On the Observability of Nonlinear and Switched Systems

Wei Kang 1 Jean-Pierre Barbot 2, 3 Liang Xu 4
2 ALIEN - Algebra for Digital Identification and Estimation
Inria Lille - Nord Europe, Inria Saclay - Ile de France, Ecole Centrale de Lille, X - École polytechnique, CNRS - Centre National de la Recherche Scientifique : UMR8146
Abstract : In this paper, new concept of observability are introduced for both nonlinear systems and switched systems. The new definitions are applicable to a much broader family of problems of estimation including unmeasured state variables, unknown input, and unknown parameters in control systems. It is also taken into account the notion of partial observability which is useful for complex or networked systems. For switched systems, the relationship between the observability and hybrid time trajectories is analyzed. It is proved that a switched system might be observable even when individual subsystems are not. Another topic addressed in this paper is the measure of observability, which is able to quantitatively define the robustness and the precision of observability. It is shown that a system can be perfectly observable in the traditional sense, but in the case of high dimensions, it is practically unobservable (or extremely weekly observable). Moreover, computational algorithm for nonlinear systems is developed to compute the observability with precision. Several examples are given to illustrate the fundamentals and the usefulness of the results.
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Submitted on : Saturday, November 6, 2010 - 1:05:06 PM
Last modification on : Wednesday, January 23, 2019 - 10:29:23 AM


  • HAL Id : inria-00533451, version 1



Wei Kang, Jean-Pierre Barbot, Liang Xu. On the Observability of Nonlinear and Switched Systems. Ghosh, Bijoy; Martin, Clyde F.; Zhou, Yishao. Emergent Problems in Nonlinear Systems and Control, 393, Springer, 2010, Lecture Notes in Control and Information Sciences,, 978-3-642-03626-2. ⟨inria-00533451⟩



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