Global Stabilization of Feedback Non-Linearizable Nonlinear Systems without Strict Triangular Condition

This paper studies a global stabilization problem for a class of high-order nonlinear systems in a cascaded chain form. The high-order cascade systems considered in this paper are feedback non-linearizable and non-affine in the control variables without the strict triangular condition, and therefore this global stabilization problem cannot be directly handled by any existing method. It is shown that under some suitable assumptions on such a nonlinear system the global stabilization problem is solvable and a globally stabilizing smooth state feedback controller can be recursively constructed, using the so-called adding one power integrator technique recently proposed by Lin and Qian (Systems and Control Letters, vol. 39 (2000), pp. 339-351) together with the back-stepping technique. A simple numerical example is worked out to demonstrate the effectiveness of the proposed controllers.