Lyapunov Equations VI

Owning Palette: Linear Algebra VIs

Requires: Full Development System

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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Select an instance Real Lyapunov EquationsComplex Lyapunov Equations

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Real Lyapunov Equations

	A contains matrix A in the Lyapunov equation. A must be a square matrix or upper quasi-triangular matrix in canonical Schur form.
	B contains matrix B in the Lyapunov equation.
	matrix type is the type of A. Set the type of A to speed up the computation of X and avoid unnecessary computation. 0 General 3 Upper Triangular (default)
	equation type specifies the type of Lyapunov equation. 0 Continuous (default)—Solves the continuous Lyapunov equation. 1 Discrete—Solves the discrete Lyapunov equation.
	X returns the solution to the Lyapunov equation.
	scale returns the scaling factor of the Lyapunov equation.
	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.

Complex Lyapunov Equations

	A contains matrix A in the Lyapunov equation. A must be a square matrix or upper triangular matrix.
	B contains matrix B in the Lyapunov equation.
	matrix type is the type of A. Set the type of A to speed up the computation of X and avoid unnecessary computation. 0 General 3 Upper Triangular (default)
	equation type specifies the type of Lyapunov equation. 0 Continuous (default)—Solves the continuous Lyapunov equation. 1 Discrete—Solves the discrete Lyapunov equation.
	X returns the solution to the Lyapunov equation.
	scale returns the scaling factor of the Lyapunov equation.
	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.

Lyapunov Equations Details

The following equation defines the continuous Lyapunov equation:

AX + XA^H = αB

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 _i + ^*_j ≠ 0 for all eigenvalues of A, where ^* is the complex conjugate of .

The following equation defines the discrete Lyapunov equation:

AXA^H – X = αB

where A^H 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 _i^*_j ≠ 1 for all eigenvalues of A, where ^* is the complex conjugate of .