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Input control in nonnegative matrix equations
Authors:D. J. Hartfiel
Affiliation: a Mathematics Department Texas, A&M University College Station, Texas
Abstract:In this paper we consider the nonnegative matrix system ciA+uiB=ci+1 where the nonnegative matrix A is allowed to vary, within bounds. The cone control problem is to find a nonnegative matrix B such that if Ci is a nonnegative vector in a specified cone, then there is a nonnegative vector ui such that ci+1 is in that cone. We extend this problem to input control by finding a B such that the cone, generated by the rows of B, is as small as possible. Thus, the percent distribution of ∣uiB∣ through the states of the sustem by uiB is either constant or varies little.
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