Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 63, Issue 8, Pages 2633-2640Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2017.2767824
Keywords
Backstepping method; coupled ordinary differential equations-hyperbolic equations; nonlocal term; wave equation
Funding
- National Natural Science Foundation of China [61673061]
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This paper solves the problem of boundary feedback stabilization of a class of coupled ordinary differential equations-hyperbolic equations with boundary, trace, and integral nonlocal terms. Using the backstepping approach, the controller is designed by formulating an integral operator, whose kernel is required to satisfy a coupled hyperbolic partial integral differential equation. By applying the method of successive approximations, the kernel's well-posedness is given. We prove the exponential stability of the origin of the system in a suitable Hilbert space. Moreover, a wave system with nonlocal terms is stabilized by applying the above result.
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