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

分类： 数学 >> 控制和优化 提交时间： 2022-12-12

陈巧玲 郑军 朱谷川

摘要： 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.

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