The classical Cayley-Hamilton theorem is extended to continuous-time linear systems with delays. The matrices of the system with delays satisfy algebraic matrix equations with coefficients of the characteristic polynomial.
Institute of Control and Industrial Electronics,Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland
Busłowicz M. and Kaczorek T. (2004): Reachability and minimum energy control of positive linear discrete-time systems with one delay. - Proc. 12-th Mediterranean Conf. s Control and Automation, Kasadasi, Turkey: Izmir (on CD-ROM).
Chang F.R. and Chan C.N. (1992): The generalized Cayley-Hamilton theorem for standard pencis. - Syst. Contr. Lett., Vol. 18, No. 192, pp. 179-182
Gałkowski K. (1996): Matrix description of multivariable polynomials. - Lin. Alg. and Its Applic., Vol. 234, No. 2, pp. 209-226.
Gantmacher F.R. (1974): The Theory of Matrices. - Vol. 2.-Chelsea: New York.
Kaczorek T. (19921993): Linear Control Systems. -Vols. I, II, Tauton: Research Studies Press.
Kaczorek T. (1994): Extensions of the Cayley-Hamilton theorem for 2D continuous-discrete linear systems. - Appl. Math. Comput. Sci., Vol. 4, No. 4, pp. 507-515.
Kaczorek T. (1995a): An existence of the Cayley-Hamilton theorem for singular 2D linear systems with non-square matrices. - Bull. Pol. Acad. Techn. Sci., Vol. 43,No. 1, pp. 39-48.
Kaczorek T. (1995b): An existence of the Cayley-Hamilton theorem for nonsquareblock matrices and computation of the left and right inverses of matrices. -Bull. Pol. Acad. Techn. Sci., Vol. 43, No. 1, pp. 49-56.
Kaczorek T. (1995c): Generalization of the Cayley-Hamilton theorem for nonsquare matrices.- Proc. Int. Conf. Fundamentals of Electrotechnics and Circuit Theory XVIII-SPETO, Ustron-Gliwice, Poland, pp. 77-83.
Kaczorek T. (1998): An extension of the Cayley-Hamilton theorem for a standard pair of block matrices. - Appl. Math. Comput. Sci., Vol. 8, No. 3, pp. 511-516.
Kaczorek T. (2005): Generalization of Cayley-Hamilton theorem for n-D polynomial matrices. - IEEE Trans. Automat. Contr., No. 5, (in press).
Lancaster P. (1969): Theory of Matrices. -New York, Academic, Press.
Lewis F.L. (1982): Cayley-Hamilton theorem and Fadeev's method for the matrix pencil [sE-A]. - Proc. 22nd IEEE Conf. Decision and Control, San Diego, USA, pp. 1282-1288.
Lewis F.L. (1986): Further remarks on the Cayley-Hamilton theorem and Fadeev's method for the matrix pencil [sE-A]. - IEEE Trans. Automat. Contr., Vol. 31, No. 7, pp. 869-870.
Mertizios B.G and Christodoulous M.A. (1986): On the generalized Cayley-Hamilton theorem. - IEEE Trans. Automat. Contr., Vol. 31, No. 1, pp. 156-157.
Smart N.M. and Barnett S. (1989): The algebra of matrices in n-dimensional systems. - Math. Contr. Inf., Vol. 6, No. 1, pp. 121-133.