By Hak-Keung Lam, Allen Leung
In this ebook, the state of the art fuzzy-model-based (FMB) dependent regulate ways are lined. A accomplished assessment in regards to the balance research of type-1 and type-2 FMB keep watch over structures utilizing the Lyapunov-based technique is given, providing a transparent photo to researchers who wish to paintings in this box. a large choice of continuous-time nonlinear regulate structures reminiscent of state-feedback, switching, time-delay and sampled-data FMB regulate platforms, are coated. briefly, this publication summarizes the hot contributions of the authors at the balance research of the FMB regulate structures. It discusses complex balance research concepts for varied FMB keep watch over platforms, and founds a concrete theoretical foundation to help the research of FMB regulate platforms on the learn point. The research result of this ebook provide numerous mathematical methods to designing solid and well-performed FMB keep an eye on platforms. additionally, the consequences widen the applicability of the FMB regulate strategy and support positioned the bushy controller in perform. a variety of complex analytical and mathematical research recommendations could be hired to enquire the approach balance and function of FMB-based regulate structures in a rigorous demeanour. specified research and derivation steps are given to reinforce the clarity, allowing the readers who're unusual with the FMB keep watch over structures to keep on 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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Extra resources for Stability Analysis of Fuzzy-Model-Based Control Systems: Linear-Matrix-Inequality Approach
Sample text
With c = p and mi (x(t)) = wi (x(t)) for all i connected in a closed loop, is asymptotically stable if the following LMIs given in the following h steps are satisfied, where h = 0, 1, 2, · · · , and d ≥ 2. The dimension of the multi-indices in the hmax = f loor d−1 2 iteration step h is denoted by dh = d − 2h. 1. (Initialization) Choose the degree of the fuzzy summation as d ≥ 2 and set T Qi [0] = Qi1 i2 ···id for i ∈ Id and h = 0. Define matrices Qj [0] = Qj [0] ∈ n×n for j ∈ P (i), i ∈ Id+o .
2. 1 offers a great deal of design flexibility to the fuzzy controller as the membership functions can be freely designed. This favourable property leads to a simple controller structure which may lower the computational demand and implementation cost. 1 exhibits an inherent robustness property. As the stability conditions are not related to the membership functions of both the TS fuzzy model and the fuzzy controller, the fuzzy controller can stabilize the nonlinear plant subject to parameter uncertainties which are embedded in the membership functions of the TS fuzzy model.
2. 4586 DRFC stands for Decay-Rate Fuzzy Controller. Staircase-Membership-Function Approach The Lyapunov stability theory is one of the mathematical tools to investigate the system stability of FMB control systems. It was shown in [15, 122] that the FMB control system is guaranteed to be asymptotically stable if the solution to a set of LMIs can be found numerically by using some convex programming techniques. 2), the system stability of the FMB control system is p p guaranteed by the satisfaction of i=1 j=1 wi mj Qij < 0.