Controller Design using Piecewise Lyapunov Functions based on Filippov First Order Theory

A controller design for a class of Takagi-Sugeno (T-S) fuzzy models is given, in which piecewise Lyapunov functions are used with the aim to improve the feasibility of certain linear matrix inequalities (LMIs) related to the controller design. First, the state space is partitioned into certain cells based on the T-S fuzzy model. In order to deal with the system behaviour between cells, the Filippov convex method is adopted by viewing the system behaviour in any adjacent cells as the discontinuous right-hand side first-order ordinary differential equations. Finally, certain LMIs, which guarantee the asymptotic stability of the closed-loop control system and determine the related parameters in the controller, are established.