This paper is concerned with the robust exponential synchronization problem of a class of chaotic delayed neural networks with different parametric uncertainties. A novel impulsive control scheme (so-called dual-stage impulsive control) is proposed. Based on the theory of impulsive functional differential equations, a global exponential synchronization error bound together with some new sufficient conditions expressed in the form of linear matrix inequalities (LMIs) is derived in order to guarantee that the synchronization error dynamics can converge to a predetermined level. Furthermore, to estimate the stable region, a novel optimization control algorithm is established, which can deal with the minimum problem with two nonlinear terms coexisting in LMIs effectively. The idea and approach developed in this paper can provide a more practical framework for the synchronization of multiperturbation delayed chaotic systems. Simulation results finally demonstrate the effectiveness of the proposed method.

This paper is concerned with further studies on control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, a novel slack variable technique, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions with arbitrary degrees, is presented by developing an efficient augmented multi-indexed matrix approach. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected into sets of augmented multi-indexed matrices. Thus, more information about the underlying normalized fuzzy weighting functions is involved into control synthesis. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved significantly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.