Stabilizing any SISO LTI plant with an arbitrarily large uncertain gain and delay

Handling delays and uncertain parameters in control systems is difficult and of long-standing interest. In this paper, we consider the problem of stabilizing any single-input single-output (SISO) linear time invariant (LTI) controllable/observable plant with an arbitrarily large uncertain gain and time delay; to do so, we propose a non-linear time varying (NLTV) controller. Despite being NLTV, the proposed controller is relatively simple, the non-linearity is mild and the time variation is periodic; furthermore, the controller is able to provide not only bounded-input bounded-output stability, but is also able to provide linear-like bounds on the plant state when subject to an initial condition and noise.