$H_\infty $ Control for 2-D Fuzzy Systems With Interval Time-Varying Delays and Missing Measurements

In this paper, we consider the H∞ control problem for a class of 2-D Takagi-Sugeno fuzzy described by the second Fornasini-Machesini local state-space model with time delays and missing measurements. The state delays are allowed to be time-varying within a known interval. The measurement output is subject to randomly intermittent packet dropouts governed by a random sequence satisfying the Bernoulli distribution. The purpose of the addressed problem is to design an output feedback controller such that the closed-loop system is globally asymptotically stable in the mean square and the prescribed H∞ performance index is satisfied. By employing a combination of the intensive stochastic analysis and the free weighting matrix method, several delay-range-dependent sufficient conditions are presented that guarantee the existence of the desired controllers for all possible time-delays and missing measurements. The explicit expressions of such controllers are derived by means of the solution to a class of convex optimization problems that can be solved via standard software packages. Finally, a numerical simulation example is given to demonstrate the applicability of the proposed control scheme.

[1]  G. Marchesini,et al.  State-space realization theory of two-dimensional filters , 1976 .

[2]  Hamid Reza Karimi,et al.  Robust Observer Design for Unknown Inputs Takagi–Sugeno Models , 2013, IEEE Transactions on Fuzzy Systems.

[3]  Lizhen Li,et al.  New approach to H ∞  filtering of two‐dimensional T‐S fuzzy systems , 2013 .

[4]  Hamid Reza Karimi,et al.  New Delay-Dependent Exponential $H_{\infty}$ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Ligang Wu,et al.  Reliable Filtering With Strict Dissipativity for T-S Fuzzy Time-Delay Systems , 2014, IEEE Transactions on Cybernetics.

[6]  Huijun Gao,et al.  Filtering for uncertain 2-D discrete systems with state delays , 2007, Signal Process..

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

[8]  W. Marsden.  I and J , 2012 .

[9]  Zidong Wang,et al.  On Nonlinear $H_{\infty }$ Filtering for Discrete-Time Stochastic Systems With Missing Measurements , 2008, IEEE Transactions on Automatic Control.

[10]  James Lam,et al.  H∞ model reduction of Markovian jump linear systems , 2003, Syst. Control. Lett..

[11]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[12]  Xin-Ping Guan,et al.  Delay-dependent guaranteed cost control for T-S fuzzy systems with time delays , 2004, IEEE Transactions on Fuzzy Systems.

[13]  Zidong Wang,et al.  Robust state estimation for two-dimensional stochastic time-delay systems with missing measurements and sensor saturation , 2014, Multidimens. Syst. Signal Process..

[14]  Jianbin Qiu,et al.  A Combined Adaptive Neural Network and Nonlinear Model Predictive Control for Multirate Networked Industrial Process Control , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[15]  Hamid Reza Karimi,et al.  Local Capacity $H_{\infty}$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays , 2010, IEEE Transactions on Automation Science and Engineering.

[16]  Zidong Wang,et al.  State estimation for two‐dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays , 2014 .

[17]  Panos Louvieris,et al.  Robust Synchronization for 2-D Discrete-Time Coupled Dynamical Networks , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[18]  Peng Shi,et al.  Adaptive Fault Diagnosis for T–S Fuzzy Systems With Sensor Faults and System Performance Analysis , 2014, IEEE Transactions on Fuzzy Systems.

[19]  James Lam,et al.  Finite-Horizon ${\cal H}_{\infty}$ Control for Discrete Time-Varying Systems With Randomly Occurring Nonlinearities and Fading Measurements , 2015, IEEE Transactions on Automatic Control.

[20]  Ahmad Haidar,et al.  Delay-range-dependent control synthesis for time-delay systems with actuator saturation , 2008, Autom..

[21]  Daniel W. C. Ho,et al.  Stability of Takagi–Sugeno Fuzzy Delay Systems With Impulse , 2007, IEEE Transactions on Fuzzy Systems.

[22]  Zidong Wang,et al.  Robust filtering with stochastic nonlinearities and multiple missing measurements , 2009, Autom..

[23]  L. Ghaoui,et al.  A cone complementarity linearization algorithm for static output-feedback and related problems , 1996, Proceedings of Joint Conference on Control Applications Intelligent Control and Computer Aided Control System Design.

[24]  Huijun Gao,et al.  Improved Hinfinite control of discrete-time fuzzy systems: a cone complementarity linearization approach , 2005, Inf. Sci..

[25]  Huijun Gao,et al.  H∞ Fuzzy Control for Systems With Repeated Scalar Nonlinearities and Random Packet Losses , 2009, IEEE Trans. Fuzzy Syst..

[26]  Yugang Niu,et al.  Filtering For Discrete Fuzzy Stochastic Systems With Sensor Nonlinearities , 2010, IEEE Transactions on Fuzzy Systems.

[27]  Carlos E. de Souza,et al.  Gain-scheduled control of two-dimensional discrete-time linear parameter-varying systems in the Roesser model , 2013, Autom..

[28]  Jinling Liang,et al.  Robust stabilisation for a class of stochastic two-dimensional non-linear systems with time-varying delays , 2013 .

[29]  Jianbin Qiu,et al.  Static-Output-Feedback ${\mathscr H}_{\bm \infty }$ Control of Continuous-Time T - S Fuzzy Affine Systems Via Piecewise Lyapunov Functions , 2013, IEEE Transactions on Fuzzy Systems.

[30]  Jun Hu,et al.  H ∞  sliding mode observer design for a class of nonlinear discrete time‐delay systems: A delay‐fractioning approach , 2012 .

[31]  Shengyuan Xu,et al.  Stability and Stabilization of Uncertain 2-D Discrete Systems with Stochastic Perturbation , 2005, Multidimens. Syst. Signal Process..

[32]  Zidong Wang,et al.  Envelope-constrained H∞ filtering with fading measurements and randomly occurring nonlinearities: The finite horizon case , 2015, Autom..

[33]  Raquel Caballero-Águila,et al.  Optimal state estimation for networked systems with random parameter matrices, correlated noises and delayed measurements , 2015, Int. J. Gen. Syst..

[34]  Zidong Wang,et al.  $H_\infty$ Fuzzy Control With Randomly Occurring Infinite Distributed Delays and Channel Fadings , 2014, IEEE Transactions on Fuzzy Systems.

[35]  Gang Feng,et al.  Robust H∞ Control for Discrete-Time Fuzzy Systems With Infinite-Distributed Delays , 2009, IEEE Trans. Fuzzy Syst..

[36]  Huijun Gao,et al.  New Delay-Dependent Exponential H ∞ Synchronization for Uncertain Neural Networks With Mixed Time Delays , 2009 .

[37]  Hamid Reza Karimi,et al.  Novel Stability Criteria for T--S Fuzzy Systems , 2014, IEEE Transactions on Fuzzy Systems.

[38]  Ahmed El Hajjaji,et al.  H∞ Filtering of Two-Dimensional T-S Fuzzy Systems , 2014, Circuits Syst. Signal Process..

[39]  Hamid Reza Karimi,et al.  Local capacity H∞ control for production networks of autonomous work systems with time-varying delays , 2009, 2009 European Control Conference (ECC).

[40]  Daniel W. C. Ho,et al.  Robust $H_{\infty }$ Fuzzy Output-Feedback Control With Multiple Probabilistic Delays and Multiple Missing Measurements , 2010, IEEE Transactions on Fuzzy Systems.

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

[42]  H. Su,et al.  Reliable $H_\infty$ Control for Discrete-Time Fuzzy Systems With Infinite-Distributed Delay , 2009 .