On local synchronisability of nonlinear networked systems with a unit inner-coupling matrix and switching topology

The local synchronisation of the nonlinear networked systems with switching topology is studied in this article for the special case in which the inner-coupling matrix is a unit matrix. The critical idea is to convert synchronisation problem to consensus problem such that the switching topology can be dealt with effectively without any extra assumption on the relationship among the involved topologies. A novel local synchronous criterion consisting of the maximum Lyapunov exponent of nodal self-dynamics and the consensus convergent rate of the switching topology is given. To illustrate the effectiveness of the analytical results, two numerical examples on chaos synchronisation are simulated, respectively, for the periodic switching case and randomly switching case.     

一类离散切换模糊系统的稳定性

针对离散模糊系统,提出一类离散切换模糊系统的稳定性问题.使用切换技术及单Lyapunov函数、多Lyapunov函数方法构造出连续状态反馈控制器,使得相应的闭环系统渐近稳定,同时设计可以实现系统全局渐近稳定的切换律.模型中的每个切换系统的子系统是离散模糊系统,取常用的平行分布补偿PDC控制器,主要条件以凸组合和矩阵不等式的形式给出,具有较强的可解性.计算机仿真结果表明设计方法的可行性与有效性.     

A general approach for synchronisation of nonlinear networked systems with switching topology

This article investigates synchronisation of a nonlinear networked system with switching topology. By defining a common synchronisation manifold for each possible switching topology, exponential synchronisation of a nonlinear networked system can be assessed by the exponential stability of a reduced nonlinear system corresponding to the concerned system, wherein the communication graph can be directed and weighted and the inner-linking matrix might be singular. In particular, a synchronisation criterion consisting of the self-dynamics of isolated nodes and the consensus dynamics of a linear switched system is given. Two numerical simulations of synchronisation are presented to illustrate the effectiveness of the analytical results for the periodic and random switching cases.     

一类离散时间切换系统鲁棒控制器设计

考虑一类非线性离散时间切换系统的鲁棒二次镇定和渐近镇定问题．利用公共李亚普诺夫函数方法和多李亚普诺夫函数方法，分别设计了切换系统鲁棒状态反馈控制器和输出反馈控制器，保证了切换系统的二次稳定性和渐近稳定性．仿真结果验证了所提出算法的有效性．     

Synchronisation control of composite chaotic systems

Synchronisation conditions are studied for composite chaotic systems with complex compound structure and the signum function based on the theorem of zero-solution stability for a class of linear time-varying systems with countable discontinuous points. The synchronisation controller and its gain range are deduced according to the stability theorem, where the gain of the controller can speed synchronisation. Numerical simulation further proves the control theory and the validity of the synchronisation controller. The proposed controller can be widely applied in those chaotic systems with switch functions or other hybrid chaotic systems.     

Stability of discrete-time switched systems with admissible edge-dependent switching signals

The problem of stability is studied in this paper for a class of discrete-time switched systems with unstable subsystems. Two new definitions of slow switching and fast switching on the basis of admissible edge-dependent average dwell time are proposed, respectively. Some conditions are established by using multiple Lyapunov function method to guarantee the global uniform exponential stability of discrete-time switched systems. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results.     

多时滞离散切换系统的动态输出反馈H∞控制

借助多Lyapunov函数方法,研究一类具有多时滞的离散切换系统的鲁棒[H∞]控制问题。假设切换系统的每个子系统都不能实现鲁棒[H∞]控制,基于切换动态输出反馈控制策略,给出了系统存在鲁棒[H∞]干扰抑制水平[γ]可切换镇定的充分条件,并表示成与时滞相关的线性矩阵不等式（LMI）形式,还分别给出了切换律和动态输出反馈控制器的设计方案。最后用仿真例子说明了结论的有效性。     

一类时滞切换系统的稳定性分析

利用时滞分解和平均驻留时间方法讨论一类时滞切换系统的稳定性问题.定义了更为一般的Lyapunov函数,结合Jensen积分不等式和倒数凸组合技术得到的线性矩阵不等式条件具有更小的保守性和更低的计算复杂性给出的仿真算例进一步验证了所得结果的有效性.     

一类非线性离散切换系统基于观测器的指数镇定

对一类离散非线性切换系统, 考虑了基于观测器的指数镇定问题. 借助微分中值定理(DMVT), 将非线性切换系统转化为线性参数(LPV)切换系统. 当状态变量不完全可获得时, 基于多Lyapunov函数方法, 给出系统在基于观测器的输出反馈控制器下指数镇定的充分条件. 所设计的滞后切换规则能够避免产生滑动模态. 并且将结果推广到系统方程含有不确定性的情况. 最后, 仿真例子说明了设计方法的有效性.     

一类多输入级联非线性切换系统的全局镇定

研究一类带有部分线性系统的多输入级联非线性切换系统的全局镇定问题. 首先, 给出保证线性部分有一致规范型的充分条件. 其次, 利用一致规范型及其零动态的共同二次Lyapunov函数设计状态反馈使得线性部分在任意切换律下镇定. 最后, 通过构造共同Lyapunov函数能实现闭环系统在任意切换律下的全局渐近稳定性.     

一类非线性切换系统任意切换采样控制设计

本文针对一类具有非严格反馈形式的非线性切换系统,在输出只在采样点可获得的情况下,提出了一种基于模糊采样观测器的自适应输出反馈控制方法.该方法降低了现有任意切换控制研究结果中因共同控制思想导致的控制器设计的保守性,避免了迭代过程对虚拟控制的反复求导引发的计算爆炸现象及控制器高增益的弊端.切换的自适应律突显了每个子系统的特...     

一类线性切换系统具有H∞性能指标的二次稳定

研究了一类线性切换系统具有H_∞扰动衰减度二次稳定问题.这类线性切换系统由两个子系统组成,并且每个子系统都不是具有H_∞扰动衰减度二次稳定的.利用单Lyapunov函数方法,得到了线性切换系统具有H_∞扰动衰减度二次稳定的充分条件,同时由凸组合系统设计出确保线性切换系统二次稳定且具有H_∞扰动衰减度的切换律.进一步,还给出了线性切换系统具有H_∞扰动衰减度二次稳定的必要条件.最后的仿真实例表明了结论的有效性.     

Non-linear adaptive sliding mode switching control with average dwell-time

In this article, an adaptive integral sliding mode control scheme is addressed for switched non-linear systems in the presence of model uncertainties and external disturbances. The control law includes two parts: a slide mode controller for the reduced model of the plant and a compensation controller to deal with the non-linear systems with parameter uncertainties. The adaptive updated laws have been derived from the switched multiple Lyapunov function method, also an admissible switching signal with average dwell-time technique is given. The simplicity of the proposed control scheme facilitates its implementation and the overall control scheme guarantees the global asymptotic stability in the Lyapunov sense such that the sliding surface of the control system is well reached. Simulation results are presented to demonstrate the effectiveness and the feasibility of the proposed approach.     

具有一步随机通讯时延的网络化切换系统H∞滤波

针对数据包在网络中传输的一步随机时延情形,研究任意切换律作用下的离散切换系统的H∞滤波问题.时延数据包包含系统的测量输出信号和切换信号,其时延由一个满足Bernoulli分布的随机变量来描述.选用切换Lyapunov函数,设计全阶和降阶的切换滤波器使得滤波误差系统在均方意义下指数稳定且具有扰动衰减度γ.滤波器的参数通过...     

Simultaneous state and output disturbance estimations for a class of switched linear systems with unknown inputs

The paper considers the issues of state estimation and output disturbance reconstruction for a class of switched linear systems with unknown inputs. A singular switched system is derived from the original switched system by taking the output disturbance as a part of a new extended state vector. For the constructed singular switched system, a robust sliding-mode switched observer which can not only estimate the states of original switched system but also reconstruct output disturbances is proposed, where the switching of the observer is synchronous with that of the switched system. A sufficient condition is provided to guarantee the existence of the switched observer by the feasibility of an optimisation problem with linear matrix inequality constraint, and the corresponding switching signal with average dwell time is designed such that the convergence of the estimation error system is proven to be exponential. Based on the state estimation of singular switched system, the methods of state estimation and output disturbance reconstruction of original switched system are proposed. Finally, the simulation results confirm the predicted performance of the proposed methods.     

一类离散时间切换混杂系统鲁棒控制

由于切换规则的存在使得切换混杂控制系统的稳定性研究变得极为复杂,如何针对给定的系统设计适当的控制器和切换规则没有统一的方法.本文考虑一类线性不确定离散时间切换混杂系统的鲁棒二次镇定和渐近镇定问题.利用公共李雅普诺夫函数方法和多李雅普诺夫函数方法,分别设计了切换混杂系统鲁棒状态反馈控制器和鲁棒输出反馈控制器,保证了切换混杂系统的二次稳定性和渐近稳定性.仿真结果验证了所提算法的正确有效性.     

Adaptive output feedback tracking control for a class of uncertain switched nonlinear systems under arbitrary switching

This paper investigates the problem of adaptive output feedback tracking for uncertain switched nonlinear systems, under arbitrary switching. First, an adaptive output feedback controller is designed, which ensures the boundedness of all the closed-loop signals. Then, a novel adaptive-based robust output feedback control is proposed to drive the tracking error to zero, in which the bound of disturbances is not required to be known in advance. Both control algorithms are based on the common Lyapunov function method, without any restrictions on dwell time. To evaluate the performance of the proposed output feedback control schemes, a numerical example is presented and discussed.     

Model predictive control of distributed networked control systems with quantization and switching topology

This work is concerned with the robust model predictive control (MPC) for a class of distributed networked control systems (NCSs), in which the input quantization and switching topology are both considered. By utilizing the sector bound approach, the NCSs with quantization are converted into the linear systems with sector bound uncertainties. The topology switching is governed by a switching signal and the dynamic behavior is modeled as a switched control system. A new robust MPC design technique is derived to minimize the upper bound of a weighted quadratic performance index. Moreover, the conditions of both the recursive feasibility of the MPC design and the stability of the resulting closed‐loop system are developed. Finally, simulation results are presented to verify the effectiveness of the proposed MPC design.     

切换系统不变集的输出反馈镇定

利用一个非负函数V (x), 推广了小时间状态模可观测和大时间状态模可观测的定义, 提出了小时间V (x)可观测和大时间V (x)可观测的概念. 利用V (x)可观测的概念, 讨论了子系统无源的切换系统不变集的有界输出反馈镇定及动态输出反馈镇定. 利用多Lyapunov函数证明了闭环系统渐近稳定. 仿真例子验证了文中结论正确性.     

Asymptotic stability and disturbance attenuation properties for a class of networked control systems

In this paper, stability and disturbance attenuation issues for a class of Networked Control Systems (NCSs) under uncertain access delay and packet dropout effects are considered. Our aim is to find conditions on the delay and packet dropout rate, under which the system stability and H∞ disturbance attenuation properties are preserved to a desired level. The basic idea in this paper is to formulate such Networked Control System as a discrete-time switched system. Then the NCSs’ stability and performance problems can be reduced to the corresponding problems for switched systems, which have been studied for decades and for which a number of results are available in the literature. The techniques in this paper are based on recent progress in the discrete-time switched systems and piecewise Lyapunov functions.