Lyapunov Stability Analysis Of Some Non-Linear Systems:- Ekeke Miracle D

ABSTRACT This work is concerned with Lyapunov stability analysis of some non-linear systems. In the process two methods of determining the stability ofsome non-linear systems was considered and they include Lyapunov direct method and indirect method. In the direct method, a suitable Lyapunov function which is positive definite was chosen. We then showed that if the time derivative ofthe function is negative semi-definite, the system is stable, ifthe time derivative is negative definite the system is asymptotically stable and if the time derivative is positive definite then the system is unstable. In the indirect method, the system was linearized about the equilibrium point using the Jacobian matrix and then the eigen values of the matrix were analyzed. Ifthe eigen values has negative real parts then the system is asymptotically stable, if at least one eigen values ofthe system with a zero real part, then the test is inconclusive. We efficient and general tool for analyzing the stability ofsome non-linear systems.