Title | Optimal evaluation of linear time-varying systems using reachable sets |
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Authors | M. S. Sorokina^{1}^{1}Lobachevsky State University of Nizhny Novgorod |

Annotation | The paper is devoted to reachable sets of linear time-varying systems under uncertain initial states and disturbances with a bounded uncertainty measure. The uncertainty measure is the sum of a quadratic form of the initial state and the integral over the finite-time interval from a quadratic form of the disturbance. Method of evaluation of ellipsoidal reachable sets has been cosidered for such systems. Applying this method allows to find minimal ellipsoidal set that is defined by optimal observer. Numerical modeling with the Mathieu-Hill equation for parametric vibrations and resonance illustrates this method. |

Keywords | reachable sets, ellipsoidal sets, chemical reaction, optimal observer |

Citation | Sorokina M. S. ''Optimal evaluation of linear time-varying systems using reachable sets'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, October 8-11, 2020). Saransk: SVMO Publ, 2020. - pp. 252-258. Available at: http://conf.svmo.ru/files/2020/papers/article14.pdf. - Date of access: 03.12.2021. |

**© SVMO, National Research Mordovia State University, 2021**

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