Stability and Feedback Control of Nonlinear Systems

In this paper, new results for stability and feedback control of nonlinear systems are proposed. The results are obtained by using the Lyapunov indirect method to approximate the behavior of the uncontrolled nonlinear system’s trajectory near the critical point using Jacobian method and designing state feedback controller for the stabilization of the controlled nonlinear system using the difference in response between the set point and actual output values of the system. Next, the Lyapunov-Razumikhin method is used to determine sufficient conditions for the stabilization of the system. Examples are given with simulation output studies to verify the theoretical analysis and numerical computations using MATLAB