On the Robustness of Linear Stabilizing Feedback Control for Linear Uncertain Systems

We investigate linear time-invariant scalar input systems with constant uncertainties that are not required to satisfy matching conditions. In a previous paper, the existence of stabilizing discontinuous controllers are established under three assumptions for such systems. The first assumption requires controllability of the system for each uncertainty. The second is a condition on an uncertain Lyapunov equation and the third is a boundness condition related to the controllability matrix. In this paper, using the same assumptions we show the existence of a linear stabilizing control. Our result is related to the high gain theorem of classical control.