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.     

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.      

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.     

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.     

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。     

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     

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.      

存在多路数据丢失的线性离散时变系统故障检测滤波器设计

本文研究一类存在多路测量数据丢失的线性离散时变系统故障检测滤波器设计问题,系统的数据丢失现象由一族在给定区间范围内取值的相互无关的随机变量描述.采用基于观测器的鲁棒Hx故障检测滤波器作为残差产生器,通过引入新的随机变量,将故障检测滤波器的设计问题转化为一类具有乘性噪声影响的随机时变系统有限时间域内的Hx滤波问题运用Ly...     

线性离散时滞系统的D稳定容错控制

采用状态反馈和带时滞的状态反馈控制律,基于Lyapunov稳定性理论和Riccati方程,针对线性离散一步时滞系统,研究了执行器失效后有一定性能保证的D稳定容错控制问题。在给出对执行器失效具有完整性的D稳定容错控制系统需满足的一个充分条件的基础上,给出了控制器的设计方法和步骤,并推广至传感器失效情况。仿真结果证实了这种方法的有效性,与仅引入状态反馈控制律相比,此方法有更好的动态响应性能。最后指出了时滞状态反馈增益矩阵的选取原则。     

Orthogonal Embeddings of Linear Time-Varying Systems

 Given a contractive linear system T which is represented as a causal linear contractive operator on a Hilbert space H, we study the question: When does there exist an isometric or unitary causal extension of T to H⊕H? Here causality is formulated as a lower triangularity condition and we assume the same causality structure for the extension. This question is often referred to as the generalized Darlington synthesis problem for linear time-varying systems. Date received: November 26, 2001. Date revised: June 19, 2002.     

The Brockett Problem for Linear Discrete Control Systems

The Brockett problem for linear discrete control systems is studied. A method for designing time-varying stabilizing feedback is developed. The Brockett problem for second-order systems with scalar feedback and nondegenerate transfer function is shown to have a positive solution.     

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．     

On Uniform Stabilization of Discrete-Time Linear Parameter-Varying Control Systems

For discrete-time polytopic linear parameter-varying systems, the uniform exponential stability, which is equivalent to the asymptotic stability and includes the quadratic stability as a special case, is characterized by the union of an increasing family of linear matrix inequality conditions. On the other hand, in certain cases, nonconservative synthesis of uniformly stabilizing controllers is achieved via a system of finite number of linear matrix inequalities if the controller is allowed to have finite memory of past parameters. Two such cases are robust state feedback (in a relaxed sense) against polytopic parameter variations, and multiple output injections under polytopic fusion rules.     

Anisotropy-Based Filtering for Linear Discrete Time-Varying Systems with Multiplicative Noises on a Finite Horizon

Automation and Remote Control - We consider the anisotropy-based filtering problem for a linear discrete time-varying multiplicative noise system on a finite time horizon. A random disturbance with...     

具有时变状态滞后2-D离散系统的稳定与镇定(英文)

针对一类由局部状态空间(LSS)Fornasini-Marchesini(FM)第二模型描述的,具有时变状态滞后的2-D离散系统,其中时变滞后项的上、下界均为正实数,研究了其稳定性和控制综合问题。首先,利用Lyapunov-Krasovski泛函方法,提出了系统的稳定性准则。再根据这一准则,分别设计状态反馈和动态输出反馈控制器保证系统的稳定性。状态反馈控制律和输出反馈矩阵可由线性矩阵不等式(LMI)求得。最后,通过数值算例说明所得结果的有效性。     

On Asymptotic Stabilization of Linear Discrete-time Systems with Saturated State Feedback

As saturation is involved in the stabilizing feedback control of a linear discrete-time system, the original global-asymptotic stabilization (GAS) may drop to region-asymptotic stabilization (RAS). How to test if the saturated feedback system is GAS or RAS? The paper presents a criterion to answer this question, and describes an algorithm to calculate an invariant attractive ellipsoid for the RAS case. At last, the effectiveness of the approach is shown with examples.     

一类线性切换系统的鲁棒状态反馈镇定

考虑一类标称系统存在共同Lyapunov函数的切换系统的鲁棒镇定问题.在不确定性不满足匹配条件下,设计出鲁棒状态反馈控制器,并在给定的切换策略下,确保闭环系统在其平衡点处渐近稳定.仿真结果表明所设计控制器是有效的.     

含区间时变时滞的线性不确定系统非脆弱鲁棒控制

针对一类时滞是时变的且属于一个已知区间的线性系统,利用Lyapunov-Krasovskii泛函方法,结合积分不等式方法,以线性矩阵不等式的形式,给出了区间时滞线性系统的时滞相关鲁棒稳定性准则,并设计了非脆弱鲁棒控制器。数值算例表明,所得结论是有效的,具有更低的保守性。     

Reducibility of Linear Time-Varying Systems of Special Form with Control and Measurements

Journal of Computer and Systems Sciences International - This paper considers some classes of linear time-varying systems with control and output vectors that can be reduced to time-invarint...