Fuzzy impulsive control for uncertain nonlinear systems with guaranteed cost

In this paper, a guaranteed cost fuzzy impulsive control (GCFIC) problem is addressed for uncertain continuous-time nonlinear systems which can be represented by the Takagi–Sugeno (T–S) fuzzy model with parametric uncertainties. Based on the T–S fuzzy model, a novel time-varying Lyapunov function is initially constructed to derive the existence condition of guaranteed cost fuzzy impulsive controllers, which cannot only exponentially stabilize the uncertain fuzzy system, but also provide an upper bound on the quadratic cost function. Then, two procedures for designing suboptimal guaranteed cost fuzzy impulsive controllers are given in the sense of minimizing an upper bound of the cost function: one casts the controller design into a parameter-dependent linear matrix inequality (LMI) optimization problem and the other casts the controller design into a sequential minimization problem subject to LMI constraints by using the cone complementary linearization (CCL) algorithm. Finally, an example is presented to illustrate the effectiveness of the proposed method.