Stability and smoothness conditions for switching fuzzy systems

Describes stability and smoothness conditions for switching fuzzy systems. We first present a switching fuzzy system that has locally Takagi-Sugeno fuzzy models and switches them according to states, external variables and/or time. A switching fuzzy controller is constructed by mirroring the structure of the switching fuzzy system. LMI stability conditions are derived to design the switching fuzzy controller in Tanaka et al. (2000). Switching of several controllers causes non-continuity of control input at switching points. The phenomenon influences important control performance, e.g., ride quality in vehicle control. We derive a smoothness condition to avoid the phenomenon. The smoothness condition is also represented via LMIs. A stable switching fuzzy controller satisfying the smoothness condition is designed by simultaneously solving both of LMIs. The design technique is applied to trajectory control of an R/C hovercraft. The simulation and experimental results far the trajectory control show the validity of the switching fuzzy control