PDC and Non-PDC fuzzy control with relaxed stability conditions for contintuous-time multiplicative noised fuzzy systems |
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| Authors: | Wen-Jer Chang Cheung-Chieh Ku Chia-Hao Chang |
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| Institution: | 1. School of Electrical and Information Engineering, Anhui University of Technology, Ma’anshan 243002, China;2. School of Mathematical Sciences, Liaocheng University, Liaocheng Shandong 252059, PR China;3. School of Automation and Electrical Engineering, Linyi University, Linyi 276005, China;1. College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110819, PR China;2. State Key Laboratory of Synthetical Automation of Process Industries, Northeastern University, Shenyang, Liaoning 110819, PR China |
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| Abstract: | This paper presents a relaxed scheme of fuzzy controller design for continuous-time nonlinear stochastic systems that are constructed by the Takagi–Sugeno (T–S) fuzzy models with multiplicative noises. Through Nonquadratic Lyapunov Functions (NQLF) and Non-Parallel Distributed Compensation (Non-PDC) control law, the less conservative Linear Matrix Inequality (LMI) stabilization conditions on solving fuzzy controllers are derived. Furthermore, in order to study the effects of stochastic behaviors on dynamic systems in real environments, the multiplicative noise term is introduced in the consequent part of fuzzy systems. For decreasing the conservatism of the conventional PDC-based fuzzy control, the NQLF stability synthesis approach is developed in this paper to obtain relaxed stability conditions for T–S fuzzy models with multiplicative noises. Finally, some simulation examples are provided to demonstrate the validity and applicability of the proposed fuzzy controller design approach. |
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