CSOIS Interval computation technical report series-2: Impulse response boundary calculation based on power of interval matrix

In this report, the impulse response boundary of discrete-time, linear, time-invariant systems with interval uncertainty is studied. The key problem of determining the impulse response of such systems is to find the boundaries of the power of an interval matrix at a specified order. To estimate the bounds of the power of an interval matrix, interval perturbation theory is used. Two different methods are developed. The first method uses first-order perturbation theory based on eigenpair-decomposition and the second method finds the sensitivity of the perturbation from the nominal matrix to the power of the interval matrix to develop a computation based on the vertex matrices of an interval matrix. Through numerical examples the usefulness of the suggested method is illustrated. Index Terms Linear time invariant, interval uncertainty, power of interval matrix, matrix perturbation theory.