Last Modified: June 25, 2019

Solves the Lyapunov matrix equation.

The matrix type of matrix *A*.

Specifying the matrix type allows this node to execute more quickly by avoiding unnecessary computations, which could introduce numerical inaccuracy.

Name | Value | Description |
---|---|---|

General | 0 | A matrix that you cannot describe with one of the other categories. |

Upper Triangular | 3 | An upper triangular. |

**Default: **Upper Triangular

Matrix *A* in the Lyapunov equation.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

This input must be a square matrix or upper quasi-triangular matrix in canonical Schur form.

Matrix *B* in the Lyapunov equation.

This input accepts a 2D array of double-precision, floating point numbers or 2D array of complex double-precision, floating point numbers.

Type of Lyapunov equation.

Name | Value | Description |
---|---|---|

Continuous | 0 | Solves the continuous Lyapunov equation. |

Discrete | 1 | Solves the discrete Lyapunov equation. |

**Default: **Continuous

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an **error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

**Default: **No error

Solution to the Lyapunov equation.

Scaling factor of the Lyapunov equation.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

The following equation defines the continuous Lyapunov equation:

*A**X* + *X**A*^{H} = α*B*

where *A*^{H} is the conjugate transpose of *A* and α is a scaling factor used to avoid overflow in *X*.

The continuous Lyapunov equation has a unique solution if and only if λ_{i} + λ^{*}_{j} ≠ 0 for all eigenvalues of *A*, where λ^{*} is the complex conjugate of λ.

The following equation defines the discrete Lyapunov equation:

*A**X**A*^{H} - *X* = α*B*

where *A*^{H} is the conjugate transpose of *A* and alpha is a scaling factor used to avoid overflow in *X*.

The discrete Lyapunov equation has a unique solution if and only if λ_{i}λ^{*}_{j} ≠ 1 for all eigenvalues of *A*, where λ^{*} is the complex conjugate of λ.

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: Not supported

Web Server: Not supported in VIs that run in a web application