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Observer-based control of a class of time-delay nonlinear systems having triangular structure. (English) Zbl 1207.93015
Summary: Time-delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering. It has been shown in the literature that the existence of a stabilizing observer-based controller is related to delay-dependent conditions that are generally satisfied for a small time delay. Motivating works towards reducing the conservatism of the results are among the on-going research topics especially when partial-state measurements are imposed. This paper investigates the problem of observer-based stabilization of a class of time-delay nonlinear systems written in triangular form. First, we show that a delay nonlinear observer is globally convergent under the global Lipschitz condition of the system nonlinearity. Then, it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay. An illustrative example is provided to approve the theoretical results.

93B07 Observability
93C10 Nonlinear systems in control theory
93D20 Asymptotic stability in control theory
93C15 Control/observation systems governed by ordinary differential equations
Full Text: DOI
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