# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE 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.
• 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.

## ExamplesExamplesopen allclose all

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

Solve a discrete algebraic Riccati equation:

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

Verify the solution:

 In[3]:=
 Out[3]=