Abstract
Abstract This paper is concerned with the boundary control of the fractional wave equation when the boundary is subject to persistent external disturbances. By developing the sliding mode control approach to infinite-dimensional fractional order systems, the fractional order sliding mode boundary control law is designed for the infinite dimensional setting. Moreover, based on the fractional asymptotical stability theorem, the asymptotical stability for the fractional wave equation under the control strategies proposed is addressed. Finally, numerical examples are provided to illustrate the viability of the theoretical results.
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