scholarly journals Synthesis of Polynomial Fuzzy Model-Based Designs with Synchronization and Secure Communications for Chaos Systems with H∞ Performance

Processes ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 2088
Author(s):  
Gwo-Ruey Yu ◽  
Yong-Dong Chang ◽  
Chih-Heng Chang
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Numerical Simulations ◽  
Fuzzy System ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Secure Communications ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Fuzzy Compensator

This paper presents the sum of squares (SOS)-based fuzzy control with H∞ performance for a synchronized chaos system and secure communications. To diminish the influence of the extrinsic perturbation, SOS-based stability criteria of the polynomial fuzzy system are derived by using the polynomial Lyapunov function. The perturbation decreasing achievement is indexed in a H∞ criterion. The submitted SOS-based stability criteria are more relaxed than the existing linear matrix inequality (LMI)-based stability criteria. The cryptography scheme based on an n-shift cipher is combined with synchronization for secure communications. Finally, numerical simulations illustrate the perturbation decay accomplishment of the submitted polynomial fuzzy compensator.

scholarly journals A Reconstruction Procedure Associated with Switching Lyapunov Function for Relaxing Stability Assurance of T-S Fuzzy Mode

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Yau-Tarng Juang ◽  
Chih-Peng Huang ◽  
Chung-Lin Yan
Keyword(s):  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Fuzzy Model ◽  
Alternative Form ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
State Variables ◽  
Stability Criteria ◽  
Quadratic Lyapunov Function ◽  
Reconstruction Procedure

This paper proposes a novel reconstruction procedure to lessen the conservatism of stability assurance of T-S Fuzzy Mode. By dividing the state variables into some bounded regions, the considered T-S fuzzy model can be first transferred to an alternative form via a reconstructing procedure. Thus, we can attain some relaxing stability criteria based on the switching quadratic Lyapunov function (SQLF) method. Notably, these proposed conditions are explicitly formulated by linear matrix inequality (LMI) form and can handily be evaluated by current software tools. Finally some illustrative examples are given to experimentally demonstrate the validity and merit of the proposed method.

A passivity-based observer for neural mass models

2018 ◽  
Vol 36 (3) ◽  
pp. 701-711
Author(s):  
Xian Liu ◽  
Cheng-Xia Sun ◽  
Qing Gao ◽  
Zhi-Wang Chen
Keyword(s):  
System Theory ◽  
Linear Matrix Inequality ◽  
Numerical Simulations ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Structure Characteristics ◽  
Novel Approach ◽  
Neural Mass ◽  
Passive Theory

Abstract This paper presents a novel approach of designing a stabilizing observer for neural mass models which can simulate distinct rhythms in electroencephalography (EEG). Due to the structure characteristics, neural mass models are expressed as Lurie systems. The stabilizing observer is designed by using the Lurie system theory and the passive theory. The observer matrices are constructed via solutions of some linear matrix inequality (LMI) conditions. Numerical simulations are used to demonstrate the efficiency of the results.

Nonlinear Position Control of Digital Hydraulic Cylinder Despite Disturbance

2014 ◽  
Vol 998-999 ◽  
pp. 638-641
Author(s):  
Shi Jie Xu ◽  
J.F. Xing ◽  
Li Kun Peng
Keyword(s):  
Control System ◽  
Lyapunov Function ◽  
Linear Matrix Inequality ◽  
Nonlinear Model ◽  
Position Control ◽  
Hydraulic Cylinder ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Nonlinear Controller ◽  
Position Control System

A nonlinear controller is presented for a digital hydraulic cylinder against disturbance. We first establish the nonlinear model of digital hydraulic cylinder position control system. Then a Lyapunov function and a nonlinear controller are presented. The controller designing problem is translated into the problem of solving a linear matrix inequality. The experiment results show that the controller proposed by this paper has much better performance than traditional one.

scholarly journals Construction of Lyapunov Function for Power System based on Solving Linear Matrix Inequality

2005 ◽  
Vol 125 (5) ◽  
pp. 461-468
Author(s):  
Atsushi Ishigame ◽  
Hiromu Sakaguchi ◽  
Jun Takashima ◽  
Shirou Suzaki
Keyword(s):  
Lyapunov Function ◽  
Power System ◽  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Matrix Inequality

Novel Approach to Robust Stability Criteria of Uncertain System with Time-Varying Delay

2013 ◽  
Vol 631-632 ◽  
pp. 1189-1194
Author(s):  
Chao Deng ◽  
Zhao Di Xu ◽  
Yu Bai ◽  
Xin Yuan Wang
Keyword(s):  
Linear Matrix Inequality ◽  
Robust Stability ◽  
Uncertain System ◽  
Linear Matrix ◽  
Convexity Property ◽  
Time Varying ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Time Varying Delay ◽  
Varying Delay

This paper considers the robust stability criteria of uncertain system with time-varying delay. Firstly, by exploiting a new Lyapunov function that optimizes the segment of time delay and using the convexity property and free-weight method of the Linear Matrix Inequality, delay-dependent stability condition can be obtained for the asymptotical stability of the nominal system. Secondly, basing on the obtained condition, the corresponding linear matrix inequality can be obtained for the uncertain system. Finally, an example is given to demostrate the effectiveness and the merit of the proposed method.

scholarly journals Pinning Synchronization of Delayed Neural Networks with Nonlinear Inner-Coupling

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Yangling Wang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Linear Matrix Inequality ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Stability Criteria ◽  
Delayed Neural Networks ◽  
Delay Dependent

Without assuming the symmetry and irreducibility of the outer-coupling weight configuration matrices, we investigate the pinning synchronization of delayed neural networks with nonlinear inner-coupling. Some delay-dependent controlled stability criteria in terms of linear matrix inequality (LMI) are obtained. An example is presented to show the application of the criteria obtained in this paper.

scholarly journals Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Bin Wang ◽  
Hongbo Cao ◽  
Yuzhu Wang ◽  
Delan Zhu
Keyword(s):  
Linear Matrix Inequality ◽  
Fractional Order ◽  
Stability Condition ◽  
Chaos Synchronization ◽  
Linear Time ◽  
Three Dimensional ◽  
Fuzzy Model ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Integer Order

This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI) interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D) chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

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