Robustness of fractional-order boundary control of time fractional wave equations with delayed boundary measurement using the simple predictor

Abstract

In this paper, we analyse the robustness of the fractional wave equation with a fractional-order boundary controller subject to delayed boundary measurement. Conditions are given to guarantee stability when the delay is small. For large delays, the Smith predictor is applied to solve the instability problem and the scheme is proved to be robust against a small difference between the assumed delay and the actual delay. The analysis shows that fractional-order controllers are better than integer order controllers in the robustness against delays in the boundary measurement. © 2007 Springer.