Ouyang, HuaPetersen, Ian RichardUgrinovskii, Valery2026-07-032026-07-0397839026610051474-6670ORCID:/0000-0003-4856-9450/work/219177638https://hdl.handle.net/1885/733812392This paper addresses a stability analysis problem and synthesis problem for pendulum-like systems with multiple nonlinearities. A method for analysing the Lagrange stability of a pendulum-like system with multiple nonlinearities is proposed. In order to study the synthesis problem, the paper develops an Extended Strict Bounded Real Lemma for unstable systems. A sufficient condition for Lagrange stabilization is proposed in terms of an algebraic Riccati equation with a sign infinite solution. An algorithm is given to solve the algebraic Riccati equation for a Lagrange stabilizing solution and thus gives a control law to stabilize the system in the sense of Lagrange stability.enApplication of nonlinear analysis and designNonlinear system controlRobustness analysis200810.3182/20080706-5-KR-1001.330079961018388