Low frequency Lagrange stabilization for pendulum‐like systems

Abstract

In this article, the low frequency Lagrange stabilization issue is investigated for a pendulum-like system. To this end, an H ∞ control method is developed for converting the frequency-domain stabilization condition into an H ∞ norm bound requirement in low frequency domain. With the aid of a generalized Kalman-Yakubovich-Popov (KYP) lemma, time-domain matrix inequality conditions are derived to assure both pendulum-like and low frequency Lagrange stability properties for the closed-loop system. Furthermore, an output feedback Lagrange stabilization controller is constructed via feasible solutions of a certain set of linear matrix inequalities. An illustrative example is provided to verify the effectiveness and superiority of the proposed controller.