Lyapunov Equations VI
- Updated2025-07-30
- 2 minute(s) read
Solves the Lyapunov matrix equation. The data types you wire to the A and B inputs determine the polymorphic instance to use.
The following equation defines the continuous Lyapunov equation:
AX + XAH = αBwhere 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 = αBwhere 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.