Extension of The Cayley-Hamilton Theorem to Continuous-time Linear Systems With Delays

Kaczorek, T.

International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 2, pp. 231-234.

Résumé

The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices A_0, A_1, dots, A_h in R^n times n of the system with h delays dot xleft(t right) = A_0 xleft(t right) + sum_i = 1^h A_i xleft( t - hi right) + Buleft( t right) satisfy nh + 1 algebraic matrix equations with coefficients of the characteristic polynomial pleft( s,wright) = det left[ I_n s - A_0 - A_1 w - cdots - A_h w^h right], w = e^- hs.

Détail

Keywords: Cayley-Hamilton theorem, continuous time, linear system, delay, extension
Mots-clés : twierdzenie Cayleya-Hamiltona, czas ciągły, system liniowy, opóźnienie, rozszerzenie

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