Stabilizing any SISO LTI plant with an arbitrarily large unknown delay and unknown B matrix

Handling delays and uncertain parameters in control systems is difficult and of long-standing interest. In this paper, we consider the problem of bounded-input bounded-output stabilizing any single-input single-output, linear time-invariant, controllable/observable plant with an arbitrarily large unknown time delay and a large amount of uncertainty in the B matrix of the state-space model. Despite being nonlinear time-varying, the proposed controller is relatively simple, the non-linearity is mild and the time variation is periodic; furthermore, the controller also guarantees the exponential decay of any initial conditions.