Local Stabilization for Uncertain T-S Fuzzy Systems Based on a Mixed Type-1/2 Control Strategy
摘要
This paper investigates the problem of local stabilization for Takagi-Sugeno (T-S) fuzzy systems with uncertainties. First, a mixed type-1/2 T-S fuzzy system is established to represent the uncertain nonlinear systems, where the membership functions (MFs) of the T-S fuzzy model are divided into two parts: the first part contains uncertain parameters, while the second part does not. Then, a mixed type-1/2 fuzzy control scheme, where the controller partly shares MFs with the system, is proposed to locally stabilize the T-S fuzzy systems. In this scheme, some of the MFs of the controller are designed to match the MFs of the system without uncertainties, while the remaining MFs of the controller can be freely designed. The purpose of designing the mixed control scheme is to make better use of the information of MFs as well as maintain the flexibility of the design. Furthermore, synthesis conditions for the mixed type-1/2 fuzzy controller are derived to ensure that the system state can be restricted into the local objective region. Different from conventional methods, with the help of the set-theoretic description, the information of the MFs, which do not contain parameters uncertainties, can be fully utilized in the synthesis of the mixed type-1/2 fuzzy controller such that the conservatism of the design can be reduced. In the end, three examples are given to illustrate the efficacy of the proposed controller scheme.