Stability of predictor-based feedback for nonlinear systems with distributed input delay

Abstract

We consider Ponomarev’s recent predictor-based control design for nonlinear systems with distributed input delays and remove certain restrictions to the class of systems by performing the stability analysis differently. We consider nonlinear systems that are not necessarily affine in the control input and whose vector field does not necessarily satisfy a linear growth condition. Employing a nominal feedback law, not necessarily satisfying a linear growth restriction, which globally asymptotically, and not necessarily exponentially, stabilizes a nominal transformed system, we prove global asymptotic stability of the original closed-loop system, under the predictor-based version of the nominal feedback law, utilizing estimates on solutions. We then identify a class of systems that includes systems transformable to a completely delay-free equivalent for which global asymptotic stability is shown employing similar tools. For these two classes of systems, we also provide an alternative stability proof via the construction of a novel Lyapunov functional. Although in order to help the reader to better digest the details of the introduced analysis methodology we focus on nonlinear systems without distributed delay terms, we demonstrate how the developed approach can be extended to the case of systems with distributed delay terms as well.