scholarly journals Nonfragile RobustH∞Filter Design for a Class of Fuzzy Stochastic Systems with Stochastic Input-to-State Stability

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Ze Li ◽  
Feng Gu ◽  
Yuqing He ◽  
Wanjun Hao
Keyword(s):  
Stochastic Systems ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Error System ◽  
Stochastic Input ◽  
Takagi Sugeno ◽  
Varying Delay

The nonfragileH∞filtering problem for a kind of Takagi-Sugeno (T-S) fuzzy stochastic system which has a time-varying delay and parameter uncertainties has been studied in this paper. Sufficient conditions for stochastic input-to-state stability (SISS) of the fuzzy stochastic systems are obtained. Attention is focused on the design of a nonfragileH∞filter such that the filtering error system can tolerate some level of the gain variations in the filter and theH∞performance level also could be satisfied. By using the SISS result, the approach to design the nonfragile filter is proposed in terms of linear matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.

scholarly journals RobustH∞Filtering for Uncertain Discrete-Time Fuzzy Stochastic Systems with Sensor Nonlinearities and Time-Varying Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Mingang Hua ◽  
Pei Cheng ◽  
Juntao Fei ◽  
Jianyong Zhang ◽  
Junfeng Chen
Keyword(s):  
Discrete Time ◽  
Stochastic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Error System ◽  
Varying Delay

The robust filtering problem for a class of uncertain discrete-time fuzzy stochastic systems with sensor nonlinearities and time-varying delay is investigated. The parameter uncertainties are assumed to be time varying norm bounded in both the state and measurement equations. By using the Lyapunov stability theory and some new relaxed techniques, sufficient conditions are proposed to guarantee the robustly stochastic stability with a prescribedH∞performance level of the filtering error system for all admissible uncertainties, sensor nonlinearities, and time-varying delays. These conditions are dependent on the lower and upper bounds of the time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods.

scholarly journals Delay-Dependent RobustL2-L∞Filtering for a Class of Fuzzy Stochastic Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ze Li ◽  
Xinhao Yang
Keyword(s):  
Stochastic Systems ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Time Varying Delay ◽  
Mean Square Stability ◽  
Error System ◽  
Delay Dependent ◽  
Takagi Sugeno ◽  
Varying Delay ◽  
Filtering Problem

This paper is concerned with theL2-L∞filtering problem for a kind of Takagi-Sugeno (T-S) fuzzy stochastic system with time-varying delay and parameter uncertainties. Parameter uncertainties in the system are assumed to satisfy global Lipschitz conditions. And the attention of this paper is focused on the stochastically mean-square stability of the filtering error system, and theL2-L∞performance level of the output error with the disturbance input. The method designed for the delay-dependent filter is developed based on linear matrix inequalities. Finally, the effectiveness of the proposed method is substantiated with an illustrative example.

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.

scholarly journals Nonfragile H∞ Filter Design for Nonlinear Continuous-Time System with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Zhongda Lu ◽  
Guoliang Zhang ◽  
Yi Sun ◽  
Jie Sun ◽  
Fangming Jin ◽  
...  
Keyword(s):  
Continuous Time ◽  
Filter Design ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Time Varying ◽  
Decoupling Method ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Delay Dependent

This paper investigates nonfragile H∞ filter design for a class of continuous-time delayed Takagi-Sugeno (T-S) fuzzy systems with interval time-varying delays. Filter parameters occur multiplicative gain variations according to the filter’s implementation, to handle this variations, a nonfragile H∞ filter is presented and a novel filtering error system is established. The nonfragile H∞ filter guarantees the filtering error system to be asymptotically stable and satisfies given H∞ performance index. By constructing a novel Lyapunov-Krasovskii function and using the linear matrix inequality (LMI), delay-dependent conditions are exploited to derive sufficient conditions for nonfragile designing H∞ filter. Using new matrix decoupling method to reduce the computational complexity, the filter parameters can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, numerical examples are given to show the effectiveness of the proposed method.

scholarly journals Delay-Dependent RobustH∞Filtering of the Takagi-Sugeno Fuzzy Stochastic Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Ze Li ◽  
Xin-Hao Yang
Keyword(s):  
Stochastic Systems ◽  
Design Method ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Mean Square Stability ◽  
Error System ◽  
Delay Dependent ◽  
Takagi Sugeno

This paper is concerned with the problem of the robustH∞filtering for the Takagi-Sugeno (T-S) fuzzy stochastic systems with bounded parameter uncertainties. For a given T-S fuzzy stochastic system, this paper focuses on the stochastically mean-square stability of the filtering error system and theH∞performance level of the output error and the disturbance input. The design method for delay-dependent filter is developed based on linear matrix inequalities. Finally, the effectiveness of the proposed methods is substantiated with an illustrative example.

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.

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.

Guaranteed Cost Control Approach for a Class of T-S Fuzzy Descriptor Delay Systems

2012 ◽  
Vol 241-244 ◽  
pp. 1148-1153 ◽  
Author(s):  
Wei Hua Tian ◽  
Li Xia Li ◽  
Wei Deng ◽  
Yan Zhao
Keyword(s):  
Controller Design ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Delay Systems ◽  
Linear Matrix ◽  
Control Approach ◽  
Time Varying Delay ◽  
Guaranteed Cost ◽  
Takagi Sugeno ◽  
Varying Delay

A new guaranteed cost controller design approach for a class of Takagi-Sugeno (T-S) fuzzy descriptor systems with time-varying delay is presented. Based on the fuzzy rules and weights, the less conservative sufficient conditions for the existence of guaranteed cost controllers via state feedback are given in terms of linear matrix inequalities (LMIs). This method includes the interactions of the different subsystems into one matrix. And the design of optimal guaranteed cost controller can be formulated to a convex optimization problem. At last, a numerical example is given to illustrate the effectiveness of the proposed method and the perfect performance of the optimal guaranteed cost controller.

scholarly journals Robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach

2018 ◽  
Vol 10 (1) ◽  
pp. 168781401774539 ◽  
Author(s):  
Min Xu
Keyword(s):  
Fuzzy Systems ◽  
Design Procedure ◽  
Linear Matrix ◽  
Delta Operator ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Operator Approach ◽  
Time Varying Delay ◽  
Takagi Sugeno ◽  
Varying Delay

The problem of robust ℋ∞ filtering design for Takagi–Sugeno fuzzy systems with time-varying delay via delta operator approach is investigated. The time-varying delay and parameter uncertainties are assumed to be of an internal-like type and a structured linear fractional form, respectively. Based on a Lyapunov–Krasovskii functional in delta domain, robust ℋ∞ filter scheme is proposed. Then, a sufficient condition is established for the existence of the desired filter in terms of linear-matrix inequalities. A numerical example is provided to illustrate the design procedure of the present method.

scholarly journals Event-Based Nonfragile H∞ Filter Design for Networked Control Systems with Interval Time-Varying Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Zhongda Lu ◽  
Guangtao Ran ◽  
Guoliang Zhang ◽  
Fengxia Xu
Keyword(s):  
Networked Control Systems ◽  
Filter Design ◽  
Linear Matrix ◽  
Time Varying ◽  
Sampled Data ◽  
Interval Time ◽  
Time Varying Delay ◽  
Error System ◽  
Varying Delay ◽  
Event Triggered

This paper first investigates the event-triggered nonfragile H∞ filter design for a class of nonlinear NCSs with interval time-varying delay. An event-triggered scheme is addressed to determine sampled data to be transmitted so that network communication resource can be saved significantly. The nonfragile filter design is assumed to include multiplicative gain variations according to the filter’s implement. Under the event-triggered scheme, the filtering error system is modeled as a system with interval time-varying delay. By constructing a new Lyapunov-Krasovskii functional and employing Wirtinger inequality, a sufficient condition is derived, which guarantees that the filtering error system is asymptotically stable with the prescribed H∞ performance. The nonfragile filter parameters are obtained by solving a set of linear matrix inequalities. Two numerical examples are given to show the usefulness and the effectiveness of the proposed method.

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