Finite-/Fixed-Time Stability of Nonautonomous Functional Differential Inclusion: Lyapunov Approach Involving Indefinite Derivative

A Dynamic Gain Fixed-Time Robust ZNN Model for Time-Variant Equality Constrained Quaternion Least Squares Problem With Applications to Multiagent Systems

A dynamic gain fixed-time (FXT) robust zeroing neural network (DFTRZNN) model is proposed to effectively solve time-variant equality constrained quaternion least squares problem (TV-EQLS). The proposed approach surmounts the shortcomings of conventional numerical algorithms which fail to address time-variant problems. The DFTRZNN model is constructed with a novel dynamic gain parameter and a novel activation function (NAF), which differs from previous zeroing neural network (ZNN) models. Moreover, the comprehensive theoretical derivation of the FXT stability and robustness of the DFTRZNN model is presented in detail. Simulation results further confirm the availability and superiority of the DFTRZNN model for solving TV-EQLS. Finally, the consensus protocols of multiagent systems are presented by utilizing the design scheme of the DFTRZNN model, which further demonstrates its practical application value.

On Finite/Fixed-Time Stability Theorems of Discontinuous Differential Equations

We investigated the finite/fixed-time stability (FNTS/FXTS) of discontinuous differential equations (DDEs) in this paper. To cope with differential equations that were discontinuous on the right-hand side, we utilized the Filippov solution, which is widely used in engineering. Under the framework of the Filippov solution, we transformed this issue into an FNTS/FXTS problem in the corresponding functional differential inclusion. We proposed some new FNTS/FXTS criteria, which will have important applications in the field of control engineering. It is worth mentioning that the coefficient function in the inequality satisfied by the Lyapunov function (LF) could be indefinite. Moreover, our paper gave a new estimation for the settling time (ST). Finally, two illustrative examples were given to demonstrate the validity and feasibility of the proposed criteria.