l1 filtering for continuous-discrete T-S fuzzy positive Roesser model

Abstract This paper addresses the positive filter design problem for a class of continuous-discrete Roesser model in Takagi-Sugeno fuzzy form. Both the observer-based and the general form of filters are designed with l1 performance constraint. By utilizing the co-positive Lyapunov function approach, sufficient criteria are derived in the form of linear programming, which not only guarantee the existence of the positive lower-bounding/upper-bounding filters but also assure the resulting filtering error system to be asymptotically stable and having a prescribed l1-gain performance index. In addition, the explicit design schemes for the corresponding filter parameters are also presented. Finally, two numerical examples are provided to illustrate effectiveness of the proposed results.

[1]  Daniel W. C. Ho,et al.  Robust ${{\cal H}}_{\infty}$ Filtering for Markovian Jump Systems With Randomly Occurring Nonlinearities and Sensor Saturation: The Finite-Horizon Case , 2011, IEEE Transactions on Signal Processing.

[2]  Fuad E. Alsaadi,et al.  Robust ${\mathscr {H}}_{\infty }$ Filtering for a Class of Two-Dimensional Uncertain Fuzzy Systems With Randomly Occurring Mixed Delays , 2017, IEEE Transactions on Fuzzy Systems.

[3]  Lihua Xie,et al.  H/sub /spl infin// reduced-order approximation of 2-D digital filters , 2001 .

[4]  Yang Xiao.  Stability, controllability and observability of 2-D continuous-discrete systems , 2003, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03..

[5]  Qi Zhou,et al.  A new delay-range-dependent H∞ filter design for T-S nonlinear systems , 2014, J. Frankl. Inst..

[6]  Jun Shen.  Analysis and Synthesis of Dynamic Systems with Positive Characteristics , 2017 .

[7]  Huiping Li,et al.  Robust H∞ filtering for nonlinear stochastic systems with uncertainties and Markov delays , 2012, Autom..

[8]  Graziano Chesi,et al.  Necessary and Sufficient LMI Conditions for Stability and Performance Analysis of 2-D Mixed Continuous-Discrete-Time Systems , 2014, IEEE Transactions on Automatic Control.

[9]  Gang Feng,et al.  Analysis and Synthesis of Fuzzy Control Systems , 2010 .

[10]  Jinling Liang,et al.  Controller synthesis for switched T–S fuzzy positive systems described by the Fornasini–Marchesini second model , 2018 .

[11]  J. Lam,et al.  Exponential stability analysis and l1 synthesis of positive T-S fuzzy systems with time-varying delays , 2017 .

[12]  Jianbin Qiu,et al.  H∞ filtering for two-dimensional continuous-time Markovian jump systems with deficient transition descriptions , 2015, Neurocomputing.

[13]  T. Kaczorek.  Positive 1D and 2D Systems , 2001 .

[14]  James Lam,et al.  Positive filtering for positive Takagi-Sugeno fuzzy systems under l1 performance , 2015, Inf. Sci..

[15]  Tong Heng Lee,et al.  $H_{\infty} $ Filter Design for Nonlinear Systems With Time-Delay Through T–S Fuzzy Model Approach , 2008, IEEE Transactions on Fuzzy Systems.

[16]  Truong Q. Nguyen,et al.  Robust mixed generalized H/sub 2//H/sub /spl infin// filtering of 2-D nonlinear fractional transformation systems , 2005, IEEE Transactions on Signal Processing.

[17]  Zhengrong Xiang,et al.  Stability, L1-gain and control synthesis for positive switched systems with time-varying delay , 2013 .

[18]  Richard H. Middleton,et al.  Asymptotic and exponential stability of nonlinear two-dimensional continuous-discrete Roesser models , 2016, Syst. Control. Lett..

[19]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[20]  Graziano Chesi,et al.  Robust stability and performance analysis of 2D mixed continuous-discrete-time systems with uncertainty , 2016, Autom..

[21]  Gang Feng,et al.  Stability and $l_1$ Gain Analysis of Boolean Networks With Markovian Jump Parameters , 2017, IEEE Transactions on Automatic Control.

[22]  R. Roesser.  A discrete state-space model for linear image processing , 1975 .

[23]  Jian Shen,et al.  Finite frequency filter design for nonlinear 2-D continuous systems in T-S form , 2017, J. Frankl. Inst..

[24]  Lan Wang,et al.  Switched mechanisms for stability and l1-gain analysis of T-S fuzzy positive systems described by the F-M second model , 2018, J. Frankl. Inst..

[25]  Dan Zhang,et al.  Robust fuzzy-model-based filtering for nonlinear networked systems with energy constraints , 2017, J. Frankl. Inst..

[26]  Xiaoming Chen,et al.  ℓ1-induced state-bounding observer design for positive Takagi-Sugeno fuzzy systems , 2017, Neurocomputing.

[27]  Seid Miad Zandavi,et al.  Simplex filter: A novel heuristic filter for nonlinear systems state estimation , 2016, Appl. Soft Comput..

[28]  Krzysztof Galkowski,et al.  Higher order discretisation methods for a class of 2-D continuous-discrete linear systems , 1999 .

[29]  Weiqun Wang,et al.  Generalised Kalman–Yakubovich–Popov lemma with its application in finite frequency positive realness control for two-dimensional continuous-discrete systems in the Roesser model form , 2015 .

[30]  Fuchun Sun,et al.  Reduced-order Hinfinity filtering for linear systems with Markovian jump parameters , 2005, Syst. Control. Lett..

[31]  Jie Zhang,et al.  Design of a modified repetitive-control system based on a continuous-discrete 2D model , 2012, Autom..

[32]  Fuad E. Alsaadi,et al.  H∞ filtering for two-dimensional systems with mixed time delays, randomly occurring saturations and nonlinearities , 2015, Int. J. Gen. Syst..

[33]  Qing-Long Han,et al.  I1-gain performance analysis and positive filter design for positive discrete-time Markov jump linear systems: A linear programming approach , 2014, Autom..

[34]  Huijun Gao,et al.  ℋ︁∞ and l2–l∞ filtering for two‐dimensional linear parameter‐varying systems , 2007 .

[35]  Huijun Gao,et al.  ${\cal H}_{\infty}$ Estimation for Uncertain Systems With Limited Communication Capacity , 2007, IEEE Transactions on Automatic Control.

[36]  Shengyuan Xu,et al.  Reduced-order H∞ filtering for stochastic systems , 2002, IEEE Trans. Signal Process..

[37]  Weimin Chen,et al.  Stability and robust stabilization of 2-D continuous–discrete systems in Roesser model based on KYP lemma , 2017, Multidimens. Syst. Signal Process..

[38]  E. Rogers,et al.  Stability analysis for a class of 2D continuous–discrete linear systems with dynamic boundary conditions , 1999 .

[39]  Qingling Zhang,et al.  L1 fuzzy observer design for nonlinear positive Markovian jump system , 2018 .

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