An analogue to the A$(\vartheta)$-stability concept for implicit-explicit BDF methods

2020 ◽  
Vol 58 (6) ◽  
pp. 3475-3503
Author(s):  
Georgios Akrivis ◽  
Emmanouil Katsoprinakis
Keyword(s):  
Bdf Methods ◽  
Stability Concept

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

scholarly journals (M,β)-Stability of Positive Linear Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Octavian Pastravanu ◽  
Mihaela-Hanako Matcovschi
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Transient Behavior ◽  
Short Term ◽  
Time Dynamics ◽  
The Right ◽  
Long Term Behavior ◽  
Stability Concept

The main purpose of this work is to show that the Perron-Frobenius eigenstructure of a positive linear system is involved not only in the characterization of long-term behavior (for which well-known results are available) but also in the characterization of short-term or transient behavior. We address the analysis of the short-term behavior by the help of the “(M,β)-stability” concept introduced in literature for general classes of dynamics. Our paper exploits this concept relative to Hölder vectorp-norms,1≤p≤∞, adequately weighted by scaling operators, focusing on positive linear systems. Given an asymptotically stable positive linear system, for each1≤p≤∞, we prove the existence of a scaling operator (built from the right and left Perron-Frobenius eigenvectors, with concrete expressions depending onp) that ensures the best possible values for the parametersMandβ, corresponding to an “ideal” short-term (transient) behavior. We provide results that cover both discrete- and continuous-time dynamics. Our analysis also captures the differences between the cases where the system dynamics is defined by matrices irreducible and reducible, respectively. The theoretical developments are applied to the practical study of the short-term behavior for two positive linear systems already discussed in literature by other authors.

scholarly journals Extending convergence of BDF methods for a class of nonlinear strongly stiff problems

2000 ◽  
Vol 126 (1-2) ◽  
pp. 121-130 ◽  
Author(s):  
Aiguo Xiao ◽  
Shoufu Li ◽  
Hongyuan Fu ◽  
Guangnan Chen
Keyword(s):  
Stiff Problems ◽  
Bdf Methods

scholarly journals On the three term recurrence relation and BDF methods

2020 ◽  
Author(s):  
Larissa Ferreira Marques ◽  
Vanessa Botta ◽  
Messias Meneguette
Keyword(s):  
Recurrence Relation ◽  
Bdf Methods ◽  
Three Term Recurrence Relation

Scale and modify for the second and third order BDF methods

2009 ◽  
Vol 53 (2-3) ◽  
pp. 261-280 ◽  
Author(s):  
Allison Heard
Keyword(s):  
Third Order ◽  
Bdf Methods

Optimal feedback control of twin rotor MIMO system with a prescribed degree of stability

2016 ◽  
Vol 4 (4) ◽  
pp. 226-238 ◽  
Author(s):  
Santosh Kumar Choudhary
Keyword(s):  
Optimal Control ◽  
Tracking Control ◽  
Mimo System ◽  
Control Solution ◽  
Content Type ◽  
Degree Of Stability ◽  
Twin Rotor Mimo System ◽  
Posture Stabilization ◽  
Twin Rotor ◽  
Stability Concept

Purpose The purpose of this paper is to investigate an optimal control solution with prescribed degree of stability for the position and tracking control problem of the twin rotor multiple input-multiple output (MIMO) system (TRMS). The twin rotor MIMO system is a benchmark aerodynamical laboratory model having strongly non-linear characteristics and unstable coupling dynamics which make the control of such system for either posture stabilization or trajectory tracking a challenging task. Design/methodology/approach This paper first describes the dynamical model of twin rotor MIMO system (TRMS) and then it adopts linear-quadratic regulator (LQR)-based optimal control technique with prescribed degree of stability to achieve the desired trajectory or posture stabilization of TRMS. Findings The simulation results show that the investigated controller has both static and dynamic performance; therefore, the stability and the quick control effect can be obtained simultaneously for the twin rotor MIMO system. Originality/value The articles on LQR optimal controllers for TRMS can also be found in many literatures, but the prescribed degree of stability concept was not discussed in any of the paper. In this work, new LQR with the prescribed degree of stability concept is applied to provide an optimal control solution for the position and tracking control problem of TRMS.

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