A parameter varying lyapunov function approach for tracking control for Takagi-Sugeno class of nonlinear systems

A reference model tracking control technique for nonlinear systems based on the Takagi-Sugeno model is proposed. The control design synthesis is aimed to reduce the tracking error for all bounded reference inputs and disturbances and to guarantee ℒ₂ gain performance. A nonlinear static output feedback controller is proposed to tackle this problem. Unlike the approaches using a single quadratic Lyapunov function, a parameter varying quadratic Lyapunov function is employed in our approach. The controller synthesis is formulated in terms of a feasibility problem of a set of linear matrix inequalities, which can be efficiently solved. A simulation example of a two-link robot system demonstrates the tracking performance and the validity of the proposed approach.