Stability analysis of nonlinear systems using dynamic-Routh´s stability criterion: A new approach

In this paper, we proposed a new method to analyze the condition and region of stability of nonlinear time-varying systems by introducing the notions of dynamic poles and dynamic-Routh´s stability method. The stability analysis is carried out in a special type of complex plane called g(t)-plane which is similar to the traditional s-plane where both real and imaginary axis have time dependent parameters. The theorem is established and numerical examples from literature are solved with simulation results to show the efficacy and accuracy of the proposed method. The phase plane curve is presented for showing the stability condition of the nonlinear time varying systems.