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Control System Design - Index | Book Contents |
Appendix D
| Section D.2
D. Properties of Continuous-Time Riccati Equations
D.2 Solutions of the CTARE
The Continuous Time
Algebraic Riccati Equation (CTARE) has
many solutions, because it is a matrix quadratic equation. The
solutions can be characterized as follows.
Lemma D.3
Consider the following CTARE:
 |
(D.2.1) |
(i) |
The CTARE can be expressed as |
 |
(D.2.2) |
|
|
where
is defined in (D.1.8).
|
(ii) |
Let
be defined so that |
 |
(D.2.3) |
|
|
where
are any partitioning of the
(generalized) eigenvalues of
such that, if
is
equal to
for same ,
then
for some .
|
|
Let |
 |
(D.2.4) |
|
|
Then
is a solution of the
CTARE.
|
Proof
|