一类变系数四阶梁方程的反馈控制

State feedback control for a class of variable coefficients fourth-order beam equations

研究一类四阶分布参数系统的状态反馈控制问题。所考虑的分布参数系统由一类变系数四阶梁方程组成。针对这类四阶分布参数系统的特点,通过构造适当的Lyapunov泛函,给出了系统的状态反馈控制律。当反馈控制律应用于系统时,闭环系统的状态向量于L^(2)(0,l)×L^(2)(0,l)空间上是全局渐近稳定的。最后,通过仿真实例验证了该方法的有效性。

This article studies the state feedback control problem for a class of fourth-order distributed parameter systems composed of a class of variable coefficient fourth-order beam equations.Based on the characteristics of the systems,the state feedback control laws were proposed for such systems by means of constructing an appropriate Lyapunov function.When the feedback control laws are applied to the systems,the state vectors of the closed-loop systems are globally asymptotically stable on L^(2)(0,l)×L^(2)(0,l).Finally,a simulation example was given to show the effectiveness of this method.