State-space representations for 2×2 hyperbolic systems with boundary inputs

摘要: The paper discusses different abstract state-space representations for a class of linear distributed parameter systems hyperbolic type defined on one-dimensional spatial domain. It starts with the homogeneous state equation including unbounded formal operator. Based semigroup approach, some theoretical results well-posedness and internal stability considered are given here. Next, boundary observation operators introduced, taking typical inputs configuration as well pointwise observations variables. Consequently, is extended to so-called control state/signal form. Finally, most classical representation involving (A, B, C)-triple state, input output together definition Pritchard-Salamon infinite-dimensional systems.