Abstract
This paper is based on the Takagi-Sugeno (T-S) fuzzy models to construct a coronary artery system (CAS) T-S fuzzy controller and considers the uncertainties of system state parameters in CAS. We propose the fuzzy model of CAS with uncertainties. By using T-S fuzzy model of CAS and the use of parallel distributed compensation (PDC) concept, the same fuzzy set is assigned to T-S fuzzy controller. Based on this, a PDC controller whose fuzzy rules correspond to the fuzzy model is designed. By constructing a suitable Lyapunov-Krasovskii function (LKF), the stability conditions of the linear matrix inequality (LMI) are exported. Simulation results show that the method proposed in this paper is correct and effective and has certain practical significance.
Highlights
Since Pecora and Caroll proposed chaotic synchronization in 1990 [1], synchronization control of chaotic systems has developed rapidly and has become one of the most important topic during the past 30 years [2,3,4,5,6,7,8,9,10,11,12]
Simulation results show that the method proposed in this paper is correct and effective and has certain practical significance
Takagi-Sugeno (T-S) fuzzy model can provide the approximation of nonlinear features by fuzzy mixing of multiple local linear models with appropriate membership functions, by using fuzzy rules, the dynamic nonlinear systems are approximated to the set of the local linear input and output relation, and the whole fuzzy model is obtained by smoothing the set of the local linear model with the fuzzy piecewise membership function
Summary
Since Pecora and Caroll proposed chaotic synchronization in 1990 [1], synchronization control of chaotic systems has developed rapidly and has become one of the most important topic during the past 30 years [2,3,4,5,6,7,8,9,10,11,12]. In order to solve the synchronization problem of chaotic systems, many methods have been proposed, such as feedback control method [13, 14], continuous sliding mode method [15, 16], and fuzzy control method [17, 18]. Application of higher-order sliding mode adaptive controller is in reference [23] They use a synchronization controller to synchronize the chaotic motion state of the diseased vessels to that of the normal vessels, so as to achieve the goal of treatment. In order to further reduce the conservativeness of system stability analysis, we study the stability of chaotic time-delay synchronous control systems by using the method in [26].
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