Stabilization Of A Class Of Nonlinear Systems With Block-feedforward Structure

Some nonlinear systems can be transformed into special triangular configuration systems by a diffeomorphism and a feedback transformation under certain conditions. Lyapunov-based recursive design methods can be used to stabilize such system according to its specific structure. Backstepping can be used to a class of strict-feedback lower-triangular systems and a lot of results are achieved. At the same time, its limitation to a class of pure feedback systems motivated the development of other recursive procedures, such as forwarding. When using forwarding to deal with systems with upper-triangular structure, it is very difficult to gain analytical expression of the cross-term of the Lyapunov function constructed at each step. Thus the results in this aspect are limited.This thesis uses forwarding based on control Lyapunov function (CLF) to stabilize a class of nonlinear control systems with block-upper triangular configuration. Control laws are designed to achieve global asymptotic stability and local exponential stability (GAS/LES) for the system. At the same time, the thesis considers the problem of robust stabilization for a class of uncertain nonlinear systems with block-upper triangular structure, and the control law gained at last can guarantee robust global asymptotic stability and local quadratic stability (RGAS/LQS) for the system. The thesis is organized as follows:The thesis reviews the achievements on nonlinear systems and introduces some fundamental tools which will be used in the subsequent analysis of the internal structure of nonlinear systems firstly. Then, the thesis considers global stabilization of a class of nonlinear control systems with upper-triangular structure. A general feedback control law designed by using forwarding based on CLF achieves GAS/LES for the system under the stabilizable conditions constructed. The aforementioned system will be extended and introduced an unknown uncertain parameter in the systems. Forwarding is used to design stabilizing controllers which can assure both RGAS/LQS for the system. Some conclusions and outlooks are illustrated finally.