We announce a new construction of a stabilizing feedback law for nonlinear globally asymptotically controllable (GAC) systems. Given a control affine GAC system, our feedback renders the closed loop system input to state stable with respect to actuator errors and small observation noise. We also announce a variant of our result for fully nonlinear GAC systems.

We present constructions of a local and global common Lyapunov function for a finite family of pairwise commuting globally asymptotically stable nonlinear systems. The constructions are based on an iterative procedure, which at each step invokes a converse Lyapunov theorem for one of the individual systems. Our results extend a previously available one which relies on exponential stability of t...

where x(t) denotes the density of the prey population and y(t) the density of predators. Parameters r, K, s, Y , and m are positive constants denoting the intrinsic growth rate and the carrying capacity of the prey, the death rate of the predator in the absence of prey, the yield constant, and the maximal growth rate of the predator, respectively. The function f(x) denotes the response function...

We study a class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs of strategies to which revising agents are switching are always exceeded by the improvements in the payoffs of strategies which revising agents are abandoning. We prove that the set of Nash equilibria of a s...

This paper presents two alternative navigation solutions for autonomous vehicles based on direction and depth measurements, in addition to relative velocity readings, with globally asymptotically stable (GAS) error dynamics. A constant unknown drift velocity disturbance is also assumed present during the operation of the agent, which is explicitly considered in the system dynamics. The observab...

In chaos synchronization, the main goal is to design such controller(s) that synchronizes the states of master and slave system asymptotically globally. This paper studied and investigated the synchronization problem of two identical Chen, and identical Tigan chaotic systems and two non-identical Chen and Tigan chaotic systems using Non-linear active control algorithm. In this study, based on L...

The purpose of this paper is to solve a global asymptotic stabilization problem for a nonlinear control system on a Riemannian manifold. As well known, a system on a noncontractible manifold is not globally asymptotically stabilizable via a C feedback law. This problem results from the existence of multiple singular points of such a controlled system. It is shown that if all the singular points...

In this paper we present observer design procedures for a class of bi-modal piecewise linear systems in both continuous and discrete time. We propose Luenberger-type observers, and derive sufficient conditions for the observation error dynamics to be globally asymptotically stable, in the case when the system dynamics is continuous over the switching plane. When the dynamics is discontinuous, w...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

In this paper, by taking full consideration of distributed delay, demographics and contact heterogeneity of the individuals, we present a detailed analytical study of the Susceptible-Infected-Removed (SIR) epidemic model on complex population networks. The basic reproduction number [Formula: see text] of the model is dominated by the topology of the underlying network, the properties of individ...