• Title, Summary, Keyword: Hurwitz stable

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ON STABILITY OF A POLYNOMIAL

  • KIM, JEONG-HEON;SU, WEI;SONG, YOON J.
    • Journal of applied mathematics & informatics
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    • v.36 no.3_4
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    • pp.231-236
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    • 2018
  • A polynomial, $p(z)=a_0z^n+a_1z^{n-1}+{\cdots}+a_{n-1}z+a_n$, with real coefficients is called a stable or a Hurwitz polynomial if all its zeros have negative real parts. We show that if a polynomial is a Hurwitz polynomial then so is the polynomial $q(z)=a_nz^n+a_{n-1}z^{n-1}+{\cdots}+a_1z+a_0$ (with coefficients in reversed order). As consequences, we give simple ratio checking inequalities that would determine unstability of a polynomial of degree 5 or more and extend conditions to get some previously known results.

Comparison of Routh-Hurwitz and Absolute Stability Criteria in Application to Scaled Telerobotics Systems (스케일 텔레 로보틱스 시스템에 적용된 Routh-Hurwitz와 절대 안정도 기준의 비교)

  • Gaponov, Igor;Cho, Hyun Chan;Jeon, Hong-Tae
    • Journal of the Institute of Electronics and Information Engineers
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    • v.50 no.11
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    • pp.171-179
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    • 2013
  • This paper presents a comparative study on application of Routh-Hurwitz and Llewellyn absolute stability criteria to a scaled telerobotic system. The dynamic equations of the telerobotic system are given, and the transfer function of the system is obtained for further stability analysis. The stable margins of controller gains are obtained using both stability analysis methods, and the differences in the results are described and explained. The paper is concluded by a numerical example verifying performed stability analysis.

New Upper Bounds for the CALE: A Singular Value Decomposition Approach

  • Savov, Svetoslav G.;Popchev, Ivan P.
    • International Journal of Control, Automation, and Systems
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    • v.6 no.2
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    • pp.288-294
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    • 2008
  • Motivated by the fact that upper solution bounds for the continuous Lyapunov equation are valid under some very restrictive conditions, an attempt is made to extend the set of Hurwitz matrices for which such bounds are applicable. It is shown that the matrix set for which solution bounds are available is only a subset of another stable matrices set. This helps to loosen the validity restriction. The new bounds are illustrated by examples.

A Study of Stability Analysis on Nonlinear Dynamic Vibration Absorber Acting on Damped Main Vibration Systems (선형진동계에 작용하는 비선형진흡진기에 관한 안정성해소 연구)

  • 안찬우;박일수;박동환
    • Journal of Ocean Engineering and Technology
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    • v.6 no.1
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    • pp.62-68
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    • 1992
  • In this study, a system coupled with the nonlinear dynamic vibration absorber was modelled, and its equation of motion was analized by the harmonic balance method to obtain the amplitude ratio. And also, the stability analysis was done by the Routh Hurwitz method. In the vibration systems coupled with the nonlinear dynamic vibration absorber, the unstable region and the jump phenomenon can be ramarkably affected by the damping ratio. The stable and unstable region that obtained to differential method excellently agreed to the result of the stability analysis of Routh Hurwitz.

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A Note on Schur Stability of Real Weighted Diamond Polynomials

  • Otsuka, Naohisa;Ichige, Koichi;Ishii, Rokuya
    • 제어로봇시스템학회:학술대회논문집
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    • pp.421-424
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    • 2004
  • This paper presents a sufficient condition for the real weighted diamond polynomials to be Schur stable using bilinear transformation and Kharitonov's theorem.

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Design of Single-input Direct Adaptive Fuzzy Logic Controller Based on Stable Error Dynamics

  • Park, Byung-Jae
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.1 no.1
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    • pp.44-49
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    • 2001
  • For minimum phase systems, the conventional fuzzy logic controllers (FLCs) use the error and the change-of-error as fuzzy input variables. Then the control rule table is a skew symmetric type, that is, it has UNLP (Upper Negative and Lower Positive) or UPLN property. This property allowed to design a single-input FLC (SFLC) that has many advantages. But its control parameters are not automatically adjusted to the situation of the controlled plant. That is, the adaptability is still deficient. We here design a single-input direct adaptive FLC (SDAFLC). In the AFLC, some parameters of the membership functions characterizing the linguistic terms of the fuzzy rules are adjusted by an adaptive law. The SDAFLC is designed by a stable error dynamics. We prove that its closed-loop system is globally stable in the sense that all signals involved are bounded and its tracking error converges to zero asymptotically. We perform computer simulations using a nonlinear plant and compare the control performance between the SFLC and the SDAFLC.

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AN EASILY CHECKING CONDITION FOR THE STAVILITY TEST OF A FAMILY OF POLYNOMIALS WITH NONLIMEARLY PERTURBED COEFFICIENTS

  • Kim, Young-Chol;Hong, Woon-Seon
    • 제어로봇시스템학회:학술대회논문집
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    • pp.5-9
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    • 1995
  • In many cases of robust stability problems, the characteristic polynomial has real coefficients which or nonlinear functions of uncertain parameters. For this set of polynomials, a new stability easily checking algorithm for reducing the conservatism of the stability bound are given. It is the new stability theorem to determine the stability region just in parameter space. Illustrative example show that the presented method has larger stability bound in uncertain parameter space than others.

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On the Design of Simple-structured Adaptive Fuzzy Logic Controllers

  • Park, Byung-Jae;Kwak, Seong-Woo
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.3 no.1
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    • pp.93-99
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    • 2003
  • One of the methods to simplify the design process for a fuzzy logic controller (FLC) is to reduce the number of variables representing the rule antecedent. This in turn decreases the number of control rules, membership functions, and scaling factors. For this purpose, we designed a single-input FLC that uses a sole fuzzy input variable. However, it is still deficient in the capability of adapting some varying operating conditions although it provides a simple method for the design of FLC's. We here design two simple-structured adaptive fuzzy logic controllers (SAFLC's) using the concept of the single-input FLC. Linguistic fuzzy control rules are directly incorporated into the controller by a fuzzy basis function. Thus some parameters of the membership functions characterizing the linguistic terms of the fuzzy control rules can be adjusted by an adaptive law. In our controllers, center values of fuzzy sets are directly adjusted by an adaptive law. Two SAFLC's are designed. One of them uses a Hurwitz error dynamics and the other a switching function of the sliding mode control (SMC). We also prove that 1) their closed-loop systems are globally stable in the sense that all signals involved are bounded and 2) their tracking errors converge to zero asymptotically. We perform computer simulations using a nonlinear plant.

On the Structure of the Transfer Function which can be Structurally Stabilized by the PID, PI, PD and P Controller

  • Kang, Hwan-Il;Jung, Yo-Won
    • 제어로봇시스템학회:학술대회논문집
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    • pp.286-286
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    • 2000
  • We consider a negative unity feedback control system in which Che PIO, PI, PD or P controller and a transfer function having only poles are in cascade, We define the notion of the structural polynomial which means that there exists a subdomain of the coefficient space in which the polynomial is Hurwitz (left half plane stable) polynomial. We obtain the necessary and sufficient condition of the structure of the transfer function of which the characteristic polynomial is a structural polynomial, In addition, this paper present another necessary and sufficient condition for the existence of a constant gain controller with which the characteristic polynomial is structurally stable, For the structurally stabilizable P controller, it is allowed that the transfer function may not to all pole plants.

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Dynamic Characteristics of Automated Guideway Transit (AGT) Vehicles (무인자동안내방적 경량전철 시스템의 동특성에 관한 연구)

  • 송창민;이우식
    • Journal of the Korean Society for Railway
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    • v.4 no.1
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    • pp.1-8
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    • 2001
  • In this paper, the dynamics and stability of the automated guideway transit (AGT) vehicles with rubber tires are investigated. Two types of AGT systems are considered: the bogie-type and steering-type systems. The critical speeds for the dynamic instability of lateral and yawing motions are investigated by use of the Routh-Hurwitz's stability criterion. It is shown that the bogie-type AGT vehicles are likely to be stable within the range of practical operating speed, whereas it is not true for the steering-type AGT vehicles. It is also shown that the control performance of steering-type AGT vehicles can be improved by choosing proper steering gains of the closed-loop steering control system.

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