scholarly journals Disturbance Observer-Based Linear Matrix Inequality for the Synchronization of Takagi-Sugeno Fuzzy Chaotic Systems

IEEE Access ◽  
2020 ◽  
pp. 1-1
Author(s):  
Van-Nam Giap ◽  
Shyh-Chour Huang ◽  
Quang Dich Nguyen ◽  
Te-Jen Su
Keyword(s):  
Linear Matrix Inequality ◽  
Disturbance Observer ◽  
Chaotic Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Takagi Sugeno

Comments on “Takagi–Sugeno fuzzy control for a wide class of fractional-order chaotic systems with uncertain parameters via linear matrix inequality”

2019 ◽  
Vol 26 (9-10) ◽  
pp. 643-645
Author(s):  
Xuefeng Zhang
Keyword(s):  
Fuzzy Control ◽  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Wide Class ◽  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Uncertain Parameters ◽  
Matrix Inequality ◽  
Takagi Sugeno

This article shows that sufficient conditions of Theorems 1–3 and the conclusions of Lemmas 1–2 for Takasi–Sugeno fuzzy model–based fractional order systems in the study “Takagi–Sugeno fuzzy control for a wide class of fractional order chaotic systems with uncertain parameters via linear matrix inequality” do not hold as asserted by the authors. The reason analysis is discussed in detail. Counterexamples are given to validate the conclusion.

scholarly journals A novel anti-swing and position control method for overhead crane

2019 ◽  
Vol 103 (1) ◽  
pp. 003685041988353
Author(s):  
Xuejuan Shao ◽  
Jinggang Zhang ◽  
Xueliang Zhang ◽  
Zhicheng Zhao ◽  
Zhimei Chen
Keyword(s):  
Linear Matrix Inequality ◽  
Decay Rate ◽  
Position Control ◽  
Control Method ◽  
Control Variable ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Overhead Crane ◽  
Nonlinear Dynamic Model ◽  
Takagi Sugeno

Based on Takagi–Sugeno fuzzy modeling and linear matrix inequality with decay rate, this article presents a novel anti-swing and position control scheme for overhead cranes. First, the simplified nonlinear dynamic model is proposed by adopting a virtual control variable method to reduce the number of nonlinear terms. Then, the Takagi–Sugeno fuzzy model is constructed using sector nonlinear technique, and the anti-swing and position controller of overhead crane is designed based on a linear matrix inequality with decay rate. Finally, the proposed control method is compared with the traditional Takagi–Sugeno fuzzy control method, and robustness of the system is discussed. The simulation results demonstrate that the proposed method is feasible and effective.

Robust H∞ Output Feedback Control Design for Takagi-Sugeno Systems with Markovian Jumps: A Linear Matrix Inequality Approach

2006 ◽  
Vol 128 (3) ◽  
pp. 617-625 ◽  
Author(s):  
Sing Kiong Nguang ◽  
Peng Shi
Keyword(s):  
Feedback Control ◽  
Linear Matrix Inequality ◽  
Output Feedback ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Control Design ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Linear Matrix Inequality Approach ◽  
Takagi Sugeno

This paper investigates the H∞ output feedback control design for a class of uncertain nonlinear systems with Markovian jumps which can be described by Takagi-Sugeno models. Based on a linear matrix inequality (LMI), LMI-based sufficient conditions for the existence of a robust output feedback controller, such that the L2-gain from an exogenous input to a regulated output is less than or equal to a prescribed value, are derived. An illustrative example is used to demonstrate the effectiveness of the proposed design techniques.

scholarly journals LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1128
Author(s):  
Hamede Karami ◽  
Saleh Mobayen ◽  
Marzieh Lashkari ◽  
Farhad Bayat ◽  
Arthur Chang
Keyword(s):  
Linear Matrix Inequality ◽  
State Feedback ◽  
Chaotic Systems ◽  
Nonlinear Function ◽  
Observer Design ◽  
System Stability ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Estimation Errors ◽  
Suggested Approach

In this study, the observer-based state feedback stabilizer design for a class of chaotic systems in the existence of external perturbations and Lipchitz nonlinearities is presented. This manuscript aims to design a state feedback controller based on a state observer by the linear matrix inequality method. The conditions of linear matrix inequality guarantee the asymptotical stability of the system based on the Lyapunov theorem. The stabilizer and observer parameters are obtained using linear matrix inequalities, which make the state errors converge to the origin. The effects of the nonlinear Lipschitz perturbation and external disturbances on the system stability are then reduced. Moreover, the stabilizer and observer design techniques are investigated for the nonlinear systems with an output nonlinear function. The main advantages of the suggested approach are the convergence of estimation errors to zero, the Lyapunov stability of the closed-loop system and the elimination of the effects of perturbation and nonlinearities. Furthermore, numerical examples are used to illustrate the accuracy and reliability of the proposed approaches.

Global Sliding Mode Control Via Linear Matrix Inequality Approach for Uncertain Chaotic Systems With Input Nonlinearities and Multiple Delays

2018 ◽  
Vol 13 (3) ◽  
Author(s):  
Mona Afshari ◽  
Saleh Mobayen ◽  
Rahman Hajmohammadi ◽  
Dumitru Baleanu
Keyword(s):  
Sliding Mode Control ◽  
Linear Matrix Inequality ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Matrix Inequality ◽  
Mode Control ◽  
Global Sliding Mode Control ◽  
Uncertain Chaotic Systems

This paper considers a global sliding mode control (GSMC) approach for the stabilization of uncertain chaotic systems with multiple delays and input nonlinearities. By designing the global sliding mode surface, the offered scheme eliminates reaching phase problem. The offered control law is formulated based on state estimation, Lyapunov–Krasovskii stability theory, and linear matrix inequality (LMI) technique which present the asymptotic stability conditions. Moreover, the proposed design approach guarantees the robustness against multiple delays, nonlinear inputs, nonlinear functions, external disturbances, and parametric uncertainties. Simulation results for the presented controller demonstrate the efficiency and feasibility of the suggested procedure.

GLOBAL ROBUST SYNCHRONIZATION OF A CLASS OF NONAUTONOMOUS CHAOTIC SYSTEMS WITH PARAMETER MISMATCH VIA VARIABLE SUBSTITUTION CONTROL

2011 ◽  
Vol 21 (05) ◽  
pp. 1369-1382 ◽  
Author(s):  
YUN CHEN ◽  
XIAOFENG WU ◽  
ZHIFANG GUI
Keyword(s):  
Linear Matrix Inequality ◽  
Chaotic Systems ◽  
Phase Mismatch ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Single Variable ◽  
Parameter Mismatch ◽  
Robust Synchronization ◽  
Variable Substitution

This paper investigates global robust synchronization of a class of nonautonomous chaotic systems with parameter mismatch under the master–slave variable substitution control. A criterion of linear matrix inequality (LMI) for the global robust synchronization is rigorously proven and the corresponding synchronization error bound is analytically estimated. The LMI criterion is then applied to the gyrostat systems, obtaining some simple and optimized algebraic criteria for global robust synchronization of the master–slave gyrostat systems with time-varying phase mismatch under single-variable substitution configurations, further verified in a numerical example.

Composite hierarchical anti-disturbance control for stochastic systems with multiple heterogeneous disturbances

2019 ◽  
Vol 41 (15) ◽  
pp. 4398-4408
Author(s):  
Yongli Wei ◽  
Xinjiang Wei ◽  
Huifeng Zhang ◽  
Jian Han
Keyword(s):  
Neural Network ◽  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Disturbance Observer ◽  
Composite System ◽  
Stochastic Systems ◽  
Dynamic Performance ◽  
Nonlinear Function ◽  
Linear Matrix ◽  
Matrix Inequality

This paper studies the problem of anti-disturbance control for a class of stochastic systems with multiple heterogeneous disturbances, which include the white noise and the non-harmonic disturbance with unknown nonlinear function. An adaptive disturbance observer is constructed to estimate the non-harmonic disturbances with unknown nonlinear function, which is approximated by neural network. A composite hierarchical anti-disturbance control (CHADC) scheme is designed by integrated Lyapunov function and linear matrix inequality (LMI), such that the expected dynamic performance of the composite system is achieved. Finally, simulations show that the approach is proper and effective.

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