Stability of Cyclic Dynamical Systems

1975 ◽  
Vol 97 (4) ◽  
pp. 393-398
Author(s):  
J. R. Dickerson ◽  
P. Erickson
Keyword(s):  
Dynamical Systems ◽  
Closed Loop ◽  
The State ◽  
Exact Results ◽  
The Stability ◽  
Stability Results

The stability of a closed loop of vehicles which are controlled by identical functions of the state of neighboring vehicles is investigated. The paper is divided into two parts, formulation and stability results for cyclic dynamical systems and, application of these results to three example problems with comparison to exact results when possible.

scholarly journals Distributed Coordination of Fractional Dynamical Systems with Exogenous Disturbances

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Hongyong Yang ◽  
Fujun Han ◽  
Fei Liu ◽  
Huixia Liu ◽  
Mei Zhao
Keyword(s):  
Dynamical Systems ◽  
Multiagent Systems ◽  
State Observer ◽  
The State ◽  
Distributed Coordination ◽  
External Disturbances ◽  
Reference Tracking ◽  
Exogenous Disturbances ◽  
The Stability ◽  
Fractional Dynamical System

Distributed coordination of fractional multiagent systems with external disturbances is studied. The state observer of fractional dynamical system is presented, and an adaptive pinning controller is designed for a little part of agents in multiagent systems without disturbances. This adaptive pinning controller with the state observer can ensure multiple agents' states reaching an expected reference tracking. Based on disturbance observers, the controllers are composited with the pinning controller and the state observer. By applying the stability theory of fractional order dynamical systems, the distributed coordination of fractional multiagent systems with external disturbances can be reached asymptotically.

Adaptive Global Stability of Nonlinear Pure-Feedback Systems With Unknown Time-Varying Delays

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Jun Guo ◽  
Yao Wang ◽  
Yuming Bo
Keyword(s):  
Time Delay ◽  
Coordinate Transformation ◽  
Stability Theory ◽  
Closed Loop ◽  
Uniform Boundedness ◽  
The State ◽  
Time Varying ◽  
Feedback Systems ◽  
The Stability ◽  
Delay Dependent

Abstract This paper investigates the backstepping control problem for nonlinear pure-feedback systems with time-varying delays. A virtual controller is designed to counteract the effects caused by the state perturbation of time delay, and improve the stability of the system. The assumption on delay-dependent nonlinearities is further relaxed by a backstepping auxiliary controller and a Lyapunov–Krasovskii functional. A suitable coordinate transformation is introduced to reduce the complexity of computation caused by nonaffine structures. The globally uniform boundedness of the closed-loop signals and the asymptotical stability of the state are proved by Lyapunov–Krasovskii stability theory. Finally, the effectiveness of our method is demonstrated by two illustrations.

Epitaxial Growth in Dislocation-Free Strained Alloy Films

2002 ◽  
Vol 715 ◽  
Author(s):  
Zhi-Feng Huang ◽  
Rashmi C. Desai
Keyword(s):  
Deposition Rate ◽  
Elastic Moduli ◽  
Composition Dependence ◽  
Critical Thickness ◽  
Lattice Misfit ◽  
Misfit Strain ◽  
Joint Stability ◽  
Alloy Films ◽  
The Stability ◽  
Stability Results

AbstractThe morphological and compositional instabilities in the heteroepitaxial strained alloy films have attracted intense interest from both experimentalists and theorists. To understand the mechanisms and properties for the generation of instabilities, we have developed a nonequilibrium, continuum model for the dislocation-free and coherent film systems. The early evolution processes of surface pro.les for both growing and postdeposition (non-growing) thin alloy films are studied through a linear stability analysis. We consider the coupling between top surface of the film and the underlying bulk, as well as the combination and interplay of different elastic effects. These e.ects are caused by filmsubstrate lattice misfit, composition dependence of film lattice constant (compositional stress), and composition dependence of both Young's and shear elastic moduli. The interplay of these factors as well as the growth temperature and deposition rate leads to rich and complicated stability results. For both the growing.lm and non-growing alloy free surface, we determine the stability conditions and diagrams for the system. These show the joint stability or instability for film morphology and compositional pro.les, as well as the asymmetry between tensile and compressive layers. The kinetic critical thickness for the onset of instability during.lm growth is also calculated, and its scaling behavior with respect to misfit strain and deposition rate determined. Our results have implications for real alloy growth systems such as SiGe and InGaAs, which agree with qualitative trends seen in recent experimental observations.

Cracking national integration after the events (the Arab Spring) and its impact On regional stability

2019 ◽  
Vol 3 (6) ◽  
pp. 1
Author(s):  
Muhannad Al Janabi Al Janabi
Keyword(s):  
Arab Spring ◽  
The State ◽  
The Political ◽  
Prominent Feature ◽  
Regional Stability ◽  
National Integration ◽  
Arab Region ◽  
Political Media ◽  
The Stability ◽  
The Arab Spring

Since late 2010 and early 2011, the Arab region has witnessed mass protests in Tunisia, Egypt, Libya, Syria, Yemen, Iraq, Bahrain and other countries that have been referred to in the political, media and other literature as the Arab Spring. These movements have had a profound effect on the stability of the regimes Which took place against it, as leaders took off and contributed to radical reforms in party structures and public freedoms and the transfer of power, but it also contributed to the occurrence of many countries in an internal spiral, which led to the erosion of the state from the inside until it became a prominent feature of the Arab) as is the case in Syria, Libya, Yemen and Iraq.

IMPACT OF GOVERNMENT DEBT ON FINANCIAL SECURITY OF UKRAINE

2017 ◽  
Author(s):  
Olena Pikaliuk ◽  
◽  
Dmitry Kovalenko ◽  
Keyword(s):  
Economic Development ◽  
Public Debt ◽  
Positive Impact ◽  
The State ◽  
Financial Security ◽  
State Budget ◽  
The Public ◽  
Debt Security ◽  
The Stability ◽  
The Impact

One of the main criteria for economic development is the size of the public debt and its dynamics. The article considers the impact of public debt on the financial security of Ukraine. The views of scientists on the essence of public debt and financial security of the state are substantiated. An analysis of the dynamics and structure of public debt of Ukraine for 2014-2019. It is proved that one of the main criteria for economic development is the size of public debt and its dynamics. State budget deficit, attracting and using loans to cover it have led to the formation and significant growth of public debt in Ukraine. The volume of public debt indicates an increase in the debt security of the state, which is a component of financial security. Therefore, the issue of the impact of public debt on the financial security of Ukraine is becoming increasingly relevant. The constant growth and large amounts of debt make it necessary to study it, which will have a positive impact on economic processes that will ensure the stability of the financial system and enhance its security.

A simulation apparatus for the experimental study of batch reactor control methods

1986 ◽  
Vol 51 (6) ◽  
pp. 1259-1267
Author(s):  
Josef Horák ◽  
Petr Beránek
Keyword(s):  
Experimental Study ◽  
Closed Loop ◽  
Dynamic Properties ◽  
Batch Reactor ◽  
Exothermic Reaction ◽  
Electric Heating ◽  
Batch Reactors ◽  
Exchange Area ◽  
The Stability ◽  
Methods Of Control

A simulation apparatus for the experimental study of the methods of control of batch reactors is devised. In this apparatus, the production of heat by an exothermic reaction is replaced by electric heating controlled by a computer in a closed loop; the reactor is cooled with an external cooler whose dynamic properties can be varied while keeping the heat exchange area constant. The effect of the cooler geometry on its dynamic properties is investigated and the effect of the cooler inertia on the stability and safety of the on-off temperature control in the unstable pseudostationary state is examined.

Adaptive attitude-tracking control of spacecraft considering on-orbit refuelling

2020 ◽  
pp. 014233122097313
Author(s):  
Yiqi Xu
Keyword(s):  
Tracking Control ◽  
Closed Loop ◽  
Closed Loop System ◽  
Tracking Errors ◽  
Attitude Tracking ◽  
Control Scheme ◽  
Inertia Model ◽  
And Performance ◽  
Attitude Tracking Control ◽  
The Stability

This paper studies the attitude-tracking control problem of spacecraft considering on-orbit refuelling. A time-varying inertia model is developed for spacecraft on-orbit refuelling, which actually includes two processes: fuel in the transfer pipe and fuel in the tank. Based upon the inertia model, an adaptive attitude-tracking controller is derived to guarantee the stability of the resulted closed-loop system, as well as asymptotic convergence of the attitude-tracking errors, despite performing refuelling operations. Finally, numerical simulations illustrate the effectiveness and performance of the proposed control scheme.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

scholarly journals Phase Synchronization Is the Amplified Result by the Hilbert Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Chi Lu ◽  
Hsing-Chung Ho ◽  
Chen-An Chan ◽  
Chia-Ju Liu ◽  
Jiann-Shing Lih ◽  
...  
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Hilbert Transform ◽  
Phase Synchronization ◽  
Nonlinear Dynamical Systems ◽  
The State ◽  
Nonlinear Dynamical ◽  
Large Correlation ◽  
Current Usage ◽  
The Hilbert Transform

We investigate the interplay between phase synchronization and amplitude synchronization in nonlinear dynamical systems. It is numerically found that phase synchronization intends to be established earlier than amplitude synchronization. Nevertheless, amplitude synchronization (or the state with large correlation between the amplitudes) is crucial for the maintenance of a high correlation between two time series. A breakdown of high correlation in amplitudes will lead to a desynchronization of two time series. It is shown that these unique features are caused essentially by the Hilbert transform. This leads to a deep concern and criticism on the current usage of phase synchronization.

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