离散Markov跳变系统事件触发H_∞量化输出反馈控制
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摘要
主要考虑了基于事件触发机制的离散Markov跳变系统的量化H∞输出反馈控制问题,对系统的建模、稳定性分析、控制器设计等三个方面进行了研究;首先,提出了事件触发通信机制来确定当前采样数据是否能够传输到控制器当中;其次,在传感器与控制器之间引入对数量化器,利用扇形有界方法,量化采样数据达到降低网络中的数据传输速率的目的;接下来,考虑网络诱导时延建立一种具有外部扰动的Markov跳变时滞系统;构造Lyapunov-Krasovskii泛函,利用线性矩阵不等式(LMIs)得到使闭环系统渐近稳定且满足H∞性能指标的充分条件,在此基础上设计相应的输出反馈控制器;最后通过数值仿真来证明本文所提方法的有效性。
The problem of event-triggered H∞output feedback control for a class of discrete Markov jump systems with quantization is investigated.The three aspects of system modeling,stability analysis and controller design are studied respectively.Firstly,an event-triggered communication mechanism is proposed to determine whether the sampled data can be transmitted to the controller.Secondly,aquantizer is introduced between the sensor and the controller.Sector bound approach is used to quantify the sampled data,which can reduce the data transmission rate in the network.Next,through the analysis of network induced delay,a Markov jump time-delay system with external disturbances is established.The Lyapunov-Krasovskii functional is constructed.And the sufficient conditions in terms of linear matrix inequalities(LMIs)for the closed-loop system to be asymptotically stable with a prescribed H∞performance index are obtained.The corresponding output feedback controller is also designed.Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.
The problem of event-triggered H∞output feedback control for a class of discrete Markov jump systems with quantization is investigated.The three aspects of system modeling,stability analysis and controller design are studied respectively.Firstly,an event-triggered communication mechanism is proposed to determine whether the sampled data can be transmitted to the controller.Secondly,aquantizer is introduced between the sensor and the controller.Sector bound approach is used to quantify the sampled data,which can reduce the data transmission rate in the network.Next,through the analysis of network induced delay,a Markov jump time-delay system with external disturbances is established.The Lyapunov-Krasovskii functional is constructed.And the sufficient conditions in terms of linear matrix inequalities(LMIs)for the closed-loop system to be asymptotically stable with a prescribed H∞performance index are obtained.The corresponding output feedback controller is also designed.Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.
引文
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[14]Hu Songlin,Yue Dong.Event-triggered control design of linear networked systems with quantizations[J].ISA Transactions,2012,51(1):153-162.
[15]Fu Minyue,Xie Lihua.The sector bound approach to quantized feedback control[J].IEEE Transactions on Automatic Control,2005,50(11):1698-1711.
[16]Xiong Junlin,Lam J.Stabilization of networked control systems with a logic ZOH[J].IEEE Transactions on Automatic Control,2009,54(2):358-363.
[17]Xie Lihua,Fu Minyue,De Souza C E.H∞control and quadratic stabilization of systems with parameter uncertainty via output feedback[J].IEEE Transactions on Automatic Control,1992,37(8):1253-1256.
[18]Wu Zhengguang,Su Hongye,Chu Jian,et al.Improved delaydependent stability condition of discrete recurrent neural networks with time-varying delays[J].IEEE Transactions on Neural Networks,2010,21(4):692-697.
[19]Zhang Jin,Peng Chen,Fei Minrui,et al.Output feedback control of networked systems with a stochastic communication protocol[J].Journal of the Franklin Institute,2016,354(9):3838-3853.
[2]Cheng Jun,Park Ju H,Liu Yajuan,et al.Finite-time H∞fuzzy control of nonlinear Markovian jump delayed systems with partly uncertain transition descriptions[J].Fuzzy Sets&Systems,2017,314:99-115.
[3]张鹏,宫占霞.网络控制系统H∞指数稳定容错控制器的设计[J].计算机测量与控制,2016,24(2):88-90.
[4]Peng Chen,Yang Taicheng.Event-triggered communication andH∞control co-design for networked control systems.[J].Automatica,2013,49(5):326-332.
[5]Shi Peng,Wang Huijiao,Lim Chengchew.Network-based eventtriggered control for singular systems with quantizations[J].IEEETransactions on Industrial Electronics,2016,63(2):1230-1238.
[6]Qu Fenglin,Guan Zhihong,He Dongxi,et al.Event-triggered control for networked control systems with quantization and packet losses[J].Journal of the Franklin Institute,2015,352(3):974-986.
[7]Zha Lijuan,Fang Jianan,Li Xiaofang,et al.Event-triggered output feedback H∞control for networked Markovian jump systems with quantizations[J].Nonlinear Analysis Hybrid Systems,2017,24:146-158.
[8]Peng Chen,Zhang Jin.Event-triggered output feedback H∞control for networked control systems with time varying sampling[J].Control Theory&Applications,Iet,2015,9(9):1384-1391.
[9]Xiao Nan,Xie Lihua,Fu Mingyue.Stabilization of Markov jump linear systems using quantized state feedback[J].Automatica,2010,46(10):1696-1702.
[10]Wang Huijiao,Xue Anke,Wang Junhong,et al.Event-based H∞filtering for discrete-time Markov jump systems with network-induced delay[J].Journal of the Franklin Institute,2017,354(14):6170-6189.
[11]Rasool F,Huang D,Nguang S K.Robust H∞output feedback control of discrete-time networked systems with adaptive quantizers[J].International Journal of Systems Science,2011,60(60):2381-2386.
[12]Hu Songlin,Yue Dong.Event-based H∞filtering for networked system with communication delay[J].Signal Processing,2012,92(9)2029-2039.
[13]Yue Dong,Tian Engang,Han Qinglong.A delay system method for designing event-triggered controllers of networked control systems[J].IEEE Transactions on Automatic Control,2013,58(2):475-481.
[14]Hu Songlin,Yue Dong.Event-triggered control design of linear networked systems with quantizations[J].ISA Transactions,2012,51(1):153-162.
[15]Fu Minyue,Xie Lihua.The sector bound approach to quantized feedback control[J].IEEE Transactions on Automatic Control,2005,50(11):1698-1711.
[16]Xiong Junlin,Lam J.Stabilization of networked control systems with a logic ZOH[J].IEEE Transactions on Automatic Control,2009,54(2):358-363.
[17]Xie Lihua,Fu Minyue,De Souza C E.H∞control and quadratic stabilization of systems with parameter uncertainty via output feedback[J].IEEE Transactions on Automatic Control,1992,37(8):1253-1256.
[18]Wu Zhengguang,Su Hongye,Chu Jian,et al.Improved delaydependent stability condition of discrete recurrent neural networks with time-varying delays[J].IEEE Transactions on Neural Networks,2010,21(4):692-697.
[19]Zhang Jin,Peng Chen,Fei Minrui,et al.Output feedback control of networked systems with a stochastic communication protocol[J].Journal of the Franklin Institute,2016,354(9):3838-3853.
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