Abstract
The problem of synthesizing an asymptotic observer for a linear system with \(l\) measurable outputs \(y=Cx\) and \(m\) unknown inputs \(f(t)\) acting on the system through the matrix \(D\) is considered. A case of hyperoutput systems is examined; such systems have output dimensions larger than that of an unknown input (\(l>m\)). Ways of constructing observers are well-known for such systems when matrix \(CD\) (the transfer matrix from input \(f(t)\) to output \(y(t)\)) is of full rank. The case \(\textrm{rank}(CD)<m\) is considered. To solve the problem, the concept of relative order is generalized to the case of non-quadratic systems. Using this concept, a sufficient condition for the existence of an observer is formulated, and an algorithm for synthesizing the observer is proposed.
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Funding
The work was supported by the Russian Foundation for Basic Research, project nos. 18-07-00540 and 18-51-00004.
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Translated by E. Oborin
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Fomichev, V.V., Kraev, A.V. & Tevdoradze, S.Z. Synthesizing Asymptotic Observers for Hyperoutput Systems with Uncertainty upon Transfer Matrix Degeneracy. MoscowUniv.Comput.Math.Cybern. 44, 44–52 (2020). https://doi.org/10.3103/S0278641919040058
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DOI: https://doi.org/10.3103/S0278641919040058