时滞不确定采样控制系统的鲁棒稳定性

本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法.因为采样系统的对象是连续时间的,所以对象中的时滞也应该是按连续时间来处理.文中指出,一个整数倍时滞是稳定的采样系统,可能会因为有并不很大的连续时间时滞而失稳.定义了一个新的变量w(t),用来描述这个不确定连续时间时滞带来的动特性.将w(t)的反馈回路分成与时滞无关和有关的两个部分,并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法.用修正z-变换法和仿真验证了这个由图解解析所求得的解.本方法既可用于采样系统,也可用于一般的连续时间系统.     

一类结构不确定性的离散时滞大系统的分散镇定

研究了一类离散时滞大系统的时滞相关鲁棒分散镇定问题, 系统的不确定与标称系统具有结构相似性. 通过构造性的差分格式, 将时滞相关鲁棒分散镇定控制器的存在条件转化为一列线性矩阵不等式的可行解问题. 提出了控制时滞及控制器的时滞鲁棒性概念, 在获得分散镇定控制器的同时给出了鲁棒时滞上界的求解, 因此比现有文献的结果更具有实际应用价值.     

线性不确定时滞系统的鲁棒指数稳定性

针对带有时变有界的不确定参数和状态时滞的线性不确定时滞系统,研究其时滞依赖型具有指定收敛率的鲁棒指数稳定性问题。通过应用Lyapunov-Krasovskii稳定性定理方法,合理建立Krasovskii泛函,利用线性矩阵不等式方法导出了系统鲁棒指数稳定且具有指定收敛率的判据。所得结论采用线性矩阵不等式表示,与时滞参数的导数无关,克服了通常所得结论与时滞导数有关,且要求时滞参数导数小于常数1的限制。应用实例证明了设计方案切实可行。     

时滞系统的降维状态预测观测器及预测控制器设计

研究控制项含有时滞的线性系统的预测控制问题.利用被控对象的预测输出向量和系统的控制向量,设计了一种降维状态预测观测器,并将该状态观测器用于时滞控制系统的最优状态反馈控制中.利用该状态预测观测器可将闭环系统的时滞项移至系统闭环结构之外,从而最优控制规律完全可以按无时滞系统进行设计.由性能指标计算公式表明,该预测控制器关于二次型性能指标是次优的.     

Global stabilization of high-order nonlinear time-delay systems by state feedback

We consider the problem of global stabilization by state feedback for a class of high-order nonlinear systems with time-delay. By developing a novel dynamic gain-based backstepping approach, a state feedback controller independent of the time-delay is explicitly constructed with the help of appropriate Lyapunov–Krasovskii functionals. The precise knowledge (even the upper bound) of the time-delay is not required. It is proved that the states of the nonlinear time-delay systems can be regulated to the origin while all the closed loop signals are globally bounded. Finally, both physical and academic examples are given to illustrate the applications of the proposed scheme.     

Application of the observer/Kalman filter identification method to unknown time-delay disturbed systems and the associated optimal digital tracker design

ABSTRACT

Many practical systems are described as unknown multi-input-multi-output (MIMO) time-delay systems with unknown disturbances. The properties and performance of multi-time-delay MIMO systems are quite different compared to delay-free systems, in particular if the time-delay is long. In addition, for practical implementation digital controllers are often required instead of analog controllers. This paper presents: (i) an overview of the mathematical modelling based on the observer/Kalman filter identification (OKID) method, with some insight on known/unknown MIMO systems; (ii) a study of the pole-zero maps of the identified delay-free system and the known/unknown time-delay system for various sampling periods; (iii) a development of the explicit pole-zero map of the sampled-data MIMO neutral system with multiple discrete and disturbed time delays; (iv) an utilisation of the OKID method for known/unknown time-delay sampled-data MIMO systems with unknown disturbances; (v) an extension of the existing equivalent-input-disturbance (EID) estimator, to determine a robust tracker for the unknown time-delay system with unknown disturbances; and (vi) an investigation on the unknown time-delay system with stable or unstable zeros to determine which traditional or customised tracker can be applied. In addition, simulation studies are performed on the relationship between pole-zero maps and delay times.     

An implicit self-tuning technique for processes with variable time-delay

Most implicit self-tuning schemes are based on least-squares k-step-ahead prediction over the system time-delay. On systems where the time-delay is variable the use of such self-tuning algorithms presents problems. For the case when there is a significant variation in the time-delay, it has been thought necessary either to determine the actual time-delay explicitly or to use explicit self-tuning schemes. Neither is in fact necessary, and it is shown in this paper how an implicit scheme may be used for such systems. In the proposed scheme, knowledge of the system time-delay is not required. A simulation example and a practical application are included which demonstrate the capability of the technique when dealing with systems having variable time delay.     

Lurie滞后反馈控制系统绝对稳定的鲁棒扰动界

本文应用Lyapunov方法讨论了具有时滞反馈的 Lurie控制系统的鲁棒绝对稳定性,给出了具有一个和多个滞后反馈的Lurie控制系统的绝对 鲁棒稳定的充分条件．用本文的结论可直接计算具有时滞反馈的Lurie控制系统绝对稳定的 鲁棒扰动上界．文末给出了应用本文结论的例子．     

线性定常时滞系统全时滞渐近稳定的充分代数判据

本文探讨了线性定常时滞系统全时滞渐近稳定性问题,并给出了简单实用的稳定性充分 代数判据.     

Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities

The problem of global asymptotic stability analysis and controller synthesis for a class of discrete linear time-delay systems with state saturation nonlinearities is investigated. With the introduction of a free matrix whose infinity norm is less than or equal to 1, the state of discrete linear time-delay systems with state saturation is bounded by a convex hull, which makes it feasible to apply a suitable Lyapunov functional to obtain a sufficient condition for global asymptotic stability. It is also shown that this condition can be extended to controller synthesis and discrete time-delay systems with partial state saturation. The obtained results are expressed in terms of matrix inequalities that can be solved by the presented iterative linear matrix inequality approach. The effectiveness of these results is demonstrated by some numerical examples.     

一类具有非线性饱和执行器的不确定时滞系统鲁棒控制

研究一类具有非线笥饱和执行器朱确定线性时滞系统的鲁棒性镇定问题。所考虑的不确定时滞系统具有时变未知且有界的不确定参数和状态时滞。提出了新的鲁棒可镇定判据和相应的鲁棒无记忆状态反馈控制器设计方法。数值仿真例子说明了所提出方法的有效性。     

Decentralised robust stabilisation of uncertain large-scale interconnected time-delay systems with unknown upper bounds of uncertainties

The problem of decentralised robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. In the paper, the upper bounds of delayed state perturbations, uncertainties, interconnection terms, and external disturbances are assumed to be completely unknown, and the delays are assumed to be any non-negative constants. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of adaptation-free decentralised local robust state feedback controllers can be constructed. In addition, it is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly ultimately bounded. Finally, as an application to the practical mechanical systems, some simulations of a numerical example are provided to demonstrate the validity of the theoretical results.     

时滞系统的自抗扰控制综述

时滞系统的控制一直是具有挑战性的普遍问题, 而自抗扰控制思想近年来被广泛地应用于时滞系统中. 在简要概述自抗扰控制原理的基础上, 介绍了应用自抗扰控制思想解决时滞系统问题的常用设计方法, 总结了自抗扰控制器的参数整定方法. 最后, 对今后的进一步研究进行了展望.     

一类非线性广义系统的时滞相关耗散控制

针对一类带有非线性摄动的广义时滞系统,研究了时滞相关的鲁棒耗散问题.讨论了此类非线性广义时滞系统的鲁棒耗散性.同时对此类非线性广义时滞系统的二次稳定性进行了研究,分别用线性矩阵不等式（LMI）的方法给出了充分条件,也给出了时滞相关的鲁棒耗散的时滞上界.并且,给出了时滞相关的鲁棒耗散的状态反馈控制器.最后,通过例子验证了定理的可行性.     

具有多个未知常时滞线性系统的时滞无关稳定性

本文针对线性时滞系统包括时滞在系统建立了时滞无关的稳定性判据，所考虑的时滞可以是多任意未知常时滞，故所得结果是对滞无关的，针对线性时滞大系统的一个说明例子比较证明了所建立的结果好于文献中存在的结果。     

Stability analysis for discrete-time switched time-delay systems

The stability analysis problem is studied in this paper for a class of discrete-time switched time-delay systems. By using a newly constructed Lyapunov functional and the average dwell time scheme, a delay-dependent sufficient condition is derived for the considered system to be exponentially stable. The obtained results provide a solution to one of the basic problems in discrete-time switched time-delay systems, that is, to find a switching signal for which the switched time-delay system is exponentially stable. Two illustrative examples are given to demonstrate the effectiveness of the proposed results.     

Delay-dependent consensus condition for a class of fractional-order linear multi-agent systems with input time-delay

The consensus problem of a class of fractional-order linear multi-agent systems with distributed control containing input time-delay is investigated. By adopting the frequency domain analysis and generalised Nyquist criterion for the fractional-order time-delay systems, the delay-dependent consensus condition is obtained. Then, we are interested in finding the maximum time-delay tolerance and give an exact formula for calculating the maximum time-delay to maintain the system is consensusable. As illustrated by the numerical examples, the proposed theoretical results work effectively and accurately.     

延时系统输入状态稳定性的Lyapunov逆理论

研究了延时系统输入状态稳定性的局部Lipschitz连续的Lyapunov逆理论. 针对含有任意可测局部本质有界扰动的延时系统, 一个局部Lipschitz连续的Lyapunov泛函被证实是存在的, 如果该系统是鲁棒渐进稳定的. 根据该结论, 延时系统输入状态稳定性的Lyapunov特征被进一步得到.     

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     

离散多步时滞系统的容错控制研究

针对离散多步时滞系统,基于Lyapunov稳定性理论,采用具有状态反馈及时滞状态反馈的控制律,推出了当执行器或传感器发生失效故障时闭环系统仍能保持渐近稳定需满足的充分条件;并利用LMI给出了不依赖时滞的线性离散多步时滞系统的容错控制器的通用求解方法;讨论了该方法对具有不同时滞步数离散多步时滞系统容错的普适性。以执行器失效故障为例,仿真结果证明了该方法的有效性。