LASIECKA I. Mathematical Control Theory of Coupled PDEs [M]. Philadelphia: Society for Industrial and Applied Mathematics, 2002.
KRSTIC M, SMYSHLYAEV A. Boundary Control of PDEs [M]. Philadelphia: Society for Industrial and Applied Mathematics, 2008.
SMYSHLYAEV A, KRSTIC M. Adaptive Control of Parabolic PDEs [M]. Princetion: Princeton University Press, 2010.
ANTONIO S G, KRSTIC M. Control of PDE-ODE Cascades with Neumann Interconnections [J]. Journal of the Franklin Institute, 2010, 347(1): 284-314. doi: 10.1016/j.jfranklin.2009.09.005
HE C H, XIE C K, ZHEN Z Y. Explicit Control Law of a Coupled Reaction-Diffusion Process [J]. Journal of the Franklin Institute, 2017, 354(5): 2087-2101. doi: 10.1016/j.jfranklin.2017.01.013
TANG S X, XIE C K. Stabilization for a Coupled PDE-ODE Control System [J]. Journal of the Franklin Institute, 2011, 348(8): 2142-2155. doi: 10.1016/j.jfranklin.2011.06.008
ZHEN Z Y, XIE C K, SI Y C, et al. Stabilization of the Second Order Parabolic System by Boundary Control[J]. Control Theory Applications, 2018, 35: 859-867.
TANG S X, XIE C K. State and Output Feedback Boundary Control for a Coupled PDE-ODE System [J]. Systems & Control Letters, 2011, 60(8): 540-545.
ZHOU Z C, GUO C L. Stabilization of Linear Heat Equation with a Heat Source at Intermediate Point by Boundary Control [J]. Automatica, 2013, 49(2): 448-456. doi: 10.1016/j.automatica.2012.11.005
LIU X L, XIE C K. Control Law in Analytic Expression of a System Coupled by Reaction-Diffusion Equation [J]. Systems & Control Letters, 2020, 137: 104643.
LEI Y, LIU X L, XIE C K. Stabilization of an ODE-PDE Cascaded System by Boundary Control [J]. Journal of the Franklin Institute, 2020, 357(14): 9248-9267. doi: 10.1016/j.jfranklin.2020.07.007
祝晶, 刘星岚, 谢成康. 圆柱体温度稳定的一种新方法[J]. 西南师范大学学报(自然科学版), 2020, 45(5): 45-50.
BACCOLI A, PISANO A, ORLOV Y. Boundary Control of Coupled Reaction-Diffusion Processes with Constant Parameters [J]. Automatica, 2015, 54: 80-90. doi: 10.1016/j.automatica.2015.01.032
ZHAO A L, XIE C K. Stabilization of Coupled Linear Plant and Reaction-Diffusion Process [J]. Journal of the Franklin Institute, 2014, 351(2): 857-877. doi: 10.1016/j.jfranklin.2013.09.012
SI Y C, XIE C K, ZHEN Z Y, et al. Local Stabilization of Coupled Nonlinear Parabolic Equations by Boundary Control [J]. Journal of the Franklin Institute, 2018, 355(13): 5592-5612. doi: 10.1016/j.jfranklin.2018.06.008
CAVALCANTI M M, FERNNDEZ-CARA E, FERREIRA A L. Null Controllability of some Nonlinear Degenerate 1D Parabolic Equations [J]. Journal of the Franklin Institute, 2017, 354(14): 6405-6421. doi: 10.1016/j.jfranklin.2017.08.015
YU X, XU C, CHU J. Local Exponential Stabilization of Fisher's Equation Using the Backstepping Technique [J]. Systems & Control Letters, 2014, 74: 1-7.
WU H N, WANG J W, LI H X. Fuzzy Boundary Control Design for a Class of Nonlinear Parabolic Distributed Parameter Systems [J]. IEEE Transactions on Fuzzy Systems, 2014, 22(3): 642-652. doi: 10.1109/TFUZZ.2013.2269698
HASAN A, AAMO O M, FOSS B. Boundary Control for a Class of Pseudo-Parabolic Differential Equations [J]. Systems & Control Letters, 2013, 62(1): 63-69.
HASAN A, AAMO O M, KRSTIC M. Boundary Observer Design for Hyperbolic PDE-ODE Cascade Systems [J]. Automatica, 2016, 68: 75-86. doi: 10.1016/j.automatica.2016.01.058
HASAN A, TANG S X. Local Exponential Stabilization of a Coupled Burgers' PDE-ODE System[C]//IEEE 56th Annual Conference on Decision and Control. New York: IEEE Press, 2017: 2479-2484.
NIKDEL P, SHEIKHOLESLAM F, ZEKRI M, et al. Backstepping Boundary Control Design for a Cascaded Viscous Hamilton-Jacobi PDE-ODE System [J]. IET Control Theory & Applications, 2021, 15(14): 1832-1848.