scholarly journals Dynamics of Physical Autonomous Robotic Network With Constant And Time-Varying Communication Delays

2021 ◽  
Author(s):  
Kuei-Fang Hsueh ◽  
Isam Al-Darabsah ◽  
Mohammad Al Janaideh ◽  
Sue Ann Campbell ◽  
Deepa Kundur
Keyword(s):  
Time Delay ◽  
Traffic Congestion ◽  
Autonomous Robots ◽  
Autonomous Vehicle ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Communication Delays ◽  
Delay Function ◽  
Flow Equilibrium ◽  
The Stability

Abstract A Connected Autonomous Vehicle Network (CAVN) is an emerging paradigm that can reduce traffic congestion by allowing vehicles to cooperatively behave according to information out of the line of sight and improve traffic flow by decreasing inter-vehicular gaps on roadways. In this paper, the stability of CAVN with constant and time-varying communication delays is studied. When the time delay depends on time, the semi-discretization method is used to study the plant stability of the flow equilibrium of CAVN and construct approximate stability regions charts over control gain space. To study the influence of time-varying delay, a constant delay is considred as the average value of the time delay function. Then, explicit sufficient conditions are provided for the stability of the flow equilibrium and study the string stability of the CAVN. The proposed controller is validated using simulations and experimentally with a platoon of four autonomous robots under time-varying delays.

scholarly journals Discrete-time systems with time-varying time delay: Stability and stabilizability

2006 ◽  
Vol 2006 ◽  
pp. 1-10 ◽  
Author(s):  
El-Kébir Boukas
Keyword(s):  
Time Delay ◽  
Discrete Time ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Design Algorithm ◽  
Time Varying Delay ◽  
Discrete Time Systems ◽  
Varying Time Delay ◽  
The Stability ◽  
Time Systems

This paper deals with the class of linear discrete-time systems with varying time delay. The problems of stability and stabilizability for this class of systems are considered. Given an upper bound and a lower bound on the time-varying delay, sufficient conditions for checking the stability of this class of systems are developed. A control design algorithm is also provided. All the results developed in this paper are in the LMI formalism which makes their solvability easier using existing tools. A numerical example is provided to show the effectiveness of the established results.

scholarly journals Global Exponential Robust Stability of Static Interval Neural Networks with Time Delay in the Leakage Term

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guiying Chen ◽  
Linshan Wang
Keyword(s):  
Neural Networks ◽  
Time Delay ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Leakage Term ◽  
Interval Neural Networks ◽  
Global Exponential Robust Stability ◽  
The Stability ◽  
Delay Differential ◽  
Delay Differential Inequality

The stability of a class of static interval neural networks with time delay in the leakage term is investigated. By using the method ofM-matrix and the technique of delay differential inequality, we obtain some sufficient conditions ensuring the global exponential robust stability of the networks. The results in this paper extend the corresponding conclusions without leakage delay. An example is given to illustrate the effectiveness of the obtained results.

Exponential stability and periodicity of memristor-based recurrent neural networks with time-varying delays

2017 ◽  
Vol 10 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Wei Zhang ◽  
Chuandong Li ◽  
Tingwen Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Inclusion Theory ◽  
The Stability

In this paper, the stability and periodicity of memristor-based neural networks with time-varying delays are studied. Based on linear matrix inequalities, differential inclusion theory and by constructing proper Lyapunov functional approach and using linear matrix inequality, some sufficient conditions are obtained for the global exponential stability and periodic solutions of memristor-based neural networks. Finally, two illustrative examples are given to demonstrate the results.

scholarly journals Mathematical analysis of a cancer model with time-delay in tumor-immune interaction and stimulation processes

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kaushik Dehingia ◽  
Hemanta Kumar Sarmah ◽  
Yamen Alharbi ◽  
Kamyar Hosseini
Keyword(s):  
Time Delay ◽  
Immune Responses ◽  
Periodic Solutions ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Cancer Model ◽  
Delay Effect ◽  
Discrete Time Delay ◽  
The Stability ◽  
Vital Parameters

AbstractIn this study, we discuss a cancer model considering discrete time-delay in tumor-immune interaction and stimulation processes. This study aims to analyze and observe the dynamics of the model along with variation of vital parameters and the delay effect on anti-tumor immune responses. We obtain sufficient conditions for the existence of equilibrium points and their stability. Existence of Hopf bifurcation at co-axial equilibrium is investigated. The stability of bifurcating periodic solutions is discussed, and the time length for which the solutions preserve the stability is estimated. Furthermore, we have derived the conditions for the direction of bifurcating periodic solutions. Theoretically, it was observed that the system undergoes different states if we vary the system’s parameters. Some numerical simulations are presented to verify the obtained mathematical results.

Co-operative 3D salvo attack of multiple missiles under switching topologies subject to time-varying communication delays

2019 ◽  
Vol 123 (1262) ◽  
pp. 464-483
Author(s):  
X.L. Ai ◽  
L.L. Wang ◽  
Y.C. Shen
Keyword(s):  
Initial Conditions ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Communication Delays ◽  
Proportional Navigation ◽  
Stationary Target ◽  
Switching Topologies ◽  
Guidance Law ◽  
Multiple Missiles ◽  
Proportional Navigation Guidance

ABSTRACTThis study focuses on the co-operative salvo attack problem of multiple missiles against a stationary target under jointly connected switching topologies subject to time-varying communication delays. By carefully exploring certain features of the typical pure proportional navigation guidance law, a two-stage distributed guidance scheme is proposed without any information on time-to-go in this study to realise the simultaneous attack of multiple missiles. In the first guidance stage, a co-operative guidance law is proposed using local neighbouring communications only to achieve consensus on range-to-go and heading error to provide favourable initial conditions for the latter phase, in which switching topologies and time-varying communication delays are taken into account when obtaining sufficient conditions of consensus in terms of linear matrix inequalities. Then, missiles disconnect from each other and are guided individually by the typical pure proportional navigation guidance law with the same navigation gain to realise salvo attack in the second guidance phase. Finally, numerical simulations are carried out to clearly validate the theoretical results.

Reduced-order observer-based consensus control of linear multi-agent systems over directed networks with nonuniform communication delays

2020 ◽  
pp. 014233122093430
Author(s):  
Qiuzhen Wang ◽  
Jiangping Hu ◽  
Yiyi Zhao ◽  
Bijoy Kumar Ghosh
Keyword(s):  
Time Varying ◽  
Communication Delays ◽  
Multi Agent Systems ◽  
Consensus Control ◽  
Reduced Order ◽  
Reduced Order Observer ◽  
Multi Agent ◽  
The Stability ◽  
Output Information ◽  
Theoretical Results

This paper considers a consensus control of a general linear multi-agent system with time-varying communication delays. Since each agent can only use the relative output information from its neighbors, a reduced-order observer-based control protocol is proposed to guarantee consensus on the directed communication network. The stability of the closed-loop system is analyzed for the cases with uniform delays and nonuniform time-varying delays, respectively. Moreover, the upper bounds of the communication delays are obtained respectively for the two cases. Finally, two numerical examples are provided to illustrate the proposed theoretical results.

scholarly journals A Panoramic Sketch about the Robust Stability of Time-Delay Systems and Its Applications

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-26
Author(s):  
Baltazar Aguirre-Hernández ◽  
Raúl Villafuerte-Segura ◽  
Alberto Luviano-Juárez ◽  
Carlos Arturo Loredo-Villalobos ◽  
Edgar Cristian Díaz-González
Keyword(s):  
Time Delay ◽  
Dynamical Systems ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Time Delay Systems ◽  
Complex Dynamical Systems ◽  
The Stability ◽  
Numerical Approaches

This paper presents a brief review on the current applications and perspectives on the stability of complex dynamical systems, with an emphasis on three main classes of systems such as delay-free systems, time-delay systems, and systems with uncertainties in its parameters, which lead to some criteria with necessary and/or sufficient conditions to determine stability and/or stabilization in the domains of frequency and time. Besides, criteria on robust stability and stability of nonlinear time-delay systems are presented, including some numerical approaches.

Bifurcation and stability of periodic solutions of differential equations with state-dependent delays

2003 ◽  
Vol 14 (1) ◽  
pp. 3-14 ◽  
Author(s):  
D. SCHLEY
Keyword(s):  
Time Delay ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Perturbation Methods ◽  
Population Models ◽  
Delay Function ◽  
State Dependent ◽  
The Stability ◽  
Bifurcation And Stability

We consider periodic solutions which bifurcate from equilibria in simple population models which incorporate a state-dependent time delay of the discrete kind. The delay is a function of the current size of the population. Solutions near equilibria are constructed using perturbation methods to determine the sub/supercriticality of the bifurcation and hence their stability. The stability of the bifurcating solutions depends on the qualitative form of the delay function. This is in contrast to the stability of an equilibrium, which is determined purely by the actual value of this function at the equilibrium.

State feedback observer-based control design for linear descriptor systems with multiple time-varying delays

2020 ◽  
Vol 37 (4) ◽  
pp. 1218-1236
Author(s):  
V N Phat ◽  
P Niamsup ◽  
N H Muoi
Keyword(s):  
State Feedback ◽  
Design Method ◽  
Sufficient Conditions ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Feedback Controllers ◽  
Delay Function ◽  
Delay Dependent

Abstract In this paper, we propose an linear matrix inequality (LMI)-based design method to observer-based control problem of linear descriptor systems with multiple time-varying delays. The delay function can be continuous and bounded but not necessarily differentiable. First, by introducing a new set of improved Lyapunov–Krasovskii functionals that avoid calculating the derivative of the delay function, we obtain new delay-dependent sufficient conditions for guaranteeing the system to be regular, impulse-free and asymptotically stable. Then, based on the derived stability conditions, we design state feedback controllers and observer gains via LMIs, which can be solved numerically in standard computational algorithms. A numerical example with simulation is given to demonstrate the efficiency and validity of the proposed deign.

Dynamic Stability of a Nonlinear Cylindrical Shell

1984 ◽  
Vol 51 (4) ◽  
pp. 852-856 ◽  
Author(s):  
A. Tylikowski
Keyword(s):  
Cylindrical Shell ◽  
Sufficient Conditions ◽  
Middle Surface ◽  
Elastic Cylindrical Shell ◽  
Time Varying ◽  
Liapunov Method ◽  
Linearized Problem ◽  
Nonlinear Shell ◽  
The Stability ◽  
Radial Loading

The stability of the undeflected middle surface of a uniform elastic cylindrical shell governed by Ka´rma´n’s equations is studied. The shell is being subjected to a time-varying axial compression as well as a uniformly distributed time-varying radial loading. Using the direct Liapunov method sufficient conditions for deterministic asymptotic as well as stochastic stability are obtained. A relation between stability conditions of a linearized problem and that of Ka´rma´n’s equations is found. Contrary to the stability theory of nonlinear plates it is established that the linearized problem should be modified to ensure the stability of the nonlinear shell. The case when the shell is governed by the Itoˆ stochastic nonlinear equations is also discussed.

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