Discrete-Time Adaptive Control of Uncertain Sampled-Data Systems with Uncertain Input Delay: A Reduction

This study proposes a discrete-time adaptive control approach for uncertain single-input single-output linear time-invariant sampled-data systems with uncertain, constant input time delay that has a known upper-bound, without explicitly estimating the time delay. To cope with the unknown time delay, a reduction approach similar to that proposed by Artstein in 1982 is used, which results in a delay-free system that simplifies the control law design. In addition, the proposed control approach is capable of coping with bounded exogenous disturbances. A rigorous stability analysis shows that the proposed control approach drives the system output to a bound around the reference signal asymptotically, in the presence of an exogenous disturbance. Moreover, simulation results are shown to verify the approach.