Stability , Chaos Tests with Adaptive and Feedback Control Methods for 3D Discrete - Time Dynamical System

Maysoon M. Aziz; Omar M. Jihad

In this paper, a three dimensional non linear discrete - time dynamical system was introduced, The numerical solution was carried by Newton's Raphson method. The basic properties was investigated by mean of it's fixed points , bifurcation and numerical diagrams. Stability analysis measured by eigenvalues of the characteristic equation roots ، Lyapunov function and Jury's test which all show that the system is unstable . Chaos diagnose was calculated by Lyapunov exponent and binary test , the maximum value of Lyapunov exponent is obtain as (L_max= 3.8), Lyapunov dimension is obtain as (D_L= 2.0872) and binary test (0-1) is obtain as (k = 0.9942≈1), which all shows the system is highly chaotic. Finally, the system was controlled effectively by designed feedback and adaptive controllers , the results after controls were very good system trajectories are stable and regular.

Select Volume / Issues:

• Volume 12,Issue 2,Mar. 2021

Year:

2021

Type of Publication:

Article

Keywords:

Stability; Chaotic System; Lyapunov Function; Lyapunov Exponent; Lyapunov Dimension; Adaptive Control; Feedback Control

Journal:

IJECCE

Volume:

12

Number:

2

Pages:

31-42

Month:

March

ISSN:

2249-071X