Related Experiment Video
Updated: Sep 2, 2025

Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays
Published on: May 29, 2017
Finite-time stability of state-dependent delayed systems and application to coupled neural networks
Xinyi He1, Xiaodi Li2, Shiji Song3
1School of Mathematics and Statistics, Shandong Normal University, Ji'nan, 250014, PR China.
Abstract:
Finite-time stability and stabilization problems of state-dependent delayed systems are studied in this paper. Different from discrete delays and time-dependent delays which can be well estimated over time, the information of state-dependent delays is usually hard to be estimated, especially when states are unknown or unmeasurable. To guarantee the stability of state-dependent delayed systems in the framework of finite time, a Razumikhin-type inequality is used, following which estimations on the settling time and the region of attraction are proposed. Moreover, the relationship between the variation speed of state-dependent delays and the size of the region of attraction is proposed. Then as an application of the theoretical result, finite-time stabilization is studied for a set of nonlinear coupled neural networks involving state-dependent transmission delay, where the design of memoryless finite-time controllers is addressed. Two numerical examples are given to show the effectiveness of the proposed results.
Related Concept Videos
Stability
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
State Space Representation
Consider an RLC circuit, a...
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
Multimachine Stability
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
Linear time-invariant Systems
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...

