Interval algorithm for membership-set identification of linear time-invariant system

An interval algorithm was presented for parameter set estimation of a linear time-invariant system with the Unknown-But-Bounded (UBB) noise. In virtue of interval mathematics, the algorithm objective is in seeking the minimal hyper-rectangle (or interval vector) of parameters which is compatible with the measurements and the bounded noise, and its recursive formula were derived. Convergence of the algorithm was analyzed. The center estimation of parameters can not only be obtained, but also the uncertain bounds on them. Numerical examples illustrate its small computation efforts and higher accuracy in comparison with Fogel's algorithm and the least squares algorithm.