الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Stability analysis is one of the most important issues in analysis and design of fuzzy control systems. In control engineering problems, a desirable feature is asymptotic stability in the large. For nonlinear systems, the system may be not asymptotically stable in the large, then the problem becomes that of determining the largest region of asymptotic stability that is
called the domain of attraction.
At first, the effect of the number of membership functions of the fuzzy controller’s
input variables on the stability boundaries of a fuzzy control system is studied. A nonlinear single input-single output (SISO) plant in controllable canonical form with linear quadratic regulator (LQR) fuzzy controller is considered. The simulation was carried out, first for two membership functions, with different simulation points. It was noticed that inside the indefinite stability region there are some stable states, this means that the estimated stability boundaries were not optimal. Then, the simulation is carried out for different numbers of . membership functions: three, five, and seven membership functions. It is shown, by simulation and analytically, that the number of membership functions has no effect on the
stability boundaries of the system.
Two methods based on the second m:ethod of Lyapunov are used for testing the
stability of the fuzzy control system, namely: linear matrix. inequalities (LMIs) algorithm, and variable gradient method, the estimated domain of attraction was still small. A new approach is introduced to determine the most proper Lyapunov function that satisfies the largest domain of attraction using genetic algorithms (GAs). This approach resulted in a Lyapunov function, which satisfies a largest domain of attraction, but it is not the optimal. So, a numerical algorithm is introduced to determine the optimum boundaries of asymptotic stability region using the results of the genetic algorithms,
The introduced GA approach and the numerical algorithm are applied to a fourth order system, which is an experimental single-link flexible joint robot manipulator, where the state-space representation was not in the controllable canonical form and it is transformed into the controllable canonical form via a nonlinear transformation. The stability analysis was carried out through the projections of the fourth-order hypersurface on the various state planes that were used to define the system. The simulation was carried out for both the transformed system in the controllable canonical form and the original system for different simulation points. It was shown that the nonlinear transformation does not affect the results
of the stability analysis of the original system, since the genetic algorithm approach gave the largest estimation of the domain of attraction and the numerical algorithm determined the optimal stability boundaries for the two forms of state-space representation of the considered system.