Robust <inline-formula> <tex-math notation="LaTeX">${L_1}$</tex-math> </inline-formula> Observer-Based Non-PDC Controller Design for Persistent Bounded Disturbed TS Fuzzy Systems

Abstract

This paper proposes a new method for bounded input bounded output stabilization and robust ${{{\bf L}}_1}$ observer-based controller design of a class of nonlinear systems described by Takagi–Sugeno (TS) models. The sufficient conditions of nonparallel distributed compensation (non-PDC) controller design are derived in terms of linear matrix inequalities (LMIs) in a way that the effect of external persistent bounded disturbance is alleviated on the amplitude of the TS system states. The main contributions of this paper can be categorized in two classes. First, a novel method for minimizing the ${{{\bf L}}_1}$ performance upper bound is proposed which leads to less number of pre-fixed scalar terms and less computational time. Second, we utilize nonquadratic Lyapunov function to reduce the conservativeness of proposed conditions and make them applicable to wider classes of TS fuzzy systems. Finally, several numerical examples are presented to test the validity of the proposed approaches of this paper. In particular, TS fuzzy model of a helicopter system is derived and the proposed controller is applied to the original nonlinear plant. Simulation results verify the effectiveness of our approaches, even in the presence of white noise.