A stabilization method of inhomogeneous ladder networks with nonlinear elements

In the paper, different structures of electric ladder networks are considered: RC, RL, and RLC. Such systems are composed of resistors, inductors and capacitors connected in series. The elements of the network are not identical and have nonlinear characteristics. The network's dynamic behavior can be mathematically described by nonlinear differential equations. A class of robust feedback controls is designed to stabilize the system. The asymptotic stability of the closed-loop system is analyzed and proved by the use of Lyapunov functionals and LaSalle's invariance principle. The results of computer simulations are included to verify theoretical analysis and mathematical formulation.