# Arthur E. Frazho

**1980 - Professor**

## Degrees

B.S.E., The University of Michigan, Ann Arbor, Computer Engineering, 1973M.S.E., The University of Michigan, Ann Arbor, Computer Information and Control Engineering, 1974

Ph.D., The University of Michigan, Ann Arbor, Computer Information and Control Engineering, 1977

## Contact

701 W. Stadium Ave.West Lafayette, IN 47907-2045

Office: ARMS 3201

Office Phone: +1 765 49-45976

Email: arthur.e.frazho.1@purdue.edu

## Interests

Control systems## Awards and Major Appointments

2006 - The W. A. Gustafson Award (teaching award)## Research Areas

This research develops and applies operator theory to problems in deterministic and stochastic control systems. These techniques are used to design models for both linear and nonlinear control systems. We also obtain fast recursive algorithms for computing reduced order models. This also yields a theory of Hinfinity controller reduction and pole placement with applications to large space structure control. Finally, these techniques are used to solve problems in signal processing and inverse scattering theory.## Publications

Mane, M., DeLaurentis, D., and Frazho, A., "A Markov Perspective on Development Interdependencies in Networks of Systems," Journal of Mechanical Design, Vol. 133, No. 10, Oct. 2011 pp. 101009-1 to 101009-9.A.E. Frazho, M.A. Kaashoek and A.C.M. Ran: "Right invertible multiplication oper- ators and stable rational matrix solutions to an associate Bezout equation, I. the least squares solution," Integral Equations and Operator Theory. 70 (2011), no. 3, 395-418.

A.E. Frazho, M.A. Kaashoek and A.C.M. Ran: "Right invertible multiplication oper- ators and stable rational matrix solutions to an associate Bezout equation, I. the least squares solution," Integral Equations and Operator Theory. 70 (2011), no. 3, 395-418.

Frazho, A.E., Kaashoek, M.A., Ran, A.C.M., "The Non-symmetric Discrete Algebraic Riccati Equation and Canonical Factroization of Rational Matrix Functions on the Unit Circle," Integral Equations and Operator Theory 66 (2010), pp. 215-229.

Du, D., Bhosri, W., & Frazho, A.E., "Multirate Filterbank Design: A Relaxed Commutant Lifting Approach IEEE Transactions on Signal Processing," Vol.-58 No. 4 (2010), pp. 2102-2112.

Frazho, A.E., Kaashoek, M.A., "A Contractive Operator View on an Inversion Formula of Gohberg-Heinig," Operator Theory: Advances and Applications, Vol. 202, (2010), pp. 223-252.

Frazho A., and Bhosri W., An Operator Perspective on Signals and Systems. Operator Theory: Advances and Applications, vol. 204, Birkhhauser-Verlag, Basel, 2010.

Frazho, A.E., ter Horst, S., and Kaashoek, M.A., "Relaxed Communtant Lifting: An Equivalent Version and a New Application,"

*Operator Theory: Advances and Applications*,

**187**(2008), pp. 157-168.

Frazho A.E., ter Horst, S., & Kaashoek, M.A., "All Solutions to the Relaxed Commutant Lifting Problem,"

*Acta Sci. Math.*(Szeged)},

**72**(2006), pp. 299-318.

Frazho, A.E., ter Horst, S., & Kaashoek, M.A., "Coupling and Relaxed Commutant Lifting,"

*Integral Equations and Operator Theory*,

**54**(2006), pp. 33-67.

Yagci, B., Frazho, A.E., and Sumali, H., "Determining the extension of a hydraulic cylinder using spectral estimation,"

*Journal of Sound and Vibration*, Vol. 279 (2005), pp. 487-496.

Biswas, A., Foias, C., and Frazho, A.E., "An intertwining property of positive Toeplitz operators,"

*Journal of Operator Theory*, Vol. 54, No. 2 (2005), pp. 301-322.

Bhosri, W., Frazho, A.E., and Yagci, B., "Maximal Nevanlinna-Pick Interpolation for Points in the Open Unit Disc," in Recent Advances in Operator Theory and Its Applications, Operator Theory: Advances and Applications, Vol. 160, Eds. Marinus A. Kaashoek, Sebastiano Seatzu, and Cornelis van der Mee, Boston: Birkhäuser, 2005, pp. 41-52.

Frazho, A.E., Yagci, B., and Sumali, H., "On Sinusoid Estimation in Nonstationary Noise,"

*Institute of Electrical and Electronics Engineers (IEEE) Transactions on Automatic Control*, Vol. 49, No. 5, (2004), pp. 777-781.

Frazho, A.E. and Kaashoek, M.A., "A Naimark Dilation Perspective on Nevalinna-Pick Interpolation,"

*Integral Equations and Operator Theory*,

**49**(2004), pp. 323-378.

**Book**

Frazho A., and Bhosri W.,

*An Operator Perspective on Signals and Systems. Operator Theory: Advances and Applications*, Vol. 204, BirkhÄauser-Verlag, Basel, 2010.

Corless, M.J., and Frazho, A.E.,

*Linear Systems and Control: An Operator Perspective*, Marcel Dekker, New York, 2003.

Foias C., Frazho A. E., Gohberg I., and Kaashoek M.,

*Metric Constrained Interpolation, Commutant Lifting and Systems. Operator Theory: Advances and Applications*, Vol. 100, BirkhÄauser-Verlag, Basel, 1998.

Foias C., and A. Frazho A. E.,

*The Commutant Lifting Approach to Interpolation Problems. Operator Theory: Advances and Applications*, Vol. 44, BirkhÄauser-Verlag, Basel, 1990.

## Conference Proceedings, Presentations, Invited Lectures

Du, D., Bhosri, W., Frazho. A., "Multirate Filterbank Design: Relaxed Commutant Lifting Approach," Allerton Conference in Communication Control and Computing, September 24, 2008, 8 pages.Invited Presentation, "Relaxed Commutant Lifting and Limit Theorems: Numerical Examples," Vrije Universiteit, Amsterdam, Netherlands, November 30, 2007.