gdare (Control System Toolbox)

Generalized solver for discrete-time algebraic Riccati equations.

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

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.

See Also
dare Solver for discrete-time algebraic Riccati equations

gcare Generalized solver for continuous-time algebraic Riccati equations

gcare gensig