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Stabilization of linear strict-feedback systems with delayed integrators. (English) Zbl 1218.93073
Summary: The problem of compensation of input delays for unstable linear systems was solved in the late 1970s. Systems with simultaneous input and state delay have remained a challenge, although exponential stabilization has been solved for systems that are not exponentially unstable, such as chains of delayed integrators and systems in the ‘feedforward’ form. We consider a general system in strict-feedback form with delayed integrators, which is an example of a particularly challenging class of exponentially unstable systems with simultaneous input and state delays, and design a predictor feedback controller for this class of systems. Exponential stability is proven with the aid of a Lyapunov-Krasovskii functional that we construct using the PDE backstepping approach.

MSC:
93D15 Stabilization of systems by feedback
93C05 Linear systems in control theory
93D30 Lyapunov and storage functions
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