# Robust stabilization by linear output delay feedback

French, Mark, Ilchmann, Achim and Mueller, Markus (2009) Robust stabilization by linear output delay feedback. SIAM Journal on Control and Optimization, 48, (4 ), 2533-2561.

The main result establishes that if a controller $C$ (comprising of a linear feedback of the output and its \emph{derivatives}) globally stabilizes a (nonlinear) plant $P$, then global stabilization of $P$ can also be achieved by an output feedback controller $C[h]$ where the output derivatives in $C$ are replaced by an Euler approximation with sufficiently small delay $h>0$. This is proved within the conceptual framework of the nonlinear gap metric approach to robust stability. The main result is then applied to finite dimensional linear minimum phase systems with unknown coefficients but known relative degree and known sign of the high frequency gain. Results are also given for systems with non-zero initial conditions.