State-feedback H<inf>&#x221E;</inf> control of LPV T-S fuzzy systems using piecewise Lyapunov functions

Abstract

This paper studies the linearization and control design for a class of Affine Nonlinear Parameter Varying (ANPV) systems. In advance, a kind of Takagi-Sugeno (T-S) fuzzy modeling procedure with homogeneous consequent part based on the ANPV system is proposed to deal with the nonlinearity and the LPV T-S fuzzy system is obtained. Then, taking the LPV T-S fuzzy system as the control design model, the piecewise parameter-dependent Lyapunov function is introduced for the LPV T-S fuzzy gain scheduling control. Especially, the statefeedback ∞ control design of the LPV T-S fuzzy system is studied and the sufficient conditions are given in LMIs form. Finally, a numerical example is provided to validate the availability of the approaches. The simulation results show the universal approximation ability of the LPV T-S fuzzy system to the nonlinearity and the effectiveness of the LPV T-S fuzzy gain scheduling control.