Related Experiment Video
Updated: Aug 20, 2025

Experimental Methods to Study Human Postural Control
Published on: September 11, 2019
Stability analysis of Hadamard and Caputo-Hadamard fractional nonlinear systems without and with delay
Bin-Bin He1, Hua-Cheng Zhou2, Chun-Hai Kou3
1College of Science, Zhejiang University of Technology, Hangzhou, 310023 Zhejiang People's Republic of China.
Abstract:
This paper handles with the Hadamard and the Caputo-Hadamard fractional derivative and stability of related systems without and with delay. Firstly, the derivative inequalities are obtained, which is indispensable in applying the theorems derived in this paper. Then, for systems without delay, we get the stability results by using the Lyapunov direct method and for systems with delay, we explore two useful inequalities to verify the stability. Examples are presented with numerical simulations to illustrate the effectiveness of our results.
More Related Videos
Related Concept Videos
Second Order systems II
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,...
Pole and System Stability
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's...
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
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....

