Integral-Type Feedback Controller and Application to the Stabilization of Heat Equation with Boundary Input Delay

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Abstract: In this paper, we consider the stabilization of Heat-equation with boundary delayed control by a new kind of feedback controller. The new feedback controller is of the integral form in spatial variable, which is called the integral-type feedback controller. Our goal of the present paper is to select appropriate kernel functions such that the closed-loop system is exponentially stable. Here we mainly give a method of selecting kernel functions. To prove the stability of the closed-loop system, we design a target system which is exponentially stable, and then construct a revertible and bounded linear transformation that establishes the equivalence between the target system and the closed-loop system.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #39

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Xiaopei Liu, Genqi Xu, "Integral-Type Feedback Controller and Application to the Stabilization of Heat Equation with Boundary Input Delay," WSEAS Transactions on Mathematics, vol. 17, pp. 311-318, 2018, DOI:
Xiaopei Liu, Genqi Xu. Integral-Type Feedback Controller and Application to the Stabilization of Heat Equation with Boundary Input Delay. WSEAS Transactions on Mathematics. 2018;17:311-318.
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