gives the matrix that is the stabilizing solution of the continuous algebraic Riccati equation .
solves the equation .
- In , denotes the conjugate transpose.
- The equation has a unique, symmetric, positive semidefinite solution if is stabilizable, is detectable, , and . Consequently, all eigenvalues of the matrix are negative and the solution is stabilizing.
- The solution is positive definite when is controllable and is observable.
- RiccatiSolve supports a Method option, with the following possible settings:
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" also applies to exact and symbolic matrices.
Introduced in 2010
(8.0)| Updated in 2014