Abstract
This paper concerns the prediction of switching times for switching linear systems. The instance when a state trajectory exceeds a predefined threshold signal can be determined for input signals and time-varying thresholds without calculating the state-trajectories explicitly. This is obtained by transforming the switching conditions in the Orthogonal Function Domain of the Legendre polynomials. The problem of predicting the event time can be transposed into the problem of finding the minimal, positive and real root of a polynomial. In general, the event time can not be determined exactly, but approximated with sufficient accuracy.
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Kwiatkowski, A., Lichtenberg, G., Schild, A. (2003). Event Prediction for Switching Linear Systems with Time Varying Thresholds Using Orthogonal Functions. In: Maler, O., Pnueli, A. (eds) Hybrid Systems: Computation and Control. HSCC 2003. Lecture Notes in Computer Science, vol 2623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36580-X_24
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DOI: https://doi.org/10.1007/3-540-36580-X_24
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