TS fuzzy robust L1 control for nonlinear systems with persistent bounded disturbances

Abstract

In this paper, a novel technique for Takagi–Sugeno (TS) model-based robust L1 controller design of nonlinear systems is proposed. Two synthesis methods based on quadratic and non-quadratic Lyapunov functions are considered. To design the robust stabilizing controller, a new approach for deriving sufficient conditions associated with the L1 performance criterion in terms of strict linear matrix inequality is proposed. This novel technique results in less pre-chosen scalar design variables and calculation burden. Furthermore, deriving the controller synthesis conditions via a non-quadratic Lyapunov function (NQLF) relaxes the obtained conditions. Therefore, the proposed approaches not only efficiently minimize the effect of persistent bounded disturbance, but also are applicable for wider classes of TS systems. Furthermore, some new lemmas are proposed to facilitate strict LMI formulation and to provide more degrees of freedom. Finally, several numerical and practical examples are presented to show the merits of this paper.