一类非线性广义系统的精确线性化和极点配置一步设计

针对非线性广义系统控制问题,将非线性系统的精确线性化、极点配置一步设计和Zubov＇s方法应用于非线性广义系统控制问题.首先给出非满秩阵化为满秩阵的方法,进而得到非线性广义系统的状态空间实现的算法,然后利用Zubov＇s方法,通过解一个拟线性偏微分方程,完成该状态空间实现的精确线性化、极点配置一步设计,从而得到非线性广义系统的精确线性化、极点配置的一步控制.该方法回避了苛刻的对合条件,使问题化繁为简,化难为易.将该方法应用于Logistic增长的SIS传染病数学模型的一步控制,其目的为控制消除该传染病.仿真数据表明：该方法行之有效.

Single-step design of feedback linearization with pole placement for nonlinear singular system

This paper applies single-step design of the nonlinear system and Zubov＇s method to the control for a class of nonlinear singular system. Firstly, this paper derives the algorithm for the state-space realization of the nonlinear singular system; then, by Zubov＇s method and solving a quasilinear partial differential equations, this paper realizes the feedback linearization and the pole placement in a single step. This paper obtains the single-step design of feedback linearization with the pole placement for nonlinear singular system. This method bypasses the set of restrictive conditions that arise in geometric exact feedback linearization, so make hard things simple. The proposed approach is finally applied in a SIS model with logistic growth, whose ultimate aim is to eliminate the disease. The simulation result proved the feasibility and the effectiveness of the proposed method.