# Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework

@article{Wu2011ModelAF,
title={Model Approximation for Discrete-Time State-Delay Systems in the T–S Fuzzy Framework},
author={Ligang Wu and Xiaojie Su and Peng Shi and Jianbin Qiu},
journal={IEEE Transactions on Fuzzy Systems},
year={2011},
volume={19},
pages={366-378}
}
• Ligang Wu, +1 author J. Qiu
• Published 1 April 2011
• Mathematics, Computer Science
• IEEE Transactions on Fuzzy Systems
This paper is concerned with the problem of H∞ model approximation for discrete-time Takagi-Sugeno (T-S) fuzzy time-delay systems. For a given stable T- S fuzzy system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well in an H∞ performance but is also translated into a linear lower dimensional system. By applying the delay partitioning approach, a delay-dependent sufficient condition is proposed for the asymptotic… Expand
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#### References

SHOWING 1-10 OF 48 REFERENCES
H ∞ model reduction for discrete time-delay systems: delay-independent and dependent approaches
• Mathematics
• 2004
This paper investigates the problem of H ∞ model reduction for linear discrete-time state-delay systems. For a given stable system, our attention is focused on the construction of reduced-orderExpand
ℋ ∞ model reduction for linear parameter-varying systems with distributed delay
• Mathematics, Computer Science
• Int. J. Control
• 2009
A sufficient condition is proposed for the asymptotic stability with an ℋ∞ performance of the error system by using the parameter-dependent Lyapunov functional method and two different approaches are developed to solve the model reduction problem. Expand
Robust H∞ Control for Discrete-Time Fuzzy Systems With Infinite-Distributed Delays
• Computer Science
• IEEE Trans. Fuzzy Syst.
• 2009
By using the linear matrix inequality (LMI) technique, sufficient conditions are derived for ensuring the exponential stability as well as the H∞ performance for the closed-loop fuzzy control system. Expand
Weighted H∞ model reduction for linear switched systems with time-varying delay
• Mathematics, Computer Science
• Autom.
• 2009
By applying the average dwell time approach and the piecewise Lyapunov function technique, delay-dependent/deley-independent sufficient conditions are proposed in terms of linear matrix inequality (LMI) to guarantee the exponential stability and the weighted @?"~ performance for the error system. Expand
Stability and Stabilization of Delayed T--S Fuzzy Systems: A Delay Partitioning Approach
• Mathematics, Computer Science
• IEEE Transactions on Fuzzy Systems
• 2009
The delay partitioning approach to solving the problems of stability analysis and stabilization for continuous time-delay Takagi-Sugeno fuzzy systems is proposed and the problem of stabilization via the so-called parallel distributed compensation scheme is solved. Expand
Reliable $H_\infty$ Control for Discrete-Time Fuzzy Systems With Infinite-Distributed Delay
• Computer Science
• IEEE Transactions on Fuzzy Systems
• 2012
The reliable H∞ control problem is solved for discrete-time Takagi-Sugeno (T-S) fuzzy systems with infinite-distributed delay and actuator faults, and an explicit expression of the desired controller is given. Expand
H∞ filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities
• Mathematics, Computer Science
• Autom.
• 2008
This paper aims at designing a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square, while achieving the prescribed H"~ disturbance rejection attenuation level. Expand
A note on the robust stability of uncertain stochastic fuzzy systems with time-delays
• Mathematics, Computer Science
• IEEE Trans. Syst. Man Cybern. Part A
• 2004
The T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay, and sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Expand
A New Approach to Guaranteed Cost Control of T-S Fuzzy Dynamic Systems With Interval Parameter Uncertainties
• Mathematics, Medicine
• IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics)
• 2009
This paper investigates the problem of guaranteed cost control for Takagi-Sugeno fuzzy dynamic systems with interval parameter uncertainties by utilizing the instrumental idea of delay dividing, a new Lyapunov-Krasovskii functional is introduced, which leads the resultant conditions to be much less conservative than most existing results in the literature. Expand
Controller Failure Analysis for T-S Fuzzy Systems with Time-Varying Delay via a Switched Approach
• Mathematics
• 2008 3rd International Conference on Innovative Computing Information and Control
• 2008
This paper deals with the problem of controller failure analysis for T-S fuzzy systems with time-varying delay. The T-S fuzzy systems can be stabilized by a pre-designed state feedback controller.Expand