Subjects: Mathematics >> Control and Optimization. submitted time 2022-12-12
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
Subjects: Mathematics >> Mathematics （General） submitted time 2018-09-18
Abstract： This paper studies Lyapunov inequalities of a class of higher-order nonlinear differential equations, which is a further discussion and extension of the relevant conclusions of "Lyapunov-type inequalities for ψ-Laplacian equations"
Peer Review Status:Awaiting Review
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