Sharif Digital Repository

In this paper, a diffusive predator-prey system with general functional responses and prey-tactic sensitivities is studied. Providing such generality, we construct a Lyapunov function and we show that the positive constant steady state is locally and globally asymptotically stable. With an eye on the biological interpretations, a numerical simulation is performed to illustrate the feasibility of the analytical findings  

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link’s transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link’s transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to... 

This paper is concerned with global analysis of a delay SVEIR epidemiological model in a population of varying size. By using Lyapunov stability method and LaSalle's invariance principle for delay systems, we prove that when there is no endemic equilibrium, the disease free equilibrium is globally asymptotically stable, otherwise the endemic equilibrium is globally stable  

In this paper, a class of uncertain piecewise affine (PWA) systems, subject to system and measurement external disturbances are studied. The uncertainties are assumed to be norm bounded and the external disturbance signals belong to the L2 space. The problem of optimizing the system response in the H?sense, by means of a piecewise affine observer-controller, is formulated as an optimization problem subject to a number of constraints in the form of matrix inequalities. The derived constraints are obtained by considering a partially piecewise quadratic Lyapunov function in combination with the general conditions for H?stability. Then the uncertain PWA approximation of the nonlinear attitude... 

In a wireless powered communication network, an energy access point (EAP) supplies the energy needs of the network nodes through radio frequency wave transmission, and the nodes store the received energy in their batteries for their future data transmission. In this paper, we propose an online stochastic policy that jointly controls energy transmission from the EAP to the nodes and data transfer among the nodes. Our proposed policy is designed using a quadratic Lyapunov function to capture the limitations on the energy consumption of the nodes imposed by their battery level. The proposed policy is adaptive to different channel statistics of the network. We provide theoretical analysis for... 

In this paper, an oscillatory condition is obtained for fractional order relay feedback systems. This condition is derived by time domain representation of the response of the fractional order relay feedback system on the basis of the Mittag-Leffler functions. Also, using an inequality, which has been recently proved for fractional derivative of convex Lyapunov functions, an invariant set is found for the under-study fractional order relay feedback system. The obtained results are validated by numerical examples  

In this note, it is shown that the Lyapunov function-based analyses done in the above-titled article to design a backstepping sliding mode controller contain some drawbacks. These drawbacks include ignoring some terms in simplification of time-derivative of the considered Lyapunov functions, which do not vanish in a finite-time. Moreover, by presenting a counterexample, it is revealed that the finite-time convergence of the error signals cannot be necessarily concluded from a Lyapunov function-based inequality used in the aforementioned article. © 2004-2012 IEEE  

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link’s transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link’s transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to... 

In this paper a nonlinear control method based on Lyapunov stability theorem is proposed to design an adaptive controller for synchronizing two different chaotic systems. It is assumed that the unknown parameters of the drive and the response chaotic systems are time varying. It is shown that the proposed scheme can identify the system parameters if the system parameters are time invariant and the richness conditions is satisfied. To demonstrate the effectiveness of the proposed technique it has been applied to Lorenz-Chen dynamic systems, as drive-response systems. Simulation results indicate that the proposed adaptive controller has a high performance in synchronizing two chaotic systems.... 

This paper will consider the mathematical definition of chaos (in sense of Devaney) in order to select appropriate chaos tests. The tests chosen according to investigate the properties mentioned in the definition. In fact, these are prerequisites of chaoticity. Either it will be represented that "sensitivity dependence on initial conditions" is not equivalent to chaos, although some researchers considering it. Hence, it is implied that checking all of the properties mentioned in the definition are required to establish chaos. As our case study, some sample stocks were selected from Tehran Stock Exchange (TSE) and the chosen tests implemented on their returns time series. Incoming results... 

This paper presents chaos synchronization between two different chaotic systems when the parameters of the drive and response systems are fully unknown and uncertain. Based on Lyapunov stability theory, an adaptive control law is designed such that the two different chaotic systems are to be synchronized. The proposed technique is applied to achieve chaos synchronization for the Chen and Lorenz dynamical systems. Numerical simulations are implemented to verify the results. © 2005 IEEE  

The dynamics driven interaction between the bubbles in a cavitation cluster is known to be a complex phenomenon indicative of a highly active nonlinear as well as chaotic behavior in ultrasonic fields. By considering the cluster of encapsulated microbubble with a thin elastic shell in ultrasonic fields, in this paper, the dynamics of microbubbles has been studied via applying the methods of chaos physics. Bifurcation, Lyapunov exponent, and time series are plotted with respect to variables such as amplitude, initial bubble radius, frequency and viscosity. The findings of the study indicate that a bubble cluster undergoes a chaotic unstable region as the amplitude and frequency of ultrasonic... 

In this investigation, the stability analysis of a rotating elastic stepped shaft is studied and the sufficient condition for system stability in the sense of Lyapunov is derived. The model consists of an elastic stepped shaft which is clamped rigidly to a rotary device. From the model's point of view, the entire length of shaft is partitioned into uniform segments with different characteristics. The Lyapunov direct method is applied in this survey where the Hamilton function has been chosen as the candidate Lyapunov function. Since the dynamical mode shapes of the shaft are required for the stability analysis, the shaft has been modeled by the Euler- Bernoulli beam theory and the... 

In this study, adaptive observer-based synchronization of chaotic systems is considered. The master and slaves systems have different dynamics and it is assumed that the master system parameters are unknown while its states are available. First, it is assumed that the slave system parameters are known but its states are not completely available. It is shown that an observer for the slave system can be designed and applied for the purpose of synchronization. Based on a Lyapunov function, an adaptive law for master parameters estimation and a control law for the synchronization goal are extracted. Stability of the entire system including the observer dynamics has been proved. Further, it is... 

This study deals with proposing a Lyapunov-based technique for stability analysis of fractional order time-delay systems. The proposed technique is constructed on the basis of modifying the convex part of a class of Lyapunov-Krasovskii functionals commonly used in stability analysis of integer order time-delay systems. As a consequence for this achievement, it is revealed that the Lyapunov-Krasovskii-based stability conditions in integer order time-delay systems can result in stability of their fractional order counterparts defined based on Caputo/Riemann-Liouville derivative operators with orders in the range (0,1). The applicability of the study results is shown through three different...