Computation of Impulse-Response Gramian for Interval Systems

Abstract

This paper presents an impulse response gramian for the interval systems. To reduce the higher-order interval systems, two methods used to evaluate the impulse response gramian are computed in the frequency domain. The first method is based on Routh technique with () table to evaluate energy integrals for finding the diagonal impulse response gramian. The second method is based on the Inners technique to compute the diagonal elements of the Gramian matrix, while the off-diagonal elements are obtained by the Markov parameters. The method is computationally simple but the reduced-order stable interval systems are difficult to obtain. To overcome this problem, the reduced-order model is developed based on Kharitonov's theorem. The advantage of the proposed technique is useful for system identification and reduction technique. Illustrative examples are included and results are compared and stability of the reduced-order model is guaranteed.