Fuzzy logic based gain-scheduled techniques

This paper is concerned with the analysis and synthesis problems for linear parameter-varying (LPV) systems. An LPV system resembles a linear system that generally depends on scheduling parameters in a nonlinear fashion. Without any structural assumption on the model, Lyapunov function based analysis and synthesis approaches involve solving infinite number of linear matrix inequalities. Motivated by the capability of Takagi-Sugeno (T-S) fuzzy logic in managing nonlinearity, a blended multiple model representation is proposed to approximate the LPV model over the scheduling parameters set. In light of the affine parameter-dependent structure in local model, parameter-dependent Lyapunov function based analysis and synthesis approaches are presented. “Convexifying” technique is exploited to obtain finite dimensional optimization problem. A pendulum control problem is given to demonstrate the validity of the theoretical results.