Discrete-Time Adaptive Control for Systems with Input Time-Delay and Non-sector Bounded Nonlinear Functions

This paper presents a discrete-time adaptive control approach for nonlinear systems with input delay. The nonlinearity is assumed to be non-sector bounded, resulting in the key technical lemma being inapplicable. The main aim of this paper is to present a general implementation inspired from Kanellakopoulos and Fu, et al. for italic uncertain scalar and multivariable input delay systems with uncertain parameters as well as uncertain input gain. While it has been shown by Kanellakopoulos and Fu, et al . that it is possible to design adaptive control laws that compensate for the growth of the nonlinearity for single parameter scalar systems, a rigorous analysis of multiple parameter systems is not shown. In this paper, it is shown that an adaptive controller design that compensates for the growth of the nonlinearity is possible for both multiple parameter scalar and multivariable systems with input delay. Rigorous stability proofs and simulations are presented to verify the validity of the approach.