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Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…
The Master Stability Function is a robust and useful tool for determining the conditions of synchronization stability in a network of coupled systems. While a comprehensive classification exists in the case in which the nodes are chaotic…
Novel criteria for global asymptotic stability of nonlinear uncertain finite-dimensional systems are presented. The results are obtained by a combination of the "discretization approach" and the ideas contained in the proof of the original…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
Nonlinear dynamical systems possessing an invariant subspace in the phase space and chaotic or stochastic motion within the subspace often display on-off intermittency close to the threshold of stability of the subspace. In a class of…
Research on synchronization of coupled oscillators has helped explain how uniform behavior emerges in populations of non-uniform systems. But explaining how uniform populations engage in sustainable non-uniform synchronization may prove to…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
The concept of boolean autonomous deterministic regular asynchronous system has its origin in switching theory, the theory of modeling the switching circuits from the digital electrical engineering. The attribute boolean vaguely refers to…
Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for…
In this paper, we study geometric features of orientation-preserving random dynamical systems on the circle driven by memoryless noise that exhibit stable synchronisation: we consider crack points, invariant measures, and the link between…
A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
This note studies the robust output feedback stabilization problem of a class of multi-input multi-output invertible nonlinear systems, for which an "ideal" state feedback based on feedback linearization can be designed under certain mild…
Synchronization is an important behavior that characterizes many natural and human made systems composed by several interacting units. It can be found in a broad spectrum of applications, ranging from neuroscience to power-grids, to mention…
Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum…
This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
"Synchronization of two dynamical systems" is the term used to describe the phenomenon when two or more systems gradually change their states or behaviors to become similar or identical. This can happen in a lot of fields, such as physics,…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…