References
- D.G. Aronson, The asymptotic speed of propagation of a simple epidemic, NSF-CBMS Regional Conference Nonlinear Diffusion Equations, University of Houston, Houston, TEX, 1976, Research Notes in Mathematics, No. 14, Pitman, London, 1977, pp. 1–23
- Crandall , M and Rabinowitz , P . 1980 . “ Mathematical theory of bifurcation ” . In Bifurcation Phenomena in Mathematical Physics and Related Topics , Edited by: Bardos , C and Bessis , D . 3 – 46 . Dordrecht : Reidel .
- Kuznetsov , YA . 1998 . Elements of Applied Bifurcation Theory , New York : Springer .
- Marsden , JE and McCracken , MF . 1976 . The Hopf Bifurcation and its Applications , Berlin : Springer-Verlag .
- McCaughan , F . 1990 . Bifurcation analysis of axial flow compressor stability . SIAM J. Appl. Math. , 50 : 1232 – 1253 .
- Xiao , M . 2008 . Quantitative characteristic of rotating stall and surge for Moore-Greitzer PDE model of an axial compressor . SIAM J. Appl. Dyn. Syst. , 7 ( 1 ) : 39 – 62 .
- Landau , L and Lifshitz , E . 1959 . Fluid Mechanics , Oxford : Pergamon .
- Xiao , M . 2006 . Characterization of critical eigenvalues of axial flow engine compressor PDE model . Appl. Anal. , 85 ( 9 ) : 1123 – 1142 .
- Xiao , M and Başar , T . 2001 . Center manifold of the viscous Moore-Greitzer PDE model . SIAM J. Appl. Math. , 61 ( 3 ) : 855 – 869 .
- Crandall , M and Rabinowitz , P . 1977 . The Hopf bifurcation theorem in infinite dimensions . Arch. Ration. Mech. Anal. , 67 : 53 – 72 .
- Chow , S and Mallet-Paret , J . 1977 . Integral averaging and bifurcation . J. Differ. Eqns , 26 : 112 – 159 .
- Abed , E and Fu , J . 1986 . Local feedback stabilization and bifurcation control, I. Hopf bifurcation . Syst. Control Lett. , 7 : 11 – 17 .
- Abed , E and Fu , J . 1987 . Local feedback stabilization and bifurcation control, II. Stationary bifurcation . Syst. Control Lett. , 8 : 467 – 473 .
- Colonius , F and Kliemann , W . 1995 . Controllability and stabilization of one dimensional systems near bifurcation points . Syst. Control Lett. , 24 : 87 – 95 .
- Kang , W . 1998 . Bifurcation and normal form of nonlinear control systems, Part I . SIAM J. Control Optim. , 1 ( 36 ) : 193 – 212 .
- Kang , W . 1998 . Bifurcation and normal form of nonlinear control systems, Part II . SIAM J. Control Optim. , 1 ( 36 ) : 213 – 232 .
- Kang , W . 2000 . Bifurcation control via state feedback for systems with a single uncontrollable mode . SIAM J. Control Optim. , 38 : 1428 – 1452 .
- Hamzi , B , Kang , W and Barbot , J-P . 2004 . Analysis and Control of Hopf Bifurcations . SIAM J. Control Optim. , 42 ( 6 ) : 2200 – 2220 .
- Gu , G , Chen , X , Sparks , AG and Banda , SS . 1999 . Bifurcation stabilization with local output feedback linearization of nonlinear systems . SIAM J. Control Optim. , 30 : 934 – 956 .
- Iooss , G and Joseph , DD . 1980 . Elementary Stability and Bifurcation Theory , New York : Springer .
- Carr , J . 1981 . Applications of Centre Manifold Theory , New York : Springer-Verlag .
- Liaw , DC and Abed , EH . 1996 . Active control of compressor stall inception: A bifurcation theoretic approach . Automatica , 32 : 109 – 115 .
- Xiao , M and Başar , T . 2000 . Analysis and control of multi-mode axial flow compression system models . ASME J. Dyn. Syst. Meas. Control , 122 ( 3 ) : 393 – 401 .
- Zaslavsky , B . 1996 . Feedback stabilization of connected nonlinear oscillators with uncontrollable linearization . Syst. Control Lett. , 27 ( 3 ) : 181 – 185 .
- Xiao , M and Kang , W . 2003 . “ Control of Hopf bifurcations for infinite-dimensional nonlinear systems ” . In New Trends in Nonlinear Dynamics and Control and their Application , Edited by: Kang , W , Xiao , M and Borges , C . 101 – 116 . Berlin : Springer-Verlag .
- Kato , T . 1995 . Perturbation Theory for Linear Operators , Berlin : Springer .
- Moore , FK and Greitzer , EM . 1986 . A theory of post-stall transients in axial compression systems: Part I–Development of equations . ASME J. Eng. Gas Turbines Power , 108 : 68 – 76 .
- Day , IJ , Greitzer , EM and Cumpsty , NA . 1978 . Prediction of compressor performance in rotating stall . J. Eng. Power , 100 : 1 – 14 .