Abstract
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 using matrix differential Riccati equation. Applying this method allows to find minimal ellipsoidal set that is defined by optimal observer. Besides, linear time-varying system with parametric time-varying uncertainty is being examined. Evaluation of ellipsoidal reachable sets is also given in the article. Applying the both methods is demonstrated with numerical modeling with the Mathieu-Hill equation for parametric vibrations and resonance illustrates this method and pendulum equation. Euler iterative method is applied to compute required evaluations.
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