Structural Properties of Linear Generalized Systems
نویسنده
چکیده
Abstract: Generalized linear systems are considered, which contain in their state-space representation matrices with elements functions of bounded variation and controls in the space of regulated functions. The Perron-Stieltjes integral is used to obtain a variation-of-parameters formula. On this basis the formula of the state of the system as well as the input-output map are derived. The fundamental concepts of controllability and reachability are analysed in this approach by means of two controllability and reachability Gramians. An optimal control is provided which solves the problem of the minimum energy transfer. The observability of these generalized systems is studied. In the case of completely observable systems a formula is obtained which recovers the initial state from the exterior data. The duality between the concepts of controllability and observability is emphasized as well as Kalman’s canonical form.
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