BUILT-IN MATHEMATICA SYMBOL

# 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 OptionsDetails 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.
• The eigenvalues of the Hamiltonian matrix must not contain any symbolic expressions.
• RiccatiSolve supports a Method option. The following explicit settings can be specified:
•  "Eigensystem" use eigenvalue decomposition "Schur" use Schur decomposition
• By default, eigenvalue decomposition is used to obtain the solution.
• The setting Method->"Schur" works only with approximate numerical matrices.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Solve a continuous algebraic Riccati equation:

 Out[2]=

Verify the solution:

 Out[3]=