solve the continuous Lyapunov equation - Maple Help

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LinearAlgebra[LyapunovSolve] - solve the continuous Lyapunov equation

Calling Sequence

LyapunovSolve( A, C )

LyapunovSolve( A, C, isgn )

LyapunovSolve( A, C, isgn, outopts, tranA, schurA )

Parameters

A

-

Matrix; input matrix of dimension m x m

C

-

Matrix; second input matrix of dimension m x m

isgn

-

(optional) {-1,1}; indicates the sign of the term X . A (second term)

outopts

-

(optional); constructor options for Matrix output

tranA

-

(optional) `transpose[A]` = {truefalse,identical(transpose,hermitiantranspose)} ; specifies operation on A prior to solving

schurA

-

(optional) `Schur[A]` = truefalse; specifies whether A is in Schur form

Description

• 

The LyapunovSolve command computes the solution to the continuous Lyapunov matrix equation A.X+isgnX.A* =scaleC 

• 

The returned solution is an expression sequence consisting of the Matrix X followed by the scalar scale.

• 

This routine operates in the floating-point domain. Hence, the entries in the Matrix arguments must necessarily be of type complex(numeric).

  

The continuous Lyapunov equation is a special case of the Sylvester equation.

Examples

withLinearAlgebra:

A,Q:=IdentityMatrix2$2

A,Q:=1001,1001

(1)

X,k:=LyapunovSolveA,Q

X,k:=0.5000000000000000.0.0.500000000000000,1.

(2)

A.X+X.A%T=k.Q

1.0.0.1.=1.0.0.1.

(3)

X,k:=LyapunovSolveA,Q,1

Warning, Matrices have common or very close eigenvalues; perturbed values were used to solve the equation

X,k:=4.5035996273705010150.0.4.503599627370501015,1.

(4)

See Also

LinearAlgebra, LinearAlgebra[SchurForm], LinearAlgebra[SylvesterSolve]


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