Solves the Lyapunov matrix equation. The data types you wire to the A and B inputs determine the polymorphic instance to use.


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Inputs/Outputs

  • c2dcdb.png A —

    A contains matrix A in the Lyapunov equation. A must be a square matrix or upper triangular matrix.

  • c2dcdb.png B —

    B contains matrix B in the Lyapunov equation.

  • ci32.png matrix type —

    matrix type is the type of A.

    Set the type of A to speed up the computation of X and avoid unnecessary computation.

    0General
    3Upper Triangular (default)
  • ci32.png equation type —

    equation type specifies the type of Lyapunov equation.

    0Continuous (default)—Solves the continuous Lyapunov equation.
    1Discrete—Solves the discrete Lyapunov equation.
  • i2dcdb.png X —

    X returns the solution to the Lyapunov equation.

  • idbl.png scale —

    scale returns the scaling factor of the Lyapunov equation.

  • ii32.png error —

    error returns any error or warning from the VI. You can wire error to the Error Cluster From Error Code VI to convert the error code or warning into an error cluster.

    • The following equation defines the continuous Lyapunov equation:

    AX + XAH = αB

    where AH 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 λi + λ*j ≠ 0 for all eigenvalues of A, where λ* is the complex conjugate of λ.

    The following equation defines the discrete Lyapunov equation:

    AXAH – X = αB

    where AH is the conjugate transpose of A and α is a scaling factor used to avoid overflow in X.

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