Algebraic approach to the analysis of linear static systems with interval uncertainty (Q1386957)

The paper considers the mathematical and computational aspects of the analysis of an interesting class of linear static systems subject to interval uncertainty. The inputs \(a\) are categorized as disturbing or controlling and the outputs \(b\) are categorized as regulating or stabilizing. The input, the outputs and the states, \(x\), are related by the static equation \(F(a,x)=b\). All inputs and outputs belong to their respective intervals. The problem of estimating the states under various assumptions on the system realization is considered. A new algebraic approach to internal algebraic estimation of solution sets of interval linear equations is proposed; it is based on substituting the initial problem by the problem of finding the algebraic solution of an auxiliary system of equations in extended Kaucher arithmetic.