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D. Properties of Continuous-Time Riccati Equations

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This appendix summarizes key properties of the Continuous-Time Differential Riccati Equation (CTDRE);

$\displaystyle \frac{d\ensuremath{\mathbf{P}} }{dt}$ $\textstyle =$ $\displaystyle -\ensuremath{\mathbf{A}} ^T \ensuremath{\mathbf{P}} (t)-\ensurema... ...emath{\mathbf{B}} ^T\ensuremath{\mathbf{P}} (t)-\ensuremath{\boldsymbol{\Psi}} $ (D.0.1)
$\displaystyle \ensuremath{\mathbf{P}} (t_f)$ $\textstyle =$ $\displaystyle \ensuremath{\boldsymbol{\Psi}} _f$ (D.0.2)

and the Continuous-Time Algebraic Riccati Equation (CTARE)

\begin{displaymath} 0=-\ensuremath{\mathbf{A}} ^T\ensuremath{\mathbf{P}} -\ensu... ...f{B}} ^T\ensuremath{\mathbf{P}} -\ensuremath{\boldsymbol{\Psi}}\end{displaymath} (D.0.3)