The main purpose of this paper is to investigate the finite-time stability Hadamard fractional differential equations (HFDEs). Firstly, standard definitions HFDEs in compatible Banach spaces are proposed. In light method successive approximation and Beesack inequality with weakly singular kernel, criteria for linear nonlinear established, respectively. Then regard pure delay, a novel delayed ma...

In the current contribution, integral representations of solutions homogeneous and nonhomogeneous delay differential equation a fractional Hilfer derivative are established in terms delayed Mittag-Leffler-type matrix function two parameters. By using method variation constants, solution represented. Finite-time stability is examined with provision appropriate sufficient conditions. Finally, an ...

This paper focuses on analyzing the finite-time convergence of a nonlinear consensus algorithm for multi-agent networks with unknown inherent nonlinear dynamics. Due to the existence of the unknown inherent nonlinear dynamics, the stability analysis and the finite-time convergence analysis of the closed-loop system under the proposed consensus algorithm are more challenging than those under the...

A new guidance law utilizing variable structure control with finite time sliding sector is proposed. First, a finite time sliding sector is defined. The finite time sliding sector is a subset of state space in which the Lyapunov function candidate satisfies the finite time stability condition, in contrast to the commonly used notion of asymptotic stability in conventional sliding sector. Then, ...

This paper studies properties of homogeneous systems in a geometric, coordinate-free setting. A key contribution of this paper is a result relating regularity properties of a homogeneous function to its degree of homogeneity and the local behavior of the dilation near the origin. This result makes it possible to extend previous results on homogeneous systems to the geometric framework. As an ap...

As is apparent from most text books, the definition of a Markov process includes, in the most natural way, processes that are time inhomogeneous. Nevertheless, most modern references quickly restrict themselves to the time homogeneous case by assuming the existence of a time homogeneous transition function, a case for which there is a vast literature. The goal of this paper is to point out some...

— This paper presents an analysis approach to finite-time attraction in probability concerns with nonlinear systems described by nonlinear random differential equations (RDE). RDE provide meticulous physical interpreted models for some applications contain stochastic disturbance. The existence and the path-wise uniqueness of the finite-time solution are investigated through nonrestrictive assum...