solves the discrete algebraic Riccati equation - Maple Help

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LinearAlgebra[DARE] - solves the discrete algebraic Riccati equation

Calling Sequence

DARE(A, B, Q, R, S, options, outopts)

Parameters

A

-

Matrix(square)

B

-

Matrix

Q

-

Matrix

R

-

Matrix(square)

S

-

(optional) Matrix

options

-

(optional) constructor options for the result objects and/or equation(s) of the form output = value

outopts

-

(optional) equation(s) of the form outputoptions[o] = list, where o is one of X, L or G

Description

• 

The DARE command solves the discrete algebraic Riccati equation,

A+ .X.AXS+A+ .X.B.B+ .X.B+R-1.S+A+ .X.B+ +Q=0

• 

The optional Matrix argument S defaults to the zero Matrix.

• 

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

Examples

withLinearAlgebra:

a:=Matrix2,2,0,1,0,0

a:=0100

(1)

b:=Matrix2,2,0.5,0.7,1,0

b:=0.50.710

(2)

q:=Matrix3,2,1,0,0,1,0,0

q:=100100

(3)

r:=Matrix1,1,1

r:=1

(4)

DAREa,b,q,r

1.000000000000004.1316273595582210-164.1316273595582210-161.92116460960662

(5)

DAREa,b,q,r,output=X

1.000000000000004.1316273595582210-164.1316273595582210-161.92116460960662

(6)

DAREa,b,q,r,1,0|0,1

1.000000000000004.1316273595582210-164.1316273595582210-161.92116460960662

(7)

DAREa,b,q,r,output=X,L,G,rcond

1.000000000000004.1316273595582210-164.1316273595582210-161.92116460960662,3.3834374587393810-17+0.I0.157670780786754+0.I,0.0.157670780786754,0.705446591923427402

(8)

See Also

CARE, copyright, LinearAlgebra, LyapunovSolve, Matrix, SylvesterSolve, Vector


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