Abstract
Abstract In this paper, based on the off-axis circle criterion, a sufficient condition with a simple graphical explanation is derived to analyze the global asymptotic stability of a type of Takagi-Sugeno (T-S) fuzzy control systems in case of different constant reference inputs. Three numerical examples are given to demonstrate how to use the proposed method in analyzing the T-S fuzzy control systems.
Highlights
In the history of fuzzy control theory, the TakagiSugeno (T-S) fuzzy model 1 is a famous landmark
Since the T-S fuzzy model usually consists of a family of local linear dynamic systems, it is valuable to graphically analyze the T-S fuzzy systems in the frequency domain
The off-axis circle criterion is employed to analyze the same type of T-S fuzzy control systems
Summary
In the history of fuzzy control theory, the TakagiSugeno (T-S) fuzzy model 1 is a famous landmark. The circle criterion is applied for the stability analysis of the Mamdani type fuzzy control systems 11, 12. The circle criterion is deployed to derive sufficient stability conditions for the T-S fuzzy control systems with a graphical interpretation in the senses of Lyapunov stability 20, 21. The aim of this paper is to generalize the off-axis circle criterion-based stability condition to the T-S fuzzy control systems in case of different constant reference inputs. Our method can guarantee the global asymptotic stability of the T-S fuzzy control systems in case of different constant reference inputs.
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