The positivity and event-triggered stabilization of Takagi-Sugeno fuzzy systems with actuator saturation

Abstract

The positivity and event-triggered stabilization of Takagi-Sugeno fuzzy systems with actuator saturation are investigated in this paper. Different from the existing quadratic event-triggered mechanism (ETM), a linear ETM is constructed, which can be reduced to a time-triggered mechanism (TTM). Based on parallel distribution compensation, an event-triggered fuzzy controller is designed, and sufficient conditions under the estimation of a certain domain of attraction are proposed to ensure the ETM-based and TTM-based closed-loop systems are positive and stable. The controller gain is solved directly by the proposed conditions. And then these sufficient conditions are extended to the conditions under the estimation of the largest domain of attraction by establishing an optimization problem. Furthermore, the linear ETM is proved to exclude the Zeno behavior of the system. Finally, two simulation examples are utilized to verify the effectiveness of the proposed event-triggered control scheme.