Fuzzy Alternate Control Delayed Systems

Abstract

This paper studies the asymptotic stability of nonlin-ear systems which is regulated by using fuzzy impulsive control. First of all, the system was formulated, the Lyapunov function was constructed, and then the fuzzy control component required for the nonlinear system to exhibit global asymptotic exponential stability under the regulation of the impulsive controller was developed. A unique fuzzy concept was introduced herein, which, compared to the conventional precise counterpart, was defined to perform only scalar approximations. Subsequently, a set of conditions sufficient for global asymptotic exponential stability was proposed for the impulsive controller. Halany inequality and its key generalizations were used while working out the mathematical proofs. Finally, examples were given to verify the general results obtained and their applicability.