Sufficient Conditions for the Existence of a Н∝-infinity State Observer for Linear Continuous Dynamical Systems



The article deals with the problem of finding the observer of the state vector of linear continuous non-stationary dynamical systems with uncertainty of the initial conditions, limited external influences and measurement errors over a finite time interval. Sufficient conditions for the existence of an observer are formulated and proved on the basis of the expansion principle. Relationships are obtained for finding the parameters of the observer and the worst laws of change in external influences and measurement errors. As a limiting case, the problem of observer synthesis for stationary linear dynamical systems on a semi-infinite time interval is considered. Two applied problems of estimating the aircraft state vector based on the results of incomplete and inaccurate measurements are solved.

General Information

Keywords: robust estimation, state observer, sufficient conditions, expansion principle, game approach

Journal rubric: Data Analysis

Article type: scientific article


Received: 12.04.2023


For citation: Panteleev A.V., Yakovleva A.A. Sufficient Conditions for the Existence of a Н∝-infinity State Observer for Linear Continuous Dynamical Systems. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2023. Vol. 13, no. 2, pp. 36–63. DOI: 10.17759/mda.2023130202. (In Russ., аbstr. in Engl.)


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Information About the Authors

Andrey V. Panteleev, Doctor of Physics and Matematics, Professor, Head of the Department of Mathematical Cybernetics, Institute of Information Technologies and Applied Mathematics, Moscow Aviation Institute (National Research University), Moscow, Russia, ORCID:, e-mail:

Aleksandra A. Yakovleva, Master Student, Moscow Aviation Institute, Moscow, Russia, e-mail:



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