Synchronization of nonlinear master–slave systems under input delay and slope‐restricted input nonlinearity

This article addresses the synchronization of nonlinear master–slave systems under input time‐delay and slope‐restricted input nonlinearity. The input nonlinearity is transformed into linear time‐varying parameters belonging to a known range. Using the linear parameter varying (LPV) approach, applying the information of delay range, using the triple‐integral‐based Lyapunov–Krasovskii functional and utilizing the bounds on nonlinear dynamics of the nonlinear systems, nonlinear matrix inequalities for designing a simple delay‐range‐dependent state feedback control for synchronization of the drive and response systems is derived. The proposed controller synthesis condition is transformed into an equivalent but relatively simple criterion that can be solved through a recursive linear matrix inequality based approach by application of cone complementary linearization algorithm. In contrast to the conventional adaptive approaches, the proposed approach is simple in design and implementation and is capable to synchronize nonlinear oscillators under input delays in addition to the slope‐restricted nonlinearity. Further, time‐delays are treated using an advanced delay‐range‐dependent approach, which is adequate to synchronize nonlinear systems with either higher or lower delays. Furthermore, the resultant approach is applicable to the input nonlinearity, without using any adaptation law, owing to the utilization of LPV approach. A numerical example is worked out, demonstrating effectiveness of the proposed methodology in synchronization of two chaotic gyro systems. © 2015 Wiley Periodicals, Inc. Complexity 21: 220–233, 2016     

具有两个加性输入时滞系统的状态反馈控制

主要考虑了具有两个加性输入时滞的网络化控制系统的状态反馈控制问题.首先考虑具有两个加性时滞的系统稳定性,构造适当的Lyapunov泛函,不需要所有的矩阵正定,只需其整体正定.其次在估计Lyapunov泛函沿系统的导数时,针对时滞范围的不同,引入了不同的松弛矩阵,得出系统保守性较小的稳定条件.在此基础上,研究了系统状态反馈控制,最后得出闭环系统渐近稳定的充分条件,并给出控制器的设计方法.     

Resilient dissipative dynamic output feedback control for uncertain Markov jump Lur’e systems with time-varying delays

The resilient dissipative dynamic output feedback control problem for a class of uncertain Markov jump Lur’e systems with piecewise homogeneous transition probabilities and time-varying delays in the discrete-time domain are examined in this study. The designed controller can tolerate additive uncertainties in the controller gain matrix, which result from controller implementations. The time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. By constructing a Lyapunov–Krasovskii functional candidate, the sufficient conditions regarding the existence of desired resilient dissipative controllers are obtained in terms of linear matrix inequalities, thereby ensuring that the resulting closed-loop system is stochastically stable and strictly dissipative. Two numerical examples were established to illustrate the effectiveness of the proposed theoretical results.     

Robust tracking and model following for uncertain time‐delay systems with input nonlinearity

This article proposes a novel adaptive sliding mode control (SMC) scheme to realize the problem of robust tracking and model following for a class of uncertain time‐delay systems with input nonlinearity. It is shown that the proposed robust tracking controller guarantees the stability of overall closed‐loop system and achieves zero‐tracking error in the presence of input nonlinearity, time‐delays, time‐varying parameter uncertainties and external disturbances. The selection of sliding surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against input nonlinearity, time‐delays, parameter uncertainties, and external disturbances. Moreover, the knowledge of the upper bound of uncertainties is not required and chattering phenomenon is eliminated. Both theoretical analysis and illustrative examples demonstrate the validity of the proposed scheme. © 2014 Wiley Periodicals, Inc. Complexity 21: 66–73, 2015     

State Estimation and Reliable Control of Singular Markovian Systems with Distributed State Delays and Input Delays

This paper is concerned with state estimation and reliable control for singular Markovian jump systems with distributed state delays and input delays. Firstly, an observer is designed to estimate the system states, and a reliable controller is proposed based on the state estimates. Moreover, some conditions for the mean-square exponential admissibility of the overall closed-loop system are derived in terms of strict linear matrix inequality (LMI).     

LMI-Based Robust <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control of Uncertain Neutral Systems with State and Input Delays

Robust stabilization and robust H_∞ control problems for a class of uncertain neutral system with state and input delays are considered. By choosing a Lyapunov-Krasovskii functional, an alternative delay-dependent sufficient condition for the existence of a controller is derived in terms of linear matrix inequalities. Furthermore, a convex optimization problem can be formulated to obtain an H_∞ controller which minimizes an upper H_∞ norm bound of the closed-loop state-input delayed system.     

Global exponential synchronization of nonlinear time-delay Lur’e systems via delayed impulsive control

This paper is concerned with the global exponential synchronization problem of two identical nonlinear time-delay Lur’e systems via delayed impulsive control. Some novel impulsive synchronization criteria are obtained by introducing a discontinuous Lyapunov function and by using the Lyapunov–Razumikhin technique, which are expressed in forms of linear matrix inequalities. The derived criteria reveal the effects of impulsive input delays and impulsive intervals on the stability of synchronization error systems. Then, sufficient conditions on the existence of a delayed impulsive controller are derived by employing these newly-obtained synchronization criteria. Additionally, some synchronization criteria for two identical time-delay Lur’e systems with impulsive effects are presented by using delayed continuous feedback control. The synchronization criteria via delayed continuous feedback control can deal with the case when the impulsive control strategy fails to synchronize two identical impulsive time-delay Lur’e systems. Three numerical examples are provided to illustrate the efficiency of the obtained results.     

Synchronization schemes for coupled identical Yang–Yang type fuzzy cellular neural networks

This paper proposes an adaptive procedure to the problem of synchronization for a class of coupled identical Yang–Yang type fuzzy cellular neural networks (YYFCNN) with time-varying delays. Based on the simple adaptive controller, a set of sufficient conditions are developed to guarantee the synchronization of the coupled YYFCNN with time-varying delays. The results are much different from previous ones. It is proved that two coupled identical YYFCNN with time-varying delays can achieve synchronization by enhancing the coupled strength dynamically. In addition, this kind of controller is simple to be implemented and it is fairly robust against the effect of weak noise in the given time series. The approaches are based on using the invariance principle of functional differential equations, constructing a general Lyapunov–Krasovskii functional and employing a linear matrix inequality (LMI). An illustrative example and its simulations show the feasibility of our results. Finally, an application is given to show how to apply the presented synchronization scheme of YYFCNN to secure communication.     

Some Remarks on Distributed PCHD-Systems

Port controlled Hamiltonian systems with dissipation are a well known tool for the modeling and the controller design for plants, described by nonlinear ordinary differential equations. This contribution presents a possible extension to systems, described by partial differential equations, where the state manifold and the input space of the ODE case are replaced by new geometric structures. This approach takes dissipative effects into account and shows, how distributed ports can be introduced. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

随机时滞控制系统的均方BIBO稳定性

本文研究了具有时滞和非线性扰动的随机控制系统的均方有界输入-有界输出(BIBO)稳定.首先,探讨了具有离散时滞和非线性扰动的随机系统的均方BIBO稳定性问题,在此基础上,进一步研究带有离散时滞和分布时滞以及非线性扰动的随机系统的均方BIBO稳定性.通过设计合理的控制器,建立合适的Lyapunov泛函,结合Riccati矩阵方程,得到时滞依赖的均方BIBO稳定性条件.     

Stability and bifurcation of a nutrient-autotroph-herbivore model with nutrient recycling under two delays

In this article, a nutrient-autotroph-herbivore model with nutrient recycling is constructed. Holling type-II functional response for the relation between nutrient and autotroph while Beddington-DeAngelis-type functional response for autotroph and herbivore relation are considered here. It is plausible that the conversion of nutrient from dead biomass (autotroph and herbivore) by decomposers (i.e., bacteria and fungi) are not instantaneous, which takes times. Hereby, two different discrete time delays for the decomposition process are introduced. The local and global stability behaviours of both nondelayed and delayed models are analysed around the equilibrium points. The stability and direction of Hopf-bifurcation using normal form theory and centre manifold theorem by taking one delay as a bifurcation parameter while keeping the other one fixed in the stable interval are discussed. It is observed that if the delay increases, the system loses its stability and hence becomes unstable. It is analysed how autotroph-herbivore ecosystem can be affected by the quantity of input nutrient and the properties of delays. The quantity of nutrient and the length of delays play significant roles in determining the stability of the system since a sufficiently small amount of nutrients or a long enough delay leads to the extinction of a species.     

一类时滞系统的稳定性分析及控制器设计

研究一类具有状态时滞和输入时滞的时变时滞线性系统.首先,通过选取合适的Lyapunov-Krasovskii泛函,应用LMI方法和Lyapunov-Krasovskill稳定性定理对时滞相关的系统进行稳定性分析,并设计了相应的控制器.改进了时变时滞线性系统方面的一些结果.最后用实例验证所得到结果.     

Simultaneous stabilization: Construction of a universal stabilizer for linear plants with delay with the use of spectral reducibility

We consider the problem of the construction of a common stabilizing controller for a family of k linear stationary nth-order plants with commensurable delays in the controls and the state variables. Our approach to stabilization is based on the construction of a common two-loop stabilizer. The controller of the first (internal) loop solves the problem of reducing each plant of the family to a finite spectrum, and the controller of the second (external) contour solves the stabilization problem.     

Distributed event-triggered hybrid wired-wireless networked control with $${H_2}/{H_\infty }$$ filtering

Aiming at the fact that distributed multi-channel hybrid network-induced delays and noise interference may deteriorate the control performance of hybrid networked control systems, distributed event-triggered hybrid wired-wireless networked control with \({H_2}/{H_\infty }\) filtering is proposed. A distributed event-triggered mechanism is firstly employed to reduce communication burden, and two Markov chains are used to respectively describe different characters of network-induced delays of hybrid wired-wireless networks. Then, a \({H_2}/{H_\infty }\) filter is employed to improve the input signal precision of the controller, where a general closed-feedback filtering and control system model with distributed event-triggered parameters and network-induced delays of hybrid wired-wireless networks is proposed. Furthermore, the designed filter and controller enable the closed-feedback filtering and control system to be stochastic stability and to achieve a prescribed \({H_2}/{H_\infty }\) performance, and the relationships between the stability criteria and the maximum network-induced delays, distributed event-triggered parameters, the filter and controller parameters and the system performance parameter are established. Finally, simulation results confirm the effectiveness of the proposed method.     

纯量反馈系统同时强镇定的充分条件

一个稳定的补偿器可同时镇定n个对象(同时强镇定)等价于一个补偿器(不一定稳定)同时镇定n 1个对象(同时镇定)．两个以上对象的同时强镇定和三个以上对象的伺时镇定是线性系统中一个急待解决的公开问题．文中所作的基本假定是所有的对象具有相同的简单不稳定零点，在此条件下给出了n个对象同时强镇定的一个充分条件．当仅有一个不稳定零点时．容易检验是否同时强镇定，否则仅需确定n个对象的不稳定零点并且判定由不稳定零点导出一个相应矩阵是正定的，就能判定n个对象同时强镇定．因此是一个易于检验的充分条件．文章同时给出了n个对象同时强镇定的算法，丰富了同时强镇定的充分条件．     

Stability analysis of fractional order neutral-type systems considering time varying delays,nonlinear perturbations,and input saturation

This article investigates the robust stability of fractional order neutral-type systems involving nonlinear perturbations and time varying delays in the presence of input saturation. Design criteria, expressed in terms of linear matrix inequalities, are derived with the aid of the Lyapunov Krasovskii functional for the state feedback controller. Based on the cone complementarity linearization method, an optimization problem is also formulated for finding the controller gains subject to maximizing the domain of attraction. The main results are confirmed by numerical simulations.     

具有饱和因子的时滞广义系统的鲁棒 H SymboleB@ 控制

研究了一类具有饱和因子并含有不确定参数的变时滞广义系统的时滞相关鲁棒H∞控制,系统的状态方程和输出方程均带有时滞,且状态方程的输入和输入时滞中均含饱和因子.通过构造Lya-punov-Krasovskii泛函,利用线性矩阵不等式方法和矩阵奇异值理论,给出了时滞广义系统正则、无脉冲、渐进稳定且满足H∞范数小于给定界γ的充分条件,并给出了H∞控制器的设计方法 .数值算例说明了本文所提方法具有更小的保守性.     

Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros

Under the existence of system uncertainties, external disturbances, and input nonlinearity, complete synchronization and anti-synchronization between two chaotic gyros are achieved by introducing a novel adaptive terminal sliding mode (ATSM) controller. In the literature, by taking account of input nonlinearity, the magnitudes of bounded nonlinear dynamics of synchronous error system were required in the designed sliding mode controller. In this study, the proposed ATSM controller associated with time-varying feedback gains can tackle nonlinear dynamics according to the novel adaptive rules. These feedback gains are not necessary to be determined in advance but updated by the adaptive rules without known the magnitudes of bounded nonlinear dynamics, system uncertainties, and external disturbances. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem, and the numerical simulations are performed to verify the effectiveness of presented schemes.     

Intuitionistic Fuzzy Logic Control for Heater Fans

The concept of intuitionistic fuzzy systems, including intuitionistic fuzzy sets and intuitionistic fuzzy logic, was introduced by Atanassov as a generalization of fuzzy systems. Intuitionistic fuzzy systems provide a mechanism for communication between computing systems and humans. In this paper, we describe the development of an intuitionistic fuzzy logic controller for heater fans, developed on the basis of intuitionistic fuzzy systems. Intuitionistic fuzzy inference systems and defuzzification techniques are used to obtain crisp output (i.e., speed of the heater fan) from an intuitionistic fuzzy input (i.e., ambient temperature). The speed of the heater fan is calculated using intuitionistic fuzzy rules applied in an inference engine using defuzzification methods.     

Triangular configuration of uncertain systems stabilizable by means of feedback controller

The uncertain linear systems with time-varying delays and limited measurable states variables are shown to have special configuration, called triangular configuration, to be stabilizable by means of state variable feedback controller. This configuration indicates the location of uncertainties among system parameters including input and output coefficients.