Closed-form boundary State feedbacks for a class of 1-D partial integro-differential equations

By Andrey Smyshlyaev, Miroslav Krstic. IEEE Transactions on Automatic Control, 2004

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Stabilization and controllability of first-order integro-differential hyperbolic equations (2015, background): “Krstic and his co-workers (see, in particular, the pioneer articles [2,16,19] and the reference book [14]).”
Backstepping boundary control for first order hyperbolic PDEs and application to systems with actuator and sensor delays (2007, methodology): “In this paper we apply the backstepping method, recently developed for parabolic PDEs [ 22 ], [23] and second order hyperbolic PDEs [13], [14], [12], to solve a problem of stabilization of a class of first order hyperbolic PDEs.”
Boundary Control of PDEs (2008, background): “It is possible to modify the controllers developed in this chapter to achieve inverse optimality, which gives guaranteed robustness margins; see [154].”
Backstepping observers for a class of parabolic PDEs (2005, methodology): “The stabilizing kernel k2(x) for (84)–(85) was obtained in[15].”
Sliding mode control and active disturbance rejection control to the stabilization of one‐dimensional Schrödinger equation subject to boundary control matched disturbance (2014, methodology): “The non-collocated method is systematically applied, due to the introduction of backstepping method to PDEs in the last few years ([17], see also [6]), to stabilize some unstable or even anti-stable wave and heat equations ([15, 17, 27]).”