gdare

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

gdare is not recommended. Use idare instead. For more information, see Version History.

Syntax

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


Description

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

$$H-tJ=\left[\begin{array}{ccc}A& F& B\\ -Q& E\prime & -S\\ S\prime & 0& R\end{array}\right]-\left[\begin{array}{ccc}E& 0& 0\\ 0& A\prime & 0\\ 0& B\prime & 0\end{array}\right]$$

The third input ns is the row size of the A matrix.

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

• -1 if the Symplectic pencil has eigenvalues on the unit circle

• -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] = gdare(H,J,NS,'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 Symplectic pencil has eigenvalues on the unit circle.

Version History

Introduced before R2006a

R2019a: gdare not recommended

Starting in R2019a, use the idare command to solve discrete-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 gdare. Furthermore, idare includes an optional info structure to gather the implicit solution data of the Riccati equation.

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

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

There are no plans to remove gdare at this time.