2-D广义系统的特征多项式配置

Characteristic Polynomial Assignment of 2-D Singular Systems

利用代数几何方法,研究具有多输入的 2 D广义系统Roesser模型的特征多项式系数的任意配置问题.通过引入恰当形式的状态反馈,消除了 2 D广义系统的无穷远极点,得到了相应的闭环系统.以代数几何方法为工具,将此闭环系统的特征多项式配置问题转化为判别有理映射是否为到上的,推导出多输入的 2 D广义系统Roe sser模型由状态反馈几乎任意配置特征多项式系数的充分条件.利用此方法同样可对基于输出反馈的特征多项式配置问题进行研究,并给出了 2 D广义系统由输出反馈几乎任意配置特征多项式系数的充分条件,从而丰富和发展了多输入情况下的 2 D广义系统特征多项式配置的理论.

The problems of arbitrary assignment coefficients of characteristic polynomial in Roesser model of (2-D) singular systems with multi-input are investigated by the algebraic geometric method.Introducing the state feedback with proper form, the infinite poles of 2-D singular systems are eliminated.Accordingly, the closed-loop systems described by Roesser model are obtained.In terms of the theory of algebraic geometry, the problem of characteristic polynomial assignment of the closed-loop systems is transferred to the ones if a rational mapping is onto.Sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial in Roesser model of 2-D singular systems via state feedback are derived, and they are available for multi-input cases.It also has been shown that this method can be applied to assign the characteristic polynomial with output feedback.Sufficient conditions for almost arbitrary assignment coefficients of characteristic polynomial of multi-input 2-D singular systems described by Roesser model with output feedback are given.These results develop the theory of characteristic polynomial assignment of 2-D singular systems in multi-input cases.