On continuity of solutions for parabolic control systems and input-to-state stability. (English) Zbl 1514.47118
Summary: 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.
MSC:
| 47N70 | Applications of operator theory in systems, signals, circuits, and control theory |
| 47D06 | One-parameter semigroups and linear evolution equations |
| 93C20 | Control/observation systems governed by partial differential equations |
| 93D20 | Asymptotic stability in control theory |
| 35K90 | Abstract parabolic equations |
Keywords:
abstract parabolic control system; admissible operator; Orlicz space; bounded functional calculus; \(H^\infty\) calculus; input-to-state stabilityReferences:
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