Abstract
In this paper, we presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical examples to illustrate the efficiency of frequency domain-based condition.
Highlights
Among various fuzzy modeling themes, the Takagi-Sugeno (T-S) model [1] has been one of the most popular modeling frameworks
We presented a sufficient condition on the frequency domain for the absolutely stable analysis of the Takagi-Sugeno (T-S)fuzzy control system, based on the Popov’s criterion. we use some numerical examples to illustrate the efficiency of frequency domain-based condition
T-S fuzzy models can be as universal approximator any smooth nonlinear control systems cab be approximated by T-S fuzzy models and any smooth nonlinear state feedback controller can be approximated by the parallel distributed compensation (PDC) controller [2]
Summary
Among various fuzzy modeling themes, the Takagi-Sugeno (T-S) model [1] has been one of the most popular modeling frameworks. Bode and Nyquist plots, which are often used in the frequency response methods, can provide a graphic insight into the control system under investigation. In [5] the stability of the Mamdani fuzzy control system is explored based on the Popov’s criterion, which is a frequency domain-based sufficient condition, so as to guarantee the stability of nonlinear feedback systems. Popov’s criterion is a frequency response method and it evaluate absolutely stable for a system that the forward path is a linear timeinvariant system, and the feedback part is a memoryless nonlinearity. Popov’s criterion is utilized to drive the frequency domain-based sufficient condition, which provide a graphical interpretation for the stability analysis of the T-S fuzzy control systems
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