Geng-Sheng Wang

Endpoint Asymptotics of Optimal Stabilization Prefactors

Consider the stabilizable finite-dimensional linear control system $\dot x=Ax+Bu$. For a prescribed decay rate $\delta>0$, we define the optimal stabilization prefactor $$ \hat{C}(\delta) := \inf_{K\in\mathbb{R}^{m\times n}} \sup_{t\ge0}e^{\delta t}\|e^{(A+BK)t}\|. $$ We determine its asymptotic behavior as $\delta$ ap...