A membership-function-dependent approach for stability analysis and controller synthesis of Takagi–Sugeno models

This paper presents a new approach for stability analysis and controller design of Takagi–Sugeno (TS) models. The analysis considers information derived from existing or induced order relations among the membership functions. Partitioning of the state-space and the use of piecewise Lyapunov functions (PWLF) arise naturally as a consequence of induced order relations. Conditions under the novel approach can be expressed as linear matrix inequalities (LMIs) facilitating the inclusion of performance design. Examples are provided to show the advantages over the classical quadratic approach.