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Polytopic observer designs for uncertain linear systems
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DOI：10.1016/j.ejcon.2025.101338.png)
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Abstract
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This article introduces polytopic observer designs for discrete- and continuous-time linear systems with bounded uncertainties. In particular, by noting that polytopes are equivalent to constrained zonotopes with intervals in their generator spaces, we propose two choices of generators to fix the order of the polytopic observer. Moreover, this observation enables us to leverage existing interval observers to find interval estimates in the augmented generator space before projecting them onto the original state space as polytopes/constrained zonotopes. Further, we prove that the polytopic observers are at least as good as interval observers for the same uncertain linear system in terms of the volumes of their set estimates and the error system gains. As a side contribution, we also introduce a more computationally efficient approach to obtain interval observer gains. Finally, we demonstrate and discuss the effectiveness of the proposed approach on a broad range of examples.
Keywords:
Observers for linear systems
Polytopic observers
Uncertain systems
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