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A priori bounds and periodic solutions for a class of planar systems with applications to LotkaVolterra equations
Feedback control of noise in a 2D nonlinear structural acoustics model
1.  Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 276958212, United States 
2.  ICASE, NASA Langley Research Center, Hampton, VA 23681, United States 
[1] 
Andrew D. Lewis, David R. Tyner. Geometric Jacobian linearization and LQR theory. Journal of Geometric Mechanics, 2010, 2 (4) : 397440. doi: 10.3934/jgm.2010.2.397 
[2] 
Sanling Yuan, Yongli Song, Junhui Li. Oscillations in a plasmid turbidostat model with delayed feedback control. Discrete and Continuous Dynamical Systems  B, 2011, 15 (3) : 893914. doi: 10.3934/dcdsb.2011.15.893 
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Shu Zhang, Jian Xu. Timevarying delayed feedback control for an internet congestion control model. Discrete and Continuous Dynamical Systems  B, 2011, 16 (2) : 653668. doi: 10.3934/dcdsb.2011.16.653 
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Guirong Jiang, Qishao Lu. The dynamics of a PreyPredator model with impulsive state feedback control. Discrete and Continuous Dynamical Systems  B, 2006, 6 (6) : 13011320. doi: 10.3934/dcdsb.2006.6.1301 
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Haiying Jing, Zhaoyu Yang. The impact of state feedback control on a predatorprey model with functional response. Discrete and Continuous Dynamical Systems  B, 2004, 4 (3) : 607614. doi: 10.3934/dcdsb.2004.4.607 
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Junyoung Jang, Kihoon Jang, HeeDae Kwon, Jeehyun Lee. Feedback control of an HBV model based on ensemble kalman filter and differential evolution. Mathematical Biosciences & Engineering, 2018, 15 (3) : 667691. doi: 10.3934/mbe.2018030 
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Yuan Tan, Qingyuan Cao, Lan Li, Tianshi Hu, Min Su. A chanceconstrained stochastic model predictive control problem with disturbance feedback. Journal of Industrial and Management Optimization, 2021, 17 (1) : 6779. doi: 10.3934/jimo.2019099 
[8] 
Pedro M. Jordan. Finiteamplitude acoustics under the classical theory of particleladen flows. Evolution Equations and Control Theory, 2019, 8 (1) : 101116. doi: 10.3934/eect.2019006 
[9] 
Kazuyuki Yagasaki. Optimal control of the SIR epidemic model based on dynamical systems theory. Discrete and Continuous Dynamical Systems  B, 2022, 27 (5) : 25012513. doi: 10.3934/dcdsb.2021144 
[10] 
Qizhen Xiao, Binxiang Dai. Heteroclinic bifurcation for a general predatorprey model with Allee effect and state feedback impulsive control strategy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 10651081. doi: 10.3934/mbe.2015.12.1065 
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Qiying Hu, Chen Xu, Wuyi Yue. A unified model for state feedback of discrete event systems II: Control synthesis problems. Journal of Industrial and Management Optimization, 2008, 4 (4) : 713726. doi: 10.3934/jimo.2008.4.713 
[12] 
Heinz Schättler, Urszula Ledzewicz. Perturbation feedback control: A geometric interpretation. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 631654. doi: 10.3934/naco.2012.2.631 
[13] 
Barbara Kaltenbacher. Mathematics of nonlinear acoustics. Evolution Equations and Control Theory, 2015, 4 (4) : 447491. doi: 10.3934/eect.2015.4.447 
[14] 
Antonio Fernández, Pedro L. García. Regular discretizations in optimal control theory. Journal of Geometric Mechanics, 2013, 5 (4) : 415432. doi: 10.3934/jgm.2013.5.415 
[15] 
K. Renee Fister, Jennifer Hughes Donnelly. Immunotherapy: An Optimal Control Theory Approach. Mathematical Biosciences & Engineering, 2005, 2 (3) : 499510. doi: 10.3934/mbe.2005.2.499 
[16] 
Rohit Gupta, Farhad Jafari, Robert J. Kipka, Boris S. Mordukhovich. Linear openness and feedback stabilization of nonlinear control systems. Discrete and Continuous Dynamical Systems  S, 2018, 11 (6) : 11031119. doi: 10.3934/dcdss.2018063 
[17] 
Fatihcan M. Atay. Delayed feedback control near Hopf bifurcation. Discrete and Continuous Dynamical Systems  S, 2008, 1 (2) : 197205. doi: 10.3934/dcdss.2008.1.197 
[18] 
Elena Braverman, Alexandra Rodkina. Stabilization of difference equations with noisy proportional feedback control. Discrete and Continuous Dynamical Systems  B, 2017, 22 (6) : 20672088. doi: 10.3934/dcdsb.2017085 
[19] 
Daniel Franco, Chris Guiver, Phoebe Smith, Stuart Townley. A switching feedback control approach for persistence of managed resources. Discrete and Continuous Dynamical Systems  B, 2022, 27 (3) : 17651787. doi: 10.3934/dcdsb.2021109 
[20] 
K.F.C. Yiu, K.L. Mak, K. L. Teo. Airfoil design via optimal control theory. Journal of Industrial and Management Optimization, 2005, 1 (1) : 133148. doi: 10.3934/jimo.2005.1.133 
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