矩阵方程AZB-Z=C的多项式解法

THE SOLVING PROCESS OF MATRX EQUATION AZB-Z=C BY POLYNOMIAL

在研究离散动力系统稳定性时,需要解矩阵方程A^TZA—Z=C.众所周知,该方程的解法非常冗繁.本文讨论了AZB—Z=C解的相容性,给出了求解公式,该公式只是A,B,C的多项式,解法和结果比目前见到的简洁.同时对离散动力系统A(t+l)=Ax(t)+f(t,x(t))所构造的Liapunov函数给出了明确的表达式.

We need to solve the matrix equation AXB-X=C for study stability of dynamical systems. Well known,the solving process of matrix equation AXB -X = C is Very hard. This paper , we discussed compatibitity of solution of AXB - X = C and gived a formula soving for this equation. The formulo only is polynomial abut matrix ,A,B,C.