Barbagallo, A., Sipp, D. & Schmid, P. 2009 Closed-loop control of an open cavity flow. Part 2. Reduced-order models based on balanced truncation. J. Fluid Mech. 641, 1–50.
Chen, C. T. 1970 Introduction to Linear System Theory. Rinehart and Winston.
Cross, M. C. & Hohenberg, P. C. 1993 Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112.
Drazin, P. G. & Reid, W. H. 1982 Hydrodynamic Stability. Cambridge Monographs on Mechanics and Applied Mechanics, Cambridge University Press.
Gottlieb, D. & Orszag, S. A. 1981 Numerical Analysis of Spectral Methods: Theory and Applications. SIAM.
Holmes, P., Lumley, J. L. & Berkooz, G. 1998 Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge University Press.
Howle, L. E. 1997 Linear stability analysis of controlled Rayleigh–Bénard convection using shadowgraphic measurement. Phys. Fluids 9, 3111–3113.
Lall, S., Marsden, J. E. & Glavaski, S. 2002 A subspace approach to balanced truncation for model reduction of nonlinear control systems. Intl J. Robust Nonlinear Control 12, 519–535.
Ma, Z., Ahuja, S. & Rowley, C. W. 2009 Reduced order models for control of fluids using the eigensystem realization algorithm. Theor. Comput. Fluid Dyn. (in press).
Ma, Z., Rowley, C. W. & Tadmor, G. 2010 Snapshot-based balanced truncation for linear time-periodic systems. IEEE Trans. Autom. Control 55 (2), 469–473.
Newell, A. C. & Whitehead, J. A. 1969 Finite bandwidth, finite amplitude convection. J. Fluid Mech. 38, 279–303.
Or, A. C., Cortelezzi, L. & Speyer, J. L. 2001 Robust feedback control of Rayleigh–Bénard convection. J. Fluid Mech. 437, 175–202.
Or, A. C. & Speyer, J. L. 2003 Active suppression of finite-amplitude Rayleigh–Bénard convection. J. Fluid Mech. 483, 111–128.
Or, A. C. & Speyer, J. L. 2005 Gain-scheduled controller for the suppression of convection at high Rayleigh number. Phys. Rev. E 71, 046302-1.
Or, A. C. & Speyer, J. L. 2008 Model reduction of input-output dynamical systems by proper orthogonal decomposition. J. Guid. Control Dyn. 31, 322–328.
Rowley, C. W. 2005 Model reduction for fluids, using balanced proper orthogonal decomposition. Intl J. Bifurcation Chaos 15, 997–1013.
Scherpen, J. M. A. 1993 Balancing for nonlinear systems. Syst. Control Lett. 21, 143–153.
Schlüter, A., Lortz, D. & Busse, F. H. 1965 On the stability of steady finite amplitude convection. J. Fluid Mech. 23, 129–144.
Tang, J. & Bau, H. H. 1998 Experiments on the stabilization of the no-motion state of a fluid layer heated from below and cooled above. J. Fluid Mech. 363, 153–171.
Willcox, K. & Peraire, J. 2002 Balanced model reduction via the proper orthogonal decomposition. AIAA J. 40, 2323–2330.