Two Notes on System Identification.
MICHIGAN UNIV ANN ARBOR SYSTEMS ENGINEERING LAB
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Given a finite set xi,yi of ordered pairs from X x Y where X, Y are hilbert spaces over the same filed, there are numerous techniques for constructing a function, f, on X to Y such that fxi yi. However, when X, Y have a causality structure and f must be causal then the data interpolation problem is much more complicated. In the paper two interpolation methods namely linear interpolation and interpolation via generalized Lagrange polynomials are considered. It is shown that these techniques can be modified to accomodate the causality constraint. The development is indicative of the modifications that must be made in any existing data interpolation algorithm if causal interpolation is required. Also an invariance property of the power functions which has important implications in the causal interpolation of experimental data is examined. Necessary and sufficient conditions for the invariance property are derived. It is shown that only sets composed of powers of a single function satisfy the invariance criteria. Author
- Theoretical Mathematics