BUILT-IN MATHEMATICA SYMBOL

# DiscreteRiccatiSolve

DiscreteRiccatiSolve[{a, b}, {q, r}]
gives the matrix that is the stabilizing solution of the discrete algebraic Riccati equation .

DiscreteRiccatiSolve[{a, b}, {q, r, p}]
solves .

## Details and OptionsDetails and Options

• 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.
• The eigenvalues of the symplectic matrix must not contain any symbolic expressions.
• DiscreteRiccatiSolve supports a Method option. The following explicit settings can be specified:
•  "Eigensystem" uses eigenvalue decomposition "Schur" uses Schur decomposition
• The default setting selects for exact matrices and as the primary method for real matrices.
• Method->"Schur" only works with real matrices.

## ExamplesExamplesopen allclose all

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

Solve a discrete algebraic Riccati equation:

 Out[2]//MatrixForm=

Verify the solution:

 Out[3]=