# dlyap

## 语法

```X = dlyap(A,Q) X = dlyap(A,B,C) X = dlyap(A,Q,[],E) ```

## 说明

`X = dlyap(A,Q)` 求解离散时间李雅普诺夫方程 AXAT − X + Q = 0

`X = dlyap(A,B,C)` 求解西尔维斯特方程 AXB – X + C = 0

`X = dlyap(A,Q,[],E)` 求解广义离散时间李雅普诺夫方程 AXAT – EXET + Q = 0

## 诊断

```Solution does not exist or is not unique. ```

## 算法

`dlyap` 对李雅普诺夫方程使用 SLICOT 例程 SB03MD 和 SG03AD，对西尔维斯特方程使用 SB04QD (SLICOT)。

## 参考

[1] Barraud, A.Y., “A numerical algorithm to solve A XA - X = Q,” IEEE® Trans. Auto. Contr., AC-22, pp. 883-885, 1977.

[2] Bartels, R.H. and G.W. Stewart, "Solution of the Matrix Equation AX + XB = C," Comm. of the ACM, Vol. 15, No. 9, 1972.

[3] Hammarling, S.J., “Numerical solution of the stable, non-negative definite Lyapunov equation,” IMA J. Num. Anal., Vol. 2, pp. 303-325, 1982.

[4] Higham, N.J., ”FORTRAN codes for estimating the one-norm of a real or complex matrix, with applications to condition estimation,” A.C.M. Trans. Math. Soft., Vol. 14, No. 4, pp. 381-396, 1988.

[5] Penzl, T., ”Numerical solution of generalized Lyapunov equations,” Advances in Comp. Math., Vol. 8, pp. 33-48, 1998.

[6] Golub, G.H., Nash, S. and Van Loan, C.F. “A Hessenberg-Schur method for the problem AX + XB = C,” IEEE Trans. Auto. Contr., AC-24, pp. 909-913, 1979.

[7] Sima, V. C, “Algorithms for Linear-quadratic Optimization,” Marcel Dekker, Inc., New York, 1996.