LinearAlgebra - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Linear Algebra : LinearAlgebra Package : Solvers : LinearAlgebra/LyapunovSolve

LinearAlgebra

  

LyapunovSolve

  

solve the continuous Lyapunov equation

 

Calling Sequence

Parameters

Options

Description

Examples

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

Options

• 

The isgn argument designates the sign of the second term of the left hand side of the equation. The default value of this argument is 1.

• 

The constructor options provide additional information (readonly, shape, storage, order, datatype, and attributes) to the Matrix constructor that builds the result. These options may also be provided in the form outputoptions=[...], where [...] represents a Maple list.  If a constructor option is provided in both the calling sequence directly and in an outputoptions option, the latter takes precedence (regardless of the order).

• 

The tranA argument specifies whether the first Matrix argument A should be transposed prior to solving. The default value of this argument is false.

• 

The schurA argument specifies whether to omit reduction of the first Matrix argument to Schur form. This avoids unnecessary computation in the case that the first Matrix argument is already in Schur form. The default value of this argument is false.

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,QIdentityMatrix2$2

A,Q:=1001,1001

(1)

X,kLyapunovSolveA,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,kLyapunovSolveA,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]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam