一类广义Lyapunov矩阵方程的正定解

摘要

研究了双线性系统中的一类广义Lyapunov矩阵方程的正定解。基于混合单调算子不动点定理，给出新的存在正定解的充分条件，构造了求其正定解的不动点迭代方法，并给出了迭代误差估计公式。数值实验表明新方法是可行的。%In this paper, we consider the positive definite solution of a class of generalized Lyapunov matrix equation, which arises in the bilinear systems. Based on the fixed point theorem for mixed monotone operator, a new sufficient condition for the existence of a unique positive definite solution is derived. A fixed point iterative method is proposed to compute the unique positive definite solution, and its error estimation is also given. Finally, a numerical example is presented to illustrate the feasibility of the proposed method.