INTERVAL SYSTEMS

A simple and direct method of approximating
higher order interval systems by lower order interval systems
based on Routh approximation without using reciprocal
transformation. Two numerical examples have been discussed
to illustrate the procedures. The errors between the original and
reduced order models are compared.

The paper proposes mixed methods for
reducing the order of interval systems i.e., systems having
uncertain but bounded parameters. The denominator of the
reduced order model is obtained by the differentiation method
and numerator is derived by applying mixed methods such as
differentiation method, factor division and Cauer second form.
A numerical example has been discussed to illustrate the
procedures. The errors between the original higher order and
reduced order models have also been highlighted to support
the effectiveness of the proposed methods.

This paper presents a mixed method for reducing order of the large scale interval systems using the Routh approximation and factor division method. The denominator coefficients of reduced order model is determined by using Routh approximation and numerator coefficients are obtained by using Factor division method. The mixed methods are simple and guarantee the stability of the reduced model if the original system is stable. A numerical example is discussed to illustrate the usefulness of the proposed method.

The paper proposes a mixed method for reducing
the order of discrete time interval systems. The numerator and
denominator of the reduced order model is obtained by
forming  table and combining factor division method and
Cauer second form. Bilinear transformation (z = p+1) is used
during the process of higher order discrete interval systems
before applying reduction method. The proposed method shows
that it is well suited to reduce both denominator and numerator
interval discrete polynomials. The proposed method is compared
with the existing methods of discrete interval system reduction. A
numerical example has been discussed to illustrate the procedure.
Accuracy of the system stability has been verified by using step
response.

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 is computed in the frequency domain. The first method is based on Routh technique with (α − β) 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.