Robust energy-to-peak filter design for a class of unstable polytopic systems with a macroeconomic application
•The notion and the design method of robust energy-to-peak filtering has been extended to a class of unstable systems. The basic tool is the theory of set stability.•It is shown that the derivation of the design conditions for the robust filters can be performed both for continuous- and discrete-tim...
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Veröffentlicht in: | Applied mathematics and computation 2022-05, Vol.420, p.126729, Article 126729 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | •The notion and the design method of robust energy-to-peak filtering has been extended to a class of unstable systems. The basic tool is the theory of set stability.•It is shown that the derivation of the design conditions for the robust filters can be performed both for continuous- and discrete-time systems simultaneously in unified frames.•The developed filter is applied to a macroeconomic problem, which was not solvable with the methods proposed in the literature before.
This paper deals with the robust energy-to-peak filtering problem for linear continuous- and discrete-time systems with polytopic uncertainties. Motivated by a macroeconomic application, the notion of the robust energy-to-peak filter is extended to a class of unstable systems by making use of the results on stability with respect to noncompact sets. Parameter-dependent Lyapunov approach and Finsler’s lemma are used to establish sufficient conditions for the existence of energy-to-peak filter such that the error system is asymptotically stable with respect to a subspace and a prescribed energy-to-peak performance is guaranteed. The conditions are formulated in terms of linear matrix inequalities (LMIs). Two numerical examples modified from the literature are provided to demonstrate the effectiveness of the proposed method. The results are also successfully applied to the estimation of the so called potential GDP using real data. |
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ISSN: | 0096-3003 1873-5649 |
DOI: | 10.1016/j.amc.2021.126729 |