Prescribed-time stabilization of reaction-diffusion equation by output feedback

In this work, we consider the problem of prescribed-time stabilization of a reaction-diffusion equation by means of time-varying feedback control. Our approach is the backstepping method, where a new target equation whose state converges to zero in a prescribed time and with a desired trajectory is utilized. By characterizing the growth-in-time of the solution of the resulting backstepping kernel equations, we establish fixed-time stabilization of the plant with a feedback controller that converges to zero within the prescribed time. Next, we present a state observer whose error converges to zero in a prescribed-time, accompanied by an output feedback result for which the separation principle is verified.

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