Sylvester Equation Observability

Available identifiers

MaRDI QIDQ6674464

Sylvester equation for the observability of a linear control system

Description

Except for the use of the reduced matrices (tilde-notation), there is a formal similarity with the Lyapunov equations for the calculations of Gramians. However, note the sign change in the CC term.

---

Defining Formula: $\tilde{A}Y+Y{A}^{*}-C{\tilde{C}}^{*}=0$

$A$ symbol represents Control System Matrix A

$C$ symbol represents Control System Matrix C

$\tilde{A}$ symbol represents Control System Matrix A (Reduced)

$\tilde{C}$ symbol represents Control System Matrix C (Reduced)

$Y$ symbol represents Unknown Matrix

---

---