On the Cayley-Hamilton theorem for two-dimensional systems

Ciftcibasi, T.; Yüksel, Oğuz Kaan

doi:10.1109/tac.1982.1102890

Cited by 20 publications

(1 citation statement)

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“…The Cayley-Hamilton theorem have been investigated for the matrix pencil case A (s) = A 0 + A 1 s by [5] and the respective relative Cayley-Hamilton theorem by [4]. The Cayley-Hamilton theorem has been extended to matrix polynomials [2], [14], [15], to standard and singular two variable matrix pencils [7], [8], [10], [11], [18] and M-D matrix pencils by [9], [17]. The reason of interest in the Caley-Hamilton theorem is due to its applications in control systems i.e.…”

Section: Introductionmentioning

confidence: 99%

On the computation of the minimal polynomial of a two-variable polynomial matrix

Tzekis

Karampetakis

2005

The Fourth International Workshop on Multidimensional Systems, 2005. NDS 2005.

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The main contribution of this work is to provide an algorithm for the computation of the minimal polynomial of a two variable polynomial matrix, based on the solution of linear matrix equations. The whole theory is implemented via an illustrative example.theorem, characteristic polynomial. be the matrices thar contains the i mod r columns of the matrix @ and Ki be the matrices that contain the i columns ufthe matrix 5. (12) has the following sofurion P200!P201!p210,P200 E RP211 = 0,PlOo = 0 PlOl = -P20o,P10z = -1 -PZOl PllO = --P200,PllI = -1 -pz10 -p20l,Pllz = 0 PlZO = -1 -P210,?7121 = O,P122 = 0 PO00 o!pOOI 0, PW2 = 0, Po03 0, PO10 = 0 PO11 = p2001p012 1 -k p2Dl,p013 = 0 PO20 = 0,POZl E 1 +P2101P022 = 0 PO23 = 07P030 = 0 Po31 = 0, PO32 0, PO33 = 0 and thergfore an annihilatingpolynomiai of third order is given by i=o j=o k=O

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