Stabilization of Discrete-Time Time-Varying Systems Subject to Unbounded Distributed Input Delays

The stabilization problem of two categories of discrete-time linear time-varying (LTV) systems subject to unbounded distributed input delays is investigated in this article. A truncated predictor feedback law is first built for a category of systems under some common assumptions. Then, under some weakened assumptions, a predictor-type feedback law is developed for the other category of more general systems. The global exponential stability of the closed-loop systems is proved. Furthermore, the result on the truncated predictor feedback control law includes many existing results on LTV systems subject to bounded input delays and linear time-invariant (LTI) systems subject to unbounded input delays as special cases. Finally, the results of simulations validate the effectiveness of the developed control laws.