Discussion on "A State Observer for a Class of Nonlinear Systems with Multiple Discrete and Distributed Time Delays

Olivier Sename (1)

1 LAG - Laboratoire d'automatique de Grenoble

Although many works have been devoted to the analysis and control of time-delay systems during the last decades [1, 2, 3], much less have concerned the observer design problem while in practice the state variables may be not all measured. As illustration recent studies concern the observer design or analysis, as [4, 5, 6, 7], as well as [8, 9, 10] in the nonlinear case. Problems solved in the reported results include algebraic approaches to the study of observability properties for time-delay systems and the corresponding observer design (in the linear and nonlinear cases), eventually with unknown input. In this paper by Alfredo Germani and Pierdomenico Pepe, a new design of state observers for nonlinear SISO systems with delays is proposed. It follows previous au- thors' contributions on this topic as [8, 9, 10]. Here, a speci¯c class of nonlinear systems is considered, i.e. systems with multiple noncommensurate as well as distributed delays (which greatly improves the existing results), but such that the output and its n¡1 derivatives depend on the present value of the system variables and do not depend on their past ones (which is a hard restriction). A nonlinear observer is proposed, extending the results in [11]. Then, under Lipschitz hypotheses, the global or local convergence of the estimation error is proved, for any prescribed decay rate. In this study some of the questions that can arise are the following: - what system representations can be considered ? - what kind of observability property is to be used ? - how to ensure global or local convergence of the ob- server ?

Domaines: Automatique / Robotique

Olivier Sename. Discussion on "A State Observer for a Class of Nonlinear Systems with Multiple Discrete and Distributed Time Delays. European Journal of Control, 2005, 11, pp.206-208. ⟨hal-00368541⟩