# RiccatiSolve

RiccatiSolve[{a,b},{q,r}]

gives the matrix that is the stabilizing solution of the continuous algebraic Riccati equation .

RiccatiSolve[{a,b},{q,r,p}]

solves the equation .

# Details and Options

• 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.

# Examples

open allclose all

## Basic Examples(1)

Solve a continuous algebraic Riccati equation:

 In[1]:=
 In[2]:=
 Out[2]=

Verify the solution:

 In[3]:=
 Out[3]=