Circuit Theory Approach To Stability and Passivity Analysis of Nonlinear Dynamical Systems

Abstract

In this paper, we address the problem of global asymptotic stability and strong passivity analysis of nonlinear time-varying systems controlled by a second-order vector differential equation. First, we obtain this equation from a nonlinear time varying network of the circuit theory. Then, we construct the Lyapunov candidate function directly from the physical meaning of the given system. By the way, we review a number of previous results from the point view of Lyapunov's direct method. Our system with its real energy function generalize and improve upon some well-known studies. The new concept facilitates the formulation of the energy (Lyapunov) function from the power-energy relationship of the given system. Then, we also realized that the time derivative of the Lyapunov function for a given dynamical systems is the negative value of the power dissipated in the system. Therefore, with the proposed approach, one can inspect the result of the time derivative of the energy function for a given physical system. Finally, two examples (one with simulations) are used to illustrate the superiority and validity of the obtained results.