研究由~Fornasini-Marchesini(简记F-M)第二模型描述的状态饱和~2-D~离散系统的渐近稳定性.定义参数~$s_i$~将系统表示成部分状态饱和~2-D~离散系统;
构造具有较少限制的矩阵~$Q$~并引入参数~$\beta$,利用~Lyapunov~方法给出了系统全局渐近稳定性的新的判别条件;设计了基于线性矩阵不等式的求解算法,
并通过数值算例验证了算法的有效性.

In this paper, the globally asymptotical stability of 2-D discrete-time systems described by the Fornasini-Marchesini (F-M) second model is studied. By
defining the parameter si, the systems are expressed as 2-D discrete-time systems with partial state saturation. By constructing a matrix Q with fewer constraints and introducing a parameter , a new criterion of globally asymptotical stability is given by applying Lyapunov method. In order to achieve the stability discrimination, an algorithm based on LMIs is designed. In the end, a numerical example is given to show the effectiveness of the proposed algorithm.