I need some algorithms to solve the Algebraic Riccati equation

hi,

I need some algorithm to solve Algebraic Riccati equation. what is the algorithm behind the Matlab function dare/care?

I need to write the algorithm with simple instructions, cause I need to write it in a S function or embedded matlab function in simulink.

Answer 1

[Zunding Xiao]

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., III and A.J. Laub, "Generalized Eigenproblem Algorithms and Software for Algebraic Riccati Equations," Proc. IEEE®, 72 (1984), pp. 1746-1754