Related papers: A Novel Criterion for Unpredictable Motions
New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of…
Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
Synchronization of chaotic system may occur only when the largest conditional Lyapunov exponent of the driven system is negative. The synchronization with positive conditional Lyapunov reported in a recent paper (Phys. Rev. E, {\bf 56},…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…
We use Lyapunov-like functions and convex optimization to propagate uncertainty in the initial condition of nonlinear systems governed by ordinary differential equations. We consider the full nonlinear dynamics without approximation,…
The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the…
We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the…
This paper investigates the problem of synchronization for nonlinear systems. Following a Lyapunov approach, we firstly study global synchronization of nonlinear systems in canonical control form with both distributed…
We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we…
We show, using generic globally-coupled systems, that the collective dynamics of large chaotic systems is encoded in their Lyapunov spectra: most modes are typically localized on a few degrees of freedom, but some are delocalized, acting…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
We study the problem of robust global stabilization in control-affine systems, focusing on dynamic uncertainties in the control directions \emph{and} the presence of topological obstructions that prevent the existence of smooth global…
We study synchronization of random one-dimensional linear maps for which the Lyapunov exponent can be calculated exactly. Certain aspects of the dynamics of these maps are explained using their relation with a random walk. We confirm that…
We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization…
We propose a general Langevin equation describing the universal properties of synchronization transitions in extended systems. By means of theoretical arguments and numerical simulations we show that the proposed equation exhibits,…
During the past decades, the question of existence and properties of a random attractor of a random dynamical system generated by an S(P)DE has received considerable attention, for example by the work of Gess and R\"ockner. Recently some…
We prove a converse Lyapunov theorem for boundedness of reachability sets for a general class of control systems whose flow is Lipschitz continuous on compact intervals with respect to trajectory-dominated inputs. We show that this…
Transitions between inverse anticipatory, inverse complete and inverse lag synchronizations are shown to occur as a function of the coupling delay in unidirectionally coupled time-delay systems with inhibitory coupling. We have also shown…