带有随机测量数据丢失及切换拓扑的传感器网络分布式$l_2-l_infty$滤波器设计

研究一类具有测量数据随机丢失以及网络拓扑结构随机切换的分布式$l_2-l_\infty$滤波器设计问题.在分布式滤波器网络,每个本地滤波器估计系统的状态不仅基于节点自身信息,而且利用网络拓扑中邻居节点的信息.首先,采用已知概率分布的二进制序列描述传感器测量数据的随机丢失,Markov链描述滤波器网络拓扑结构的切换;其次,构造一个Lyapunov函数来分析滤波误差系统的$l_2-l_\infty$性能,并研究其均方指数稳定性;再次,通过线性矩阵不等式(LMI)技术,给出分布式$l_2-l_\infty$滤波器的设计方法;最后, 通过数值例子验证所提方法的有效性.     

离散切换线性系统的异步滤波器设计

利用模型依赖的平均驻留时间策略研究离散异步切换线性系统的指数H_∞滤波问题.考虑到在实际问题中,所设计的模型依赖的全阶滤波器的切换往往会滞后于其相应的子系统,将子系统的运行区间划分为与滤波器匹配的区间和不匹配的区间.针对两种工作模态,利用模型依赖的平均驻留时间切换策略和μ依赖的多Lyapunov函数方法完成滤波器的设计,并使得增广得到的异步滤波误差系统全局一致指数稳定且满足指数H_∞性能指标.该滤波器存在的充分条件在文中以线性矩阵不等式的形式给出.最后通过数值仿真验证所提方法的有效性.     

基于周期动态事件触发的网络化切换系统的分析与控制

针对网络化系统研究具有模态依赖平均驻留时间(MDADT)和异步的线性切换系统的周期动态事件触发$H_\infty$控制.与已有切换系统事件触发方式不同,周期动态事件触发引入动态事件触发参数,且具有最小的事件触发间隔下界,在降低数据发送数量的同时,能够有效避免奇诺行为;利用MDADT方法和多Lyapunov函数技术,给出闭环系统具有指数稳定和$H_\infty$加权性能的充分条件;在此基础上,针对周期动态事件触发机制中可能存在的异步问题,提出相应的控制器设计准则.最后,通过算例验证所得结果的优越性.     

切换系统H_/H∞异步切换故障检测滤波器设计

研究混合H_/H_∞框架下,切换系统的异步故障检测滤波器的 设计问题.使用$H_-$性能指标和加权$H_\infty$性能指标表示 残差对于故障的敏感性以及对于扰动的鲁棒性.首先,利用多Lyapunov函数方 法和平均驻留时间技术,得到初步的异步切换滤波器设计条件; 然后,使用松 弛变量的方法解除Lyapunov矩阵和系统矩阵的耦合,得到进一步的设计结 果,并将其表示为线性矩阵不等式形式; 最后,通过仿真例子验证了所提出 方法的有效性.     

连续切换LPV系统的鲁棒H∞滤波

探究连续切换线性参数变化(LPV)系统的鲁棒H∞滤波问题.对于整个参数变化空间,传统方法是设计单一LPV滤波器,具有较大的保守性.为此,利用多参数依赖Lyapunov函数设计了切换LPV系统的多参数依赖鲁棒H∞滤波器,以降低设计的保守性.考虑了平均驻留时间切换逻辑,所设计的鲁棒H∞滤波器能够确保滤波误差系统指数稳定且具有一定的H∞扰动抑制水平.数值仿真实例验证了所提出方法的有效性.     

基于模型依赖驻留时间的异步切换控制

研究在模型依赖平均驻留时间切换策略下切换线性系统的异步切换控制问题,同时考虑模型依赖的控制器滞后时间的约束问题.在实际情况下,信号传输和系统检测等原因会导致控制器的切换滞后于子系统.基于这类情况,首先将子系统运行的区间划分为子系统与控制器相匹配的区间和非匹配的区间,根据模型依赖的驻留时间策略设计出各子系统的控制器;然后,结合模型依赖的控制器滞后时间、系统参数和Lyapunov稳定条件推导出合适的驻留时间设计参数,且使得异步切换系统全局一致指数稳定;最后通过数值仿真验证了所提出方法的有效性.     

具有状态时滞的离散时间切换系统的H∞ 滤波器设计: 依赖状态的切换方法

讨论一类时滞离散时间切换系统的H∞滤波器的设计问题.首先,当所有子系统都稳定时,基于切换Lyapunov函数和Finsler引理,得到了滤波误差系统渐近稳定且具有指定的H∞性能指标的充分条件,即使切换系统的每个子系统均不稳定,通过利用多Lyapunov函数方法和依赖状态的切换技术仍能保证切换系统稳定;然后,设计了H∞滤波器,并得到滤波误差系统满足指定的H∞性能指标的充分条件;最后,通过数值算例验证了所提出方法的有效性.     

分数阶时变切换系统有限时间异步控制

针对一类时变切换系统,当考虑子系统具有分数阶(Fractional Order)特性时,提出了一种基于模型依赖平均驻留时间方法的有限时间稳定性条件及异步切换控制策略.借助Caputo分数阶导数引理和切换Lyapunov函数,利用矩阵不等式技术提出了分数阶时变切换系统有限时间稳定的充分条件.将有限时间稳定的结果进一步推广到有限时间有界的情形,利用平均驻留时间思想提出了分数阶时变切换系统有限时间有界的充分条件,基于该条件设计了系统的异步切换控制器.所给出的设计方法将系统异步切换控制问题转化为矩阵不等式组的求解问题.通过数值仿真验证了所提控制方法的有效性.     

Delta算子切换系统的鲁棒滤波器研究

研究了一类参数不确定线性Delta算子切换系统的鲁棒H∞滤波器设计问题。提出利用多Lyapunov函数和平均驻留时间方法,以线性矩阵不等式的形式给出了参数不确定Delta算子滤波误差切换系统指数稳定性条件,并进行了肌性能分析,从而进一步给出Delta算子切换系统鲁棒肌滤波器存在的充分条件和设计方法。所设计的滤波器不但保证系统参数不确定时闭环系统指数稳定,而且满足所期望的H∞性能指标。仿真结果证明了设计方法的有效性和可行性。     

基于局部交叠异步切换的网络控制系统故障检测

针对存在时变短时延和丢包的网络控制系统故障检测问题,将非线性对象建模为线性切换系统.考虑工程中存在的局部交叠切换律,将切换系统划分为若干局部交叠切换于系统.同时,考虑滤波器切换滞后引起的异步切换问题,进一步将系统增广为局部交叠异步切换系统.在此基础上,结合公共Lyapunov函数和平均驻留时间方法,以LMI形式给出检测滤波器设计方法.最后,通过某网络化飞行器的全包线飞行验证了所提出方法的有效性.     

Stability and stabilization of continuous‐time switched systems: A multiple discontinuous convex Lyapunov function approach

In this paper, the problems of stability and stabilization are considered for a class of switched linear systems with slow switching and fast switching. A multiple convex Lyapunov function and a multiple discontinuous convex Lyapunov function are first introduced, under which the extended stability and stabilization results are derived with a mode‐dependent average dwell time switching strategy, where slow switching and fast switching are exerted on stable and unstable subsystems, respectively. These two types of Lyapunov functions are established in a constructive manner by virtue of a set of time‐varying functions. By using our proposed approaches, larger stability regions of system parameters are identified, and tighter bounds can be obtained for the mode‐dependent average dwell time. New mode‐dependent and time‐varying controllers are constructed for a class of switched control systems with stabilizable and unstabilizable subsystems as well. All the stability and stabilization conditions can be given in terms of strict linear matrix inequalities (LMIs), which can be checked easily by using recently developed algorithms in solving LMIs. Finally, two numerical examples are provided to show the effectiveness of the obtained results compared with the existing results.     

基于反馈无源化的切换非线性系统H∞跟踪控制

针对切换非线性系统,提出一种基于反馈无源化的H_∞跟踪控制策略.首先,提出依赖状态切换的控制方法,在子系统不满足有界参考弱最小相位这一标准假设时,给出解决H_∞跟踪问题的充分条件,通过零状态可检测条件保证切换系统的内部稳定性,并利用无源不等式验证切换非线性系统满足H_∞跟踪性能;然后,提出依赖时间切换的跟踪策略,得到H_∞跟踪问题的可解性条件,该方法不依赖系统内部状态进行切换,将系统输出和参考信号之间的误差作为控制输入,并计算出切换系统满足的平均驻留时间;最后,给出仿真算例,以验证结果的正确性.     

Exponential Stability and Asynchronous Stabilization of Switched Systems With Stable and Unstable Subsystems

This paper deals with the exponential stability and asynchronous stabilization of continuous‐time switched systems. By delicately constructed piecewise Lyapunov‐like functions and the minimum dwell time switching method, exponential stability of the switched systems with stable or unstable subsystems is obtained. Based on the result of the stability, the problem of controller design of the switched systems under asynchronous switching is also solved, and the delay that causes asynchronous phenomena can be unbounded. The stability results and control laws of the switched systems are formulated in the form of linear matrix inequalities that are numerically feasible. Finally, two illustrative numerical examples are presented to show the effectiveness of the obtained theoretical results.     

Exponential H∞ Filtering for Discrete‐Time Switched State‐Delay Systems Under Asynchronous Switching

The exponential H_∞ filtering problem of discrete‐time switched state‐delay systems under asynchronous switching is considered in this paper. The objective is to design a full‐order or reduced‐order switched filter guaranteeing the exponential stability with the weighted H_∞ performance of the filtering error system. A sufficient condition for the exponential stability with the weighted H_∞ performance of the filtering error system is provided based on delay‐dependent multiple Lyapunov‐Krasovskii functionals. The gains of the filter can be obtained by solving a set of linear matrix inequalities. A numerical example is presented to demonstrate the effectiveness of the developed results.     

Exponential H∞ filtering for nonlinear discrete‐time switched stochastic systems with mixed time delays and random missing measurements

This paper is concerned with the exponential H_∞ filtering for a class of nonlinear discrete‐time switched stochastic hybrid systems with mixed time delays and random missing measurements. The switched system under study involves stochastic disturbance, time‐varying discrete delay, bounded distributed delay and nonlinearity. Attention is focused on the design of a mode‐dependent filter that guarantees the exponential stability in the mean‐square sense and a prescribed H_∞ noise attenuation level for the filtering error dynamics. By constructing a new Lyapunov functional and using the average dwell time scheme, a new delay‐dependent sufficient condition for the existence of the filter is presented in terms of linear matrix inequalities. A numerical example is finally given to show the effectiveness of the proposed design method. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Fault detection for continuous‐time switched systems under asynchronous switching

In this paper, the problem of fault detection for continuous‐time switched systems under asynchronous switching is investigated. The designed fault detection filter is assumed to be asynchronous with the original systems. Attention is focused on designing a fault detection filter such that the estimation error between the residual and the fault is minimized in the sense of H _∞ norm. By employing piecewise Lyapunov function and average dwell time techniques, a sufficient condition for the existence of such a filter is exploited in terms of certain linear matrix inequalities. Finally, an example of a switched electrical circuit is provided to illustrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

时滞半Markov跳变神经网络系统事件驱动故障检测滤波器设计

本文针对一类具有时滞的半Markov跳变神经网络系统,研究其基于滤波器的故障检测问题.首先,通过引入一种事件驱动通讯机制和一个滤波器,并将时变时滞以及网络诱导时滞考虑进来,建立残差系统,将故障检测问题转化为求解满足一定H∞性能指标的滤波问题.然后,基于Lyapunov-Krasovskii(L–K)泛函方法,通过利用时滞乘积型L–K泛函思想、积分不等式、改进逆凸矩阵不等式等方法,以线性矩阵不等式形式给出故障检测滤波器的设计方法.最后,数值仿真结果验证本文所设计故障检测滤波器的有效性与优越性.     

Asynchronous H∞ filtering for linear switched systems with average dwell time

This paper is concerned with the H_∞ filtering problem for a class of continuous-time linear switched systems with the asynchronous behaviours, where ‘asynchronous’ means that the switching of the filters to be designed has a lag to the switching of the system modes. By using the Lyapunov-like functions and the average dwell time technique, a sufficient condition is obtained to guarantee the asymptotic stability with a weighted H_∞ performance index for the filtering error system. Moreover, the results are formulated in the form of linear matrix inequalities that are numerical feasible. As a result, the filter design problem is solved. Finally, an illustrative numerical example is presented to show the effectiveness of the results.