In this paper, we present necessary and sufficient stability and robust stability conditions for two-dimensional (2D) systems described by the Fornasini-Marchesini (FM) second model in terms of the discriminant systems of polynomial. This paper simplifies the traditional method of stability into a tractable method by the fractional linear transformation (FLT). More specifically, we reduce the stability analysis to a easy issue whether some polynomials are positive definite. Then we use the same idea to consider the stabilization and robust stabilization issues. Finally, the effectiveness of the proposed results is demonstrated by a practical example and two numerical examples.

在本文中，我们针对多项式的判别系统，针对由Fornasini-Marchesini（FM）第二模型描述的二维（2D）系统，提供了必要且充分的稳定性和鲁棒稳定性条件。本文通过分数线性变换（FLT）将传统的稳定性方法简化为易于处理的方法。更具体地说，我们将稳定性分析简化为一个简单的问题，即某些多项式是否为正定的。然后，我们使用相同的想法来考虑稳定性和鲁棒性稳定性问题。最后，通过一个实际例子和两个数值例子证明了所提出结果的有效性。