Survey on the stability of networked control systems

The insertion of the communication network in the feedback control loop makes the analysis and design of a network control system more complex, and induces some issues that degrade the control system’s performance and even cause system instability. The main aspects are focused on the stability analysis of Network Control Systems (NCSs) with network-induced delays, data packet dropouts, and multiple-packet transmission. These issues must be considered in the design of an NCS. This work summarizes the main research results, and remarks on some related handling approaches and techniques. The main purpose of the survey is to present the new research state of NCSs and to point out some fields of future work.     

Survey on the stability of networked control systems

The insertion of the communication network in the feedback control loop makes the analysis and design of a network control system more complex, and induces some issues that degrade the control system’s performance and even cause system instability. The main aspects are focused on the stability analysis of Network Control Systems (NCSs) with network-induced delays, data packet dropouts, and multiple-packet transmission. These issues must be considered in the design of an NCS. This work summarizes the main research results, and remarks on some related handling approaches and techniques. The main purpose of the survey is to present the new research state of NCSs and to point out some fields of future work.     

Output feedback control of networked systems

This paper considers the problem of control of networked systems via output feedback. The controller consists of two parts: a state observer that estimates plant state from the output when it is available via the communication network, and a model of the plant that is used to generate a control signal when the plant output is not available from the network. Necessary and sufficient conditions for the exponential stability of the closed loop system are derived in terms of the networked dwell time and the system parameters. The results suggest simple procedures for designing the output feedback controller proposed. Numerical simulations show the feasibility and efficiency of the proposed methods.     

Input-to-state stability for networked control systems via an improved impulsive system approach

This paper presents a novel impulsive system approach to input-to-state stability (ISS) analysis of networked control systems (NCSs) with time-varying sampling intervals and delays. This approach is based upon the new idea that an NCS can be viewed as an interconnected hybrid system composed of an impulsive subsystem and an input delay subsystem. A new type of time-varying discontinuous Lyapunov-Krasovskii functional, which makes full use of the information on the piecewise-constant input and the bounds of the network delays, is introduced to analyze the ISS property of NCSs. Linear matrix inequality based sufficient conditions are derived for ISS of NCSs with respect to external disturbances. When applied to the approximate tracking problem for NCSs, the derived ISS result provides bounds on the steady-state tracking error. Numerical examples are provided to show the efficiency of the proposed approach.     

Stability analysis of networked control systems with time-varying sampling periods

In this paper, we present an interval model of networked control systems with time-varying sampling periods and time-varying network-induced delays and discuss the problem of stability of networked control systems using Lyapunov stability theory. A sufficient stability condition is obtained by solving a set of linear matrix inequalities. In the end, the illustrative example demonstrates the correctness and effectiveness of the proposed approach.     

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.     

Delay-dependent stability and stabilization criteria of networked control systems with multiple time-delays

This paper deals with the problem of delay-dependent stability and stabilization for networked control systems(NCSs)with multiple time-delays. In view of multi-input and multi-output(MIMO) NCSs with many independent sensors and actuators, a continuous time model with distributed time-delays is proposed. Utilizing the Lyapunov stability theory combined with linear matrix inequalities(LMIs) techniques, some new delay-dependent stability criteria for NCSs in terms of generalized Lyapunov matrix equation and LMIs are derived. Stabilizing controller via state feedback is formulated by solving a set of LMIs. Compared with the reported methods, the proposed methods give a less conservative delay bound and more general results. Numerical example and simulation show that the methods are less conservative and more effective.     

Delay-dependent stability and stabilization criteria of networked control systems with multiple time-delays

This paper deals with the problem of delay-dependent stability and stabilization for networked control systems（NCSs）with multiple time-delays. In view of multi-input and multi-output（MIMO） NCSs with many independent sensors and actuators, a continuous time model with distributed time-delays is proposed. Utilizing the Lyapunov stability theory combined with linear matrix inequalities（LMIs） techniques, some new delay-dependent stability criteria for NCSs in terms of generalized Lyapunov matrix equation and LMIs are derived. Stabilizing controller via state feedback is formulated by solving a set of LMIs. Compared with the reported methods, the proposed methods give a less conservative delay bound and more general results. Numerical example and simulation show that the methods are less conservative and more effective.     

Stochastic stability of networked control systems with network-induced delay and data dropout

This paper deals with the stochastic stability of networked control systems with the presence of network- induced delay and transmitted data dropout. Based on the Lyapunov approach, sufficient conditions for the mean-square stability of the networked control system are derived subject that the sequence of transmission interval is driven by an identically independently distributed sequence and by a finite state Markov chain, respectively. Stabilization controllers are constructed in terms of linear matrix inequalities correspondingly. An example is provided to illustrate our results.     

网络控制系统稳定性的图理论

针对具有有界时延和数据包丢失的网络控制系统,提出了一种新的稳定性判据.基于Lyapunov方法和图论理论,给出非线性离散和连续刚络控制系统渐近稳定的充分条件,获得保持这两类系统稳定的最大允许时延界.得到控制器设计方法.并且,利用区间矩阵的谱特征.给出网络控制系统区间稳定的充分条件.设计算法,获得比例积分反馈控制器增益.算例表明所提方法的有效性.     

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.     

Absolute stability and stabilization for Lurie networked control systems

This paper investigates the problem of absolute stability and stabilization for 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. By considering the relationship between the network‐induced delay and its upper bound, an improved stability criterion for networked control system is proposed. Furthermore, the resulting condition is extended to design a state feedback controller by employing an improved cone complementary linearization (ICCL) algorithm. A numerical example is worked out to illustrate the effectiveness and the benefits of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Predictive observer‐based control for networked control systems with network‐induced delay and packet dropout

This paper addresses the stability analysis and synthesis problems for a class of networked control systems (NCSs) under effects of both network‐induced delay and packet dropout. The motivation comes from the increasing NCS applications where the full state vector is not available. To handle the concerned problems, two predictive observer‐based controllers are constructed. The first one is a memoryless controller with the predictive observer collocated with the plant. The second one, with the predictive observer colocated with the controller, uses the last effective plant information as well as the knowledge of the plant dynamics. The stability conditions of NCSs are derived via both network‐condition‐dependent Lyapunov function and common quadric Lyapunov function. The corresponding controller design problems are also solved based upon the obtained stability conditions. Simulation and experimental results are given to demonstrate the effectiveness of the proposed approaches. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Modelling and control of networked control systems with both network-induced delay and packet-dropout

A new switched linear system model is proposed to describe the networked control system (NCS) with both network-induced delay and packet-dropout. A sufficient condition is derived for the exponential stability of the closed-loop NCS, and the obtained condition establishes the quantitative relation between the packet-dropout rate and the stability of the NCS. Design procedures for the state feedback stabilising controllers are also presented by using the augmenting technique. An illustrative example is provided to demonstrate the effectiveness of the proposed method.     

网络控制系统中的稳定性研究

网络控制系统中由于通讯网络的引入产生了不确定的网络延时、数据包丢失以及数据包时序错乱等问题，这些问题严重影响了系统的稳定性能甚至引起了系统的不稳定。为了保证系统的稳定性应根据网络控制系统中出现的时延问题设计控制器，本文针对线性和非线性控制对象提出了控制器模型。     

多时滞不确定网络控制系统的时滞独立稳定判据

针对一类多输入多输出（MIMO）网络控制系统．在考虑多重分布时滞和不确定性的情况下．建立了该系统的连续时闻数学模型．利用Lyapunov稳定性理论,结合线性矩阵不等式（LMI）方法和S-过程,给出了基于LMI形式的时滞独立渐近稳定判据．通过这些判据,能分析和判定具有多重时滞和不确定性的网络控制系统的时滞独立渐近稳定性．与已有的方法相比,该方法更加有效且求解方便．数值仿真结果表明了该方法的有效性．     

网络控制系统的时延相关状态反馈控制器设计

研究了具有时延、丢包和数据包时序错乱的网络控制系统镇定问题.为了有效提高系统的控制性能,本文根据网络控制系统的特点提出一种时延相关状态反馈控制方法,并将闭环网络控制系统建模为离散时间切换模型.在此基础上,通过构造依赖于参数的Lyapunov函数给出了闭环网络控制系统的稳定条件和镇定控制器设计方法.仿真结果和实验结果表明所提方法的有效性和可用性.     

Model predictive control for networked control systems

This paper investigates the problem of model predictive control for a class of networked control systems. Both sensor‐to‐controller and controller‐to‐actuator delays are considered and described by Markovian chains. The resulting closed‐loop systems are written as jump linear systems with two modes. The control scheme is characterized as a constrained delay‐dependent optimization problem of the worst‐case quadratic cost over an infinite horizon at each sampling instant. A linear matrix inequality approach for the controller synthesis is developed. It is shown that the proposed state feedback model predictive controller guarantees the stochastic stability of the closed‐loop system. Copyright © 2008 John Wiley & Sons, Ltd.