Generalized Inverses for a Special Structure Matrix Appearing in Control

Athanasios Pantelous, Athanasios D. Karageorgos

Abstract


In the literature of control and system theory, several explicit formulae for solving structural systemsand computing the inverse of those are appeared regularly. Recently, getting inspired from an interesting application ofcontrol for the change of the initial state of a linear system of higher order in (almost) zero time, the need for the inputcalculation, and the matrix properties of different types of generalized inverses for a special structure matrix, like

where lambda != mu != 0 have been derived, studied and considered further in the present paper. The above matrix is appearedfor the very first time in the literature of matrix theory, according to the authors’ knowledge. Two numerical examplesare also provided.


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References


S.L. Campbell and C.D. Meyer, Jr (1979), Generalized inverses of linear transformations, Dover Publications, USA.

S.C. Gupta, and L. Hasdorff, Changing the state of a linear system by use of normal function and its derivatives,

International Journal of Electronics, 14 (1963) 351-359.

S.C. Gupta, Transform and state variable methods in linear systems, Wiley New York, U.S.A, 1966.

A.D. Karageorgos, A.A. Pantelous and G.I. Kalogeropoulos, Transferring instantly the state of higher-order linear

descriptor (regular) differential systems using impulsive inputs, Journal of Control Science and Engineering, 2009

(2009) 1-32.

A.A. Pantelous, N. Karcanias and G. Halikias (2012), Approximating distributional behaviour of linear differential

systems using Gaussian function and its derivatives, International Journal of Control, 85 (7) (2012) 830-841.

A.A. Pantelous and A.D. Karageorgos, Generalized inverses of the structural matrices appearing in Control (2012)

(submitted).


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