H∞ networked control of two inverted pendulums coupled by a spring

We consider the H∞ control of two inverted pendulums coupled by a spring. Such a plant, with its controller separated away by a serial communication network, is modeled as an unstable time-delay system with two nonlinear terms corresponding to the torques by gravity and spring force, respectively. Quadratic upper bound estimations for these two nonlinear terms lead to the applicability of linear matrix inequality (LMI) technique to the stabilization of the system. We use a method of completing the square to estimate some integrals in computing of the derivative of the Lyapunov-Krasovskii functional.