Selective stabilization of Takagi-Sugeno fuzzy systems

This paper presents new results concerning the stability analysis and the design of state feedback controllers for continuous-time Takagi-Sugeno (T-S) fuzzy systems via fuzzy Lyapunov functions. Using the Cartesian product of simplexes, called multi-simplex, a new modeling is proposed to represent the membership functions of T-S fuzzy systems. In the multi-simplex representation, linear matrix inequality relaxations based on homogeneous polynomials matrices are provided for stability analysis and controller design. The time-derivatives of the membership functions are modeled as belonging to polytopic convex sets and may be considered unbounded if nothing is known about their upper limits. As main aspect, the method allows to synthesize control gains depending only on some premise variables selected by the designer. Numerical experiments illustrate the flexibility and advantages of the method.