在离散观测和反馈延迟下的混杂随机系统镇定（英文）

对混杂随机系统的状态反馈控制近年来引起了广泛的关注.一个更现实也更经济的情况是对状态的观测不是连续时间而是离散时间的.同时,现实中绝大多数的观测和反馈系统都或多或少会存在时滞现象.因此,讨论这种基于离散时间观测同时带有观测反馈时滞的混杂随机系统的反馈控制是很有意义的.特别地,通过使用一个李雅普诺夫泛函,不仅可以得到H无穷稳定、渐近稳定和指数稳定,而且还能显著地改善对时滞上界的要求.本文是文献[20]工作的深入和推广.     

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。     

状态和控制含多时滞的离散系统H∞容错控制

针对状态和控制输入同时具有多个时滞的线性离散时间系统,基于Lyapunov稳定性理论和线性矩阵不等式方法(LMI),采用无时滞记忆的状态反馈控制律,研究了执行器故障情况下,离散多时滞系统的H∞容错控制问题.在采用连续执行器故障模型条件下,给出了系统没有干扰输入时存在无时滞记忆的状态反馈容错控制器的充分条件;进一步,给出了在H∞扰动衰减指标约束下,系统存在无时滞记忆的状态反馈H∞容错控制器的充分条件,并将结论推广到离散故障模型的情况.仿真结果证明了所提H∞容错控制器设计方法的正确性和有效性.     

基于T—S的时滞模糊系统的鲁棒稳定与镇定问题

讨论同时具有输入及状态时滞且多个范数有界不确定的非线性时滞模糊系统的时滞相关鲁棒稳定及镇定问题。利用通用的Lyapunov—Krasovskii泛函方法,结合自由权矩阵思想和对不确定项的更精确描述,获得基于线性矩阵不等式的时滞相关稳定的充分条件并给出状态反馈控制器的设计。该条件较已有结论不仅形式简单,而且具有更小的保守性。利用Matlab软件中的LMI工具箱求解,得到保证系统鲁棒渐近稳定的最大可允许时滞上界。数值算例表明该方法是有效性的。     

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.     

线性离散时滞系统滞后相关型H ∞状态反馈控制

基于Lyapunov泛函方法,对存在状态时滞的线性离散时间系统,给出了滞后相关型无记忆H∞状态反馈控制器设计方案,通过求解相应的线性矩阵不等式即可求得满足设计要求的控制器。     

不确定离散时滞系统状态预估H∞控制

针对一类线性不确定离散时滞系统,研究了系统的鲁棒稳定性和鲁棒H∞观测控制器的设计问题.在系统状态不能直接测量的情况下,基于线性矩阵不等式方法,通过构造合适的Lyapunov函数,给出了系统新近稳定的充分条件和状态反馈控制器的设计方案,并通过求解相应的线性矩阵不等式得到满足设计要求的控制器.仿真结果表明,所设计的控制器对...     

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.

     

离散奇异时滞系统时滞依赖稳定性分析与镇定

分别研究了离散奇异时滞系统时滞依赖稳定性分析与镇定问题. 首先给出了一个新的离散奇异时滞系统时滞依赖容许性充分条件. 经过证明, 所提出的方法与现有结论相比, 具有一定的优势. 然后, 运用矩阵理论技巧,设计出状态反馈控制器保证闭环离散奇异时滞系统是容许的. 最后,两个数值例子说明了所用方法的有效性.     

线性离散时滞系统的鲁棒耗散控制

考虑线性离散时滞系统的二次型耗散控制问题.对于确定系统,给出渐近稳定且严格二次型耗散的条件和动态输出反馈控制器使闭环系统渐近稳定且严格二次型耗散.对于不确定系统,考虑不确定性具有耗散特性的情形,讨论鲁棒耗散性分析和动态输出反馈鲁棒耗散控制问题.通过构造增广系统,将不确定系统的鲁棒严格二次型耗散分析和设计转化为确定系统的情况.所得结果为离散时滞系统的无源控制和H∞控制提供了统一框架,且为离散时滞系统的分析和设计提供了一种更灵活、保守性更小的方法.     

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.     

Robust quantised control of hybrid stochastic systems based on discrete-time state and mode observations

This paper considers robust quantised feedback control for hybrid stochastic systems based on discrete-time state and mode observations. All of the existing results in this area design the quantised feedback control based on continuous observations of the state and mode for all time t ≥ 0. This is the first paper where we propose to use the quantised feedback control based on discrete-time observations of the state and mode. The key reason for this is to reduce the burden of communication by using not only the quantisation (i.e. in the direction of state axis), but also discrete-time observations of state and mode (i.e. in the direction of time axis). Thus, the designed quantised feedback controllers have to be based on discrete-time state and mode observations. Clearly, the new quantised feedback controllers are more practical and lower of cost in practice.     

Analysis and design of event‐triggered control algorithms using hybrid systems tools

This article proposes a general framework for analyzing continuous‐time systems controlled by event‐triggered algorithms. Closed‐loop systems resulting from using both static and dynamic output (or state) feedback laws that are implemented via asynchronous event‐triggered techniques are modeled as hybrid systems given in terms of hybrid inclusions. Using recently developed tools for robust stability, properties of the proposed models, including stability of compact sets, robustness, and Zeno behavior of solutions are addressed. The framework and results are illustrated by several event‐triggered strategies available in the literature, and observations about their key dynamical properties are made.     

Decentralised adaptive robust control of uncertain large-scale interconnected systems with multiple time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. It is assumed that the upper bounds of the uncertainties, interconnection terms and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed decentralised local adaptive robust state feedback controllers are completely independent of time delays, the results obtained in this article may also be applicable to a class of large-scale interconnected dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.     

Necessary and Sufficient Stability Criterion and Stabilization for Positive 2‐D Continuous‐Time Systems with Multiple Delays

This paper addresses the stability and control problem of the linear positive two‐dimensional (2‐D) continuous‐time systems in Roesser model with multiple time delays. The contribution lies in two aspects. First, a simple novel proof is provided to establish necessary and sufficient conditions of asymptotic stability for 2‐D continuous delayed systems. It turns out that the magnitude of delays has no any impact on the stability of these systems, which is completely determined by the system matrices. Second, a necessary and sufficient condition for the existence of state‐feedback controllers is proposed for general delayed 2‐D systems, which ensures the non‐negativity and the stability of the resulting closed‐loop systems. Two examples are given to validate the proposed methods.     

Delay compensation for linear systems with both state and distinct input delays

This paper is concerned with the stabilization of linear systems with both state and distinct input delays. Nested predictor feedback controllers are designed to predict the future states such that the distinct input delays that can be arbitrarily large yet bounded are compensated completely. It is shown that the compensated closed‐loop system possesses the same characteristic equation as the closed‐loop system without distinct input delays. Both continuous‐time and discrete‐time time‐delay systems are studied in this paper. Moreover, the safe implementation problem for the continuous‐time nested predictor feedback controller is solved via adding input filters. Three numerical examples show the effectiveness of the proposed approaches.     

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.     

The Liapunov's second method for continuous time difference equations

Among many other cases such as economic and lossless propagation models, continuous time difference equations are encountered as the internal dynamics in a class of non‐linear time delay systems, when controlled by a suitable state feedback which drives the output exponentially to zero. The Liapunov's second method for these infinite dimensional systems has not been extensively investigated in the literature. This paper has the aim of filling this gap. Liapunov's second method theorems for checking the stability and the asymptotic stability of this class of infinite dimensional systems are built up, in both a finite and an infinite dimensional setting. In the finite dimensional setting, the Liapunov function is defined on finite dimensional sets. The conditions for stability are given as inequalities on continuous time. No derivatives are involved, as in the dynamics of the studied systems. In the infinite dimensional setting, the continuous time difference equation is transformed into a discrete time system evolving on an infinite dimensional space, and then the classical Liapunov theorem for the system in the new form is written. In this paper the very general case is considered, that is non‐linear continuous time difference equations with multiple non commensurate delays are considered, and moreover the functions involved in the dynamics are allowed to be discontinuous, as well as the initial state. In order to study the stability of the internal dynamics in non‐linear time delay feedback systems, an exogenous disturbance is added, which goes to zero exponentially as the time goes to infinity. An example is considered, from non‐linear time delay feedback theory. While the results available in the literature are inconclusive as far as the stability of that example is concerned, such stability is proved to hold by the theorems developed in this paper, and is validated by simulation results. Copyright © 2003 John Wiley & Sons, Ltd.     

Hybrid control for wide-area power systems based on hybrid system theory

The article focuses on a new two-level hierarchical hybrid control which contains an upper layer discrete supervisory strategy and lower layer continuous decentralised coordinated control based on hybrid system theory for wide-area power system overall stability enhancement. The discrete supervisory strategies are constituted based on an information fusion technique by using wide-area measurements (WAMs) in order to supervise and switch the control actions into apposite operation mode following a large disturbance. The continuous control is designed in the form of a local state feedback decentralised controller for each generator helped by a coordinated controller, and the coordinated controller is proposed to apply the remote signals from the WAM systems for improving dynamic performance. However, unavoidable communication time delays are involved before the remote signals are received at the coordinated controller. Taking account of the multiply delays, the authors develop a delay-dependent H _∞ robust control technique based on multiple Lyapunov stability theory. Some new stability criteria for hybrid control are derived in terms of linear matrix inequality. The so-called hybrid control is demonstrated through simulation examples to achieve the best overall performance following a large disturbance.     

A model of angiogenesis by hybrid systems with delay on the piecewise constant part

An important approach towards understanding the cancer dynamics is the modeling of angiogenesis process. There have been several attempts to model this process. Among them angiogenesis models with time delays, caused by the physical distance between the tumor and the vessel, are the most realistic ones. Recent studies have suggested that those delays can cause oscillatory behavior in the angiogenesis process. In this work we employed piecewise linear hybrid systems with delay on the piecewise constant part. Our approach is based on piecewise linearization of the system behavior where the delays occur at threshold crossings and state transitions. Piecewise linear systems with a single threshold for each variable are useful in approximating and modeling the dynamical systems especially when the model might need to be calibrated by the observations. Therefore, we used piecewise linear systems where the delays are introduced in piecewise constant part of the equations. Our approach allows tractable approximation of the angiogenesis process with possible advances of incorporating more variables, involving the effect of some possible external inputs, and possible adjustment or correction of parameters by observations.