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A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno (T-S) fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.
A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno (TS) fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great Significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest TS fuzzy controller. . Comparisons are drawn between the performance of the simplest TS fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this full condition can be applied to both stable and unstable plants.