Stabilizing a first order system with an arbitrarily large time varying delay and an uncertain gain

Handling delays and uncertain parameters in control systems is difficult and of long-standing interest. In this paper, we consider the problem of stabilizing (in a bounded-input–bounded-output sense) a first order linear time invariant plant with an arbitrarily large time varying delay and an arbitrarily large uncertain gain; we propose the use of a mildly non-linear, periodic controller, which is simple to implement. We will derive a clear, simple formula relating the maximum delay duration, the location of the unstable plant pole and the bounds on the derivative of the delay for which our controller stabilizes the system.