This paper is devoted to study the Razumikhin stability theorem for a class of impulsive stochastic delay differential systems. By developing a new lemma, stochastic analysis technique, and Razumikhin approach, several novel criteria of the $p$ th moment exponential stability are derived for the related systems. The key feature of the criteria is that time-derivatives of the Razumikhin functions are allowed to be indefinite, which loosens the constraints of the existing results greatly. Finally, two examples are given to illustrate the usefulness and significance of the theoretical results.

Some Improved Razumikhin Stability Criteria for Impulsive Stochastic Delay Differential Systems

Improved Razumikhin and Krasovskii stability criteria for time-varying stochastic time-delay systems

Finite-time stability analysis and stabilization by bounded linear time-varying feedback

This paper studies the fixed-time anti-synchronization (FTAS) of discontinuous reaction–diffusion neural networks (DRDNNs) with both time-varying coefficients and time delay. First, differential inclusion theory is used to deal with the influence caused by discontinuous activations. In addition, a new fixed-time convergence theorem is used to handle the time-varying coefficients. Second, a novel state-feedback control algorithm and integral state-feedback control algorithm are proposed to realize FTAS of DRDNNs. During the generalized (adaptive) pinning control strategy, a guideline is proposed to select neurons to pin the designed controller. Furthermore, we present several criteria on FTAS by using the generalized Lyapunov function method. Different from the traditional Lyapunov function with negative definite derivative, the derivative of the Lyapunov function can be positive in this paper. Finally, we give two numerical simulations to substantiate the merits of the obtained results.

Anti-Synchronization in Fixed Time for Discontinuous Reaction–Diffusion Neural Networks With Time-Varying Coefficients and Time Delay

New fixed-time synchronization control of discontinuous inertial neural networks via indefinite Lyapunov-Krasovskii functional method

This study is concerned with stability analysis of non-linear time-varying systems by using Lyapunov function-based approach. The classical Lyapunov stability theorems are generalised in the sense that the time-derivative of the Lyapunov functions are allowed to be indefinite. The stability analysis is accomplished with the help of the scalar stable functions introduced in the author's previous study. Both asymptotic stability and input-to-state stability are considered. Particularly, for asymptotic stability, several concepts such as uniform and non-uniform asymptotic stability, and uniform and non-uniform exponential stability are studied. The effectiveness of the proposed theorems is illustrated by several numerical examples.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/iet-cta.2016.1538

Bin Zhou

Papers

Stability analysis of non-linear time-varying systems by Lyapunov functions with indefinite derivatives