Robust $H_\infty$ Filtering for Two-Dimensional Uncertain Linear Discrete Time-Varying Systems: A Krein Space-Based Method

A robust <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> filtering algorithm is proposed for two-dimensional (2-D) linear uncertain time-varying systems in this study. The considered 2-D systems are subject to unknown inputs, measurement noises, and time-varying modeling uncertainties. To appropriately deal with the system uncertainties, a new problem formulation of robust <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> filter design for 2-D uncertain systems is first presented by introducing an alternative indefinite quadratic performance function in lieu of the standard <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance index. Then, the robust 2-D <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> filter design is converted to an optimization problem of finding the positive minimum of the new indefinite quadratic performance function under certain conditions. By relating this quadratic form to a specific 2-D state-space model in Krein space, the Krein space estimation theory is used to solve the reformulated optimization problem. A recursive robust 2-D time-varying <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> filter and its explicit condition for the existence are obtained through projection techniques in 2-D Krein space. One thermal process plant is used to illustrate the effectiveness of the proposed filter.

[1]  Ling Shi,et al.  Multi-sensor Scheduling for State Estimation with Event-based, Stochastic Triggers , 2013 .

[2]  Peng Shi,et al.  Two-Dimensional Peak-to-Peak Filtering for Stochastic Fornasini–Marchesini Systems , 2018, IEEE Transactions on Automatic Control.

[3]  Dong Zhao,et al.  $H_{\infty}$ Fault Estimation for 2-D Linear Discrete Time-Varying Systems Based on Krein Space Method , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[4]  Donghua Zhou,et al.  Sensor fault reconstruction for a class of 2-D nonlinear systems with application to fault compensation , 2015, Multidimens. Syst. Signal Process..

[5]  Peter H. Bauer,et al.  Realization Using the Fornasini-Marchesini Model for Implementations in Distributed Grid Sensor Networks , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  Dong Shen,et al.  Fault diagnosis and compensation for two‐dimensional discrete time systems with sensor faults and time‐varying delays , 2017 .

[7]  Ligang Wu,et al.  Stability analysis and stabilization of 2-D switched systems under arbitrary and restricted switchings , 2015, Autom..

[8]  Donghua Zhou,et al.  Control Performance Assessment for ILC-Controlled Batch Processes in a 2-D System Framework , 2018, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[9]  Shengyuan Xu,et al.  A Generalized Kalman Filter for 2D Discrete Systems , 2004, The 2004 47th Midwest Symposium on Circuits and Systems, 2004. MWSCAS '04..

[10]  Wojciech Paszke,et al.  Robust H/sub /spl infin// filtering for Uncertain2-D continuous systems , 2005, IEEE Transactions on Signal Processing.

[11]  Zhiping Lin,et al.  Robust H Filtering for Uncertain 2-D Continuous Systems , 2005 .

[12]  Maria Elena Valcher,et al.  The general fault detection and isolation problem for 2D state-space models , 2006, Syst. Control. Lett..

[13]  Furong Gao,et al.  Robust two-dimensional iterative learning control for batch processes with state delay and time-varying uncertainties , 2010 .

[14]  Wei Xing Zheng,et al.  Generalized H2 fault detection for two-dimensional Markovian jump systems , 2012, Autom..

[15]  Peng Shi,et al.  Two-Dimensional Dissipative Control and Filtering for Roesser Model , 2015, IEEE Transactions on Automatic Control.

[16]  Okyay Kaynak,et al.  Sliding Mode Observer-Based FTC for Markovian Jump Systems With Actuator and Sensor Faults , 2017, IEEE Transactions on Automatic Control.

[17]  T. Kailath,et al.  Linear estimation in Krein spaces. I. Theory , 1996, IEEE Trans. Autom. Control..

[18]  Ligang Wu,et al.  Filtering and Control for Classes of Two-Dimensional Systems , 2015 .

[19]  T. Kaczorek.  Two-Dimensional Linear Systems , 1985 .

[20]  Steven X. Ding,et al.  Unbiased Minimum Variance Fault and State Estimation for Linear Discrete Time-Varying Two-Dimensional Systems , 2017, IEEE Transactions on Automatic Control.

[21]  T. Kailath,et al.  Linear estimation in Krein spaces. II. Applications , 1996, IEEE Trans. Autom. Control..

[22]  Lorenzo Ntogramatzidis,et al.  On Kalman filtering for 2-D Fornasini-Marchesini models , 2009, 2009 International Workshop on Multidimensional (nD) Systems.