gives the matrix that is the stabilizing solution of the discrete algebraic Riccati equation .
- In , denotes the conjugate transpose.
- The equation has a unique, symmetric, positive semidefinite solution only if is stabilizable, is detectable, , and . Consequently, all the eigenvalues of the matrix lie inside the unit circle, and the solution is stabilizing.
- The solution is positive definite when is controllable and is observable.
- DiscreteRiccatiSolve supports a Method option. The following settings can be specified:
Automatic automatically determined method "Eigensystem" based on eigen decomposition "GeneralizedEigensystem" based on generalized eigen decomposition "GeneralizedSchur" based on generalized Schur decomposition "InverseFree" a variant of "GeneralizedSchur" "MatrixSign"
- iterative method using the matrix sign function
"Newton" iterative Newton method "Schur" based on Schur decomposition
- All methods apply to approximate numeric matrices. "Eigensystem" apply to exact and symbolic matrices.
Introduced in 2010
(8.0)| Updated in 2014