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On continuity of solutions for parabolic control systems and input-to-state stability. (arXiv:1709.04261v3 [math.FA] UPDATED)
来源于:arXiv
We study minimal conditions under which mild solutions of linear evolutionary
control systems are continuous for arbitrary bounded input functions. This
question naturally appears when working with boundary controlled, linear
partial differential equations. Here, we focus on parabolic equations which
allow for operator-theoretic methods such as the holomorphic functional
calculus. Moreover, we investigate stronger conditions than continuity leading
to input-to-state stability with respect to Orlicz spaces. This also implies
that the notions of input-to-state stability and integral-input-to-state
stability coincide if additionally the uncontrolled equation is dissipative and
the input space is finite-dimensional. 查看全文>>