Globally stabilizing second order nonlinear systems by SDRE control

Infinite-horizon nonlinear regulation of second order systems using the state dependent Riccati equation (SDRE) method is considered. By a convenient parametrization of the A(x) matrix, the state dependent algebraic Riccati equation is solved analytically. Thus, the closed-loop system equations are obtained in analytical form. Global stability analysis is performed by the second method of Lyapunov. By the aforementioned parametrization, it is sufficient for the Lyapunov function derivative to be negative semi-definite to achieve global asymptotic stability. Accordingly, a relatively simple condition for global asymptotic stability of the closed-loop system is derived. Two illustrative examples are included.