We derive sufficient conditions to guarantee asymptotic stability for fuzzy-based sliding mode controllers applied to single-input single-output nonlinear systems, made in the framework of the Lyapunov functions. Such conditions also preserve the well-recognized features of both sliding mode control and Mamdani-type fuzzy control such as robustness and uncertainties treatment. In addition, the rules for tuning the cores of membership functions are also found. Real-time experiments, made on a one-link pendulum, are performed to illustrate and demonstrate the theoretical results.

Hyperchaotic systems have applications in multiple areas of science and engineering. The study and development of these type of systems helps to solve diverse problems related to encryption and decryption of information. In order to solve the chaos synchronization problem for a hyperchaotic Lorenz-type system, we propose an observer based synchronization under a master-slave configuration. The proposed methodology consists of designing a sliding-mode observer (SMO) for the hyperchaotic system. In contrast, this type of methodology exhibits high-frequency oscillations, commonly known as chattering. To solve this problem, a fuzzy-based SMO system was designed. Numerical simulations illustrate the effectiveness of the synchronization between the hyperchaotic system obtained and the proposed observer.