
ICANNGA'07 tutorial on
Selected Mathematical Equations of Contemporary Technology
Tadeusz Kaczorek
Institute of Control and
Industrial Electronics
Warsaw University
of Technology
Warsaw, Poland
The talk will be consisting of two parts. The
first part will be devoted to some recent developments of selected
mathematical matrix equations. A special attention will be focused on the
matrix Sylvester equation, the matrix Lyapunov equation and the matrix
Riccati equation. The polynomial matrix equations will be also discussed.
The numerical aspects of solutions to the equations will be considered and
illustrated by numerical examples. Some applications of the equations in
engineering problems will be also demonstrated.
The second part will be devoted to some new extensions of the classical
CayleyHamilton theorem for nD polynomial matrices, the block matrices, the
coefficients matrices of the impulse response matrices, the right and left
inverse matrices and for timevarying and nonlinear systems. It will be
shown that the extensions are useful not only in systems and control systems
theory but they can be also applied in solving many engineering problems.
Basic references

B.N.Datta, Numerical Methods for Linear Control
Systems, Amsterdam, Elsevier 2003.

T.Kaczorek, Theory of Polynomial and Rational
Matrices, SpringerVerlag,
London 2006

T.Kaczorek, Generalizations of CayleyHamilton
Theorem for nD Polynomial Matrices, IEEE Trans.Autom.
Contr.vol.50,No.5,2005,pp.671674

T.Kaczorek, An Extension of the CayleyHamilton
Theorem for Nonlinear TimeVarying Systems, Int. J. Appl. Math. Comput. Sci.
Vol.16,No.1,2006, pp. 141145.

T.Kaczorek, New Extensions of the
CayleyHamilton Theorem with Applications, Pro. 19th European Conf. on
Modelling and Simulation June 14, 2005, Riga, Latvia, pp.119124.
Tadeusz Kaczorek
received the MSc., PhD and DSc degrees from Electrical Engineering of Warsaw
University of Technology in 1956, 1962 and 1964, respectively. In the period
1968  69 he was the dean of Electrical Engineering Faculty and in the
period 1970  73 he was the prorector of Warsaw University of Technology.
Since 1971 he has been professor and since 1974 full professor at Warsaw
University of Technology. In 1986 he was elected a corresp. member and in
1996 full member of Polish Academy of Sciences. In the period 1988  1991 he
was the director of the Research Centre of Polish Academy of Sciences in
Rome. In June 1999 he was elected the full member of the Academy of
Engineering in Poland. In May 2004 he was elected the honorary member of the
Hungarian Academy of Sciences. He was awarded by the title doctor honoris
causa by the University of Zielona Góra (2002), the Technical University of
Lublin (2004), the Technical University of Szczecin (2004), Warsaw
University of Technology 2004. His research interests cover the theory of
systems and the automatic control systems theory, specially, singular
multidimensional systems, positive multidimensional systems and singular
positive 1D and 2D systems. He has initiated the research in the field of
singular 2D and positive 2D linear systems. He has published 17 books (5 in
English) and over 600 scientific papers in journals like IEEE Transactions
on Automatic Control, IEEE Transactions on Neural Networks, Multidimensional
Systems and Signal Processing, International Journal of Control, Bull. Pol.
Acad. Sciences, etc. and proceedings of conferences. He has presented more
than 80 invited papers on international conferences and world congresses. He
has given invited lectures in more than 50 universities in USA, Canada, UK,
Germany, Italy, France, Japan, Greece etc. He has been a member of many
international committees and programme committees. He
supervised over 60 Ph.D. theses. More than 20 of this PhD students became
professors in USA, UK and Japan. He is editorinchief of Bulletin of the
Polish Academy of Sciences, Techn. Sciences and editorial member of about
ten international journals.
