并由此得到鲁棒镇定控制器综合设计方法。     

离散区间线性切换正系统的镇定

这里同时考虑了快切换和慢切换两类切换情形, 即任意切换和平均驻留时间切换情形. 在这两种情形下, 均给出了系统状态反馈镇定控制器的存在条件, 所设计的控制器能够在原系统不必为正的情况下保证相应的闭环系统对于所有给定的区间不确定性不但为正而且渐近稳定. 由于所获得的控制器存在条件均被描述为了线性不等式的形式, 因此通过求解简单的线性规划问题很容易确定出所期望的控制器参数. 最后, 通过数值算例说明了本文所提出的镇定控制器设计方法的有效性.     

基于状态反馈的一类非线性系统动态输出反馈镇定

针对一类具有线性不可测量状态的非线性系统,基于状态反馈稳定控制器,利用不变流形和滑模变结构控制技术设计了动态输出反馈镇定控制器.这类控制器的结构类似于系统的状态反馈稳定控制器,在较简单的假定条件下,能够保证被控系统的状态得到渐近镇定.仿真算例表明该动态输出反馈控制器具有较强的镇定能力.     

基于反馈线性化的MIMO非最小相位系统指数镇定

针对仿射多输入多输出非线性非最小相位系统,提出了一种新的镇定方案.用反馈线性化解耦系统输入输出关系,通过高增益状态反馈镇定系统外部动态,用模型预测控制镇定内部动态,所设计控制器能保证闭环系统的指数稳定性.仿真结果表明了所提出方法的有效性和优越性.     

不确定非线性时滞系统鲁棒镇定的进一步结果

针对广义的不确定非线性时滞系统，研究了其鲁棒镇定控制器的系统的递归设计方法。通过递归地构造Lyapunov-Razumikhin函数获得了一种独立于延时的状态反馈控制律。证明了通过一些设计技术处理，由Razumikhin 条件的应用所带来的固有的设计障碍是可以被克服的，从而使得系统鲁棒镇定控制器的获得不需要任何对系统的限制条件。     

Global state control for a class of inherently higher‐order parameterized nonlinear time‐delay systems based on homogeneous domination approach

This paper addresses the problem of global state feedback stabilization for a class of inherently higher‐order parameterized nonlinear systems subject to time delay. By using the homogeneous domination approach, we construct a homogeneous state feedback controller with an adaptive strategy. A constructive design method is developed based an effective coupling of the inductive method and a sign function, leading to adaptive regulators with minimal parameterization. With the aid of a homogeneous Lyapunov‐Krasovskii functional, the closed‐loop systems can be asymptotically stabilized globally.     

Stabilization of linear systems with distributed input delay and input saturation

This paper is concerned with stabilization of a linear system with distributed input delay and input saturation. Both constant and time-varying delays are considered. In the case that the input delay is constant, under the stabilizability assumption on an auxiliary system, it is shown that the system can be stabilized by state feedback for an arbitrarily large delay as long as the open-loop system is not exponentially unstable. In the case that the input delay is time-varying, but bounded, it is shown that the system can be stabilized by state feedback if the non-asymptotically stable poles of the open-loop system are all located at the origin. In both cases, stabilizing controllers are explicitly constructed by utilizing the parametric Lyapunov equation based low gain design approach we recently developed. It is also shown that in the presence of actuator saturation and under the same assumptions on the system, these controllers achieve semi-global stabilization. Some discussions on the assumptions we impose on the system are given. A numerical example illustrates the effectiveness of the proposed stabilization approach.     

单输入中立型时滞系统的镇定

本文考虑了单输人中立型时滞系统的镇定问题。利用Byrnes等人提出的中立型时滞系统的模型,我们证明:如果系统是非奇异的,则系统可镇定的充要条件是其谱可镇定。     

Stabilization of linear systems with time‐varying input delay by event‐triggered delay independent truncated predictor feedback

This article deals with the problem of stabilization of linear systems with time‐varying input delay by an event‐triggered delay independent truncated predictor feedback law, either of the state feedback type or the output feedback type. Only the information of a delay bound rather than the delay itself is required in the design of both control laws and event‐triggering strategies. For both the state feedback case and the output feedback case, an admissible delay bound that guarantees the stabilizability of a general linear system is established, and the Zeno behavior is shown to be excluded. For linear systems with all open‐loop poles at the origin or in the open left‐half plane, stabilization can be achieved for a delay under an arbitrarily large bound.     

Robust Exponential Stability and Stabilization of a Class of Nonlinear Stochastic Time‐Delay Systems

This paper presents new exponential stability and delayed‐state‐feedback stabilization criteria for a class of nonlinear uncertain stochastic time‐delay systems. By choosing the delay fraction number as two, applying the Jensen inequality to every sub‐interval of the time delay interval and avoiding using any free weighting matrix, the method proposed can reduce the computational complexity and conservativeness of results. Based on Lyapunov stability theory, exponential stability and delayed‐state‐feedback stabilization conditions of nonlinear uncertain stochastic systems with the state delay are obtained. In the sequence, the delayed‐state‐feedback stabilization problem for a nonlinear uncertain stochastic time‐delay system is investigated and some sufficient conditions are given in the form of nonlinear inequalities. In order to solve the nonlinear problem, a cone complementarity linearization algorithm is offered. Mathematical and/or numerical comparisons between the proposed method and existing ones are demonstrated, which show the effectiveness and less conservativeness of the proposed method.     

Simultaneous stabilization of a collection of single‐input nonlinear systems based on CLFs

This paper considers the simultaneous stabilization problem of a collection of single‐input nonlinear systems. Based on the technique of control Lyapunov functions (CLFs), a sufficient condition for the existence of a simultaneously stabilizing state feedback controller is proposed. It is shown that a collection of feedback linearizable systems in canonical form can be simultaneously globally asymptotically stabilized by a single state feedback controller. Moveover, for a set of three‐order chaotic dynamical systems, the simultaneous stabilization problem is considered and a similar result is derived. All the proposed simultaneously stabilizing state feedback controllers are explicitly constructed. Numerical examples are provided to illustrate the effectiveness of the proposed schemes. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于Razumikhin 方法的随机时变时滞非线性系统的状态反馈

采用Razumikhin 方法研究一类随机时变时滞非线性系统的状态反馈镇定问题. 利用随机系统的Razumikhin-Mao 理论和反推设计方法, 设计系统的状态反馈控制器, 所设计的控制器能保证闭环系统的平衡点为依概率全局渐近稳定的. 所提出的方法能够彻底地去掉关于随机时变时滞非线性系统传统结果中所要求的时滞导数的限制. 仿真示例验证了所提出状态反馈控制器的有效性.

     

具有输入饱和的组合系统的分散控制

研究了一类具有饱和输入的组合系统的分散可镇定问题. 运用M-矩阵方法, 通过线性分散状态反馈得出具有饱和输入组合系统的可镇定的充分条件. 对于具有对称结构的组合系统, 给出了更为简单的镇定条件.     

一类线性离散时滞大系统的分散镇定

用一组线性矩阵不等式给出一类线性离散时滞大系统分散能镇定的一个充分条件,进而,通过建立和求解一个凸优化问题,提出了具有较反馈增益参数的分散稳定化状态反馈控制律的设计方法,所得到的控制器不仅使得闭环境系统是稳定的,而且还可以使得闭环系统状态具有给定的衰减度。