A full-rank IC x n matrix G ( D ) over the rational functions F ( D ) generates a rate R = k / n convolutional code C. G ( D ) is minimal if it can be realized with as few memory elements as any encoder for C, and G ( D ) is canonical if it has a minimal realization in controller canonical form. We show that G ( D ) is minimal if and only if for all rational input sequences p1 ( D ) , the span ...

Minimal realization is discussed for linear switched systems with a given switching signal. We propose consecutive forward and backward approach the time-interval of interest. The refers to extending reachable subspace at each time by taking into account nonzero space from previous mode. Afterwards, extends observable current mode observability information next account. This results in an overa...

A graph is point determining if distinct vertices have distinct neighbourhoods. A realization of a point determining graph H is a point determining graph G such that each vertex-removed subgraph G − x which is point determining, is isomorphic to H . We study the fine structure of point determining graphs, and conclude that every point determining graph has at most two realizations. A full homom...

The realization problem for positive, multivariable continuous-time linear systems with delays in state and in control is formulated and solved. Sufficient conditions for the existence of positive realizations of a given proper transfer function are established. A procedure for computation of positive minimal realizations is presented and illustrated by an example.

We analyze the computational complexity of the cost-table approach to designing multiple-valued logic circuits that is applicable to IL, CCDs, current-mode CMOS, and RTDs. We show that this approach is NP-complete. An efficient algorithm is shown for finding the exact minimal realization of a given function by a given cost-table.