Integral input-to-state stabilization in different norms for a class of linear parabolic PDEs

Subjects: Mathematics >> Control and Optimization. submitted time 2022-12-12

Chen, Qiaoling Zheng, Jun Zhu, Guchuan

Abstract：

In this paper, we study the problem of  integral input-to-state stabilization in different norms for  parabolic PDEs with integrable inputs. More precisely, we apply the method of backstepping to design a boundary  control law for certain linear   parabolic PDEs with  destabilizing terms and $L^r$-inputs, and establish  the integral  input-to-state stability   in  the spatial $L^p$-norm and $W^{1,p}$-norm, respectively, for the closed-loop system, whenever $p in 1,+ infty $ and $r in p,+ infty $.  In order to deal with singularities in the case of $p in 1,2)$, we employ  the approximative Lyapunov method to analyze  the stability in different norms. Concerning with the appearance of external inputs, we apply the   method of functional analysis and the theory of series to prove the unique existence and regularity of solution to the closed-loop system.

Peer Review Status:Awaiting Review

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