in this paper, a new alternative method for order reduction of high order systems is presented based on optimization of multi objective fitness function by using harmony search algorithm. at first, step response of full order system is obtained as a vector, then, a suitable fixed structure considered for model order reduction which order of original system is bigger than fixed structure model. ...

For the two sixth-order polynomials a(s) and b(s), Hurwitz stability of their convex combination is necessary and sufficient for the existence of a polynomial c(s) such that c(s)/a(s) and c(s)/b(s) are both strictly positive real. Our reasoning method is constructive, and is insightful and helpful in solving the general robust strictly positive real synthesis problem.

We describe the pairs (p, n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.

This paper presents a trajectory tracking control method for flexible space robot. The advantage of the method is that it is free from spill-over instability as it uses a robust overwhelming trajectory controller. The proposed controller is conceptualized for a single rotational degree of freedom case. The efficacy of the scheme is illustrated by simulation results. The stability analysis of th...

Simple proofs of the Hermite–Biehler and Routh–Hurwitz theorems are presented. The total nonnegativity of the Hurwitz matrix of a stable real polynomial follows as an immediate corollary. © 2003 Elsevier Inc. All rights reserved. AMS classification: 93D05; 34D99; 12D10; 26C05; 26C10; 30C15; 15A23; 15A48; 15A57

Beginning with Hermite’s integral representation of the Hurwitz zeta function, we derive explicit expressions in terms of elementary, polygamma, and negapolygamma functions for several families of integrals of the type ∫∞ 0 f(t)K(q, t)dt with kernels K(q, t) equal to ( e2πqt − 1 )−1 , ( e2πqt + 1 )−1 , and (sinh(2πqt))−1.

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 ...