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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.

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