Studies have shown that fractional calculus can describe and characterize a practical system satisfactorily. Therefore, the stabilization of fractional-order systems is of great significance. The asymptotic stabilization problem of delayed linear fractional-order systems (DLFS) subject to state and control constraints is studied in this article. Firstly, the existence conditions for feedback controllers of DLFS subject to both state and control constraints are given. Furthermore, a sufficient condition for invariance of polyhedron set is established by using invariant set theory. A new Lyapunov function is constructed on the basis of the constraints, and some sufficient conditions for the asymptotic stability of DLFS are obtained. Then, the feedback controller and the corresponding solution algorithms are given to ensure the asymptotic stability under state and control input constraints. The proposed solution algorithm transforms the asymptotic stabilization problem into a linear/nonlinear programming (LP/NP) problem which is easy to solve from the perspective of computation. Finally, three numerical examples are offered to illustrate the effectiveness of the proposed method.

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In this paper, we investigate the problem of sliding mode control for singular fractional-order systems that have matched uncertainties. We design an innovative integral sliding mode function and controller based on the normalizable condition. A strict linear matrix inequality-based sufficient condition is obtained for the system’s stability. The normalizable condition is eliminated by updating and developing the control method, and a sufficient and necessary condition is developed for the admissibility of the system. Lastly, verification of our method’s effectiveness is numerically conducted in two instances.

This paper investigates the local stabilization problem of delayed fractional-order neural networks (FNNs) under the influence of actuator saturation. First, the sector condition and dead-zone nonlinear function are specially introduced to characterize the features of the saturation phenomenon. Then, based on the fractional-order Lyapunov method and the estimation technique of the Mittag–Leffler function, an LMIs-based criterion is derived to guarantee the local stability of closed-loop delayed FNNs subject to actuator saturation. Furthermore, two corresponding convex optimization schemes are proposed to minimize the actuator costs and expand the region of admissible initial values, respectively. At last, two simulation examples are developed to demonstrate the feasibility and effectiveness of the derived results.

This paper addresses a new fractional order infectious disease model with saturated incidence and time delay. In the new model, the isolated population and the asymptomatic infected population are considered. The invariant region and positive analysis of the solution of the model are established. Next, the basic reproduction number is obtained by the next-generation matrix method, and the sufficient conditions for local asymptotic stability for arbitrary time delays are proposed. Finally, the correctness of the theoretical results is verified by some numerical simulations.