一类不确定系统的双曲正切模型控制器设计

Hyperbolic model control design for a class of uncertain systems

针对一类不确定时滞系统的双曲正切模型稳定控制器设计问题,给出一种基于线性矩阵不等式控制器的设计方法。该方法通过选取合适的Lyapunov-Krasovskii泛函,并引入自由权矩阵和Newton-Leibniz公式,通过解线性矩阵不等式来设计控制增益矩阵,使得系统在控制器的作用下实现稳定。数值算例仿真结果表明,该控制器可以使系统达到稳定,进而说明所给控制器设计方法的有效性。

A new controller method based on linear matrix inequality is proposed tor a class of uncertain hyperbolic systems with uncertain time delay. In this new method, an appropriate Lyapunov-Krasovskii function is selected, and free-weighting matrix technique and Newton-Leibniz formula are both introduced in linear matrix inequality. The control gain is obtained by solving linear matrix inequality, which can guarantee the stability of systems. A simulation example is provided to show the controller can stabilize the system, and therefore demonstrate the effectiveness of the proposed method.