Bumpless Transfer Control for Switched Fuzzy Systems With $L_2$-Gain Property

Abstract

This paper concentrates on the bumpless transfer control problem for a category of switched fuzzy systems with $L_2$ -gain property. A description of the bumpless transfer performance for switched fuzzy systems is introduced for the first time. A general multiple Lyapunov functions strategy is exploited to solve the bumpless transfer control problem of the switched fuzzy systems with the $L_2$ -gain property. The multiple Lyapunov functions scheme allows the disconnection of the successive Lyapunov functions when a switching happens. A criterion on the bumpless transfer performance with the $L_2$ -gain property is established, allowing each subsystem to satisfy neither the bumpless transfer performance nor the $L_2$ -gain property. Moreover, when only the $L_2$ -gain property is considered, the condition is mildly expressed in terms of matrix inequalities rather than the usual combination of matrix inequalities and matrix equalities. Finally, an example of controlling a mass-spring-damping model is offered to validate the effectiveness of the developed control strategy.