Stabilization of linear strict-feedback systems with delayed integrators |
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Authors: | Nikolaos Bekiaris-Liberis [Author Vitae] Miroslav Krstic [Author Vitae] |
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Affiliation: | Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093-0411, USA |
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Abstract: | 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. |
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Keywords: | Delay systems Predictor Strict-feedback systems |
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