in this paper, a new method is investigated for model order reduction of high order systems based on moment matching technique. in this method, at first, full order model is expanded by legendre wavelet function which is included in orthogonal functions. a suitable fixed structure model is considered as reduced order model whose parameters are unknown. these unknown parameters are determined us...

This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems ...

below) a sequence of e.0. polynomials [SI S. V. Salehi and E. P. Ryan. “On optimal nonlinear feedback regulation of linear plants,” IEEE Trans. Auiomai. Contr., vol. AC-27, pp. 1260-1264, 1982. [ IO] J . Sandor and D. Williamson. “Design of nonlinear regulators for linear plants,” IEEE Truns. Automar. Conrr.. vol. AC-22. pp. 47-50, 1977. 1111 F. G. Shinsky, Process Control Syslems. 2nd ed. New ...

We present a method, based on the Routh stability criterion, for transforming the task of finding the complex roots of a polynomial of even degree n with real coefficients to that of: (a) finding their real parts as the n/2 real roots of a polynomial of degree n(n−1)/2; (b) for each real part, calculating the corresponding imaginary part as a square root. We illustrate the method for polynomial...

Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaini...

This note presents an elementary proof of the familiar Routh-Hurwitz test. The proof is basically one continuity argument, it does not rely on Sturm chains, Cauchy index and the principle of the argument and it is fully self-contained. In the same style an extended Routh-Hurwitz test is derived, which finds the inertia of polynomials.