Linear systems on partially ordered time sets
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A point set with a partial order (poset) P is a useful "generalized time" set for linear system theory, since the fundamental concept of causality can be defined for linear operators on a function space on P. The causal-operator algebra has a rich structure, known to combinatorists. Specializing to posets which admit shift operators, some novel generalizations of time-invariance are obtained; P becomes an ordered semigroup. A Kalman-Wyman algebraic system theory is indicated for these systems.
[1] H. W. Turnbull,et al. Lectures on Matrices , 1934 .
[2] Frank Harary,et al. Graph Theory , 2016 .
[3] R. Stanley,et al. On the foundations of combinatorial theory. VI. The idea of generating function , 1972 .
[4] Bostwick F. Wyman,et al. Linear Systems over rings of operators , 1974, Category Theory Applied to Computation and Control.