RESUMEN
This paper studies the issue of adaptive fuzzy output-feedback event-triggered control (ETC) for a fractional-order nonlinear system (FONS). The considered fractional-order system is subject to unmeasurable states. Fuzzy-logic systems (FLSs) are used to approximate unknown nonlinear functions, and a fuzzy state observer is founded to estimate the unmeasurable states. By constructing appropriate Lyapunov functions and utilizing the backstepping dynamic surface control (DSC) design technique, an adaptive fuzzy output-feedback ETC scheme is developed to reduce the usage of communication resources. It is proved that the controlled fractional-order system is stable, the tracking and observer errors are able to converge to a neighborhood of zero, and the Zeno phenomenon is excluded. A simulation example is given to verify the availability of the proposed ETC algorithm.
RESUMEN
In this paper, the function projective synchronization between integer-order and stochastic fractional-order nonlinear systems is investigated. Firstly, according to the stability theory of fractional-order systems and tracking control, a controller is designed. At the same time, based on the orthogonal polynomial approximation, the method of transforming stochastic error system into an equivalent deterministic system is given. Thus, the stability of the stochastic error system can be analyzed through its equivalent deterministic one. Finally, to demonstrate the effectiveness of the proposed scheme, the function projective synchronization between integer-order Lorenz system and stochastic fractional-order Chen system is studied.
RESUMEN
This paper investigates the stability of n-dimensional fractional order nonlinear systems with commensurate order 0 <α<2. By using the Mittag-Leffler function, Laplace transform and the Gronwall-Bellman lemma, one sufficient condition is attained for the local asymptotical stability of a class of fractional order nonlinear systems with order lying in (0, 2). According to this theory, stabilizing a class of fractional order nonlinear systems only need a linear state feedback controller. Simulation results demonstrate the effectiveness of the proposed theory.