Stabilizing a SISO LTI Plant With Gain and Delay Margins as Large as Desired

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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 gain and time delay margins as large as desired; to do so, we propose the use of a non-linear time varying (NLTV) controller. Despite being NLTV, the proposed controller is relatively simple and the time variation is periodic; furthermore, the controller is noise tolerant, guarantees the exponential decay of the plant initial conditions, tolerates occasional jumps in the gain and delay and is robust to un-modelled dynamics.