Search results for "Asymptotic stability"
showing 7 items of 7 documents
On integral input-to-state stability for a feedback interconnection of parameterised discrete-time systems
2014
This paper addresses integral input-to-state stability iISS for a feedback interconnection of parameterised discrete-time systems involving two subsystems. Particularly, we give a construction for a smooth iISS Lyapunov function for the whole system from the sum of nonlinearly weighted Lyapunov functions of individual subsystems. Motivations for such a construction are given. We consider two main cases. The first one investigates iISS for the whole system when both subsystems are iISS. The second one gives iISS for the interconnected system when one of subsystems is allowed to be input-to-state stable. The approach is also valid for both discrete-time cascades and a feedback interconnection…
A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma
2016
We study diffusion of cooperation in a two-population game in continuous time. At each instant, the game involves two random individuals, one from each population. The game has the structure of a Prisoner's dilemma where each player can choose either to cooperate (c) or to defect (d), and is reframed within the field of approachability in two-player repeated game with vector payoffs. We turn the game into a dynamical system, which is positive, and propose a saturated strategy that ensures local asymptotic stability of the equilibrium (c, c) for any possible choice of the payoff matrix. We show that there exists a rectangle, in the space of payoffs, which is positively invariant for the syst…
A generalized Degn–Harrison reaction–diffusion system: Asymptotic stability and non-existence results
2021
Abstract In this paper we study the Degn–Harrison system with a generalized reaction term. Once proved the global existence and boundedness of a unique solution, we address the asymptotic behavior of the system. The conditions for the global asymptotic stability of the steady state solution are derived using the appropriate techniques based on the eigen-analysis, the Poincare–Bendixson theorem and the direct Lyapunov method. Numerical simulations are also shown to corroborate the asymptotic stability predictions. Moreover, we determine the constraints on the size of the reactor and the diffusion coefficient such that the system does not admit non-constant positive steady state solutions.
Bio-inspired evolutionary dynamics on complex networks under uncertain cross-inhibitory signals
2019
Given a large population of agents, each agent has three possiblechoices between option 1 or 2 or no option. The two options are equally favorable and the population has to reach consensus on one of the two options quickly and in a distributed way. The more popular an option is, the more likely it is to be chosen by uncommitted agents. Agents committed to one option can be attracted by those committed to the other option through a cross-inhibitory signal. This model originates in the context of honeybee swarms, and we generalize it to duopolistic competition and opinion dynamics. The contributions of this work include (i) the formulation of a model to explain the behavioral traits of the ho…
Distributed Consensus in Networks of Dynamic Agents
2006
Stationary and distributed consensus protocols for a network of n dynamic agents under local information is considered. Consensus must be reached on a group decision value returned by a function of the agents' initial state values. As a main contribution we show that the agents can reach consensus if the value of such a function computed over the agents' state trajectories is time invariant. We use this basic result to introduce a protocol design rule allowing consensus on a quite general set of values. Such a set includes, e.g., any generalized mean of order p of the agents' initial states. We demonstrate that the asymptotical consensus is reached via a Lyapunov approach. Finally we perfor…
On the qualitative analysis of the solutions of a mathematical model of social dynamics
2006
Abstract This work deals with a family of dynamical systems which were introduced in [M.L. Bertotti, M. Delitala, From discrete kinetic and stochastic game theory to modelling complex systems in applied sciences, Math. Models Methods Appl. Sci. 7 (2004) 1061–1084], modelling the evolution of a population of interacting individuals, distinguished by their social state. The existence of certain uniform distribution equilibria is proved and the asymptotic trend is investigated.
Fuzzy cooperative control of automated ground passenger vehicles
2007
In this paper a fuzzy motion control for cooperative passenger automated vehicles where there are not collisions between the closest ones is proposed. Based on the position of the target and on the initial position of each cooperative vehicle, a supervisory plans nonholonomic circular trajectories which are without intersections, while a fuzzy control strategy assures the asymptotical stability of the motion errors and the reaching of the target with low acceleration values along the planned trajectories. Based on the ISO 2631-1 standard, the saturation properties of the fuzzy maps guarantees low values of the longitudinal and lateral accelerations to assure the comfort of the passengers. T…