State-feedback H ∞ control for LPV system using T-S fuzzy linearization approach

Abstract

This paper discusses the linear parameter varying (LPV) gain scheduling control problem based on the Takagi-Sugeno (T-S) fuzzy linearization approach. Firstly, the affine nonlinear parameter varying (ANPV) description of a class of nonlinear dynamic processes is defined; that is, at any scheduling parameter, the corresponding system is affine nonlinear as usual. For such a class of ANPV systems, a kind of developed T-S fuzzy modeling procedure is proposed to deal with the nonlinearity, instead of the traditional Jacobian linearization approach. More concretely, the evaluation system for the approximation ability of the novelly developed T-S fuzzy modeling procedure is established. Consequently, the LPV T-S fuzzy system is obtained which can approximate the ANPV system with required accuracy. Secondly, the notion of piecewise parameter-dependent Lyapunov function is introduced, and then the stabilization problem and the state-feedback H ∞ control problem of the LPV T-S fuzzy system are studied. The sufficient conditions are given in linear matrix inequalities (LMIs) form. Finally, a numerical example is provided to demonstrate the availability of the above approaches. The simulation results show the high approximation accuracy of the LPV T-S fuzzy system to the ANPV system and the effectiveness of the LPV T-S fuzzy gain scheduling control. © 2013 Jizhen Liu et al.