scholarly journals Robustl2−l∞Filtering for Takagi-Sugeno Fuzzy Systems with Norm-Bounded Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Wenbai Li ◽  
Yu Xu ◽  
Huaizhong Li
Keyword(s):  
Fuzzy Systems ◽  
Filter Design ◽  
Weighting Function ◽  
Original System ◽  
Peak Performance ◽  
System 2 ◽  
Error System ◽  
Takagi Sugeno ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

We study the filter design problem for Takagi-Sugeno fuzzy systems which are subject to norm-bounded uncertainties in each subsystem. As we know that the Takagi-Sugeno fuzzy linear systems can be used to represent smooth nonlinear systems, the studied plants can also be uncertain complex systems. We suppose to design a filter with the order of the original system which is also dependent on the normalized fuzzy-weighting function; that is, the filter is also a Takagi-Sugeno fuzzy filter. With the augmentation technique, an uncertain filtering error system can be obtained and the system matrices in the filtering error system are reorganized into two categories (without uncertainties and with uncertainties). For the filtering error system, we have two objectives. (1) The first one is that the filtering error system should be robust stable; that is, the filtering error system is stable though there are uncertainties in the original system. (2) The second one is that the robust energy-to-peak performance should be guaranteed. With the well-known Finsler’s lemma, we provide the conditions for the robust energy-to-peak performance of the filtering error system in which three slack matrices are introduced. Finally, a numerical example is used to show the effectiveness of the proposed design methodology.

scholarly journals New approach to finite frequency Filter Design for two-dimensional T-S fuzzy systems

2021 ◽  
Vol 297 ◽  
pp. 01036
Author(s):  
Ben Meziane Khaddouj ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Fuzzy Systems ◽  
Filter Design ◽  
Asymptotically Stable ◽  
Two Dimensional ◽  
Finite Frequency ◽  
New Approach ◽  
Filter Model ◽  
Error System ◽  
Non Linear Systems ◽  
Takagi Sugeno

This paper considers the problem of filter design for two-dimensional (2D) discrete-time non-linear systems in Takagi-Sugeno (T-S) fuzzy mode. The problem to be solved in the paper is to find a H∞ filter model such that the filtering error system is asymptotically stable. A numerical example is employed to illustrate the validity of the proposed methods.

Finite Time Passive Reliable Filtering for Fuzzy Systems With Missing Measurements

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
S. Vimal Kumar ◽  
R. Sakthivel ◽  
M. Sathishkumar ◽  
S. Marshal Anthoni
Keyword(s):  
Finite Time ◽  
Fuzzy Systems ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Missing Measurements ◽  
Randomly Occurring Uncertainties ◽  
Error System ◽  
Takagi Sugeno ◽  
Reliable Filtering

This paper investigates the problem of robust finite time extended passive reliable filtering for Takagi–Sugeno (T–S) fuzzy systems with randomly occurring uncertainties, missing measurements, and time-varying delays. Moreover, two stochastic variables satisfying the Bernoulli random distribution are introduced to characterize the phenomenon of the randomly occurring uncertainties and missing measurements. By skillfully choosing a proper Lyapunov–Krasovskii functional (LKF), a new set of sufficient conditions in terms of linear matrix inequalities (LMI) is derived to ensure that the filtering error system is robustly stochastically finite time bounded (SFTB) with a desired extended passive performance index. Based on the obtained sufficient conditions, an explicit expression for the desired filter can be computed. Finally, two numerical examples are provided to show the effectiveness of the proposed filter design technique.

Robust Control for Uncertain Takagi–Sugeno Fuzzy Systems with Time-Varying Input Delay

2004 ◽  
Vol 127 (2) ◽  
pp. 302-306 ◽  
Author(s):  
Ho Jae Lee ◽  
Jin Bae Park ◽  
Young Hoon Joo
Keyword(s):  
Fuzzy Systems ◽  
Fuzzy Model ◽  
Input Delay ◽  
Time Varying ◽  
Convex Optimization Problem ◽  
Variation Rate ◽  
Mass Spring ◽  
Takagi Sugeno ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

A control problem of Takagi–Sugeno fuzzy systems with a time-varying input delay and norm-bounded uncertainties is addressed. The input delay is well-known in making the closed-loop stabilization difficult. A sufficient condition for the robust fuzzy-model-based stabilization is derived based on the Lyapunov–Razumikhin stability theorem, without the assumption of the variation rate on the delay. A constructive design scheme is presented in the form of the iterative convex optimization problem. The effectiveness of the proposed method is demonstrated by a numerical simulation of a nonlinear mass-spring-damper system.

Delay-Dependent L1 Filtering for LPV Systems With Parameter-Varying Delays

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
Yanhui Li ◽  
Yan Liang ◽  
Xionglin Luo
Keyword(s):  
Filter Design ◽  
Peak Performance ◽  
Linear Matrix ◽  
Compact Set ◽  
Worst Case ◽  
Lpv Systems ◽  
Error System ◽  
Parameter Varying ◽  
Space Data ◽  
Delay Dependent

The paper investigates the problems of delay-dependent L1 filtering for linear parameter-varying (LPV) systems with parameter-varying delays, in which the state-space data and the time delays are dependent on parameters that are measurable in real-time and vary in a compact set with bounded variation rate. The attention is focused on the design of L1 filter that guarantees the filtering error system to be asymptotically stable and satisfies the worst-case peak-to-peak gain of the filtering error system. In particular, we concentrate on the delay-dependent case, using parameter-dependent Lyapunov function, the decoupled peak-to-peak performance criterion is first established for a class of LPV systems. Under this condition, the admissible filter can be found in terms of linear matrix inequality (LMI) technology. According to approximate basis function and the gridding technique, the filter design problem is transformed into feasible solution problem of the finite parameter LMIs. Finally, a numerical example is provided to illustrate the feasibility of the developed approach.

scholarly journals Improved filtering H∞ finite frequency of Takagi-Sugeno fuzzy systems

2021 ◽  
Vol 12 (4) ◽  
pp. 2523
Author(s):  
Rim Mrani Alaoui ◽  
Abderrahim El-Amrani
Keyword(s):  
Fuzzy Systems ◽  
Filter Method ◽  
Linear Matrix ◽  
Fuzzy Filter ◽  
Finite Frequency ◽  
Filter Model ◽  
Error System ◽  
Takagi Sugeno ◽  
Finsler’S Lemma ◽  
Slack Matrices

The work treats the filter H∞ finite frequency (FF) in Takagi-Sugeno (T-S) two dimensional (2-D) systems described by Fornasini-Marchesini local state-space (FM LSS)models. The goal of this work is to find an FF H∞ T-S fuzzy filter model design in such a way that the error system is stable and has a reduced FF H∞ performance over FF area swith noise is established as aprerequisite. Via the use of the generalized Kalman Yakubovich Popov (gKYP) lemma, Lyapunov functions approach, Finsler’s lemma, and parameterize slack matrices, new design conditions guaranteeing the FF H∞ T-S fuzzy filter method of FM LSS models are developed by solving linear matrix inequalities (LMIs). At last, the simulation results are provided to show the effectiveness and the validity of the proposed FF T-S fuzzy of FM LSS models strategy by a practical application has been made.

H∞ Filtering for Nonlinear Systems with Time Delays via Takagi-Sugeno Fuzzy Model

2012 ◽  
Vol 557-559 ◽  
pp. 2033-2038
Author(s):  
Jun Sheng Ren ◽  
Xian Ku Zhang
Keyword(s):  
Time Delays ◽  
Controller Design ◽  
Filter Design ◽  
Estimation Error ◽  
Fuzzy Model ◽  
Error System ◽  
Delay Dependent ◽  
S Model ◽  
Takagi Sugeno ◽  
Filtering Problem

State estimation is an important topic in controller design. H∞filtering problem is discussed for fuzzy dynamical systems with time delays by using Takagi-Sugeno (T-S) model. Fuzzy H∞filter is obtained such that the filtering error system is stable and guarantees a prescribed estimation error level. Delay-dependent Lyapunov functional approach is employed to lower the conservativeness of the filter design. Therefore, the results of fuzzy H∞filter are delay-dependent. An example is given to illustrate the proposed results.

scholarly journals Improved Results on FuzzyH∞Filter Design for T-S Fuzzy Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-21 ◽  
Author(s):  
Jiyao An ◽  
Guilin Wen ◽  
Wei Xu
Keyword(s):  
Upper Bound ◽  
Fuzzy Systems ◽  
Filter Design ◽  
Linear Matrix ◽  
Time Varying ◽  
Bounded Interval ◽  
Time Varying Delay ◽  
Error System ◽  
Varying Delay ◽  
Uniformly Bounded

The fuzzyH∞filter design problem for T-S fuzzy systems with interval time-varying delay is investigated. The delay is considered as the time-varying delay being either differentiable uniformly bounded with delay derivative in bounded interval or fast varying (with no restrictions on the delay derivative). A novel Lyapunov-Krasovskii functional is employed and a tighter upper bound of its derivative is obtained. The resulting criterion thus has advantages over the existing ones since we estimate the upper bound of the derivative of Lyapunov-Krasovskii functional without ignoring some useful terms. A fuzzyH∞filter is designed to ensure that the filter error system is asymptotically stable and has a prescribedH∞performance level. An improved delay-derivative-dependent condition for the existence of such a filter is derived in the form of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

New Sufficient Conditions on H∞ Filter Design for Nonlinear T-S Fuzzy Systems with Time Delays

2012 ◽  
Vol 263-266 ◽  
pp. 162-166
Author(s):  
Su Huan Yi ◽  
Sheng Juan Huang
Keyword(s):  
Fuzzy Systems ◽  
Time Delays ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying Delay ◽  
Weighting Matrix ◽  
Decoupling Approach ◽  
Takagi Sugeno ◽  
Varying Delay

This paper focuses on the problem of H∞ filter design for continuous Takagi-Sugeno (T-S) fuzzy systems with an interval time-varying delay in the state. Based on the free weighting matrix method combined with a matrix decoupling approach, some new sufficient results are proposed in forms of linear matrix inequalities (LMIs), which can achieve much less conservative feasibility conditions. Finally, the effectiveness of the proposed method is demonstrated ba an example.

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