sylv
Solve the Sylvester equations A*X + X*B = C or A*X*B + X = C
Syntax
sylv(A, B, C, 'c') sylv(A, B, C, 'd')
Arguments
- A, B, C
three real matrices of appropriate dimensions.
- flag 'c' or 'd'
choose the type of Sylvester equation to solve.
Description
X = sylv(A, B, C, 'c') computes X
as solution of the "continuous time" Sylvester equation
A*X + X*B = C.
X = sylv(A, B, C, 'd') computes X
as solution of the modified "discrete time" Sylvester equation
A*X*B + X = C.
X = -sylv(-A, B, C, 'd') computes X
as solution of the real "discrete time" Sylvester equation
A*X*B - X = C.
Examples
A = rand(4, 4); C = rand(4, 3); B = rand(3, 3); // Continuous time Sylvester equation: X = sylv(A, B, C, 'c'); norm(A*X + X*B - C) // Modified Discrete time Sylvester equation: X = sylv(A, B, C, 'd'); norm(A*X*B + X - C) // Real Discrete time Sylvester equation: X = -sylv(-A, B, C, 'd'); norm(A*X*B - X - C)
See also
- lyap — Equation de Lyapunov
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