A formula for frequency responses of distributed systems with one spatial variable

Systems and Control Letters

Volumn 55, Issue 1, 2006, Pages 27-37

  Jovanović, Mihailo R ^a   Bamieh, Bassam ^b  

^a University of Minnesota   (United States)

^b University of California   (United States)

Author keywords

Frequency responses; Infinite dimensional systems; Two point boundary value state space realizations

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL METHODS; FREQUENCY RESPONSE; MATHEMATICAL OPERATORS; MATRIX ALGEBRA;

DIFFERENTIAL OPERATORS; HILBERT-SCHMIDT NORM; INFINITE-DIMENSIONAL SYSTEM; TWO POINT BOUNDARY VALUE STATE-SPACE REALIZATION (TPBVSR);

DISTRIBUTED PARAMETER CONTROL SYSTEMS;

EID: 28444453271     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2005.04.014     Document Type: Article

References (13)

1. P.J. Antsaklis, and A.N. Michel Linear Systems 1997 McGraw-Hill New York
2. B. Bamieh, and M. Dahleh Energy amplification in channel flows with stochastic excitation Phys. Fluids 13 2001 3258 3269
3. 2 norms for a class of infinite dimensional problems IEEE Trans. Automat. Control 48 2003 646 649
4. C.T. Chen Linear System Theory and Design 1998 Oxford University Press Oxford
5. R.F. Curtain, and H.J. Zwart An Introduction to Infinite-Dimensional Linear Systems Theory 1995 Springer New York
6. R.C. DiPrima, and G.J. Habetler A completeness theorem for non-selfadjoint eigenvalue problems in hydrodynamic stability Arch. Rat. Mech. Anal. 34 1969 218 227
7. I. Gohberg, and M.A. Kaashoek Time varying linear systems with boundary conditions and integral operators, I. The transfer operator and its properties Integral Equations Operator Theory 7 1984 325 391
8. M.R. Jovanović, modeling, analysis, and control of spatially distributed systems, Ph.D. Thesis, University of California, Santa Barbara, 2004. available at http://www.ece.umn.edu/users/mihailo/
9. M.R. Jovanović, and B. Bamieh Frequency domain analysis of the linearized Navier-Stokes equations Proceedings of the 2003 American Control Conference Denver, CO 2003 3190 3195
10. M.R. Jovanović, B. Bamieh, Componentwise energy amplification in channel flows, J. Fluid Mech. 534 (2005) 145-183.
11. S.C. Reddy, and D.S. Henningson Energy growth in viscous channel flows J. Fluid Mech. 252 1993 209 238
12. P.J. Schmid, and D.S. Henningson Stability and Transition in Shear Flows 2001 Springer New York
13. N. Young An introduction to Hilbert Spaces 1988 Cambridge University Press New York