Robust reduced-order l2-l∞ filtering for network-based discrete-time linear systems

This paper investigates the l2-l∞ filtering problem for a class of discrete-time system subject to network-induced delays. The objective is to design a reduced-order filter, such that the estimation errors converge to zero, while an l2-l∞ performance is satisfied. A Markov chain with partly unknown transition probabilities is used to describe the network-induced delay. Then, a delay-dependent linear filter is considered, whose parameters are described by the network-induced delay. By using Finsler?s lemma, sufficient conditions in terms of linear matrix inequalities (LMIs) for the existence of the desired filter are derived, which guarantee that estimation errors converge to zero with an l2-l∞ performance γ. By solving those LMIs, filter gain matrices can be calculated. Finally, numerical simulations are given to illustrate that the designed filter is successful even in the existence of network-induced delays. A network-based system is considered in this paper.The network-induced delays are modeled by a Markov chain with partly uncertain transition probabilities.A reduced-order energy-to-peak filter is designed.A numerical example illustrates the effectiveness of the proposed filtering approach.

[1]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[2]  Guang-Hong Yang,et al.  H ∞ filter design for continuous-time systems with quantised signals , 2013, Int. J. Syst. Sci..

[3]  Huijun Gao,et al.  Robust L/sub 2/-L/sub /spl infin// filtering for uncertain systems with multiple time-varying state delays , 2003 .

[4]  Wei Xing Zheng,et al.  H ∞ filtering for linear continuous-time systems subject to sensor non-linearities , 2011 .

[5]  R Yang,et al.  Delay-dependent L2-L∞ filter design forstochastic time-delay systems , 2011 .

[6]  Honghai Liu,et al.  Improved H ∞ analysis of Markovian jumping stochastic systems with time-varying delays , 2013, Int. J. Syst. Sci..

[7]  Wei Xing Zheng,et al.  H∞ filter design for nonlinear networked control systems with uncertain packet-loss probability , 2012, Signal Process..

[8]  Carlo Piccardi.  Parameter Estimation for Systems with Peak-to-Peak Dynamics , 2008, Int. J. Bifurc. Chaos.

[9]  Fei Liu,et al.  An adaptive risk-sensitive filtering method for Markov jump linear systems with uncertain parameters , 2012, J. Frankl. Inst..

[10]  K. Grigoriadis,et al.  Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities , 1997, IEEE Transactions on Aerospace and Electronic Systems.

[11]  Hui Zhang,et al.  H∞ Step Tracking Control for Networked Discrete-Time Nonlinear Systems With Integral and Predictive Actions , 2013, IEEE Transactions on Industrial Informatics.

[12]  Petros G. Voulgaris,et al.  Minimization of the Peak-to-Peak Gain in Periodic Systems Under Full State Feedback , 1996 .

[13]  Jian-xun Li,et al.  Energy-to-peak filtering for singular systems: the discrete-time case , 2008 .

[14]  Wen-an Zhang,et al.  Hinfinity filtering of network-based systems with random delay , 2009, Signal Process..

[15]  Dan Zhang,et al.  $H_\infty$ Filtering for Networked Systems With Multiple Time-Varying Transmissions and Random Packet Dropouts , 2013, IEEE Transactions on Industrial Informatics.

[16]  Hui Zhang,et al.  Robust Static Output Feedback Control and Remote PID Design for Networked Motor Systems , 2011, IEEE Transactions on Industrial Electronics.

[17]  D. Wilson.  Convolution and Hankel operator norms for linear systems , 1989 .

[18]  Hui Zhang,et al.  On Energy-to-Peak Filtering for Nonuniformly Sampled Nonlinear Systems: A Markovian Jump System Approach , 2014, IEEE Transactions on Fuzzy Systems.

[19]  Hui Zhang,et al.  Robust weighted H∞ filtering for networked systems with intermittent measurements of multiple sensors , 2011 .

[20]  Long-Yeu Chung,et al.  Robust H∞ filtering for discrete switched systems with interval time-varying delay , 2014, Signal Process..

[21]  E. Boukas,et al.  H∞ control for discrete‐time Markovian jump linear systems with partly unknown transition probabilities , 2009 .

[22]  Hui Zhang,et al.  Robust gain-scheduling energy-to-peak control of vehicle lateral dynamics stabilisation , 2014 .

[23]  Dong Yue,et al.  Event-based H∞ filtering for networked system with communication delay , 2012, Signal Process..

[24]  Vasile Dragan,et al.  H∞ filtering of periodic Markovian jump systems: Application to filtering with communication constraints , 2012, Autom..

[25]  Tongwen Chen,et al.  Hinfinity filtering for nonuniformly sampled systems: A Markovian jump systems approach , 2011, Syst. Control. Lett..

[26]  Hui Zhang,et al.  Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data , 2010 .

[27]  K. Poolla,et al.  A linear matrix inequality approach to peak‐to‐peak gain minimization , 1996 .

[28]  Lihua Xie,et al.  Kalman filtering over unreliable communication networks with bounded Markovian packet dropouts , 2009 .

[29]  Jie Yang,et al.  New results on robust energy-to-peak filtering for discrete-time switched polytopic linear systems with time-varying delay , 2008 .

[30]  Songlin Hu,et al.  Event-triggered control design of linear networked systems with quantizations. , 2012, ISA transactions.

[31]  Oswaldo Luiz V. Costa,et al.  Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises , 2011, Autom..

[32]  Peng Shi,et al.  Robust filtering for jumping systems with mode-dependent delays , 2006, Signal Process..

[33]  James Lam,et al.  Robust energy-to-peak filter design for stochastic time-delay systems , 2006, Syst. Control. Lett..

[34]  Fuwen Yang,et al.  Decentralized robust Kalman filtering for uncertain stochastic systems over heterogeneous sensor networks , 2008, Signal Process..

[35]  M. Fragoso,et al.  ℋ︁∞ filtering for discrete‐time linear systems with Markovian jumping parameters† , 2003 .

[36]  Aryan Saadat Mehr,et al.  On ${\cal H}_{\infty }$ Filtering for Discrete-Time Takagi–Sugeno Fuzzy Systems , 2012, IEEE Transactions on Fuzzy Systems.

[37]  Huazhen Fang,et al.  Kalman filter‐based adaptive control for networked systems with unknown parameters and randomly missing outputs , 2009 .

[38]  Victor Sreeram,et al.  Design of reduced-order H∞ filtering for Markovian jump systems with mode-dependent time delays , 2009, Signal Process..

[39]  James Lam,et al.  A new delay system approach to network-based control , 2008, Autom..

[40]  Haiping Du,et al.  Energy‐to‐peak control of seismic‐excited buildings with input delay , 2007 .

[41]  Lin Li,et al.  On mode-dependent H∞ filtering for network-based discrete-time systems , 2013, Signal Process..