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Adaptive backstepping control of uncertain systems with unknown input time-delay. (English) Zbl 1166.93339
Summary: We establish the robustness of adaptive controllers designed using the standard backstepping technique with respect to unmodeled dynamics involving unknown input time delay. While noting that some results on robust stabilization of non-minimum phase systems using the backstepping technique are available, we realize that the standard adaptive backstepping technique has only been shown applicable to unknown minimum phase systems. Another significance of our result is to enable the class of systems stablizable by adaptive backstepping controllers to cross the boundary of minimum phase systems, since systems with input time delay belong to non-minimum phase systems. Moreover, the ${L}_{2}$ and ${L}_{\infty }$ norms of the system output are also established as functions of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters.
##### MSC:
 93C40 Adaptive control systems 93C15 Control systems governed by ODE 93B35 Sensitivity (robustness) of control systems