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output=value

X - the Matrix which solves the equation

L - the Vector of closed-loop eigenvalues of the symplectic Matrix H

rcond - the reciprocal of the condition number of the system solved by X

G - the gain Matrix where $G={\left(B^{+}·X·B+R\right)}^{\mathrm{-1}}·{\left(S+A^{+}·X·B\right)}^{+}$.

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

The DARE command solves the discrete algebraic Riccati equation,

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.

$\mathrm{with}\left(\mathrm{LinearAlgebra}\right)\:$

$a≔\mathrm{Matrix}\left(2\,2\,\left[\left[0\,1\right]\,\left[0\,0\right]\right]\right)$

$a≔\left[\begin{array}{cc}0& 1\\ 0& 0\end{array}\right]$

$b≔\mathrm{Matrix}\left(2\,2\,\left[\left[0.5\,0.7\right]\,\left[1\,0\right]\right]\right)$

$b≔\left[\begin{array}{cc}0.5& 0.7\\ 1& 0\end{array}\right]$

$q≔\mathrm{Matrix}\left(3\,2\,\left[\left[1\,0\right]\,\left[0\,1\right]\,\left[0\,0\right]\right]\right)$

$q≔\left[\begin{array}{cc}1& 0\\ 0& 1\\ 0& 0\end{array}\right]$

$r≔\mathrm{Matrix}\left(1\,1\,\left[\left[1\right]\right]\right)$

$r≔\left[\begin{array}{c}1\end{array}\right]$

$\mathrm{DARE}\left(a\,b\,q\,r\right)$

$\left[\begin{array}{cc}1.00000000000000& \mathrm{-4.40918311571451}\times {10}^{\mathrm{-16}}\\ \mathrm{-4.40918311571451}\times {10}^{\mathrm{-16}}& 1.92116460960662\end{array}\right]$

$\mathrm{DARE}\left(a\,b\,q\,r\,\mathrm{output}=X\right)$

$\left[\begin{array}{cc}1.00000000000000& \mathrm{-4.40918311571451}\times {10}^{\mathrm{-16}}\\ \mathrm{-4.40918311571451}\times {10}^{\mathrm{-16}}& 1.92116460960662\end{array}\right]$

$\mathrm{DARE}\left(a\,b\,q\,r\,⟨⟨1\,0⟩|⟨0\,1⟩⟩\right)$

$\left[\begin{array}{cc}0.626691964175562& \mathrm{-0.0851772290376543}\\ \mathrm{-0.0851772290376543}& 1.60725718203778\end{array}\right]$

$\mathrm{DARE}\left(a\,b\,q\,r\,\mathrm{output}=\left[X\,L\,G\,\mathrm{rcond}\right]\right)$

$\left[\begin{array}{cc}1.00000000000000& \mathrm{-4.40918311571451}\times {10}^{\mathrm{-16}}\\ \mathrm{-4.40918311571451}\times {10}^{\mathrm{-16}}& 1.92116460960662\end{array}\right],\left[\begin{array}{c}3.38343745873938\times {10}^{\mathrm{-17}}+0.\mathrm{I}\\ \mathrm{-0.157670780786754}+0.\mathrm{I}\end{array}\right],\left[\begin{array}{cc}0.& 0.157670780786754\end{array}\right],0.705446591923427402$