Delay-dependent robust stability of uncertain networked control systems with multiple state time-delays

In this paper, delay-dependent robust stability for a class of uncertain networked control systems （NCSs） with multiple state time-delays is investigated. Modeling of multi-input and multi-output （MIMO） NCSs with networkinduced delays and uncertainties through new methods are proposed. Some new stability criteria in terms of LMIs are derived by using Lyapunov stability theory combined with linear matrix inequalities （LMIs） techniques. We analyze the delay-dependent asymptotic stability and obtain maximum allowable delay bound （MADB） for the NCSs with the proposed methods. Compared with the reported results, the proposed results obtain a much less conservative MADB which are more general. Numerical example and simulation is used to illustrate the effectiveness of the proposed methods.     

Asymptotic stability analysis of nonlinear real-time networked control systems

The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems （NCSs）. Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound （MADB） for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.     

网络控制系统的最大允许时延界

提出确定多输入多输出网络控制系统的最大允许时延界的新方法. 由于网络诱导时延的分布特性, 整个多输入多输出网络控制系统实际上是一个多时延系统. 利用李雅普诺夫第二方法, 得到网络控制系统时延相关渐近稳定性判据. 最大允许时延界和输出反馈镇定控制器均可通过求解矩阵不等式(LMI)得到. 仿真比较说明了本文结果的正确性和可行性.     

一种获取网络化控制系统最大允许延迟时间的新方法

提出了一种获取网络化控制系统最大允许延迟时间的新方法．该方法利用控制系统的时滞相关稳定性条件设计状态反馈控制器,得到最大允许延迟时间,并以线性矩阵不等式的形式描述．仿真实例表明了该方法是有效的,并降低了已有方法的保守性．     

Absolute stability of Lurie networked control systems

This paper is concerned with the absolute stability problem of networked control systems (NCSs) with the controlled plant being Lurie systems (Lurie NCSs), in which the network‐induced delays are assumed to be time‐varying and bounded. First, in consideration of both the time‐varying network‐induced delays and data packet dropouts, the Lurie NCSs can be modeled as a multiple‐delays Lurie system. Then, a delay‐dependent absolute stability condition is established by using the Lyapunov–Krasovskii method. Next, two approaches to controller design are proposed in the terms of simple algebra criteria, which are easily solved via the toolbox in Matlab. Furthermore, the main results can be extended to robust absolute stability of Lurie NCSs with the structured uncertainties, where robust absolute stability conditions and approaches to robust controller design are presented. Finally, two numerical examples are worked out to illustrate the feasibility and the effectiveness of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust stabilization for a class of nonlinear networked control systems

The problem of robust stabilization for a class of uncertain networked control systems （NCSs） with nonlinearities satisfying a given sector condition is investigated in this paper. By introducing a new model of NCSs with parameter uncertainty, network-induced delay, nonlinearity and data packet dropout in the transmission, a strict linear matrix inequality （LMI） criterion is proposed for robust stabilization of the uncertain nonlinear NCSs based on the Lyapunov stability theory. The maximum allowable transfer interval （MATI） can be derived by solving the feasibility problem of the corresponding LMI. Some numerical examples are provided to demonstrate the applicability of the proposed algorithm.     

含状态和输入时滞的网络控制系统镇定

研究含有更广泛被控对象的网络控制系统镇定问题．假定被控对象含有时变状态和输入时滞,采用Lyapunov-Krasovskii泛函方法分析了系统的稳定性．所提出的方法可转化为线性矩阵不等式的形式,因而可较为容易地求得控制器和广义最大允许时延．仿真结果说明了所提出方法的有效性．     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

A Switched System Approach to Robust Stabilization of Networked Control Systems with Multiple Packet Transmission

This paper considers robust stabilization of networked control systems (NCSs) with the problem of multiple packet transmission. Two parts of uncertainties are considered in this paper: norm‐bounded parameter uncertainties in the plant, and norm‐bounded parameter uncertainties in the controller. For sensor nodes and actuator nodes communicating through a limited communication channel, we are particularly interested in the case that only one packet containing part of the state information can be transmitted through a toking‐bus every time. Stability of the NCSs with multiple packet transmitted in a periodic manner is closely related to that of periodically switched systems. For NCSs with and without uncertainties in the plant and the controller, stabilizing state feedback controllers are constructed in terms of linear matrix inequalities (LMIs). Numerical examples are given to illustrate the feasibility and effectiveness of the proposed approach.     

基于传感器故障的网络化系统鲁棒容错设计

针对一类具有参数不确定的非线性网络化控制系统,基于T-S模糊模型建模,推证出了确保非线性网络化控制系统在传感器发生失效故障时具有鲁棒完整性的时滞依赖充分条件,并以求解矩阵不等式给出了容错控制器的设计方法.最后以一个仿真算例验证了文中所述方法的可行性和有效性.     

Robust reliable control design for networked control system with sampling communication

In this article, the problem of robust exponential stability and reliable stabilisation for a class of continuous-time networked control systems (NCSs) with a sample-data controller and unknown time-varying sampling rate is considered. The analysis is based on average dwell-time, Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique. The delay-dependent criteria are developed for ensuring the robust exponential stability of the considered NCSs. The obtained conditions are formulated in terms of LMIs that can easily be solved by using standard software packages. Furthermore, the result is extended to study the robust stabilisation for NCS with parameter uncertainties. A state feedback controller is constructed in terms of the solution to a set of LMIs, which guarantee the robust exponential stabilisation of NCS and the controller. Finally, numerical examples are presented to illustrate the effectiveness of the obtained results.     

具有短时延的网络控制系统的一种鲁棒控制方法

针对具有短时延的网络控制系统, 本文提出了一种基于鲁棒控制的方法来解决该类系统的稳定化控制问题. 考虑状态反馈控制律, 将闭环网络控制系统描述为一个离散时间线性不确定系统模型, 其中的不确定部分反映了时延的时变特性对系统动态的影响. 得到了该闭环网络控制系统的渐近稳定性条件, 且该条件建立了闭环网络控制系统稳定性与两个时延参数, 即允许时延上界和允许时延变换范围, 之间的定量关系. 进一步的, 还给出了稳定化反馈控制器的设计步骤. 最后通过一个示例验证了本文所提出方法的有效性.     

非线性时延网络控制系统的模糊建模与控制

针对时变网络诱导时延小于一个采样周期的非线性时延网络控制系统,讨论系统的稳定性及控制器的设计方法.利用基于“IF-THEN”规则的模糊模型近似系统中的非线性,将时延的不确定性转化为系统参数的不确定性,从而将此类非线性网络控制系统建模为一类具有参数不确定性的离散Takagi-Sugeno（T-S）模糊模型.基于建立的模型,利用Lyapunov方法和线性矩阵不等式方法,分析了系统的稳定性及模糊状态反馈控制器的设计方法,最后通过仿真实例验证了所提出方法的有效性.     

不确定TCP流模型的离散H∞鲁棒主动队列管理算法

针对TCP/IP网络存在参数时变和不确定性下的拥塞控制问题,提出一种新的基于H∞状态反馈控制的离散鲁棒主动列队管理算法(AQM).该方法针对不确定TCP流模型,将短期突发流所占据的带宽作为系统的外部干扰,同时考虑时滞和参数不确定性因素,基于Lyapunov稳定性理论和线性矩阵不等式技术,设计了离散鲁棒状态反馈控制器以保证路由器队列响应的稳定性和鲁棒性.最后,通过NS-2仿真验证了本文方法的有效性.     

Robust fuzzy tracking control for nonlinear networked control systems with integral quadratic constraints

This paper investigates the robust tracking control problem for a class of nonlinear networked control systems (NCSs) using the Takagi-Sugeno (T-S) fuzzy model approach. Based on a time-varying delay system transformed from the NCSs, an augmented Lyapunov function containing more useful information is constructed. A less conservative sufficient condition is established such that the closed-loop systems stability and time-domain integral quadratic constraints (IQCs) are satisfied while both time-varying network-induced delays and packet losses are taken into account. The fuzzy tracking controllers design scheme is derived in terms of linear matrix inequalities (LMIs) and parallel distributed compensation (PDC). Furthermore, robust stabilization criterion for nonlinear NCSs is given as an extension of the tracking control result. Finally, numerical simulations are provided to illustrate the effectiveness and merits of the proposed method.     

Non‐fragile robust control for networked control systems with long time‐varying delay,randomly occurring nonlinearity,and randomly occurring controller gain fluctuation

This paper investigates the non‐fragile robust control problem for a class of nonlinear networked control systems (NCSs) with long time‐varying delay. Both the uncertain nonlinearity and the controller gain fluctuation enter into the system in random ways, and such randomly occurring nonlinearity and randomly occurring controller gain fluctuation obey certain mutually uncorrelated Bernoulli distributed white noise sequences. A new time‐varying discrete time system model is proposed to describe the NCS. To reduce conservatism arising from modeling time‐varying parts, the time‐varying parts due to the time‐varying delay are treated as a norm‐bounded uncertainty with one nominal point using robust control techniques. Based on the obtained uncertain system model, a regular and an optimal sufficient non‐fragile controllers are derived by applying the Lyapunov stability theory and the linear matrix inequality technique, which render the closed‐loop NCS to be asymptotically stable and guarantee an upper bound of the given performance cost for all admissible uncertainties. Moreover, the existence condition and design method for the non‐fragile stabilizing controllers are also presented. Two numerical examples are provided to demonstrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

不确定多时变时滞网络控制系统的时滞相关稳定性

讨论了具有不确定性和多时变时滞的网络控制系统(NCSs)的时滞相关稳定性. 针对一类多输入多输出(MIMO)的NCSs, 在考虑网络时滞和不确定性的情况下, 建立了该系统的数学模型. 利用Lyapunov稳定性理论和线性矩阵不等式(LMI)方法, 提出了新的基于LMI形式的时滞相关稳定条件. 该方法克服了已有方法的保守性且结果更具有一般性. 最后给出实例表明该方法与现有文献结果相比, 具有较小的保守性和更好的有效性.     

时延网络控制系统的模型预测控制

针对有输入约束的不确定时延网络控制系统,提出鲁棒模型预测控制方法;其中,将不确定时延建模为范数有界的输入矩阵的不确定性．给出了鲁棒性能指标的上界和系统渐近稳定的充分条件,通过在线求解LMI凸优化问题得到状态反馈控制律．仿真例子验证了该方法的有效性．     

一种改进的网络控制系统控制器设计方法

讨论网络控制系统的状态反馈控制器设计问题。针对具有未知时变时延的网络控制系统,应用自由权矩阵方法得到系统的稳定性条件,并应用到具有时变结构不确定性的网络控制系统,在此基础上提出状态反馈控制器设计方法。数值实例表明该方法的有效性,与已有方法相比,具有较低的保守性。     

一类不确定线性系统的鲁棒自适应控制

针对一类同时具有匹配不确定性和不匹配政治面目 确定性的线性系统,首先采用李雅普诺夫稳定性定理,结合基于矩阵不等式的鲁棒控制器设计方法和变结构控制方法,设计鲁棒控制器,使得闭环系统是二次渐近稳定的,然后,利用自适应参数估计方法,设计具有匹配不确定性范数界估计能力的鲁棒自适应控制器,保证闭环系统的一致终结有界,在此基础上,进一步考虑系统中可能的未知不确定性,分析闭环系统的鲁棒性,并得到了相应的控制器设计方法。