Causality Structure of Engineering Systems
MICHIGAN UNIV ANN ARBOR DEPT OF ELECTRICAL ENGINEERING
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The report is a study of the structure of engineering systems with respect to time related behavior. The development is unconventional in not being based on system properties such as linearity, time invariance, etc. The main question of interest concerns the possibility of decomposing a general system into a sum of systems with less complex time related behavior. An analysis of characteristic properties of such systems and their interconnection with other aspects of system behavior is also made. The approach used in the study is functional analytic, making use of recently developed axiomatic structures called the group resolution space and Hilbert resolution space. This in turn permits the efficient use of powerful techniques from the Gohberg-Krein theory of Volterra operators. The most important result of the study is a canonical causality decomposition theorem. Other results include a theorem connecting the temporal properties of an open loop system to the stability of the closed loop feedback system.
- Theoretical Mathematics