Butler, K. M., and Farrell, B. F., 1992, “Three-Dimensional Optimal Perturbations in Viscous Shear Flow,” Phys. Fluids A

[CrossRef], 4 , pp. 1637–1650.

Farrell, B. F., 1988, “Optimal Excitation of Perturbations in Viscous Shear Flow,” Phys. Fluids

[CrossRef], 31 , pp. 2093–2102.

Reddy, S. C., and Henningson, D. S., 1993, “Energy Growth in Viscous Channel Flows,” J. Fluid Mech.

[CrossRef], 252 , pp. 209–238.

Reddy, S. C.Schmid, P. J., and Henningson, D. S., 1993, “Pseudospectra of the Orr–Sommerfeld Operator,” SIAM J. Appl. Math.

[CrossRef], 53 (1), pp. 15–47.

Farrell, B. F., and Ioannou, P. J., 1996, “Generalized Stability Theory. Part I. Autonomous Operators,” J. Atmos. Sci.

[CrossRef], 53 , pp. 2025–2040.

Schmid, P. J., 2007, “Nonmodal Stability Theory,” Annu. Rev. Fluid Mech.

[CrossRef], 39 , pp. 129–162.

Schmid, P. J., and Henningson, D. S., 2001, "*Stability and Transition in Shear Flows*", Springer, New York.

Trefethen, L. N., Trefethen, A. E., Reddy, S. C., and Driscoll, T., 1993, “Hydrodynamic Stability Without Eigenvalues,” Science

[CrossRef], 261 , pp. 578–584.

Jovanovic, M. R., and Bamieh, B., 2005, “Componentwise Energy Amplification in Channel Flows,” J. Fluid Mech.

[CrossRef], 534 , pp. 145–183.

Åkervik, E., Hœpffner, J., Ehrenstein, U., and Henningson, D. S., 2007, “Optimal Growth, Model Reduction and Control in a Separated Boundary-Layer Flow Using Global Eigenmodes,” J. Fluid Mech.

[CrossRef], 579 , pp. 305–314.

Bewley, T. R., and Liu, S., 1998, “Optimal and Robust Control and Estimation of Linear Paths to Transition,” J. Fluid Mech.

[CrossRef], 365 , pp. 305–349.

Chevalier, M., Hœpffner, J., Åkervik, E., and Henningson, D. S., 2007, “Linear Feedback Control and Estimation Applied to Instabilities in Spatially Developing Boundary Layers,” J. Fluid Mech., 588 , pp. 163–187.

Chevalier, M., Hœpffner, J., Bewley, T. R., and Henningson, D. S., 2006, “State Estimation in Wall-Bounded Flow Systems. Part 2: Turbulent Flows,” J. Fluid Mech.

[CrossRef], 552 , pp. 167–187.

Hœpffner, J., Chevalier, M., Bewley, T. R., and Henningson, D. S., 2005, “State Estimation in Wall-Bounded Flow Systems. Part I: Laminar Flows,” J. Fluid Mech.

[CrossRef], 534 , pp. 263–294.

Högberg, M., Bewley, T. R., and Henningson, D. S., 2003, “Linear Feedback Control and Estimation of Transition in Plane Channel Flow,” J. Fluid Mech.

[CrossRef], 481 , pp. 149–175.

Högberg, M., Bewley, T. R., and Henningson, D. S., 2003, “Relaminarization of Reτ=100 Turbulence Using Gain Scheduling and Linear State-Feedback Control Flow,” Phys. Fluids

[CrossRef], 15 , pp. 3572–3575.

Joshi, S. S., Speyer, J. L., and Kim, J., 1997, “A Systems Theory Approach to the Feedback Stabilization of Infinitesimal and Finite-Amplitude Disturbances in Plane Poiseuille Flow,” J. Fluid Mech., 332 , pp. 157–184.

Lee, K. H., Cortelezzi, L., Kim, J., and Speyer, J., 2001, “Application of Reduced-Order Controller to Turbulent Flow for Drag Reduction,” Phys. Fluids

[CrossRef], 13 , pp. 1321–1330.

Monokrousos, A., Brandt, L., Schlatter, P., and Henningson, D. S., 2008, “DNS and Less of Estimation and Control of Transition in Boundary Layers Subject to Free-Stream Turbulence,” Int. J. Heat Fluid Flow, 29 (3), pp. 841–855.

Anderson, B., and Moore, J., 1990, "*Optimal Control: Linear Quadratic Methods*", Prentice-Hall, New York.

Kwakernaak, H., and Sivan, R., 1972, "*Linear Optimal Control Systems*", Wiley Interscience, New York.

Lewis, F. L., and Syrmos, L. V., 1995, "*Optimal Control*", Wiley, New York.

Zhou, K., Doyle, J. C., and Glover, K., 2002, "*Robust and Optimal Control*", Prentice-Hall, Englewood Cliffs, NJ.

Bewley, T. R., 2001, “Flow Control: New challenges for a New Renaissance,” Prog. Aerosp. Sci.

[CrossRef], 37 , pp. 21–58.

Gal-El-Hak, M., 1996, “Modern Developments in Flow Control,” Appl. Mech. Rev., 49 , pp. 365–379.

Kim, J., 2003, “Control of Turbulent Boundary Layers,” Phys. Fluids

[CrossRef], 15 , pp. 1093–1105.

Kim, J., and Bewley, T. R., 2007, “A Linear Systems Approach to Flow Control,” Annu. Rev. Fluid Mech.

[CrossRef], 39 , pp. 383–417.

Hill, D. C., 1995, “Adjoint Systems and Their Role in the Receptivity Problem for Boundary Layers,” J. Fluid Mech.

[CrossRef], 292 , pp. 183–204.

Luchini, P., and Bottaro, A., 1998, “Gortler Vortices: A Backward-in-Time Approach to the Receptivity Problem,” J. Fluid Mech.

[CrossRef], 363 , pp. 1–23.

Chomaz, J. M., 2005, “Global Instabilities in Spatially Developing Flows: Non-Normality and Nonlinearity,” Annu. Rev. Fluid Mech.

[CrossRef], 37 , pp. 357–392.

Huerre, P., and Monkewitz, P. A., 1990, “Local and Global Instabilities in Spatially Developing Flows,” Annu. Rev. Fluid Mech.

[CrossRef], 22 , pp. 473–573.

Cohen, K., Siegel, S., McLaughlin, T., Gillies, E., and Myatt, J., 2005, “Closed-Loop Approaches to Control of a Wake Flow Modeled by the Ginzburg–Landau Equation,” Comput. Fluids, 34 , pp. 927–949.

Lauga, E., and Bewley, T. R., 2003, “The Decay of Stabilizability With Reynolds Number in a Linear Model of Spatially Developing Flows,” Proc. R. Soc. London, Ser. A

[CrossRef], 459 , pp. 2077–2095.

Lauga, E., and Bewley, T. R., 2004, “Performance of a Linear Robust Control Strategy on a Nonlinear Model of Spatially Developing Flows,” J. Fluid Mech., 512 , pp. 343–374.

Monkewitz, P., 1989, “Feedback Control of Global Oscillations in Fluid Systems,” AIAA Paper No. 89-0991.

Park, D. S., Ladd, D. M., and Hendricks, E. W., 1993, “Feedback Control of a Global Mode in Spatially Developing Flows,” Phys. Lett. A

[CrossRef], 182 , pp. 244–248.

Briggs, R. J., 1964, "*Electron-Stream Interaction With Plasmas*", MIT, Cambridge, MA.

Huerre, P., 2000, “Open Shear Flow Instabilities,” "*Perspectives in Fluid Dynamics*", Cambridge University Press, Cambridge, England, pp. 159–229.

Chomaz, J. M., Huerre, P., and Redekopp, L. G., 1991, “A Frequency Selection Criterion in Spatially Developing Flows,” Stud. Appl. Math., 84 , pp. 119–144.

Le Dizes, S., Huerre, P., Chomaz, J. M., and Monkewitz, P. A., 1996, “Linear Global Modes in Spatially Developing Media,” Philos. Trans. R. Soc. London, Ser. A, 354 , pp. 169–212.

Monkewitz, P., 1990, “The Role of Absolute and Convective Instability in Predicting the Behavior of Fluid Systems,” Eur. J. Mech. B/Fluids, 9 , pp. 395–413.

Davies, E. B., 2002, “Non-Self-Adjoint Differential Operators,” Bull. London Math. Soc.

[CrossRef], 34 , pp. 513–532.

Trefethen, L. N., 1997, “Pseudospectra of Linear Operators,” SIAM Rev.

[CrossRef], 39 (3), pp. 383–406.

Trefethen, L. N., and Embree, M., 2005, "*Spectra and Pseudospectra: The Behavior Of Nonnormal Matrices and Operators*", Princeton University Press, Princeton, NJ.

Chomaz, J. M., Huerre, P., and Redekopp, L. G., 1991, “The Effect of Nonlinearity and Forcing on Global Modes,” "*New Trends in Nonlinear Dynamics and Pattern-Forming Phenomena*" (NATO Advanced Series Institute, Series B: Physics ), P.Coullet and P.Huerre, eds., Springer, New York, pp. 259–274.

Cossu, C., and Chomaz, J. M., 1997, “Global Measures of Local Convective Instabilities,” Phys. Rev. Lett.

[CrossRef], 78 , pp. 4387–4390.

Henningson, D. S., and Åkervik, E., 2008, “The Use of Global Modes to Understand Transition and Perform Flow Control,” Phys. Fluids

[CrossRef], 20 , p. 031302.

Hunt, R. E., and Crighton, D. G., 1991, “Instability of Flows in Spatially Developing Media,” Proc. R. Soc. London, Ser. A, 435 , pp. 109–128.

Chomaz, J. M., Huerre, P., and Redekopp, L. G., 1988, “Bifurcations to Local and Global Modes in Spatially Developing Flows,” Phys. Rev. Lett.

[CrossRef], 60 , pp. 25–28.

Chomaz, J. M., Huerre, P., and Redekopp, L. G., 1987, “Models of Hydrodynamic Resonances in Separated Shear Flows,” Sixth Symposium on Turbulent Shear Flows , Toulouse, France.

Åkervik, E., Ehrenstein, U., Gallaire, F., and Henningson, D. S., 2008, “Global Two-Dimensional Stability Measures of the Flat Plate Boundary-Layer Flow,” Eur. J. Mech. B/Fluids, 27 , pp. 501–513.

Ehrenstein, U., and Gallaire, F., 2005, “On Two-Dimensional Temporal Modes in Spatially Evolving Open Flows: The Flat-Plate Boundary Layer,” J. Fluid Mech.

[CrossRef], 536 , pp. 209–218.

Trefethen, L. N., and Bau, D., 1997, "*Numerical Linear Algebra*", SIAM, Philadelphia.

Andersson, P., Berggren, M., and Henningson, D. S., 1999, “Optimal Disturbances and Bypass Transition in Boundary Layers,” Phys. Fluids

[CrossRef], 11 , pp. 134–150.

Corbett, P., and Bottaro, A., 2001, “Optimal Linear Growth in Swept Boundary Layers,” J. Fluid Mech.

[CrossRef], 435 , pp. 1–23.

Luchini, P., 2000, “Reynolds-Number-Independent Instability of the Boundary Layer Over a Flat Surface: Optimal Perturbations,” J. Fluid Mech.

[CrossRef], 404 , pp. 289–309.

Biau, D., and Bottaro, A., 2004, “Transient Growth and Minimal Defects: Two Possible Initial Paths of Transition to Turbulence in Plane Shear Flows,” Phys. Fluids

[CrossRef], 16 , pp. 3515–3529.

Giannetti, F., and Luchini, P., 2007, “Structural Sensitivity of the First Instability of the Cylinder Wake,” J. Fluid Mech.

[CrossRef], 581 , pp. 167–197.

Pier, B., 2002, “On the Frequency Selection of Finite-Amplitude Vortex Shedding in the Cylinder Wake,” J. Fluid Mech.

[CrossRef], 458 , pp. 407–417.

Provansal, M., Mathis, C., and Boyer, L., 1987, “Bénard–von Kármán Instability: Transient and Forcing Regimes,” J. Fluid Mech.

[CrossRef], 182 , pp. 1–22.

Albarède, P., and Monkewitz, P. A., 1992, “A Model for the Formation of Oblique Shedding and “Chevron” Patterns in Cylinder Wakes,” Phys. Fluids A

[CrossRef], 4 , pp. 744–756.

Monkewitz, P. A., Williamson, C. H. K., and Miller, G. D., 1996, “Phase Dynamics of Kármán Vortices in Cylinder Wakes,” Phys. Fluids

[CrossRef], 8 , pp. 91–96.

Roussopoulos, K., and Monkewitz, P., 1996, “Nonlinear Modeling of Vortex Shedding Control in Cylinder Wakes,” Physica D

[CrossRef], 97 , pp. 264–273.

Lesshafft, L., Huerre, P., Sagaut, P., and Terracol, M., 2006, “Nonlinear Global Modes in Hot Jets,” J. Fluid Mech.

[CrossRef], 554 , pp. 393–409.

Nichols, J. W., Schmid, P. J., and Riley, J. J., 2007, “Self-Sustained Oscillations in Variable-Density Round Jets,” J. Fluid Mech.

[CrossRef], 582 , pp. 341–376.

Marquillie, M., and Ehrenstein, U., 2002, “On the Onset of Nonlinear Oscillations in a Separating Boundary-Layer Flow,” J. Fluid Mech.

[CrossRef], 458 , pp. 407–417.

Ho, C. M., and Huerre, P., 1984, “Perturbed Free Shear Layers,” Annu. Rev. Fluid Mech.

[CrossRef], 16 , pp. 365–424.

Kailath, T., 1980, "*Linear Systems*", Prentice-Hall, Englewood Cliffs, NJ.

Farrell, B. F., and Ioannou, P. J., 1993, “Stochastic Forcing of the Linearized Navier–Stokes Equations,” Phys. Fluids A

[CrossRef], 5 , pp. 2600–2609.

van der Schaft, A. J., 1991, “Duality for Linear Systems: External and State Space Characterization of the Adjoint Problem,” "*Analysis of Controlled Dynamical Systems*", B.BonnardB.Bride, J.P.Gauthier, and I.Kupka, eds., Birkhäuser, Boston, pp. 393–403.

Hœpffner, J., 2006, “Stability and Control of Shear Flows Subject to Stochastic Excitations,” Ph.D. thesis, KTH Stockholm, Stockholm.

Bamieh, B., and Dahleh, M., 2001, “Energy Amplification in Channel Flows With Stochastic Excitation,” Phys. Fluids

[CrossRef], 13 , pp. 3258–3269.

Hœpffner, J., and Brandt, L., 2008, “Stochastic Approach to the Receptivity Problem Applied to Bypass Transition in Boundary Layers,” Phys. Fluids

[CrossRef], 20 , pp. 024108.

Datta, B., 2003, "*Numerical Methods for Linear Control Systems Design and Analysis*", Elsevier, New York.

Zhou, K., Salomon, G., and Wu, E., 1999, “Balanced Realization and Model Reduction for Unstable Systems,” Int. J. Robust Nonlinear Control, 9 , pp. 183–198.

Antoulas, C. A., 2005, "*Approximation of Large-Scale Dynamical Systems*", SIAM, Philadelphia.

Lumley, J. L., 1970, "*Stochastic Tools in Turbulence*", Academic, New York.

Obintata, G., and Andersson, B. D., 2001, "*Model Reduction for Control System Design*", Springer, New York.

Green, M., and Limebeer, J. N., 1995, "*Linear Robust Control*", Prentice-Hall, Englewood Cliffs, NJ.

Skogestad, S., and Postlethwaite, I., 2005, "*Multivariable Feedback Control: Analysis and Design*", 2nd ed., Wiley, New York.

Moore, B., 1981, “Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction,” IEEE Trans. Autom. Control

[CrossRef], 26 (1), pp. 17–32.

Antoulas, A. C., Sorensen, D. S., and Gugercin, S., 2001, “A Survey of Model Reduction Methods for Large-Scale Systems,” Contemp. Math., 280 , pp. 193–219.

RowleyC. W., 2005, “Model Reduction for Fluids Using Balanced Proper Orthogonal Decomposition,” Int. J. Bifurcation Chaos Appl. Sci. Eng.

[CrossRef], 15 (3), pp. 997–1013.

Willcox, K., and Peraire, J., 2002, “Balanced Model Reduction Via the Proper Orthogonal Decomposition,” AIAA J., 40 (11), pp. 2323–2330.

Sirovich, L., 1987, “Turbulence and the Dynamics of Coherent Structures. Parts I–III,” Q. Appl. Math., 45 , pp. 561–590.

Ilak, M., and Rowley, C. W., 2008, “Modeling of Transitional Channel Flow Using Balanced Proper Orthogonal Decomposition,” Phys. Fluids

[CrossRef], 20 , p. 034103.

Ahuja, S., Rowley, C. W., Kevrekidis, I. G., and Wei, M., 2007, “Low-Dimensional Models for Control of Leading-Edge Vortices: Equilibria and Linearized Models,” 45th AIAA Aerospace Sciences Meeting and Exhibit , AIAA Paper No. 2007-709.

Joslin, R. D., 1998, “Aircraft Laminar Flow Control,” Annu. Rev. Fluid Mech.

[CrossRef], 30 , pp. 1–29.

Moin, P., and Bewley, T. R., 1994, “Feedback Control of Turbulence,” Appl. Mech. Rev., 47 (6), pp. S3–S113.

Choi, H., Moin, P., and Kim, J., 1994, “Active Turbulence Control for Drag Reduction in Wall-Bounded Flows,” J. Fluid Mech.

[CrossRef], 262 , pp. 75–110.

Bewley, T. R., and Moin, P., 1994, “Optimal Control of Turbulent Channel Flows,” "*Active Control of Vibration and Noise*", ASME DE-Vol. No. 75 , E.W.Hendricks, K.W.Wang, A.H.Von Flotow, R.Shoureshi, and T.W.Farabee, eds., ASME, New York, NY.

Bewley, T. R., Moin, P., and Temam, R., 2001, “DNS-Based Predictive Control of Turbulence: An Optimal Benchmark for Feedback Algorithms,” J. Fluid Mech., 447 , pp. 179–225.

Guégan, A., Schmid, P. J., and Huerre, P., 2006, “Optimal Energy Growth and Optimal Control in Swept Hiemenz Flow,” J. Fluid Mech., 566 , pp. 11–45.

Zuccher, P., Luchini, S., and Bottaro, A., 2006, “Algebraic Growth in a Blasius Boundary Layer: Optimal and Robust Control by Mean Suction in the Nonlinear Regime,” J. Fluid Mech., 556 , pp. 189–216.

Farrell, B. F., and Ioannou, P. J., 2000, "*Flow Control: Passive, Active and Reactive Flow Management*", Cambridge University Press, London.

Gunzburger, M. D., 1995, "*Flow Control*", Springer, Berlin.

Skelton, R., Iwasaki, T., and Grigoriadis, K., 1998, "*A Unified Algebraic Approach to Linear Control Design*", Taylor & Francis, London.

Kalman, R. E., 1960, “A New Approach to Linear Filtering and Prediction Problems,” Trans. ASME Ser. D. J. Basic Eng., 82 , pp. 24–45.

Laub, A. J., 1991, “Invariant Subspace Methods for the Numerical Solution of Riccati Equations,” "*The Riccati Equation*", S.Bittanti, A.J.Laub, and J.C.Willems, eds., Springer, Berlin, pp. 163–196.

Högberg, M., 2001, “Optimal Control of Boundary-Layer Transition,” Ph.D. thesis, KTH Stockholm, Stockholm.

Doyle, J., 1978, “Guaranteed Margins for LQG Regulators,” IEEE Trans. Autom. Control

[CrossRef], 23 , pp. 756–757.

Doyle, J. C., Glover, K., Khargonekar, P. P., and Francis, B. A., 1989, “State-Space Solutions to Standard H2and H∞ Control Problems,” IEEE Trans. Autom. Control

[CrossRef], 34 , pp. 831–847.

Kailath, T., 1973, “Some New Algorithms for Recursive Estimation in Constant Linear Systems,” IEEE Trans. Inf. Theory, 19 , pp. 750–760.

Gillies, E. A., 1998, “Low-Dimensional Control of the Circular Cylinder Wake,” J. Fluid Mech.

[CrossRef], 371 , pp. 157–178.

Ahuja, S., and Rowley, C. W., 2008, “Low-Dimensional Models for Feedback Stabilization of Unstable Steady States,” 46th AIAA Aerospace Sciences Meeting and Exhibit , AIAA Paper No. 2008-553.

Weideman, J. A. C., and Reddy, S. C., 2000, “A MATLAB Differentiation Matrix Suite,” ACM Trans. Math. Softw.

[CrossRef], 26 , pp. 465–519.

Tang, T., 1993, “The Hermite Spectral Method for Gaussian-Type Functions,” J. Sci. Comput., 14 , pp. 594–606.

Abramowitz, M., and Stegun, I. E., 1964, "*Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables*", National Bureau of Standards, Washington, DC.