### Paul A. Fuhrmann

Welcome to my homepage; It is still under construction, so please excuse the mess.

## Sde Boker Workshop

Department of Mathematics,

Ben-Gurion University of the Negev,

POB 653. Beer-Sheva 84105,

Israel.

• Office Telephone: 972-8-6461616
• Home Telephone: 972-8-6469262
• e-mail:
• FAX: 972-8-6469343

Present position: Professor at the Department of Mathematics, Ben-GurionUniversity of the Negev

Research Interests:

My current research interests are in the following directions:

Algebraic System Theory, Behaviors, Observer Theory, Functional Models.

### Announcement:

In June 1996 my book: A Polynomial Approach to Linear Algebra was publishedby Springer.

A short announcementis enclosed. So are aEuropeanorder formas well as an American order form.

• You can find a collection of photos, including many members of the systemtheory community at the end of the home page.
• Any comments, suggestions for improvements are encouraged and welcome.

LECTURE NOTES:

### Books:

[3] R.W. Brockett and P.A. Fuhrmann eds. Special issue on "Linear Control Theory", Linear Algebra and its Applications, April 1983.

[4] P.A. Fuhrmann, H. Kimura and J.C. Willems eds. Special issue on "Linear Control Theory", Linear Algebra and its Applications, vols. 122-124, 1989.

[5] A.C. Antoulas, P. A. Fuhrmann, M.L.J. Hautus and Y. Yamamoto eds. Special issue on "Linear Systems", Linear Algebra and its Applications, 1993.

### Journals:

[73] P.A. Fuhrmann, "On duality in some problems of geometric control", {\em Acta Applicandae Mathematicae}, (2006), 91, 207-251.

[34] P.A. Fuhrmann, and P. S. Krishnaprasad, Towards a cell decomposition for $Rat(n)$, IMA J. Math. Contr.,Info.3 (1986), 137-150.

[15] P.A. Fuhrmann and R.W. Brockett, Normal symmetric dynamical systems,SIAM J. Control, 14 (1976), 107-119.

### Conference and Symposia Proceedings:

[9] P.A. Fuhrmann, On the partial realization problem and the recursiveinversion of Hankel and Toeplitz matrices, Contemporary Mathematics, v.47; "Linear Algebra and its Role in System Theory", Amer. Math. Soc., B. N. Datta - Editor, v.47, 149-161.

[8] P.A. Fuhrmann, Polynomial models and algebraic stability criteria,Proceedings of Joint Workshop on Synthesis of Linear and Nonlinear Systems,Bielefeld June 1981, 78-90.

[7] M.L.J. Hautus and P.A. Fuhrmann, On the zero module of rational matrix functions, Proceedings CDC Conference Albuquerque, 1980.

[6] P.A. Fuhrmann, Functional models, factorizations and linear systems,Proceedings of the NATO Advanced Study Institute on Algebraic and GeometricMethods in Linear System Theory , Harvard University June 1979, GeometricalMethods for the Theory of Linear Systems Edited by C. I. Byrnes and C.F. Martin, D. Reidel 1980, 257-282.

[5] P.A. Fuhrmann, An integrative approach to linear system theory,Proc. of the International Symposium on Mathematical Theory of Networks and Systems}, Delft July 1979, 2-13, Western Periodicals Co.

[4] P.A. Fuhrmann, On spectral minimality and fine structure of theshift realization, Distributed parameter systems: Modelling and Identification, Proceedings of the IFIP working conference, Rome 1976, Lecture Notes InControl and Information Sciences 1, Springer Verlag.

[3] P.A. Fuhrmann, Algebraic ideas in infinite dimensional system theory,Udine 1975, Lecture Notes in Economics and Mathematical Systems, vol. 13Springer Verlag 1976, 237-251.

[2] P.A. Fuhrmann, On canonical realization of sums and products ofnonrational transfer functions, Proc. of the 8th Princeton Conference on Information Sciences and Systems, 1974, 213-217.

[1] P.A. Fuhrmann, On a class of multi input-output control systemsin Hilbert space, Proc. 11th Allerton Conference on Circuit and System Theory, 1973, 30-35.

### Lecture Notes:

This is a set of lecture notes prepared for the 1998 Thematic Term on Linear Algebra and Control Theory, that took place at CIM, Coimbra,Portugal.

### Slide sets:

For the convenience of interested users, I am including several sets ofslides that I have used at various conferences. Please point out to meany mistakes that you may find. Remember: Nothing is perfect.

• This is a set of slides prepared for the IFAC Workshop on System Structureand Control that took place in Nantes, 1995. Its central themes arefactorizationand geometric control theory.
• This is a set of slides based on [54]. It deals with the parametrizationof the set of all minimal, not necessarily stable, spectralfactors.
• This is a set of slides prepared for the 1997 GAMM meeting in Regensburg.It is based on some joint work with Andrea Gombani and focuses ongeometriccontrolfrom a functional point of view.
• This set of slides was prepared for the 1997 Toeplitz Conference at TelAviv University. It reviews some applications of Toeplitzoperators to system theoretic problems. Parts are based on joint workwith Uwe Helmke, see [59].

This is a set of slides prepared for the 1997 Summer Workshop on"Mathematicsfor Systems",St. Emilion, France.

This is a set of slides prepared for the 1998 Thematic Term on LinearAlgebra and Control Theory, to take place at CIM, "Coimbra,"Portugal.

### Some Photos:

Kalman and some of his students, (L.to R.: E. Sontag, Y. Yamamoto, T. Matsuo and A.C. Antoulas). Kalman and Lions, Kalman and PF, GiorgioPicci, Roger Brockett and Jan Willems,, Brockett, Baras and Gohberg,Michel Fliess (withJan Willems and Michael Heymann in the background), grouppicture, Frascatti 1990.

Peli (Pratzel-Wolters)and UweHelmke at the Dead sea.Uwe Helmke afew years younger.PF and Raimund Ober on Massada.

The Operator Theory Conference in honour of Moshe Livsic, BGU 1997.

St. Emilion Workshop, July 1997.

Israel Gohberg's 70th Birtday Conference, Beer Sheva, 1998.