gcare

(Not recommended) Generalized solver for continuous-time algebraic Riccati equation

gcare is not recommended. Use icare instead. For more information, see Version History.

Syntax

[X,L,report] = gcare(H,J,ns)
[X1,X2,D,L] = gcare(H,...,'factor')


Description

[X,L,report] = gcare(H,J,ns) computes the unique stabilizing solution X of the continuous-time algebraic Riccati equation associated with a Hamiltonian pencil of the form

$$H-tJ=\left[\begin{array}{ccc}A& F& S1\\ G& -A^{\prime }& -S2\\ S2\prime & S1\prime & R\end{array}\right]-\left[\begin{array}{ccc}E& 0& 0\\ 0& E\prime & 0\\ 0& 0& 0\end{array}\right]$$

The optional input ns is the row size of the A matrix. Default values for J and ns correspond to E = I and R = [ ].

Optionally, gcare returns the vector L of closed-loop eigenvalues and a diagnosis report with value:

• -1 if the Hamiltonian pencil has jw-axis eigenvalues

• -2 if there is no finite stabilizing solution X

• 0 if a finite stabilizing solution X exists

This syntax does not issue any error message when X fails to exist.

[X1,X2,D,L] = gcare(H,...,'factor') returns two matrices X1, X2 and a diagonal scaling matrix D such that X = D*(X2/X1)*D. The vector L contains the closed-loop eigenvalues. All outputs are empty when the associated Hamiltonian matrix has eigenvalues on the imaginary axis.

Version History

Introduced before R2006a

R2019a: gcare is not recommended

Starting in R2019a, use the icare command to solve continuous-time Riccati equations. This approach has improved accuracy through better scaling and the computation of K is more accurate when R is ill-conditioned relative to gcare. Furthermore, icare includes an optional info structure to gather the implicit solution data of the Riccati equation.

The following table shows some typical uses of gcare and how to update your code to use icare instead.

Not Recommended	Recommended
[X,L] = gcare(H,J,NS)	[X,K,L] = icare(A,B,Q,R,S,E,G) computes the stabilizing solution X, the state-feedback gain K and the closed-loop eigenvalues L of the continuous-time algebraic Riccati equation. For more information, see icare.
[X,L,report] = gcare(H,J,NS)	[X,K,L,info] = icare(A,B,Q,R,S,E,G) computes the stabilizing solution X, the state-feedback gain K, the closed-loop eigenvalues L of the continuous-time algebraic Riccati equation. The info structure contains the implicit solution data. For more information, see icare.

There are no plans to remove gcare at this time.