不确定时滞系统的非线性保性能控制

Nonlinear Guaranteed Cost Control for Uncertain Systems with Time-delay

针对一类非线性系统和给定的性能指标,研究其保性能控制问题。基于Lyapunov稳定性理论,采用线性矩阵不等式工具,给出非线性状态反馈保性能控制器存在的一个充分条件,并依据其可行解给出相应保性能控制律的设计方法。建立一个具有线性矩阵不等式约束的凸优化问题,得到非线性系统的最优保性能控制律。仿真示例表明该方法的可行性。

For a class of nonlinear systems with norm-bounded uneextainties and state-delay, the problem of designing a nonlinear guaranteed cost state controller is considered. Based on LMI and Lyapunov stability theory, a sufficient condition for the existence of nonlinear guaranteed cost controller is derived in terrm of linear matrix inequalities, which making the dosed- loop systems local stable for all admissible ＂ uncertainties and guaranteeing the cost bounded in a limitation, such that the control law of the resulting dcsed- loop systems is obtained by solving a set of linear matrix inequalities. Furthermore, the nonlinear optimal guaranteed controller is formulated through a eonvex optimization problem. Finally, a numerical example shows the feasibility and validity of the proposed design approach.