A necessary and sufficient condition in Lyapunov robust control
We consider Lyapunov's equation \(PA+A^ TP+Q=0\), where Q is symmetric positive definite and A is in controllable companion form. We prove that a necessary and sufficient condition that A be stable is that the first row \(P_ 1\) of the P-matrix be a stable n-1 coefficient vector. This result is related to the minimum phase property of linear systems and is useful in designing robust controllers.
scientific article; zbMATH DE number 4085512
scientific article