Finite-time boundary stabilization of fractional reaction-diffusion systems

This paper investigates the boundary finite-time stabilization of fractional reaction-diffusion systems (FRDSs). First, a distributed controller is designed, and sufficient conditions are obtained to ensure the finite-time stability (FTS) of FRDSs under the designed controller. Then, a boundary controller is presented to achieve the FTS. By virtue of Lyapunov functional method and inequality techniques, sufficient conditions are presented to ensure the FTS of FRDSs via the designed boundary controller. The effect of diffusion term of FRDSs on the FTS is also investigated. Both Neumann and mixed boundary conditions are considered. Moreover, the robust finite-time stabilization of uncertain FRDSs is studied when there are uncertainties in the system’s coefficients. Under the designed boundary controller, sufficient conditions are presented to guarantee the robust FTS of uncertain FRDSs. Finally, numerical examples are presented to verify the effectiveness of our theoretical results.

Finite-time stabilization for fractional-order inertial neural networks with time varying delays

This paper deals with the finite-time stabilization of fractional-order inertial neural network with varying time-delays (FOINNs). Firstly, by correctly selected variable substitution, the system is transformed into a first-order fractional differential equation. Secondly, by building Lyapunov functionalities and using analytical techniques, as well as new control algorithms (which include the delay-dependent and delay-free controller), novel and effective criteria are established to attain the finite-time stabilization of the addressed system. Finally, two examples are used to illustrate the effectiveness and feasibility of the obtained results.

Finite-time stabilization of switched nonlinear singular systems with asynchronous switching

This paper is concerned with the finite-time stabilization of a class of switched nonlinear singular systems under asynchronous control. Asynchronism here refers to the delays in switching between the controller and the subsystem. First, the dynamic decomposition technique is used to prove that such a switched singular system is regular and impulse-free. Secondly, based on the state solutions of the closed-loop system in the matched time period and the mismatched time period of the system instead of constructing a Lyapunov function, the sufficient conditions for the finite-time stability of the asynchronous switched singular system are given, there is no limit to the stability of subsystems. Then, the mode-dependent state feedback controller that makes the original system stable is derived in the form of strict linear matrix inequalities. Finally, numerical examples are given to verify the feasibility and validity of the results.