中文摘要：

利用逆矩阵的Neumann级数形式,将在离散时间跳跃线性二次控制问题中遇到的含未知矩阵之逆的离散对偶代数Riccati方程（DCARE）转化为高次多项式矩阵方程组,然后采用牛顿算法求高次多项式矩阵方程组的异类约束解,并采用修正共轭梯度法求由牛顿算法每一步迭代计算导出的线性矩阵方程组的异类约束解或者异类约束最小二乘解,建立求DCARE的异类约束解的双迭代算法.双迭代算法仅要求DCARE有异类约束解,不要求它的异类约束解唯一,也不对它的系数矩阵做附加限定.数值算例表明,双迭代算法是有效的.

英文摘要：

By using Neumann series of inverse matrix,discrete coupled algebraic Riccati equation with unknown matrix inverse in discrete-time jump linear quadratic control problems can be transformed into the high degree polynomial matrix equations.Then Newton＇s method is applied to find different constrained solution of polynomial matrix equations, and the modified conjugate gradient method is used to solve different constrained solution or different constrained least square solution of linear matrix equations derived from each iterative step of Newton＇s method.In this way, a double iterative method is established to solve for different constrained solution of discrete coupled algebraic Riccati equation.Different constrained solution of discrete coupled algebraic Riccati equation is only required by double iterative algorithm.But it may not be unique.Besides there are not additional limits to its coefficient matrix of discrete coupled algebraic Riecati equation.The effectiveness of the double iterative method is demonstrated by numerical examples.