Síntese de sistemas estritamente reais positivos através do critério de routh-hurwitz

Given a linear time-invariant plant Gol(s) with one input and q outputs, where q > 1, a method based on the Routh-Hurwitz Stability Criterion is proposed to obtain a constant tandem matrix F ∈ ℝq, such that FGOl(s) is a minimumphase system. From this solution, the system FGol(s) is represented in state space by {A, B, FC} and a constant output feedback matrix K0 ∈ ℝ is obtained such that the feedback system {A - BK0C, B, FC} is Strictly Positive Real (SPR). The proposed procedure offers necessary and sufficient conditions for both problems. Initially, the general case, with a generic q, is analyzed. Following, the particular cases q = 2 and q = 3 are studied.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.

Proportional controllers: Direct method for stability analysis and MATLAB implementation

In most cases, the cost of a control system increases based on its complexity. Proportional (P) controller is the simplest and most intuitive structure for the implementation of linear control systems. The difficulty to find the stability range of feedback systems with P controllers, using the Routh-Hurwitz criterion, increases with the order of the plant. For high order plants, the stability range cannot be easily obtained from the investigation of the coefficient signs in the first column of the Routh's array. A direct method for the determination of the stability range is presented. The method is easy to understand, to compute, and to offer the students a better comprehension on this subject. A program in MATLAB language, based on the proposed method, design examples, and class assessments, is provided in order to help the pedagogical issues. The method and the program enable the user to specify a decay rate and also extend to proportional-integral (PI), proportional-derivative (PD), and proportional-integral-derivative (PID) controllers.

Comportamento caótico em sistemas dinâmicos e aplicação no estudo de tumores de câncer

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Semi-analytical study of the rotational motion stability of artificial satellites using quaternions

This study at aims performing the stability analysis of the rotational motion to artificial satellites using quaternions to describe the satellite attitude (orientation on the space). In the system of rotational motion equations, which is composed by four kinematic equations of the quaternions and by the three Euler equations in terms of the rotational spin components. The influence of the gravity gradient and the direct solar radiation pressure torques have been considered. Equilibrium points were obtained through numerical simulations using the softwares Matlab and Octave, which are then analyzed by the Routh-Hurwitz Stability Criterion.

Estabilidade de sistemas dinâmicos: Estudo do memristor

Pós-graduação em Matematica Aplicada e Computacional - FCT

Análise da estabilidade do movimento rotacional de satélites artificiais com quatérnions e sob a influência de torques externos

The aim of this work is to analyze the stability of the rotational motion’s artificial satellite using the Routh Hurwitz Algorithm (CRH) and the quaternions to describe the satellite’s attitude. This algorithm allows the investigation of the stability of the motion using the coefficients of the characteristic equation associated with the equation of the rotational motion in the linear form. The equations of the rotational motion are given by the four cinematic equations for the quaternion and the three equations of Euler for the spin velocity’s components. In the Euler equations are included the components of the gravity gradient torque (TGG) and the solar radiation torque (TRS). The TGG is generated by the difference of the Earth gravity force direction and intensity actuating on each satellite mass element and it depends on the mass distribution and the form of the satellite. The TRS is created by changing of the linear momentum, which happens due to the interactions of solar photons with the satellite surface. The equilibrium points are gotten by the equation of rotational motion and the CRH is applied in the linear form of these equations. Simulations are developed for small and medium satellites, but the gotten equilibrium points are not stable by CRH. However, when some of the eigenvalues of the characteristic equation are analyzed, it is found some equilibrium points which can be pointed out as stables for an interval of the time, due to small magnitude of the real part of these eigenvalue

Stability Analysis of a Run-of-River Diversion Hydropower Plant With Surge Tank And Spillway in the Head Pond

Run-of-river hydropower plants usually lack significant storage capacity; therefore, the more adequate control strategy would consist of keeping a constant water level at the intake pond in order to harness the maximum amount of energy from the river flow or to reduce the surface flooded in the head pond. In this paper, a standard PI control system of a run-of-river diversion hydropower plant with surge tank and a spillway in the head pond that evacuates part of the river flow plant is studied. A stability analysis based on the Routh-Hurwitz criterion is carried out and a practical criterion for tuning the gains of the PI controller is proposed. Conclusions about the head pond and surge tank areas are drawn from the stability analysis. Finally, this criterion is applied to a real hydropower plant in design state; the importance of considering the spillway dimensions and turbine characteristic curves for adequate tuning of the controller gains is highlighted

On the zeta-function regularization of a two-dimensional series of epsten-Hurwitz type

For a few years now, the study of quantum field theories in partially compactified space-time manifolds has acquired increasing importance in several domains of quantum physics. Let me just mention the issues of dimensional reduction and spontaneous compactification, and the multiple questions associated with the study of quantum field theories in the presence of boundaries (like the Casimir effect) and on curved space-time (manifolds with curvature and nontrivial topology), a step towards quantum gravity.

Almost strict total positivity and a class of Hurwitz polynomials

We establish sufficient conditions for a matrix to be almost totally positive, thus extending a result of Craven and Csordas who proved that the corresponding conditions guarantee that a matrix is strictly totally positive. Then we apply our main result in order to obtain a new criteria for a real algebraic polynomial to be a Hurwitz one. The properties of the corresponding extremal Hurwitz polynomials are discussed. (C) 2004 Elsevier B.V. All rights reserved.

Capitoli della teoria delle funzioni di K. Weierstrass nell'interpretazione di A. Hurwitz e S. Pincherle

Ricostruzione della teoria delle funzioni affrontata nel corso "Einleitung in die Theorie der analytischen Funktionen" tenuto da K. Weierstrass attraverso l'analisi e il confronto dei saggi di due suoi studenti: A. Hurwitz e S. Pincherle.

A finite class of orthogonal functions generated by Routh-Romanovski polynomials

It is known that some orthogonal systems are mapped onto other orthogonal systems by the Fourier transform. In this article we introduce a finite class of orthogonal functions, which is the Fourier transform of Routh-Romanovski orthogonal polynomials, and obtain its orthogonality relation using Parseval identity.

Platonos Gorgias e peri retorikes = Platons Gorgias oder von der Redekunst : worin Plato zeigt, dass Sokrates das Sittengesetz gegen die Volksführer bis zum Tode behauptet und geübt hat : mit einem Kommentar nebst Anhange worin die Vorrede des Olympiodors zu den Scholien über den Gorgias, und die brauchbarsten Anmerkungen aus Routh mitgetheilt sind /

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