By Hak-Keung Lam, Allen Leung
In this publication, the cutting-edge fuzzy-model-based (FMB) dependent keep watch over methods are coated. A accomplished evaluate concerning the balance research of type-1 and type-2 FMB keep watch over structures utilizing the Lyapunov-based procedure is given, providing a transparent photograph to researchers who wish to paintings in this box. a large choice of continuous-time nonlinear regulate platforms similar to state-feedback, switching, time-delay and sampled-data FMB keep an eye on platforms, are coated. briefly, this publication summarizes the new contributions of the authors at the balance research of the FMB regulate platforms. It discusses complex balance research strategies for numerous FMB keep watch over structures, and founds a concrete theoretical foundation to help the research of FMB keep an eye on platforms on the study point. The research result of this ebook supply quite a few mathematical techniques to designing strong and well-performed FMB keep watch over platforms. additionally, the implications widen the applicability of the FMB keep watch over process and support positioned the bushy controller in perform. a variety of complicated analytical and mathematical research recommendations may be hired to enquire the approach balance and function of FMB-based regulate platforms in a rigorous demeanour. particular research and derivation steps are given to reinforce the clarity, permitting the readers who're unexpected with the FMB keep an eye on structures to persist with the fabrics simply. Simulation examples, with figures and plots of process responses, are given to illustrate the effectiveness of the proposed FMB keep an eye on approaches.
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Additional resources for Stability Analysis of Fuzzy-Model-Based Control Systems: Linear-Matrix-Inequality Approach
1 to realize the system performance with pre-deﬁned weighting matrices J1 and J2 . 2. 16) characterized by pre-deﬁned weighting matrices J1 ≥ 0 and J2 ≥ 0 that is attenuated to the level η > 0 if any stability conditions reported in this book and the LMIs Wj < 0 for all j are satisﬁed. 4. 2. By following the MFSD analysis approach, the performance conditions can be relaxed by considering the information of the membership functions. 5. There are diﬀerent approaches reported in some published work to considering the system performance.
Yet, it is possible to widen the applicability of the FMB control approach by integrating the advantages of the PDC and non-PDC design techniques. In this chapter, the membership-function-shape-dependent (MFSD) analysis approach is employed to facilitate the stability analysis and controller synthesis. -K. F. Leung: FMB Control Systems, STUDFUZZ 264, pp. 23–58. com 24 3 Stability Analysis of FMB Control Systems under MFSD Approach consideration in the stability analysis for relaxing the stability conditions.
6) is employed to close the feedback loop. 7). 05 0 8 −b + 6 B2 = , B3 = where a and b are constant parameters. 5) are employed to check for the stability region characterized by the system parameters 2 ≤ a ≤ 12 and 2 ≤ b ≤ 12 at the interval of 1. With the help of the MATLAB LMI toolbox, the stability regions given by diﬀerent theorems are shown in Fig. 1 indicated by diﬀerent symbols. An empty point means that no feasible solution is found. 2. It can also be seen from Fig. 1 that the stability conditions in  oﬀer the most relaxed result demonstrated by the largest size of the stability region.