scholarly journals Obtaining approximate region of asymptotic stability by computer algebra: A case study

2002 ◽  
Vol 20 (1) ◽  
pp. 56 ◽  
Author(s):  
S Prakash ◽  
J Vanualailai ◽  
T Soma
Keyword(s):  
Asymptotic Stability ◽  
Computer Algebra ◽  
System Analysis ◽  
Direct Method ◽  
Quantifier Elimination ◽  
Optimization Method ◽  
Analysis And Design ◽  
The Stability ◽  
Computer Algebra Software

One of the classical problems in nonlinear control system analysis and design is to find a region of asymptotic stability by the Direct Method of Lyapunov. This paper tentatively shows, via a numercial example, that this problem can be easily solved using Quantifier Elimination (QE). In particular, if the governing equations are described by differential equations containing only polynomials, then the problem can be conveniently solved by a computer algebra software packages such as Qepcad or Redlog. In our case study, we use a simple Lyapunov function and Qepcad to estimate the stability region, and the results are verified by an optimization method based on Lagrange's method.

scholarly journals Object Oriented VS Structured Analysis and Design in System Development Courses

2019 ◽  
Vol 8 (6S3) ◽  
pp. 82-88
Keyword(s):  
System Analysis ◽  
Survey Methodology ◽  
System Development ◽  
Object Oriented ◽  
Analysis And Design ◽  
Institutions Of Higher Learning ◽  
Structured Analysis ◽  
The One ◽  
Structured Analysis And Design

Objectives: The main aim of this study was to investigate the factors that influence students’, academicians’, clients’, as well as developer’s preferences in choosing their preferred approach in system development, namely structured analysis design (SAD) or object-oriented analysis and design (OOAD). Methods: The research design was based on a survey methodology and a case study. For the survey, questionnaires were administered to 30 students and 38 academicians, who were randomly selected from several Malaysian universities. For the case study, the requirements of the information system were modeled and presented to several clients to elicit their feedback. The survey data were analyzed using SPSS Findings: The result shows that students preferred the use of OOAD approach, which clearly outnumbered those who preferred the SAD approach, which stood at 33%. Interestingly, the majority (53%) of academicians preferred the use of a mixture of both approaches. Likewise, the clients shared a similar view with the academicians, whereas the developer preferred the OOAD approach. Application/Improvements: Clearly, the findings suggest that both approaches are essential, but the one that is widely used by developers and preferred by students is OOAD, and thus should be given priority when it comes to structured analysis and design. As such, curriculum designers and institutions of higher learning, particularly those offering system analysis and design and related courses, should make the necessary changes to the existing curriculum such that the academic programs offered will be able to produce highly competent and skilled analysts and designers as required by the industry.

Operator-Based Control System Analysis and Design for Nonlinear System with Input and Output Constraints

2018 ◽  
Vol 30 (6) ◽  
pp. 950-957
Author(s):  
Shuhui Bi ◽  
Lei Wang ◽  
Shengjun Wen ◽  
Liyao Ma ◽  
◽  
...  
Keyword(s):  
Control System ◽  
Nonlinear System ◽  
System Analysis ◽  
Sufficient Conditions ◽  
Input Constraint ◽  
Analysis And Design ◽  
Input And Output ◽  
Output Constraints ◽  
The Stability ◽  
Output Constraint

Smart material-based actuators and sensors have been widely used in practice owing to their various advantages. However, in the working process of these actuators and sensors, their output responses always deduce non-smooth nonlinear constraints. The constraint resulting from the actuator is called the input constraint and the constraint caused by the sensor is called the output constraint. These input and output constraints may induce inaccuracies and oscillations, severely degrading system performance. Therefore, the input and output constraints brought about by actuators and sensors should be considered in control system design. In this paper, system analysis for a nonlinear system with input and output constraints will be considered. The effect from the input constraint to the internal signal in the control system will be discussed. Moreover, the influence of the output constraint on the whole system will be studied. Further, the sufficient conditions for maintaining the stability of the system are obtained. Then, by using the robust right coprime factorization approach, an operator-based internal model like control structure is proposed for mitigating the input and output constraints. Finally, the effectiveness of the proposed design scheme will be confirmed through numerical simulation.

scholarly journals Asymptotic Stability of Distributed-Order Nonlinear Time-Varying Systems with the Prabhakar Fractional Derivatives

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
MohammadHossein Derakhshan ◽  
Azim Aminataei
Keyword(s):  
Asymptotic Stability ◽  
Fractional Derivatives ◽  
Direct Method ◽  
Time Varying ◽  
Lyapunov Direct Method ◽  
Fractional Differential Systems ◽  
Time Varying Systems ◽  
Fractional Differential ◽  
The Stability ◽  
Distributed Order

In this article, we survey the Lyapunov direct method for distributed-order nonlinear time-varying systems with the Prabhakar fractional derivatives. We provide various ways to determine the stability or asymptotic stability for these types of fractional differential systems. Some examples are applied to determine the stability of certain distributed-order systems.

Dynamic Stability of Nonlinear Antisymmetrically-Laminated Cross-Ply Rectangular Plates

1989 ◽  
Vol 56 (2) ◽  
pp. 375-381 ◽  
Author(s):  
Andrzej Tylikowski
Keyword(s):  
Asymptotic Stability ◽  
Dynamic Stability ◽  
Material Properties ◽  
Stability Problem ◽  
Large Deflection ◽  
Direct Method ◽  
Rectangular Plates ◽  
Stability Criteria ◽  
The Stability ◽  
Liapunov's Direct Method

The dynamic stability problem is solved for rectangular plates that are laminated antisymmetrically about their middle plane and compressed by time-dependent deterministic or stochastic membrane forces. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov’s direct method. A relation between the stability of nonlinear equations and linearized ones is analyzed. An influence on the number of orthotropic layers, material properties for different classes of parametric excitation on stability domains is shown.

scholarly journals Assessing a Transition to 100% Renewable Power Generation in a Non-interconnected Area: A Case Study for La R ́Eunion Island

2021 ◽  
Author(s):  
Frederic Babonneau ◽  
Stéphane Biscaglia ◽  
David Chotard ◽  
Alain Haurie ◽  
Nicolas Mairet ◽  
...  
Keyword(s):  
Power Systems ◽  
System Analysis ◽  
Production Plan ◽  
Power Network ◽  
Investment Planning ◽  
Time Step ◽  
Renewable Power ◽  
The Stability ◽  
Expansion Model

Abstract In this paper, we present a global and multi-timescale approach for assessing energy tran- sition policies aiming at fully renewable generation in power systems of non-interconnected areas, typically islands or isolated regions. The approach links together three dynamic mod- els:(i) a capacity expansion model, ETEM-SG, proposes an investment and production plan for typical days, at the horizon 2030; (ii) a simplified dispatch model is used to validate the production plan for a full year data of weather and demand variations and; (iii) a static & dynamic power system analysis is used to assess the stability of the new power network for fast occurring events like, e.g., a sudden reduction of renewable production. The proposed three-stage approach generates a least-cost long-term investment planning that ensures a supply-demand balance at an hourly time-step and power network statibility at a few mil- lisecond time scale. The presentaion is based on a case study fully described in a report [1] made with ADEME, the French Agency for ecological transition, for the French island La R ́eunion. It shows how a reliable 100% renewable power supply is reachable by 2030, in this area.

scholarly journals On the Stability of Some Discrete Fractional Nonautonomous Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Fahd Jarad ◽  
Thabet Abdeljawad ◽  
Dumitru Baleanu ◽  
Kübra Biçen
Keyword(s):  
Asymptotic Stability ◽  
Global Stability ◽  
Direct Method ◽  
Uniform Stability ◽  
Lyapunov Direct Method ◽  
Uniform Asymptotic Stability ◽  
Fractional Difference ◽  
Nonautonomous Systems ◽  
The Stability

Using the Lyapunov direct method, the stability of discrete nonautonomous systems within the frame of the Caputo fractional difference is studied. The conditions for uniform stability, uniform asymptotic stability, and uniform global stability are discussed.

scholarly journals Improving Angle Stability by Switching Shunt Reactors in Mixed Overhead Cable Lines. An Italian 400 kV Case Study

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1187
Author(s):  
Mariano Ippolito ◽  
Fabio Massaro ◽  
Rossano Musca
Keyword(s):  
Power System ◽  
System Analysis ◽  
System Stability ◽  
Theoretical Point ◽  
Control Logic ◽  
The Stability ◽  
Cable Lines ◽  
Shunt Reactors ◽  
Mixed Line

Stringent environmental constraints make the construction of new transmission overhead lines more and more difficult. Alternatively, today it is possible to use cable lines for high (HV) and extra-high (EHV) voltage systems. The configuration of the so-called mixed lines can create some problems in the operation of the electrical system, both during steady-state and transient conditions. In particular, the system stability is one of the main concerns when analyzing the dynamic response of power systems. In this paper, the study of angular stability of a system containing a mixed line is presented: a specific control logic applied to the shunt reactors of the mixed line is proposed as improvement of the overall system stability. The proposed switching logic is first discussed from a theoretical point of view and validated with two different testing systems. Then, the existing overhead-cable lines connecting Sicily to the rest of continental Europe 400 kV power system are taken as case study for the application of the proposed switching strategy. Several simulations are performed in the power system analysis software NEPLAN360: the results show the fundamental role of the timing of the control actions applied on the shunt reactors in helping the system to keep the stability. The proposed control proves to be an effective support to the system subjected to critical contingencies, contributing decisively to avoid the angular separation between areas and therefore to preserve the stability of the system.

The Studies of Stability of Non-Interval Gray Verhulst Model

2013 ◽  
Vol 779-780 ◽  
pp. 1701-1704 ◽  
Author(s):  
Xian Sheng Fan ◽  
Xiao Chun Shi
Keyword(s):  
System Analysis ◽  
System Model ◽  
Time Interval ◽  
Interval Model ◽  
Model Stability ◽  
Analysis And Design ◽  
Development Factor ◽  
New Ideas ◽  
The Stability ◽  
Primary Problem

For the system analysis and design, the research of the stability of system model has always been the primary problem to considerate and solve, unstable system is actually not paid for use. Combining classic mathematical analysis and Lyapunov (Lyapunov) stability of the Criterion, we get the stability of the conclusions that its asymptotic stability only depend on development factor, regardless of the gray action and time interval .The research provide new ideas and methods for non-interval model stability studies.

scholarly journals Dynamic stability of functionally graded plate under in-plane compression

2005 ◽  
Vol 2005 (4) ◽  
pp. 411-424 ◽  
Author(s):  
Andrzej Tylikowski
Keyword(s):  
Asymptotic Stability ◽  
Power Law ◽  
Volume Fraction ◽  
Direct Method ◽  
Functionally Graded ◽  
Time Dependent ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Plane State ◽  
The Stability

Functionally graded materials have gained considerable attention in the high-temperature applications. A study of parametric vibrations of functionally graded plates subjected to in-plane time-dependent forces is presented. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. Material properties are graded in the thickness direction of the plate according to volume fraction power law distribution. An oscillating temperature causes generation of in-plane time-dependent forces destabilizing the plane state of the plate equilibrium. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov's direct method. Effects of power law exponent on the stability domains are studied.

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