solves the continuous algebraic Riccati equation - Maple Help

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LinearAlgebra[CARE] - solves the continuous algebraic Riccati equation

 Calling Sequence CARE(A, B, Q, R, S, options, outopts)

Parameters

 A - Matrix(square) B - Matrix Q - Matrix R - (optional) Matrix(square) S - (optional) Matrix options - (optional) constructor options for the result objects and/or equation(s) of the form keyword = value, where keyword is one of haveB or output outopts - (optional) equation(s) of the form outputoptions[o] = list, where o is one of X, L or G

Description

 • The CARE command solves the continuous algebraic Riccati equation,

${A}^{+}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}X+X\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}A-\left(S+X\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}B\right)\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{R}^{\mathrm{-1}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}{\left(S+X\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}B\right)}^{+}+Q=0$

 • The optional Matrix arguments R and S default respectively to the identity Matrix and 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

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}\right):$
 > $a:=\mathrm{Matrix}\left(\left[\left[-3,2\right],\left[1,1\right]\right]\right):$
 > $b:=\mathrm{Matrix}\left(\left[\left[0\right],\left[1\right]\right]\right):$
 > $c:=\mathrm{Matrix}\left(\left[\left[1,-1\right]\right]\right):$
 > $r:=\mathrm{Matrix}\left(\left[\left[3\right]\right]\right):$
 > $\mathrm{CARE}\left(a,b,{c}^{\mathrm{%T}}\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}.\phantom{\rule[-0.0ex]{0.5em}{0.0ex}}c,r,\mathrm{output}=\left[X,L\right]\right)$
 $\left[\begin{array}{cc}{0.589517437276262}& {1.82157472488609}\\ {1.82157472488609}& {8.81883980692312}\end{array}\right]{,}\left[\begin{array}{c}{-}{3.42578096594334}{+}{0.}{}{I}\\ {-}{1.32083158810045}{+}{0.}{}{I}\end{array}\right]$ (1)
 > $a:=\mathrm{Matrix}\left(\left[\left[0,1\right],\left[0,0\right]\right]\right):$
 > $q:=\mathrm{Matrix}\left(\left[\left[1,0\right],\left[0,2\right]\right]\right):$
 > $b:=\mathrm{Matrix}\left(\left[\left[0,0\right],\left[0,1\right]\right]\right):$
 > $\mathrm{CARE}\left(a,b,q\right)$
 $\left[\begin{array}{cc}{2.00000000000000}& {1.00000000000000}\\ {1.00000000000000}& {2.00000000000000}\end{array}\right]$ (2)
 > $\mathrm{CARE}\left(a,b,q,\mathrm{output}=X\right)$
 $\left[\begin{array}{cc}{2.00000000000000}& {1.00000000000000}\\ {1.00000000000000}& {2.00000000000000}\end{array}\right]$ (3)
 > $\mathrm{CARE}\left(a,b,q,\mathrm{output}=\left[X,L,\mathrm{rcond}\right]\right)$
 $\left[\begin{array}{cc}{2.00000000000000}& {1.00000000000000}\\ {1.00000000000000}& {2.00000000000000}\end{array}\right]{,}\left[\begin{array}{c}{-}{0.771362440687311}{+}{0.}{}{I}\\ {-}{0.788573854448794}{+}{0.}{}{I}\end{array}\right]{,}{0.427050982331351692}$ (4)