Filtering for Discrete Fuzzy Stochastic Time-Delay Systems with Sensor Saturation

This paper addresses the filtering problem for discrete fuzzy stochastic systems with time-varying delay and sensor saturation. Random noise depending on state and external disturbance is also taken into account. A decomposition approach is employed to solve the characteristic of sensor saturation. The scaled small gain (SSG) theorem is extended to the stochastic systems, which is employed to handle with the time-varying delay by transforming the original system into the form of an interconnected system consisting of two subsystems. By the proposed Lyapunov-Krasovskii function, the scaled small gains of the subsystems are analyzed, respectively. Sufficient conditions for the stochastic stability of the filtering error system with a prescribed level are established such that the gains of the filter can be obtained explicitly. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.

[1]  H. Karimi.  Optimal Vibration Control of Vehicle Engine-Body System using Haar Functions , 2006 .

[2]  Huijun Gao,et al.  A delay-dependent approach to robust H∞ filtering for uncertain discrete-time state-delayed systems , 2004, IEEE Trans. Signal Process..

[3]  Shengyuan Xu,et al.  Improved stability criterion and its applications in delayed controller design for discrete-time systems , 2008, Autom..

[4]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[5]  Peng Shi,et al.  Exponential Stability on Stochastic Neural Networks With Discrete Interval and Distributed Delays , 2010, IEEE Transactions on Neural Networks.

[6]  Honghai Liu,et al.  Reliable Fuzzy Control for Active Suspension Systems With Actuator Delay and Fault , 2012, IEEE Transactions on Fuzzy Systems.

[7]  Jianbin Qiu,et al.  Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework , 2011, IEEE Transactions on Fuzzy Systems.

[8]  Yugang Niu,et al.  Robust Filtering Design for Stochastic System With Mode-Dependent Output Quantization , 2010, IEEE Transactions on Signal Processing.

[9]  Qing-Long Han,et al.  Delay-Dependent Robust $H_{\infty}$ Filtering for Uncertain Discrete-Time Systems With Time-Varying Delay Based on a Finite Sum Inequality , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  Kemin Zhou,et al.  Robust stability of uncertain time-delay systems , 2000, IEEE Trans. Autom. Control..

[11]  Ligang Wu,et al.  A New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Time-Varying Delay Systems , 2011, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[12]  Ligang Wu,et al.  Fuzzy filtering of nonlinear fuzzy stochastic systems with time-varying delay , 2009, Signal Process..

[13]  Ming-Feng Yang,et al.  APPLICATION OF SIGNED DISTANCES METHOD TO INTEGRATE LINEAR PROGRAMMING FOR FUZZY MULTI-OBJECTIVE PROJECT MANAGEMENT , 2010 .

[14]  Yongduan Song,et al.  A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays , 2013, IEEE Transactions on Fuzzy Systems.

[15]  Huijun Gao,et al.  Mixed H2/Hinfinity output-feedback control of second-order neutral systems with time-varying state and input delays. , 2008, ISA transactions.

[16]  Raja Sengupta,et al.  An H/sub /spl infin// approach to networked control , 2005, IEEE Transactions on Automatic Control.

[17]  Hamid Reza Karimi,et al.  Observer-Based Mixed H2/H∞ Control Design for Linear Systems with Time-Varying Delays: An LMI Approach , 2008 .

[18]  Shengyuan Xu,et al.  Robust H∞ control for uncertain discrete stochastic time-delay systems , 2004, Syst. Control. Lett..

[19]  J. Chou,et al.  DESIGN OF STABLE AND QUADRATIC-OPTIMAL STATIC OUTPUT FEEDBACK CONTROLLERS FOR TS-FUZZY-MODEL-BASED CONTROL SYSTEMS: AN INTEGRATIVE COMPUTATIONAL APPROACH , 2012 .

[20]  Chung-Yao Kao,et al.  Simple stability criteria for systems with time-varying delays , 2004, Autom..

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

[22]  Guo-Ping Liu,et al.  Filtering for Discrete-Time Networked Nonlinear Systems With Mixed Random Delays and Packet Dropouts , 2011, IEEE Transactions on Automatic Control.

[23]  Min Wu,et al.  H∞ filtering for discrete-time systems with time-varying delay , 2009, Signal Process..

[24]  Xian Zhang,et al.  DELAY-RANGE-DEPENDENT ROBUST H1 FILTERING FOR SINGULAR LPV SYSTEMS WITH TIME VARIANT DELAY , 2013 .

[25]  Huijun Gao,et al.  A New Model Transformation of Discrete-Time Systems With Time-Varying Delay and Its Application to Stability Analysis , 2011, IEEE Transactions on Automatic Control.

[26]  K. Gu,et al.  Small gain problem in coupled differential‐difference equations, time‐varying delays, and direct Lyapunov method , 2011 .

[27]  Bing Chen,et al.  Robust Stability for Uncertain Delayed Fuzzy Hopfield Neural Networks With Markovian Jumping Parameters , 2009, IEEE Trans. Syst. Man Cybern. Part B.

[28]  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).

[29]  Hong Wang,et al.  LMI-BASED FAULT DETECTION FUZZY OBSERVER DESIGN WITH MULTIPLE PERFORMANCE CONSTRAINTS FOR A CLASS OF NON-LINEAR SYSTEMS: COMPARATIVE STUDY , 2011 .

[30]  Wei Yang,et al.  H∞ filtering for nonlinear stochastic systems with sensor saturation, quantization and random packet losses , 2012, Signal Process..

[31]  Taher Niknam,et al.  A NEW HYBRID FUZZY ADAPTIVE PARTICLE SWARM OPTIMIZATION FOR NON-CONVEX ECONOMIC DISPATCH , 2010 .

[32]  Hamid Reza Karimi,et al.  Stability analysis and control synthesis of neutral systems with time-varying delays and nonlinear uncertainties , 2009 .

[33]  Yugang Niu,et al.  Stabilization of Markovian jump linear system over networks with random communication delay , 2009, Autom..

[34]  Tsung-Chih Lin,et al.  ROBUST ADAPTIVE FUZZY SLIDING MODE CONTROL FOR A CLASS OF UNCERTAIN DISCRETE-TIME NONLINEAR SYSTEMS , 2012 .

[35]  James Lam,et al.  A delay-partitioning approach to the stability analysis of discrete-time systems , 2010, Autom..

[36]  Yongduan Song,et al.  ${\cal H}_{\infty}$ Model Reduction of Takagi–Sugeno Fuzzy Stochastic Systems , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).