Abstract State-Space Models for a Class of Linear Hyperbolic Systems of Balance Laws

摘要: The paper discusses and compares different abstract state-space representations for a class of linear hyperbolic systems defined on one-dimensional spatial domain. It starts with their PDE representation in both weakly strongly coupled forms. Next, the homogeneous state equation including unbounded formal operator is presented. Based semigroup approach, some results well-posedness internal stability are given. boundary observation operators introduced, assuming typical configuration inputs as well pointwise observations variables. Consequently, extended to so-called control state/signal form. classical additive statespace involving (A, B, C)-triple state, input output considered. After short discussion appropriate Hilbert spaces, factor form also Finally, resolvent system A discussed.