Modeling and SPM-dependent control of multi-rate networked control system with long time delay

In this paper, an efficient approach of modeling and control is presented for Multi-Rate Networked Control System (MRNCS) with considering long time delay. Firstly, the system is modeled as a switched system with a random switching signal which is subject to random networked-induced delay. For this, time delay is defined as a Markov chain and the model of MRNCS is obtained as a Markovian jump linear system. Afterward, a dynamic output feedback controller is designed for output tracking as well as stabilization of closed-loop system. The modeling and control of MRNCS are presented for two structures. At first, a new model of single-side MRNCS is proposed and a mode-independent controller is designed for stabilizing the system. Then the proposed modeling method is generalized to double-side MRNCS and by introducing the Set of Possible Modes (SPM) concept, an SPM-dependent controller is proposed for double-side MRNCS. To show the effectiveness of the proposed methods, some numerical results are provided on the quadruple-tank process.     

Stabilization of nonlinear networked systems with sensor random packet dropout and time-varying delay

In this paper, a nonlinear stochastic system model is proposed to describe the networked control systems (NCSs) with both random packet dropout and network-induced time-varying delay. Based on this more general nonlinear NCSs model, by choosing appropriate Lyapunov functional and employing new discrete Jensen type inequality, a sufficient condition is derived to establish the quantitative relation of maximum allowable delay upper bound, packet dropout rate and the nonlinear level to the exponential stability of the nonlinear NCSs. Design procedures for output feedback controller are also presented in terms of utilizing cone complementarities linearization algorithm or solving corresponding linear matrix inequalities (LMIs). Illustrative examples are provided to demonstrate the effectiveness of the proposed method.     

Impulsive controller for wireless networked control system: Switched system approach

The problem of stabilization for wireless networked control system (NCS) with packet dropout and time delay is studied in this article. The impulsive control law for the NCS is defined with time delay and impulse. Using a switching model, the network‐induced imperfections can be treated as three switching subsystems. Therein, in the case of packet dropout, the control law use the previous state via the first‐order hold. The impulsive control law is designed using the switched system approach and the average dwell time method. The obtained sufficient conditions which can guarantee the exponential stability of switched system are in the form of linear matrix inequalities. Finally, a numerical example is used to demonstrate the merits and applicabilities of the proposed method. © 2015 Wiley Periodicals, Inc. Complexity 21: 291–299, 2016     

Adaptive cooperative control of networked uncalibrated robotic systems with time‐varying communicating delays

This paper investigates the trajectory tracking control of the networked multimanipulator with the existence of time‐varying delays and uncertainties in both kinematics and dynamics. To address time‐varying delays in the communication links, a novel control scheme is established by the design of delay–rate‐dependent networking mutual coupling strengths. Besides, to handle the kinematic and dynamic uncertainties, an adaptive controller is designed. The proposed control scheme guarantees that the networked robotic system can track a commonly desired trajectory cooperatively with the strongly connected communication graph, uncertainties, and time‐varying communicating delays. A Lyapunov–Krasovskii functional is employed to rigorously prove the asymptotic convergence of both tracking errors and synchronization errors. The simulation results are provided to verify the effectiveness of the control method proposed by this paper.     

不确定随机时滞系统的时滞相关鲁棒镇定

研究一类不确定随机时滞系统的时滞相关鲁棒镇定问题.通过引入参数化的中立型模型变换,构造Lyapunov-krasovskii泛函,运用线性矩阵不等式方法,得到了使得闭环系统为均方指数稳定的保守性较小的时滞相关鲁棒镇定条件.     

Observer‐based dissipative control for networked control systems: A switched system approach

This article studies the problem of observer‐based dissipative control problem for wireless networked control systems (NCSs). The packet loss and time delay in the network are modeled by a set of switches, using that a discrete‐time switched system is formulated. First, results for the exponential dissipativity of discrete‐time switched system with time‐varying delays are proposed by using the average dwell time approach and multiple Lyapunov–Krasovskii function. Then, the results are extended to drive the controller design for considered wireless NCS. The attention is focused on designing an observer‐based state feedback controller which ensures that, for all network‐induced delay and packet loss, the resulting error system is exponentially stable and strictly dissipative. The sufficient conditions for existence of controllers are formulated in the form of linear matrix inequalities (LMIs), which can be easily solved using some standard numerical packages. Both observer and controller gains can be obtained by the solutions of set of LMIs. Finally, numerical examples are provided to illustrate the applicability and effectiveness of the proposed method. © 2014 Wiley Periodicals, Inc. Complexity 21: 297–308, 2015     

Stochastic stability and robust control for sampled-data systems with Markovian jump parameters

In this paper, the problems of stochastic stability and robust control for a class of uncertain sampled-data systems are studied. The systems consist of random jumping parameters described by finite-state semi-Markov process. Sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented. The conditions for the existence of a sampled-data feedback control and a multirate sampled-data optimal control for the continuous-time uncertain Markovian jump systems are also obtained. The design procedure for robust multirate sampled-data control is formulated as linear matrix inequalities (LMIs), which can be solved efficiently by available software toolboxes. Finally, a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques.     

时滞依赖型中立系统的鲁棒稳定性分析

研究了一类不确定中立型系统的时滞依赖稳定性问题.利用基于LMI正定解的存在性,给出了一个新时滞依赖型稳定性判据,相比于已有文献本文具有低的保守性.最后通过数值算例验证了本文得到的结论的正确性和有效性.     

Quantized stabilization of discrete-time systems in a networked environment

This paper is concerned with the problem of output feedback stabilization for a class of discrete-time systems with sector nonlinearities and imperfect measurements. A unified control law model is proposed to take the network-induced delay, random packet dropout and measurement quantization into consideration simultaneously. By choosing appropriate Lyapunov functional, a new stability condition, which is dependent on multiple network status, is established for the resulting closed-loop system. Based on the result, a design criterion for the static output feedback controller is formulated in the form of nonconvex matrix inequalities, and the cone complementary linearization (CCL) procedure is exploited to solve the nonconvex feasibility problem. Incidentally, a less conservative synthesis method is also developed for the state feedback stabilization purpose. Finally, two illustrative examples are provided to illustrate the effectiveness and applicability of the proposed design method.     

Stability of a class of networked control systems with Markovian characterization

This paper studies the stability problem for a class of networked control systems (NCSs) with the plant being a Markovian jump system. The random delays from the sensor to the controller and from the controller to the actuator are modeled as two Markov chains. The necessary and sufficient conditions for the stochastic stability are established. The state-feedback controller gain that depends on not only the delay modes but also the system mode is obtained through the iterative linear matrix inequality approach. An illustrative example is presented to demonstrate the effectiveness of the proposed method.     

Finite‐time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach

This article investigates the sliding mode control method for a class of chaotic systems with matched and unmatched uncertain parameters. The proposed reaching law is established to guarantee the existence of the sliding mode around the sliding surface in a finite‐time. Based on the Lyapunov stability theory, the conditions on the state error bound are expressed in the form of linear matrix inequalities. Simulation results for the well‐known Genesio's chaotic system are provided to illustrate the effectiveness of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 14–19, 2016     

Finite-time synchronization for coupled systems with time delay and stochastic disturbance under feedback control

This paper proposes a framework for finite-time synchronization of coupled systems with time delay and stochastic disturbance under feedback control. Combining Kirchhoff"s Matrix Tree Theorem with Lyapunov method as well as stochastic analysis techniques, several sufficient conditions are derived. Differing from previous references, the finite time provided by us is related to topological structure of networks. In addition, two concrete applications about stochastic coupled oscillators with time delay and stochastic Lorenz chaotic coupled systems with time delay are presented, respectively. Besides, two synchronization criteria are provided. Ultimately, two numerical examples are given to illustrate the effectiveness and feasibility of the obtained results.     

Stabilization problem of stochastic time-varying coupled systems with time delay and feedback control

The stabilization of stochastic coupled systems with time delay and time-varying coupling structure (SCSTT) via feedback control is investigated. We generalize systems with constant coupling structure to the time-varying coupling structure. Combining the graph theory with the Lyapunov method, a systematic method is provided to construct a Lyapunov function for SCSTT, and a Lyapunov-type theorem and a coefficient-type criterion are obtained to guarantee the stabilization in the sense of pth moment exponential stability. Furthermore, theoretical results are applied to analyze the stabilization of stochastic-coupled oscillators with time delay and time-varying coupling structure in order to illustrate the practicability of the results. Finally, two numerical examples are given to illustrate the effectiveness and feasibility of theoretical results.     

Stability of hybrid stochastic differential systems with switching and time delay

This article introduces a hybrid stochastic differential system with impulsive, switching and time-delay. Some stability criteria of p-moment global asymptotical stability, p-moment global exponential stability and mean square stability of this system are derived by using switching Lyapunov function approach, Itô formula, impulsive differential inequality method, and linear matrix equality techniques. Three examples are presented to demonstrate the efficiency of the obtained results.     

一类具混合时滞随机神经网络稳定性的推广与应用

将一类具有混合时滞随机神经网络均方渐近稳定的判据推广到不确定神经网络的鲁棒稳定性,所导出的判据都表示为线性矩阵不等式(LMI)的形式,可通过使用一些标准的数值方法求解.最后给出了一个简单的例子说明所提出的判定条件的有效性和可应用性.     

受控马尔可夫跳线性系统的随机鲁棒稳定性

本文讨论了受控连续和离散时间马尔可夫跳线性系统的随机鲁棒稳定性,并且给出了此时该系统发生马尔可夫跳的转移速率的一个界.     

Deterministic and stochastic approaches to supervisory control design for networked systems with time-varying communication delays

This paper proposes a supervisory control structure for networked systems with time-varying delays. The control structure, in which a supervisor triggers the most appropriate controller from a multi-controller unit, aims at improving the closed-loop performance relative to what can be obtained using a single robust controller. Our analysis considers average dwell-time switching and is based on a novel multiple Lyapunov–Krasovskii functional. We develop stability conditions that can be verified by semi-definite programming, and show that the associated state feedback synthesis problem also can be solved using convex optimization tools. Extensions of the analysis and synthesis procedures to the case when the evolution of the delay mode is described by a Markov chain are also developed. Simulations on small and large-scale networked control systems are used to illustrate the effectiveness of our approach.     

Observer-based fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts

This paper addresses the problem of fault detection for networked discrete-time infinite-distributed delay systems with packet dropouts. Both sensor-to-controller and controller-to-actuator packet dropouts are described by two different Bernoulli distributed white sequences, respectively. The problem addressed is to design an observer-based fault detection filter (FDF) such that the error between the residual and the fault is made as small as possible. Unlike most of the existing literature, we have noted that the control input of the observer is different from that of the plant because of packet dropouts in the controller-to-actuator link. Sufficient condition for the existence of the FDF is derived in terms of some linear matrix inequalities (LMIs). When these LMIs are feasible, the explicit expression of the desired FDF can also be characterized. A numerical example is exploited to show the effectiveness of the obtained results.     

State feedback stabilization of uncertain linear time‐delay systems: A nonlinear matrix inequality approach

A nonlinear matrix inequality is derived as a stabilizability condition of linear uncertain time‐delay systems. This inequality is seen as a less conservative one as well as efficient for numerical computation than the existing results as seen when solving by cone‐complementary algorithm. Copyright © 2010 John Wiley & Sons, Ltd.     

Improvement on delay dependent absolute stability of Lurie control systems with multiple time delays

Absolute stability of Lurie control systems with multiple time-delays is studied in this paper. By using extended Lyapunov functionals, we avoid the use of the stability assumption on the main operator and derive improved stability criteria, which are strictly less conservative than the criteria in [2] and [3].