On the Stability Verification of Adaptive Uncertain and Coupled Dynamical Discrete-Time Systems

In the controlled uncertain coupled dynamical systems employing standard model reference adaptive methods, stability is guaranteed either under minimally coupled dynamics or negligible system uncertainties. Thus, significant uncertainties and coupled dynamics in an uncertain system can lead to instability. In recent papers, continuous-time adaptive architectures are derived to compensate for uncertainties and coupled dynamics together. However, discretizing such algorithms doesn't guarantee the stability of the system directly since it complicates the Lyapunov analysis in discrete-time. This makes it challenging to generalize successful continuous-time adaptive control results to discrete-time environments. Thus, this article includes the stability verification for adaptive uncertain and coupled dynamical discrete-time systems and shows the efficacy of the novel controller over the standard ones through two illustrative examples.