# care

(Not recommended) Solve continuous-time algebraic Riccati equation

`care`

is not recommended. Use `icare`

instead. For more information, see Version
History.

## Syntax

## Description

## Examples

## Input Arguments

## Output Arguments

## Limitations

The $$(A,B)$$ pair must be stabilizable (that is, all unstable modes are controllable). In addition, the associated Hamiltonian matrix or pencil must have no eigenvalue on the imaginary axis. Sufficient conditions for this to hold are $$(Q,A)$$ detectable when $$S=0$$ and $$R>0$$, or

$$\left[\begin{array}{cc}Q& S\\ {S}^{T}& R\end{array}\right]>0$$

## Algorithms

`care`

implements the algorithms described in [1]. It works with the Hamiltonian matrix when R is well-conditioned and $$E=I$$; otherwise it uses the extended Hamiltonian pencil and QZ
algorithm.

## References

[1] Arnold, W.F., and A.J. Laub. “Generalized Eigenproblem
Algorithms and Software for Algebraic Riccati Equations.” *Proceedings of the IEEE* 72, no. 12 (1984): 1746–54.
https://doi.org/10.1109/PROC.1984.13083.

## Version History

**Introduced before R2006a**