Abstract
Recently, an adaptive distributed observer for a class of uncertain leader systems was established over undirected connected graphs. In this paper, we further study the same problem over directed connected graphs. It is shown that, if the graph is acyclic, then an adaptive distributed observer exists in the sense that it can not only estimate the leader’s state, but also the unknown parameters of the leader’s system matrix exponentially.
This work has been supported in part by the Research Grants Council of the Hong Kong Special Administration Region under grant No. 14201418 and in part by Projects of Major International (Regional) Joint Research Program NSFC (Grant no. 61720106011).
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Appendix
Appendix
The following lemma is rephrased from Lemma B.2.3 of [3].
Lemma 6
Consider the following linear time-varying system
where 
is Hurwitz, 
is a symmetric positive definite matrix satisfying \(A^TP+PA=-Q\) with Q some symmetric positive definite matrix, and 
is some symmetric positive definite matrix. If \(\Vert \varOmega (t)\Vert \) and \(\Vert \dot{\varOmega }(t)\Vert \) are uniformly bounded and \(\varOmega (t)\) is persistently exciting, then, the origin of system (28) is exponentially stable.
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Wang, S., Huang, J. (2019). Adaptive Distributed Observer for an Uncertain Leader over Directed Acyclic Graphs. In: Lu, H., Tang, H., Wang, Z. (eds) Advances in Neural Networks – ISNN 2019. ISNN 2019. Lecture Notes in Computer Science(), vol 11555. Springer, Cham. https://doi.org/10.1007/978-3-030-22808-8_3
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DOI: https://doi.org/10.1007/978-3-030-22808-8_3
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