Stabilization of Discrete Time-Varying Systems by Output Control

Stabilization of a discrete linear time-varying system with uniformly bounded parameters and one output by output control is studied by synthesizing an asymptotically stable observer with a given observation error attenuation rate and solving the problem of stabilization by state control through special similarity transformations.     

线性时变离散系统的状态观测器

本文放弃了Ｌｕｅｎｂｅｒｇｅｒ状态观测器理论对系统完全可观测性的要求，提出了一般线性时变离散系统的状态观测器设计方法，并对ｊ＝ｉ，ｉ－１给出了系统完全（ｉ，ｊ，Ｔｉ）－可重构这一新概念的充要条件。     

线性时变离散系统的稳定性

本文利用文[1]中的Gauss-Seidel迭代方法研究了线性时变离散系统的稳定性,得到了稳定性的若干代数判据。     

Finite-Time Stabilization of Linear Time-Varying Continuous Systems

In this technical note, the problem of finite time stabilization of linear time-varying continuous systems is considered. Necessary and sufficient conditions, based upon the solution to some Lyapunov differential matrix equations, are proposed for particular cases of interest. From these conditions, the design of time-varying state feedback controller guaranteeing the finite time closed-loop stability is presented. Numerical experiments illustrate the potentialities of the approach.      

关于线性时变离散系统的稳定性

本文研究线性时变离散系统的稳定性，采用一种解的估计技巧，简化了［１］用Ｇａｕｓｓ－Ｓｅｉｄｅｌ迭代法建立的稳定性判据的证明，并获得一些新的代数判据。     

带有时变不确定性的线性系统族的同时镇定

本文考虑了具有时变不确定性的线性系统族的状态反馈同时二次镇定问题，这个问题能更全面地刻划考虑系统的不确定性，并将其转注多个ｙａｐｕｎｏｖ方程的同一解的问题，最后给出一个数值算例。     

不确定时变时滞系统稳定性的Riccati方程法

讨论了不确定时变时滞系统的基于观测器后次稳定性问题,有两类不确定性被讨论,利用Ｌｙａｐｕｎｏｖ稳定性定理及范数不等式,我们证明了几个关于二次稳定性的定理,通过求解Ｒｉｃｃａｔｉ方程可以获得系统可二次稳定的状态反馈控制器,最后,通过实例验证了上述结果。     

Stabilization of Arbitrary Switched Linear Systems With Unknown Time-Varying Delays

We consider continuous time switched systems that are stabilized via a computer. Several factors (sampling, computer computation, communications through a network, etc.) introduce model uncertainties produced by unknown varying feedback delays. These uncertainties can lead to instability when they are not taken into account. Our goal is to construct a switched digital control for continuous time switched systems that is robust to the varying feedback delay problem. The main contribution of this note is to show that the control synthesis problem in the context of unknown time varying delays can be expressed as a problem of stabilizability for uncertain systems with polytopic uncertainties.     

离散线性多输入系统的切换反馈镇定

New idea of stabilization for discrete linear multiple-input system is proposed based on switching technique and single-input control. The system discussed here denotes coupled singleinput objects to be controlled. The central processing unit chooses an object at each discrete instant according to periodic switching strategy and controls it by local state feedback. Stabilization of a multiple-input system is turned into stabilization of single-input systems under periodic switching strategy, which is easy to be realized in practice. On the other hand, only one central processing unit can realize all local controllers, which decreases the cost and increases the usage of the resources.     

Switching Feedback Stabilization for Discrete Linear Multiple-input Systems

New idea of stabilization for discrete linear multiple-input system is proposed based on switching technique and single-input control. The system discussed here denotes coupled single-input objects to be controlled. The central processing unit chooses an object at each discrete instant according to periodic switching strategy and controls it by local state feedback. Stabilization of a multiple-input system is turned into stabilization of single-input systems under periodic switching strategy, which is easy to be realized in practice. On the other hand, only one central processing unit can realize all local controllers, which decreases the cost and increases the usage of the resources.     

周期时变线性系统的一般线性二次型最优控制

讨论周期时变线性系统的一般线性二次型最优控制问题, 即状态方程为非齐次方程且二次型性能指标包含线性项的一般情况. 给出了该问题可解的一系列充分必要条件, 同时给出了最优控制的解析构造以及最优性能指标值.     

具有状态和控制滞后的 线性时变时滞系统的输出反馈镇定

研究具有状态和控制滞后的线性时变时滞系统的静态输出反馈镇定，其设计过程只需解一个特殊的代数Ｒｉｃｃａｔｉ方程。并且指出，系统的动态输出反馈镇定问题可等价为广义系统的静态输出反馈镇定问题。最后通过实例论证了本方法的有效性。     

线性时变不确定离散系统的输出反馈鲁棒镇定研究

研究线性时变不确定离散系统的输出反馈鲁棒镇定问题。得到的动态输出反馈补偿器确保对于所有容许不确定性可以镇定被控对象。推导出动态输出反馈补偿器存在的充分条件。最后通过求解一个等价的线性时不变离散系统的标准Ｈ＾∞输出反馈控制问题,构造出线性时变不确定离散系统的动态输出反馈补偿器的系统矩阵。     

分布时滞系统的反馈镇定

求解特征矩阵是镇定时滞系统的关键问题,本文给出了系统的特征根的代数重复度与几何重复度均为一般值情况下特征矩阵的求法,即把它归结为求解一组线性代数方程的问题,并得到了该方程组有解及对应于同一特征值的解向量组线性独立的充分条件.此外,还提出了一种算法,用以处理系统对应于不同特征值的左特征向量线性相关情况下系统的镇定问题.     

Input-to-State Stabilization of Linear Systems With Quantized State Measurements

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with linear dynamics and quantized state measurements. Quantizers considered in this paper take finitely many values and have an adjustable "zoom" parameter. Building on an approach applied previously to systems with no disturbances, we develop a control methodology that counteracts an unknown disturbance by switching repeatedly between "zooming out" and "zooming in." Two specific control strategies that yield ISS are presented. The first one is implemented in continuous time and analyzed with the help of a Lyapunov function, similarly to earlier work. The second strategy incorporates time sampling, and its analysis is novel in that it is completely trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We discover that in the presence of disturbances, time-sampling implementation requires an additional modification which has not been considered in previous work     

Stabilization of Hybrid Systems by Feedback Control Based on Discrete‐Time State and Mode Observations

Recently, a kind of feedback control based on discrete‐time state observations was proposed to stabilize continuous‐time hybrid stochastic systems in the mean‐square sense. We find that the feedback control there still depends on the continuous‐time observations of the mode. However, it usually costs to identify the current mode of the system in practice. So we can further improve the control to reduce the control cost by identifying the mode at discrete times when we make observations for the state. In this paper, we aim to design such a type of feedback control based on the discrete‐time observations of both state and mode to stabilize the given hybrid stochastic differential equations (SDEs) in the sense of mean‐square exponential stability. Moreover, a numerical example is given to illustrate our results.     

含时变不确定性线性系统的鲁棒跟踪控制

本文就含时变不确定性的线性系统,研究了鲁棒跟踪控制器的设计问题。文中利用Ｒｉｃ－ｃａｔｉ方程,给出了使系统输出鲁棒跟踪某一动态输入的线性控制律,对于匹配系统,跟踪误差可以任意小,从而得到实际跟踪;对于不满足匹配条件的系统,若另一些条件成立,则跟踪误差有界。     

Inequality-Based Properties of Detectability and Stabilizability of Linear Time-Varying Systems in Discrete Time

Well-known properties of uniform detectability and uniform stabilizability are sharpened in terms of Lyapunov and Riccati inequalities for discrete-time linear time-varying systems. In particular, it is shown that the stabilizing output injection law can be taken to depend solely on a finite path of past and present system coefficients and the stabilizing state feedback law solely on a finite-path of present and future coefficients. These results are applied to time-varying systems where the system coefficients vary among a finite set, and lead to precise and computable convex conditions for the stability and dynamic-output-feedback stabilizability of such systems.      

鲁棒核主元分析的数据重构

针对野值点噪声对样本均值和协方差估计带来的不利影响,在线性鲁棒M 位置估计方法的基础上,结 合了核原理来估计协方差,提出了一种新型的鲁棒KPCA 算法．将所提出的算法应用于数据重构仿真实验,仿真测 试结果表明当样本数据中存在野值点噪声时, 由所提出的鲁棒KPCA 算法实现样本数据重构时,要比KPCA 具有更 高的重构精度, 抗野值点噪声性能更强．     

Finite-Time Stabilization of Linear Systems With Input Constraints by Event-Triggered Control

<正>Dear editor,This letter designs the event-triggered control(ETC) to achieve finite-time stabilization(FTS) of linear systems with input constraints. The key idea of the established algorithm is that the designed time-varying high-gain is only scheduled on a specified time determined by an event-triggered mechanism.