Master‐slave synchronization for delayed Lur'e systems using time‐delay feedback control

This paper deals with the problem of designing delayed feedback controllers of master‐slave synchronization for Lur'e systems with time‐variant delay (0≤τ₀≤τ(t)≤τ_m). Through partitioning the intervals [0, τ₀] and [τ₀, τ_m], respectively, and choosing two augmented Lyapunov‐Krasovskii functionals(LKFs), two delay‐dependent synchronization criteria are formulated in the form of linear matrix inequalities (LMIs), in which the conservatism can be greatly reduced by thinning the partitioning of delay intervals and employing convex combination. Thus the sufficient conditions can be derived for the existence of delayed feedback controllers, and the controller gain matrices can be achieved by solving the established LMIs. Finally, three numerical examples are given to illustrate the presented synchronization schemes. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

New Stabilization of Continuous‐Time Delayed Systems Based on Partially Delay‐Dependent Controllers

In this paper, a new approach is developed to discuss the stabilization problem for a class of continuous‐time delayed systems, which is firstly achieved by a kind of partially delay‐dependent controller. The main property of the desired controller is that both non‐delay and delay states are contained. Different from the traditional stabilization methods realized by totally non‐delay or delay state feedback controllers, both non‐delay and delay states are contained but take place asynchronously, where the probability distributions of such terms are considered in the controller design process. Based on the established model, new stabilization conditions depending on such probabilities are presented with linear matrix inequality forms. Moreover, another general case in terms of probability having uncertainty is also considered. Finally, numerical examples are used to illustrate the effectiveness and superiority of the design methods.     

Synchronization Criterion and Control Scheme for Lur'e Type Complex Dynamical Networks with Switching Topology and Coupling Time‐Varying Delay

In this paper, the synchronization problem is addressed in the context of Lur'e type complex switched network (CSN) with coupling time‐varying delay in which every node is a Lur'e system. Based on the Lyapunov–Krasovskii theory and linear matrix inequality (LMI) technique, a delay‐dependent synchronization criterion and a decentralized state feedback dynamic controller for synchronization of CSNs have been proposed. By choosing a common Lyapunov–Krasovskii functional and using the combined reciprocal convex technique, some previously ignored terms can be reconsidered and less conservative conditions can be obtained. In addition, by using an eigenvalue‐decoupling method and convex optimization theory, high‐dimension LMIs are decoupled into a set of low‐dimension ones and the computation complexity of the criterion can be significantly reduced. The effectiveness and applicability of the suggested control solution is verified and assessed through the analysis for two numerical examples.     

State and mode feedback control strategy for discrete‐time Markovian jump linear systems with time‐varying controllable mode transition probability matrix

In this article, the state and mode feedback control strategy is investigated for the discrete‐time Markovian jump linear system (MJLS) with time‐varying controllable mode transition probability matrix (MTPM). This strategy, consisting of a state feedback controller and a mode feedback controller, is proposed to ensure MJLS's stability and meanwhile improve system performance. First, a mode‐dependent state feedback controller is designed to stabilize the MJLS based on the time‐invariant part of the MTPM such that it can still keep valid even if the MTPM is adjusted by the mode feedback control. Second, a generalized quadratic stabilization cost is put forward for evaluating MJLS's performance, which contains system state, state feedback controller, and mode feedback controller. To reduce the stabilization cost, a mode feedback controller is introduced to adjust each mode's occurrence probability by changing the time‐varying controllable part of MTPM. The calculation of such mode feedback controller is given based on a value‐iteration algorithm with its convergence proof. Compared with traditional state feedback control strategy, this state and mode feedback control strategy offers a new perspective for the control problem of general nonhomogeneous MJLSs. Numerical examples are provided to illustrate the validity of the proposed strategy.     

Delay‐dependent criteria for general decay synchronization of discontinuous fuzzy neutral‐type neural networks with time‐varying delays

This paper aims to investigate the general decay synchronization analysis of discontinuous fuzzy neutral‐type neural networks. Under the framework of Filippov solutions, based on functional differential inclusions theory, inequality technique and by constructing a modified delay‐dependent Lyapunov‐Krasovskii functional, some new delay‐dependent criteria are provided to guarantee the general decay synchronization via the effective nonlinear feedback controller. The neural network model considered is more generalized, some previous fuzzy neural networks can be regard as the special cases. Moreover, some recent results on the delay‐independent criteria ensuring the general decay synchronization can also be extended and concluded. These can be seen from the given corollaries and remarks which are provided to make the comparisons and show the advantages. Finally, some numerical examples and simulations are provided to illustrate the correctness.     

Delay‐range‐dependent control of nonlinear time‐delay systems under input saturation

This paper describes a delay‐range‐dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time‐delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay‐range‐dependent and delay‐dependent stabilization problems for linear and nonlinear time‐delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay‐rate‐independent condition for control of nonlinear systems in the presence of input saturation with unknown delay‐derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L₂ gain reduction from disturbance to output is devised to address the problem of the stabilization of input‐constrained nonlinear time‐delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time‐delay network and a large‐scale chemical reactor under input saturation and varying interval time‐delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.     

Time‐ and State‐Dependent Input Delay‐Compensated Bang‐Bang Control of a Screw Extruder for 3D Printing

In this paper, a delay‐compensated bang‐bang control design methodology for the control of the nozzle output flow rate of screw extruder‐based three‐dimensional printing processes is developed. A geometrical decomposition of the screw extruder in a partially and a fully filled regions allows to describe the material convection in the extruder chamber by a one‐dimensional hyperbolic partial differential equation (PDE) coupled with an ordinary differential equation. After solving the hyperbolic PDE by the method of characteristics, the coupled PDE–ordinary differential equation's system is transformed into a nonlinear state‐dependent input delay system. The aforementioned delay system is extended to the non‐isothermal case with the consideration of periodic fluctuations acting on the material's convection speed, which represent the process variabilities due to temperature changes in the extruder chamber, resulting to a nonlinear system with an input delay that simultaneously depends on the state and the time variable. Global exponential stability of the nonlinear delay‐free plant is established under a piecewise exponential feedback controller that is designed. By combining the nominal, piecewise exponential feedback controller with nonlinear predictor feedback, the compensation of the time‐dependent and state‐dependent input delay of the extruder model is achieved. Global asymptotic stability of the closed‐loop system under the bang‐bang predictor feedback control law is established when certain conditions related to the extruder design and the material properties, as well as to the magnitude and frequency of the materials transport speed variations, are satisfied. Simulations results are presented to illustrate the effectiveness of the proposed control design. Copyright © 2017 John Wiley & Sons, Ltd.     

Fixed‐Time Synchronization of a Class of Second‐Order Nonlinear Leader‐Following Multi‐Agent Systems

The fixed‐time synchronization problem for a class of second‐order nonlinear multi‐agent systems with a leader‐follower architecture is investigated in this paper. To achieve the fixed‐time tracking task, the design procedure is divided into two steps. At the first step, a distributed fixed‐time observer is designed for each agent to estimate the leader's state in a fixed time. Then, at the second step, based on the technique of adding a power integrator, a fixed‐time tracking controller for each agent is proposed such that the estimate leader's state can be tracked in a fixed time. Finally, an observer‐based fixed‐time controller is developed such that the leader can be tracked by all the followers in a fixed time, which can be predetermined. Simulations are presented to verify the effectiveness of the proposed approach.     

An LMI approach to output‐feedback‐guaranteed cost control for uncertain time‐delay systems

This paper considers the problem of output‐feedback‐guaranteed cost controller design for uncertain time‐delay systems. The uncertainty in the system is assumed to be norm‐bounded and time‐varying. The time‐delay is allowed to enter the state and the measurement equations. A linear quadratic cost function is considered as a performance measure for the closed‐loop system. Necessary and sufficient conditions are provided for the construction of a guaranteed cost controller. These conditions are given in terms of the feasibility of LMIs which depend on a positive definite matrix and a scaling variable. A numerical algorithm is developed to search for a full order dynamic output‐feedback controller which minimizes the cost bound. Copyright © 2000 John Wiley & Sons, Ltd.     

Reliable control for a class of uncertain singular systems with interval time‐varying delay

This paper is concerned with the reliable controller design problem for a class of singular systems with interval time‐varying delay and norm‐bounded uncertainties. A more practical model of actuator failures than outages is considered. First, by constructing a novel Lyapunov–Krasovskii functional combined with Finsler's Lemma, an improved delay‐range‐dependent stability criterion for the nominal unforced singular time‐delay system is established in terms of linear matrix inequality (LMI). Then, based on this criterion, an LMI condition for the design of a reliable state feedback controller is presented such that, for all parameter uncertainties and actuator failures, the resultant closed‐loop system is regular, impulse‐free and stable. Numerical examples are proposed to illustrate the effectiveness of the proposed method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Razumikhin‐type approach on state feedback of stochastic high‐order nonlinear systems with time‐varying delay

The Razumikhin‐type approach is introduced to solve the state feedback stabilization problem for a class of stochastic high‐order nonlinear systems with time‐varying delay. Based on the general Razumikhin‐type theorem on stochastic systems established in our paper and backstepping design method, a state feedback controller is constructed to ensure the origin of closed‐loop system is globally asymptotically stable in probability. Our methodology enables us to completely remove the limitations on the derivative of delay, which is the common assumption of stochastic high‐order nonlinear systems with time‐varying delay. The efficiency of the state feedback controller is demonstrated by simulation examples. Copyright © 2017 John Wiley & Sons, Ltd.     

STABILIZATION AND H∞ CONTROL FOR UNCERTAIN STOCHASTIC TIME‐DELAY SYSTEMS VIA NON‐FRAGILE CONTROLLERS

This paper considers the problems of robust non‐fragile stochastic stabilization and H_∞ control for uncertain time‐delay stochastic systems with time‐varying norm‐bounded parameter uncertainties in both the state and input matrices. Attention is focused on the design of memoryless state feedback controllers which are subject to norm‐bounded uncertainties. For both the cases of additive and multiplicative controller uncertainties, delay‐independent sufficient conditions for the solvability of the above problems are obtained. The desired state feedback controller can be constructed by solving a certain linear matrix inequality.     

Cooperative observers and regulators for discrete‐time multiagent systems

This paper investigates the design of distributed observers for agents with identical linear discrete‐time state‐space dynamics networked on a directed graph interaction topology. The digraph is assumed to have fixed topology and contain a spanning tree. Cooperative observer design guaranteeing convergence of the estimates of all agents to their actual states is proposed. The notion of convergence region for distributed observers on graphs is introduced. It is shown that the proposed cooperative observer design has a robustness property. Application of cooperative observers is made to the synchronization problem. A command trajectory generator and pinning control are employed for synchronizing all the agents to a desired trajectory. Complete knowledge about the agent's state is not assumed. A duality principle is shown for observers and state feedback for distributed discrete‐time systems on graph topologies. Three different observer/controller architectures are proposed for dynamic output feedback regulator design, and they are shown to guarantee convergence of the estimate to the true state and synchronization of all the agents' states to the command state trajectory. This provides design methods for cooperative regulators based on a separation principle. It is shown that the observer convergence region and feedback control synchronizing region for discrete‐time systems are inherently bounded, so that the conditions for observer convergence and state synchronization are stricter than the results for the continuous‐time counterparts. This is in part remedied by using weighting of different feedback coupling gains for every agent. Copyright © 2012 John Wiley & Sons, Ltd.     

Robust quantized output feedback control for uncertain discrete time‐delay systems with saturation nonlinearity

This paper is concerned with robust quantized output feedback control problems for uncertain discrete‐time systems with time‐varying delay and saturation nonlinearity. It is assumed that the quantizer is of the saturating type. A new framework for the local boundedness stabilization of quantized feedback systems is developed. Attention is focused on finding a quantized static output feedback controller such that all trajectories of the resulting closed‐loop system starting from an admissible initial basin converge to a bounded region strictly within the initial basin. A quantized feedback controller is proposed, which comprises output feedback and the exogenous signal parts. Simulation examples are given to illustrate the effectiveness and advantage of the proposed methods. Copyright © 2014 John Wiley & Sons, Ltd.     

Discrete‐time repetitive controller for time‐delay systems with disturbance observer

A novel discrete‐time repetitive controller design for time‐delay systems subject to a periodic reference and exogenous periodic disturbances is presented. The main idea behind the proposed approach is to take advantage of the plant delay in the controller design, and not to compensate for the effect of this delay. To facilitate this concept, we introduce an appropriate time‐delay and a compensator in a positive feedback connection with the plant, such that a generator for periodic signals is constructed. Then a proportional controller is used to stabilize the closed‐loop system. The tracking control capability is thus guaranteed according to the internal model principle (IMP). In addition, to attenuate external periodic disturbances, a disturbance observer (DO) is developed to simultaneously achieve reference tracking and disturbance rejection. The possible fractional delay due to the digital discretization is handled by using a fractional delay filter approximation. The proposed controller has a simple structure, in which only a proportional parameter and a low‐pass filter are required to be chosen. The closed‐loop stability conditions and a robustness analysis under model uncertainties are studied. Numerical simulations and practical experiments on a servo motor system are conducted to verify the feasibility and simplicity of the proposed controller. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

State‐feedback stabilization for a class of stochastic time‐delay nonlinear systems

This paper investigates the problem of state‐feedback stabilization for a class of lower‐triangular stochastic time‐delay nonlinear systems without controllable linearization. By extending the adding‐a‐power‐integrator technique to the stochastic time‐delay systems, a state‐feedback controller is explicitly constructed such that the origin of closed‐loop system is globally asymptotically stable in probability. The main design difficulty is to deal with the uncontrollable linearization and the nonsmooth system perturbation, which, under some appropriate assumptions, can be solved by using the adding‐a‐power‐integrator technique. Two simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this paper.Copyright © 2011 John Wiley & Sons, Ltd.     

时滞扩散性复杂网络同步保性能控制

针对节点扩张的时滞复杂网络系统, 在节点扩张的条件下, 讨论此类系统的同步保性能控制问题. 首先采用自适应控制方法, 利用Lyapunov-Krasovskii稳定性理论,结合矩阵不等式的凸优化问题处理方法, 得出了时 滞复杂网络系统保性能控制器存在的充分条件; 当系统节点的扩张后, 在原有自适应控制器不能使系统同步稳定的条件下, 设计脉冲控制器, 利用牵制控制原理使系统达到稳定同步. 所设计的自适应动态反馈控制器在保证系统的渐近稳定条件下使系 统性能指标满足一定的要求. 最后给出一个数值仿真说明其有效性.     

Synchronization in a network of identical discrete‐time agents with uniform constant communication delay

This paper studies the synchronization problem for a network of identical discrete‐time agents with unknown uniform constant communication delay. When the agents are non‐introspective, the problem is solvable via a decentralized low‐gain‐based synchronization controller if the delay satisfies the proposed upper bound. When the agents are introspective, the synchronization problem can be solved with arbitrary bounded communication delay. Copyright © 2013 John Wiley & Sons, Ltd.     

State feedback controller design of networked control systems with interval time‐varying delay and nonlinearity

This paper proposes a method for robust state feedback controller design of networked control systems with interval time‐varying delay and nonlinearity. The key steps in the method are to construct an improved interval‐delay‐dependent Lyapunov functional and to introduce an extended Jessen's inequality. Neither free weighting nor model transformation is employed in the derivation of system stability criteria. It is shown that the maximum allowable bound on the nonlinearity could be computed through solving a constrained convex optimization problem; and the maximum allowable delay bound and the feedback gain of a memoryless controller could be derived by solving a set of linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Non‐Fragile Synchronization Control For Markovian Jumping Complex Dynamical Networks With Probabilistic Time‐Varying Coupling Delays

This paper studies the problem of non‐fragile synchronization control for Markovian jumping complex dynamical networks with probabilistic time‐varying coupling delays. By constructing a new Lyapunov–Krasovskii functional (LKF) and combining the reciprocal convex technique, sufficient conditions for the complex dynamical networks to be globally asymptotically synchronized in the mean square sense are derived. The probability distribution of the delays have been proposed and delay probability‐distribution‐dependent conditions are derived in the form of linear matrix inequalities (LMIs). The derived conditions depend not only on the size of the delay but also on the probability of the delay taking values in some intervals. Further, a non‐fragile synchronization controller is proposed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.