Boundary Feedback Stabilization of an Unstable Heat Equation

By Weijiu Liu. SIAM Journal of Control and Optimization, 2003

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Boundary Control of PDEs (2008, background): “11 Notes and References The material in this chapter is based on the ideas introduced in [113, 154, 156].”
Closed-form boundary State feedbacks for a class of 1-D partial integro-differential equations (2004, methodology): “The kernel well posedness for was shown by Liu [23], whose result has inspired the efforts that have led to this paper.”
Structured H∞‐control of infinite‐dimensional systems (2017, background): “[52], for a parallel heat flow exchanger see [53], for an unstable heat equation see [54].”
Stabilization and controllability of first-order integro-differential hyperbolic equations (2015, background): “Krstic and his co-workers (se e, in particular, the pioneer articles [3, 4, 5] and the reference book [6]).”
Null Controllability and Finite Time Stabilization for the Heat Equations with Variable Coefficients in Space in One Dimension via Backstepping Approach (2017, unknown): “In this context, the ﬁrst continuous backstepping designs were proposed for the heat equation [25, 32].”
Backstepping observers for a class of parabolic PDEs (2005, background): “(28) The exponential stability of the target system (13)–(15) and invertibility of transformation (12) (established in Theorem 1) imply the exponential stability of (9)–(11) both in L2 and H1 (see [2,12] for details and references).”