Fuzzy Control for Nonlinear Uncertain T-S Fuzzy Systems with Time-Varying Delays

2013 ◽  
Vol 341-342 ◽  
pp. 668-673
Author(s):  
Yi Min Li ◽  
Yuan Yuan Li
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Fuzzy Model ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Lmi Optimization ◽  
System A ◽  
The Stability

This paper studies the stability analysis of discrete time-varying system with parameter uncertainties and disturbances. The system under consideration is subject to time-varying non-bounded parameter uncertainties in both the state and measured output matrices. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. A fuzzy observer is used to guarantee the Lyapunov stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The control and observer matrices can be obtained by directly solving a set of linear matrix inequality (LMI) via the existing LMI optimization techniques. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

Fuzzy-Model-Based Adaptive Control for a Kind of Discrete-Time Systems with Time-Delay and Disturbances

2014 ◽  
Vol 22 (03) ◽  
pp. 453-468
Author(s):  
Yi-Min Li ◽  
Yuan-Yuan Li
Keyword(s):  
Adaptive Control ◽  
Stability Analysis ◽  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Parameter Uncertainties ◽  
Model Based ◽  
The Stability

This paper presents the stability analysis of discrete-time fuzzy-model-based adaptive control systems with time-delay, parameter uncertainties and external disturbance. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discretetime nonlinear system. A fuzzy observer is used to estimate the state of the fuzzy system, by using the estimations of states and nonlinear functions, and sufficient conditions for designing observer-based fuzzy controllers are proposed. The control and observer matrices involved can be determined by solving a set of linear matrix inequality (LMI). Finally, the numerical example carried out also demonstrate the feasibility of the design method.

scholarly journals Robust H∞ Consensus Control for Linear Discrete-Time Swarm Systems with Parameter Uncertainties and Time-Varying Delays

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Xiao Jia ◽  
Laihong Hu ◽  
Fujun Feng ◽  
Jun Xu
Keyword(s):  
Control Problem ◽  
Discrete Time ◽  
Convergence Result ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Consensus Protocol ◽  
Consensus Control ◽  
Consensus Analysis ◽  
The Stability

Robust H∞ consensus control problems of linear swarm systems with parameter uncertainties and time-varying delays are investigated. In this literature, a linear consensus protocol for high-order discrete-time swarm systems is proposed. Firstly, the robust H∞ consensus control problem of discrete-time swarm systems is transformed into a robust H∞ control problem of a set of independent uncertain systems. Secondly, sufficient linear matrix inequality conditions for robust H∞ consensus analysis of discrete-time swarm systems are given by the stability theory, and a H∞ performance level γ is determined meanwhile. Thirdly, the convergence result is derived as a final consensus value of swarm systems. Finally, numerical examples are presented to demonstrate theoretical results.

Stability Analysis for Discrete-Time Stochastic Neural Networks with Mixed Time Delays via Delay-Paritioning

2011 ◽  
Vol 228-229 ◽  
pp. 464-470
Author(s):  
Xia Zhou ◽  
Shou Ming Zhong
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Discrete Time ◽  
Time Delays ◽  
Optimization Problems ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Mixed Time Delays

This paper revisits the problem of stability analysis for discrete-time stochastic neural networks (DSNNs) with mixed time-varying delays in the state. Here the mixed time delays are assumed to be discrete and distributed time delays and the uncertainties are assumed to be time varying norm bounded parameter uncertainties. A new delay-dependent stability criterion is presented by constructing a novel Lyapunov-Krasovskii functional and utilizing the delay partitioning idea and free-weighting matrix approach, Which is less conservative than the existing ones. This criterion can be developed in the frame of convex optimization problems and then solved via standard numerical software. These conditions are formulated in the forms of linear matrix inequalities, which feasibility can be easily checked by using Matlab LMI Toolbox.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals Robust Synchronization Criterion for Coupled Stochastic Discrete-Time Neural Networks with Interval Time-Varying Delays, Leakage Delay, and Parameter Uncertainties

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Neural Networks ◽  
Discrete Time ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Leakage Term ◽  
Interval Time ◽  
Robust Synchronization ◽  
Delay Dependent ◽  
Finsler’S Lemma

The purpose of this paper is to investigate a delay-dependent robust synchronization analysis for coupled stochastic discrete-time neural networks with interval time-varying delays in networks coupling, a time delay in leakage term, and parameter uncertainties. Based on the Lyapunov method, a new delay-dependent criterion for the synchronization of the networks is derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov-Krasovskii’s functional and utilizing Finsler’s lemma without free-weighting matrices. Two numerical examples are given to illustrate the effectiveness of the proposed methods.

scholarly journals ℋ∞Performance and Stability Analysis of Linear Systems with Interval Time-Varying Delays and Stochastic Parameter Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
M. J. Park ◽  
O. M. Kwon ◽  
Ju H. Park ◽  
S. M. Lee ◽  
E. J. Cha
Keyword(s):  
Stability Analysis ◽  
Linear Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Interval Time ◽  
Stochastic Parameter ◽  
Stochastic Properties ◽  
Random Change

This paper deals with the problems ofℋ∞performance and stability analysis for linear systems with interval time-varying delays. It is assumed that the parameter uncertainties are of stochastic properties to represent random change of various environments. By constructing a newly augmented Lyapunov-Krasovskii functional, less conservative criteria of the concerned systems are introduced with the framework of linear matrix inequalities (LMIs). Four numerical examples are given to show the improvements over the existing ones and the effectiveness of the proposed methods.

Switching Model Construction and Stability Analysis for Nonlinear Systems

2006 ◽  
Vol 10 (1) ◽  
pp. 3-10 ◽  
Author(s):  
Hiroshi Ohtake ◽  
◽  
Kazuo Tanaka
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Lyapunov Function ◽  
Fuzzy Model ◽  
Function Approach ◽  
Model Construction ◽  
Switching Model ◽  
Piecewise Lyapunov Function ◽  
System A ◽  
The Stability

This paper presents switching model construction and stability analysis for a class of nonlinear systems. A switching fuzzy model newly developed in this paper is employed to represent the dynamics of a nonlinear system. A key feature of the switching fuzzy model construction is to find the so-called minimum distance sector by solving a nonlinear optimization problem. Next, we discuss the stability of a switching fuzzy model. To take advantage of the switching fuzzy model, we introduce a piecewise Lyapunov function that mirrors its structure. We show that the piecewise Lyapunov function approach provides less conservative results for the typical quadratic Lyapunov function approach. Illustrative examples demonstrate the utility of the switching model construction and the stability analysis.

Robust Switched Filtering for Time-Varying Polytopic Uncertain Systems

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Chang Duan ◽  
Fen Wu
Keyword(s):  
Lyapunov Function ◽  
Uncertain Systems ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Varying ◽  
Synthesis Conditions ◽  
Lmi Optimization ◽  
Globally Asymptotical Stability ◽  
Polytopic Uncertain Systems ◽  
Switching Filter

This paper studies the problem of designing robust switched filters for time-varying polytopic uncertain systems. The synthesis conditions for a set of filters under a min-switching rule are derived to guarantee globally asymptotical stability with optimized robust H∞ performance. Specifically, the conditions are expressed as bilinear matrix inequalities (BMIs) and can be solved by linear matrix inequality (LMI) optimization techniques. The proposed approach utilizes a piecewise quadratic Lyapunov function to reduce the conservativeness of robust filtering methods based on single Lyapunov function, thus better H∞ performance can be achieved. Both continuous and discrete-time robust filter designs are considered. To simplify filter implementation, a method to remove redundancy in min-switching filter members is also introduced. The advantages of the proposed robust switching filters are illustrated by several examples.

FUZZY LOGIC DERIVATION OF NEURAL NETWORK MODELS WITH TIME DELAYS IN SUBSYSTEMS

2005 ◽  
Vol 14 (06) ◽  
pp. 967-974 ◽  
Author(s):  
CHEN-YUAN CHEN ◽  
JOHN RONG-CHUNG HSU ◽  
CHENG-WU CHEN
Keyword(s):  
Time Delays ◽  
Fuzzy Model ◽  
Network Models ◽  
Space Representation ◽  
Linear Matrix ◽  
Neural Network Models ◽  
Lmi Optimization ◽  
Common Solution ◽  
State Space Representation ◽  
The Stability

This paper extends the Takagi-Sugeno (T-S) fuzzy model representation to analyze the stability of interconnected systems in which there exist time delays in subsystems. A novel stability criterion which can be solved numerically is presented in terms of Lyapunov's theory for fuzzy interconnected models. In this paper, we use linear difference inclusion (LDI) state-space representation to represent the fuzzy model. Then, the linear matrix inequality (LMI) optimization algorithm is employed to find common solution and then guarantee the asymptotic stability.

scholarly journals RobustH∞Fuzzy Control for Nonlinear Discrete-Time Stochastic Systems with Markovian Jump and Parametric Uncertainties

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Huiying Sun ◽  
Long Yan
Keyword(s):  
Fuzzy Control ◽  
Discrete Time ◽  
Stochastic Systems ◽  
Design Method ◽  
Fuzzy Model ◽  
Control Design ◽  
Linear Matrix ◽  
Parametric Uncertainties ◽  
Markovian Jump ◽  
Parameter Uncertainties

The paper mainly investigates theH∞fuzzy control problem for a class of nonlinear discrete-time stochastic systems with Markovian jump and parametric uncertainties. The class of systems is modeled by a state space Takagi-Sugeno (T-S) fuzzy model that has linear nominal parts and norm-bounded parameter uncertainties in the state and output equations. AnH∞control design method is developed by using the Lyapunov function. The decoupling technique makes the Lyapunov matrices and the system matrices separated, which makes the control design feasible. Then, some strict linear matrix inequalities are derived on robustH∞norm conditions in which both robust stability andH∞performance are required to be achieved. Finally, a computer-simulated truck-trailer example is given to verify the feasibility and effectiveness of the proposed design method.

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