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In this note, we develop a new robustness property of optimal regulators of nonlinear dynamic systems. The stability condition we establish presents a great advantage when compared to other stability conditions already available in the literature. It does not depend explicitly on the optimal control problem solution, allowing then a very simple and a priori analysis of the closed-loop system stability. Based on that, we propose a methodology for determining linear decentralized controllers which stabilize asymptotically a wide class of nonlinear dynamic systems. As an application example we present and discuss in detail the control design for a two-pendulum system .