Enhanced <em>H</em><sub>∞</sub> Filtering for Continuous-time State-delayed Systems

Ying Zhang; Ai-Guo Wu; Guang-Ren Duan

doi:10.1007/s11633-009-0159-7

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

doi: 10.1007/s11633-009-0159-7

1.
Institute of Information and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, PRC;
2.
Department of Automation, Harbin University of Science and Technology, Harbin 150080, PRC;
3.
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PRC

基金项目:

supported by National Natural Science Foundation ofChina (No.60772046);Program for Changjiang Scholars and Inno-vative Research Team in University;Natural Science Foundationof Heilongjiang Province (No.F2007-13)

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

1.
Institute of Information and Control, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen 518055, PRC;
2.
Department of Automation, Harbin University of Science and Technology, Harbin 150080, PRC;
3.
Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PRC

Funds:

摘要: The H filtering problem for continuous-time polytopic uncertain time-delay systems is investigated. Attention is focused on the design of full-order filters guaranteeing a prescribed H attenuation level for the filtering error system. First, a simple alternative proof is given for an improved linear matrix inequality (LMI) representation of H performance. Then, based on the performance criterion which keeps Lyapunov matrices out of the product of system dynamic matrices, a suficient condition for the existence of robust estimators is formulated in terms of LMIs, and the corresponding filter design is cast into a convex optimization problem which can be effciently handled by using standard numerical algorithms. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than some earlier results. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.
- Conservativeness /
- parameter-dependence /
- time-delay systems /
- linear matrix inequality (LMI)
Abstract: The H filtering problem for continuous-time polytopic uncertain time-delay systems is investigated. Attention is focused on the design of full-order filters guaranteeing a prescribed H attenuation level for the filtering error system. First, a simple alternative proof is given for an improved linear matrix inequality (LMI) representation of H performance. Then, based on the performance criterion which keeps Lyapunov matrices out of the product of system dynamic matrices, a suficient condition for the existence of robust estimators is formulated in terms of LMIs, and the corresponding filter design is cast into a convex optimization problem which can be effciently handled by using standard numerical algorithms. It is shown that the proposed design strategy allows the use of parameter-dependent Lyapunov functions and hence it is less conservative than some earlier results. A numerical example is employed to demonstrate the feasibility and advantage of the proposed design.
- Conservativeness /
- parameter-dependence /
- time-delay systems /
- linear matrix inequality (LMI)

[1]	J.C.Geromel,M.C.de Oliveira.H₂ and H_∞ Robust Filtering for Convex Bounded Uncertain Systems.IEEE Transactions on Automatic Control,vol.46,no.1,pp.100-107,2001.
[2]	A.G.Wu,H.F.Dong,G.R.Duan.Improved Robust H_∞ Estimation for Uncertain Continuous-time Systems.Journal of System Science and Complexity,vol.20,no.3,pp.362-369,2007.
[3]	C.E.de Souza,R.M.Palhares,P.L.D.Peres.Robust H_∞ Fitcr Design for Uncertain Linear Systems with Multiple Time-varying State Delay.IEEE Transactions on Signal Processing,vol.49,no.3,pp.569-576,2001.
[4]	X.M.Zhang,Q.L.Han.Robust H_∞ Filtering for a Class of Uncertain Linear Systems with Time-varying Delay.Automatica,vol.44,no.1,pp.157-166,2008.
[5]	Y.He,M.Wu,J.H.She,G.P.Liu.Parameter-dependent Lyapunov Functional for Stability of Time-delay Systems with Polytopic-type Uncertainties.IEEE Transactions on Automatic Control,vol.49,no.5,pp.828-832,2004.
[6]	Q.L.Han.On Robust Stability of Neutral Systems with Time-varying Discrete Delay and Norm-bounded Uncertainty.Automatica,vol.40,no.6,pp.1087-1092,2004.
[7]	A.G.Wu,G.R.Duan.On Delay-independent Stability Criteria for Linear Time-delay Systems.International Journal of Automation and Computing,vol.4,no.1,pp.95-100,2007.
[8]	H.Gao,C.Wang.A Delay-dependent Approach to Robust H_∞ Filtering for Uncertain Discrete-time State-delayed Systems.IEEE Transactions on Signal Processing,vol.52,no.6,1631-1640,2004.
[9]	A.G.Wu,G.R.Duan.Robust H_∞ Estimation for Uncertain Continuous-time Systems.In Proceedings of the 4th International Conference on Machine Learning and Cytbernetic,Guangzhou,PRC,pp.448-453,2004.
[10]	H.Y.Li,C.W.Yang.Robust H_∞ Filtering for Uncertain Linear Neutral Delay Systems.In Proceedings of the American Control Conference,Minneapolis,MN,USA,pp.14-16,2006.
[11]	A.W.Pila,U.Shaked,C.E.de Souza.H_∞ Filtering for Continuous-time Linear Systems with Delay.IEEE Transactions on Automatic Control,vol.44,no.7,pp.1412-1417,1999.
[12]	L.Xie,C.E.de Souza.On Robust Filtering for Linear Systems with Parameter Uncertainty.In Proceedings of the 34th IEEE Conference on Decision and Control,IEEE Press,New Orleans,USA,pp.2087-2092,1995.
[13]	M.C.de Oliveira,J.Bernussou,J.C.Geromel.A New Discrete-time Robust Stability Condition.System & Control Letters,vol.37,no.4,pp.261-265,1999.
[14]	R.M.Palhares,C.E.de Souza,P.L.D.Peres.Robust H_∞ Filtering for Uncertain Discrete-time State-delayed Systems.IEEE Transactions on Signal Processing,vol.49,no.8,pp.1696-1703,2001.
[15]	T.Li,Y.Jia.Improved LMI Presentations for Bounded Real Criterion of Systems with Polytopic Type Uncertainty.In Proceedings of the American Control Conference,Denver,Colorado,USA,pp.851-856,2003.

[1]	Tuo Zhou, Xi-Qin He. An Improved H_∞ Filter Design for Nonlinear Systems Described by T-S Fuzzy Models with Time-varying Delay . International Journal of Automation and Computing, 2015, 12(6): 671-678. doi: 10.1007/s11633-015-0930-x
[2]	Jun-Jun Hui, He-Xin Zhang, Xiang-Yu Kong, Xin Zhou. On Improved Delay-dependent Robust Stability Criteria for Uncertain Systems with Interval Time-varying Delay . International Journal of Automation and Computing, 2015, 12(1): 102-108. doi: 10.1007/s11633-014-0822-5
[3]	Guo-Chen Pang, Kan-Jian Zhang. Stability of Time-delay System with Time-varying Uncertainties via Homogeneous Polynomial Lyapunov-Krasovskii Functions . International Journal of Automation and Computing, 2015, 12(6): 657-663. doi: 10.1007/s11633-015-0940-8
[4]	Jian Ding, Blazej Cichy, Krzysztof Galkowski, Eric Rogers, Hui-Zhong Yang. Robust Fault-tolerant Iterative Learning Control for Discrete Systems via Linear Repetitive Processes Theory . International Journal of Automation and Computing, 2015, 12(3): 254-265. doi: 10.1007/s11633-015-0883-0
[5]	Jun-Jun Hui, He-Xin Zhang, Xiang-Yu Kong. Delay-dependent Non-fragile H_∞ Control for Linear Systems with Interval Time-varying Delay . International Journal of Automation and Computing, 2015, 12(1): 109-116. doi: 10.1007/s11633-014-0851-0
[6]	P. Balasubramaniam, T. Senthilkumar. Delay-dependent Robust Stabilization and H_∞ Control for Uncertain Stochastic T-S Fuzzy Systems with Discrete Interval and Distributed Time-varying Delay . International Journal of Automation and Computing, 2013, 10(1): 18-31 . doi: 10.1007/s11633-013-0692-2
[7]	. A Stability Criterion for Singular Systems with Two Additive Time-varying Delay Components . International Journal of Automation and Computing, 2013, 10(1): 39-45 . doi: 10.1007/s11633-013-0694-0
[8]	Imen Haj Brahim, Maha Bouattour, Driss Mehdi, Mohamed Chaabane, Ghani Hashim. Sensor Faults Observer Design with H_∞ Performance for Non-linear T-S systems . International Journal of Automation and Computing, 2013, 10(6): 563-570. doi: 10.1007/s11633-013-0754-5
[9]	Kamel Mohamed, Mohammed Chadli, Mohamed Chaabane. Unknown Inputs Observer for a Class of Nonlinear Uncertain Systems: An LMI Approach . International Journal of Automation and Computing, 2012, 9(3): 331-336. doi: 10.1007/s11633-012-0652-2
[10]	Zhong-Cai Zhang, Yu-Qiang Wu. Globally Asymptotic Stabilization for Nonlinear Time-delay Systems with ISS Inverse Dynamics . International Journal of Automation and Computing, 2012, 9(6): 634-640 . doi: 10.1007/s11633-012-0689-2
[11]	. Further Results on Delay-distribution-dependent Robust Stability Criteria for Delayed Systems . International Journal of Automation and Computing, 2011, 8(1): 23-28. doi: 10.1007/s11633-010-0550-4
[12]	K. Ramakrishnan, G. Ray. Delay-range-dependent Stability Criterion for Interval Time-delay Systems with Nonlinear Perturbations . International Journal of Automation and Computing, 2011, 8(1): 141-146. doi: 10.1007/s11633-010-0566-9
[13]	Lin-Na Zhou, Chun-Yu Yang, Qing-Ling Zhang. Observers for Descriptor Systems with Slope-restricted Nonlinearities . International Journal of Automation and Computing, 2010, 7(4): 472-478. doi: 10.1007/s11633-010-0529-1
[14]	Xu-Dong Zhao, Qing-Shuang Zeng. H_∞ Output Feedback Control for Stochastic Systems with Mode-dependent Time-varying Delays and Markovian Jump Parameters . International Journal of Automation and Computing, 2010, 7(4): 447-454. doi: 10.1007/s11633-010-0526-4
[15]	Xian-Ming Tang, Jin-Shou Yu. Stability Analysis of Discrete-time Systems with Additive Time-varying Delays . International Journal of Automation and Computing, 2010, 7(2): 219-223. doi: 10.1007/s11633-010-0219-z
[16]	Fang Qiu, Bao-Tong Cui. Improved Exponential Stability Criteria for Uncertain Neutral System with Nonlinear Parameter Perturbations . International Journal of Automation and Computing, 2010, 7(4): 413-418. doi: 10.1007/s11633-010-0522-8
[17]	Fatima El Haoussi, El Houssaine Tissir. Delay and Its Time-derivative Dependent Robust Stability of Uncertain Neutral Systems with Saturating Actuators . International Journal of Automation and Computing, 2010, 7(4): 455-462. doi: 10.1007/s11633-010-0527-3
[18]	Guang-Deng Zong, Jia Liu. New Delay-dependent Global Asymptotic Stability Condition for Hopfield Neural Networks with Time-varying Delays . International Journal of Automation and Computing, 2009, 6(4): 415-419. doi: 10.1007/s11633-009-0415-x
[19]	Fatima El Haoussi, El Houssaine Tissir. Robust H_∞ Controller Design for Uncertain Neutral Systems via Dynamic Observer Based Output Feedback . International Journal of Automation and Computing, 2009, 6(2): 164-170. doi: 10.1007/s11633-009-0164-x
[20]	Ai-Guo Wu, Guang-Ren Duan. On Delay-independent Stability Criteria for Linear Time-delay Systems . International Journal of Automation and Computing, 2007, 4(1): 95-100. doi: 10.1007/s11633-007-0095-3

点击查看大图

计量

文章访问数: 3302
HTML全文浏览量: 33
PDF下载量: 1936
被引次数: 0

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

doi: 10.1007/s11633-009-0159-7

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

计量

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

doi: 10.1007/s11633-009-0159-7

English Abstract

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

全文HTML

目录

Enhanced H∞ Filtering for Continuous-time State-delayed Systems

doi: 10.1007/s11633-009-0159-7

Enhanced H∞ Filtering for Continuous-time State-delayed Systems

计量

出版历程

Enhanced H∞ Filtering for Continuous-time State-delayed Systems

doi: 10.1007/s11633-009-0159-7

English Abstract

Enhanced H∞ Filtering for Continuous-time State-delayed Systems

全文HTML

目录

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems

Enhanced H_∞ Filtering for Continuous-time State-delayed Systems