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.

In this paper employing Routh's table, a geometrical stability criterion for the analysis of linear time-invariant system is formulated. The proposed stability criterion is applied for the system, whose characteristic equation having complex coefficients. For this Routh like table is presented with complex terms and the signs pair-wise elements with the first column of the table are observ...

This work suggests the estimation method developed in relation to the position of the robotic system (RS) operator, showing his degree of risk proneness. The base models are: Hurwitz pessimism/optimism criterion and decision trees. The problem is solved using the reverse setting: we estimate pessimism/optimism parameter of the operator (decision taker) by observing what decisions he makes when ...

Based on the generalized Routh–Hurwitz criterion, we propose a sufficient and necessary criterion for testing stability of fractional-order linear systems with order α∈1,2, called criterion. Compared existing ours involves fewer simpler expressions, which is significant analyzing robust high-dimensional uncertain systems. All these expressions are explicit ones about coefficients characteristic...

— In this note, we have shown special case on Routh stability criterion, which is not discussed, in previous literature. This idea can be useful in computer science applications.

This paper is about omitting types in logic of metric structures introduced by Ben Yaacov, Berenstein, Henson and Usvyatsov. While a complete type is omissible in some model of a countable complete theory if and only if it is not principal, this is not true for the incomplete types by a result of Ben Yaacov. We prove that there is no simple test for determining whether a type is omissible in a ...

We start from the dynamic equations of the comprimating systems (Greitzer-1976) and we make a nondimensionalizing the mass flow rate, the pressure and the time to obtain the nondimensional governing equations. To analyse the stability we apply the Routh Hourwitz criterion and we determin the useful stability range for compressor stability. We propose an interesting concept of dynamic stabilizat...

In this paper, the nonlinear dynamic system of equations, a type of nuclear ssion reactor is solved analytically and numerically. Considering that the direct solution of three-dimensional dynamical systems analysis and more in order to determine the stability and instability, in terms of algebraicsystems is dicult. Using certain situations in mathematics called Hurwitz criterion, Necessary and ...