Construction of a new Lyapunov function for a dissipative gyroscopic system using the residual energy function

2020 ◽  
Vol 21 (4) ◽  
pp. 629-634
Author(s):  
Cem Civelek ◽  
Özge Cihanbeğendi
Keyword(s):  
Lyapunov Function ◽  
Energy Function ◽  
Residual Energy ◽  
Gyroscopic System

scholarly journals Discrete Lyapunov function by means of a discrete residual energy function and stability analysis for discrete time physical systems

2021 ◽  
Author(s):  
Cem Civelek
Keyword(s):  
Stability Analysis ◽  
Lyapunov Function ◽  
Dynamic System ◽  
Discrete Time ◽  
Energy Function ◽  
Residual Energy ◽  
Discrete Time System ◽  
Dissipation Energy ◽  
Physical Systems ◽  
D Model

In this research paper beginning from the fundamental concepts, all the basic approach is introduced for short. Then after obtaining the discrete Lagrange-dissipative model ({L,D}- model for short) of a discrete time observed physical/engineering dynamic system, the model will be used to develope the discrete Hamiltonian together with discrete dissipation energy as discrete Lyapunov function and as such, a systematic method is proposed to obtain discrete Lyapunov function in form of a residual energy function for discrete (time) observed physical systems to analyze the discrete time system related to stability. Stability analysis of a discrete time observed physical dynamic system is performed using discrete Lyapunov function in form of a residual energy function consisting of Hamiltonian together with dissipation energy. Application of the method was shown using two discrete time physical examples, one of which is a coupled one and time dependent. This coupled physical discrete time example is analyzed related to stability using two different formulations, one form of which leads to a result.

Construction of Lyapunov Function for Dissipative Gyroscopic System

2011 ◽  
Vol 28 (5) ◽  
pp. 050201 ◽  
Author(s):  
Wei Xu ◽  
Bo Yuan ◽  
Ping Ao
Keyword(s):  
Lyapunov Function ◽  
Gyroscopic System

scholarly journals Morse-Bott energy function for surface Ω-stable flows

2020 ◽  
Vol 22 (4) ◽  
pp. 434-441
Author(s):  
Anna E. Kolobyanina ◽  
Vladislav E. Kruglov
Keyword(s):  
Lyapunov Function ◽  
Finite Number ◽  
Fixed Points ◽  
Structural Stability ◽  
Limit Cycles ◽  
Energy Function ◽  
Hyperbolic Fixed Points ◽  
Smale Flows ◽  
Flows On Surfaces

In this paper, we consider the class of Ω-stable flows on surfaces, i.e. flows on surfaces with the non-wandering set consisting of a finite number of hyperbolic fixed points and a finite number of hyperbolic limit cycles. The class of Ω -stable flows is a generalization of the class of Morse-Smale flows, admitting the presence of saddle connections that do not form cycles. The authors have constructed the Morse-Bott energy function for any such flow. The results obtained are an ideological continuation of the classical works of S. Smale, who proved the existence of the Morse energy function for gradient-like flows, and K. Meyer, who established the existence of the Morse-Bott energy function for Morse-Smale flows. The specificity of Ω-stable flows takes them beyond the framework of structural stability, but the decrease along the trajectories of such flows is still tracked by the regular Lyapunov function.

scholarly journals Novel stability and passivity analysis for three types of nonlinear LRC circuits

2021 ◽  
Vol 11 (2) ◽  
pp. 227-237
Author(s):  
Muzaffer Ates ◽  
Nezir Kadah
Keyword(s):  
Lyapunov Function ◽  
Energy Function ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Lyapunov Theory ◽  
Neural Systems ◽  
Theoretical Predictions ◽  
The Stability ◽  
Lyapunov Energy Function ◽  
Rlc Circuits

In this paper, the global asymptotic stability and strict passivity of three types of nonlinear RLC circuits are investigated by utilizing the Lyapunov direct method. The stability conditions are obtained by constructing appropriate Lyapunov function, which demonstrates the practical application of the Lyapunov theory with a clear perspective.  The meaning of Lyapunov functions is not clear by many specialists whose studies based on Lyapunov theory. They construct Lyapunov functions by using some properties of Lyapunov functions with much trial and errors or for a system choose candidate Lyapunov functions. So, for a given system Lyapunov function is not unique. But we insist that Lyapunov (energy) function is unique for a given physical system. In this study we highly simplified Lyapunov’s direct method with suitable tools. Our approach constructing energy function based on power-energy relationship that also enable us to take the derivative of integration of energy function. These aspects have not been addressed in the literature. This paper is an attempt towards filling this gap. The results are provided within and are of central importance for the analysis of nonlinear electrical, mechanical, and neural systems which based on the system energy perspective. The simulation results given from Matlab successfully verifies the theoretical predictions.

MONITORING THE TOPOLOGY OF GROWING DYNAMICAL NETWORKS

2010 ◽  
Vol 21 (08) ◽  
pp. 1051-1063 ◽  
Author(s):  
ZHAOYAN WU ◽  
XINCHU FU ◽  
GUANRONG CHEN
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Energy Function ◽  
Function Method ◽  
Sufficient Conditions ◽  
Adaptive Strategy ◽  
Linear Feedback ◽  
Linear Feedback Control ◽  
Lyapunov Function Method ◽  
Growing Networks

In this paper, topology monitoring of growing networks is studied. When some new nodes are added into a network, the topology of the network is changed, which needs to be monitored in many applications. Some auxiliary systems (network monitors) are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied to designing such network monitors. Based on the Lyapunov function method via constructing a potential or energy function decreasing along any solution of the system, and the LaSalle's invariance principle, which is a generalization of the Lyapunov function method, some sufficient conditions for achieving topology monitoring are obtained. Illustrative examples are provided to demonstrate the effectiveness of the new method.

Distributed Entropy Energy-Efficient Clustering algorithm for cluster head selection (DEEEC)

2020 ◽  
Vol 39 (6) ◽  
pp. 8139-8147
Author(s):  
Ranganathan Arun ◽  
Rangaswamy Balamurugan
Keyword(s):  
Energy Efficient ◽  
Clustering Algorithm ◽  
Cluster Head ◽  
Residual Energy ◽  
Energy Utilization ◽  
Sensor Nodes ◽  
Second Stage ◽  
Energy Efficient Clustering ◽  
Two Stages ◽  
Ch Selection

In Wireless Sensor Networks (WSN) the energy of Sensor nodes is not certainly sufficient. In order to optimize the endurance of WSN, it is essential to minimize the utilization of energy. Head of group or Cluster Head (CH) is an eminent method to develop the endurance of WSN that aggregates the WSN with higher energy. CH for intra-cluster and inter-cluster communication becomes dependent. For complete, in WSN, the Energy level of CH extends its life of cluster. While evolving cluster algorithms, the complicated job is to identify the energy utilization amount of heterogeneous WSNs. Based on Chaotic Firefly Algorithm CH (CFACH) selection, the formulated work is named “Novel Distributed Entropy Energy-Efficient Clustering Algorithm”, in short, DEEEC for HWSNs. The formulated DEEEC Algorithm, which is a CH, has two main stages. In the first stage, the identification of temporary CHs along with its entropy value is found using the correlative measure of residual and original energy. Along with this, in the clustering algorithm, the rotating epoch and its entropy value must be predicted automatically by its sensor nodes. In the second stage, if any member in the cluster having larger residual energy, shall modify the temporary CHs in the direction of the deciding set. The target of the nodes with large energy has the probability to be CHs which is determined by the above two stages meant for CH selection. The MATLAB is required to simulate the DEEEC Algorithm. The simulated results of the formulated DEEEC Algorithm produce good results with respect to the energy and increased lifetime when it is correlated with the current traditional clustering protocols being used in the Heterogeneous WSNs.

Developing Multi-Tier Network Design for Effective Energy Consumption of Cluster Head Selection in WSN

2016 ◽  
Vol 13 (1) ◽  
pp. 116
Author(s):  
Wan Isni Sofiah Wan Din ◽  
Saadiah Yahya ◽  
Mohd Nasir Taib ◽  
Ahmad Ihsan Mohd Yassin ◽  
Razulaimi Razali
Keyword(s):  
Sensor Network ◽  
Clustering Algorithm ◽  
Cluster Head ◽  
Residual Energy ◽  
Sensor Nodes ◽  
Cluster Head Selection ◽  
Energy Usage ◽  
Network Cluster ◽  
Fuzzy Logic Approach ◽  
The Stability

Clustering in Wireless Sensor Network (WSN) is one of the methods to minimize the energy usage of sensor network. The design of sensor network itself can prolong the lifetime of network. Cluster head in each cluster is an important part in clustering to ensure the lifetime of each sensor node can be preserved as it acts as an intermediary node between the other sensors. Sensor nodes have the limitation of its battery where the battery is impossible to be replaced once it has been deployed. Thus, this paper presents an improvement of clustering algorithm for two-tier network as we named it as Multi-Tier Algorithm (MAP). For the cluster head selection, fuzzy logic approach has been used which it can minimize the energy usage of sensor nodes hence maximize the network lifetime. MAP clustering approach used in this paper covers the average of 100Mx100M network and involves three parameters that worked together in order to select the cluster head which are residual energy, communication cost and centrality. It is concluded that, MAP dominant the lifetime of WSN compared to LEACH and SEP protocols. For the future work, the stability of this algorithm can be verified in detailed via different data and energy. 

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