一类非线性不确定系统的鲁棒镇定

Robust stabilization for a class of uncertain nonlinear systems

由于实际中的一类非线性不确定系统可以建模为具有状态矩阵和输入矩阵不确定性并受非线性摄动的线性系统,将这类系统的鲁棒镇定问题转化为求解一个线性系统的H∞状态反馈控制问题。结果表明:若该H∞状态反馈控制问题有解,则原系统可以通过状态反馈实现鲁棒镇定。给出了状态反馈矩阵,还进一步给出了具体的仿真实例。仿真结果表明:该理论是可行的,且控制器实现了对这类非线性不确定系统的鲁棒镇定。

A large number of uncertain nonlinear systems can be modeled as linear systems with nonlinear perturbations and uncertainties in both the state and input matrices. The robust stabilization problem of this class of systems is converted to a state feedback H∞ linear system control problem in this paper, The results show that if the solution of the H∞ control problem exists, the original system can be robustly stabilized by a state feedback control. The state feedback matrix is given with a numerical example. Simulation results show that the theory gives a controller that guarantees robust stabilization of this class of uncertain nonlinear systems.