Atmospheric flows exhibit fractal fluctuations and inverse power law form for power spectra indicating an eddy continuum structure for the selfsimilar fluctuations. A general systems theory for fractal fluctuations developed by the author is based on the simple visualisation that large eddies form by space-time integration of enclosed turbulent eddies, a concept analogous to Kinetic Theory of G...

Similar with the CLF method, Wieland and Allgöwer in [8] have proposed the construction of Control Barrier Functions (CBF), where the Lyapunov function is interchanged with the Barrier certificate studied in [3]. Using a CBF as in [8], one can design a universal feedback law for steering the states from the set of initial conditions to the set of terminal conditions, without violating the set o...

In this paper we propose a new robust scheme of nonpeaking nonlinear observers. The observation strategy is issued from differential algebra where the unmeasured states are given as outputs of a time-varying linear differentiator that guarantees robustness against measurement errors. We show that for a certain initial condition, the n-dimensional differentiator does not exhibit the peaking phen...

We study two identical hyperchaotic oscillators symmetrically coupled. Each oscillator represents a codimension-2 Takens–Bogdanov bifurcation under square symmetry, and was used to model a convection experiment in a time-dependent state. In the coupled system, the Lyapunov exponents behavior against the coupling parameter is used to detect changes in the dynamics, and the synchronization state ...

This paper focuses on the stabilization problem of neutral systems in the presence of control saturation. Based on a descriptor approach and the use of a modified sector condition, global and local stabilization conditions are derived using Lyapunov-Krasovskii functionals. These conditions allow to consider systems presenting time-varying delays and are formulated directly as linear matrix ineq...

In recent years, it becomes important to understand chaotic behaviors in order to analyze nonlinear dynamics because chaotic behavior can be observed in many models in the field of physics, biology, and so on. To understand chaotic behaviors, investigating mechanisms of chaos is necessary and it is meaningful to study simple models that shows chaotic behaviors. In this paper, we propose an extr...

We consider a vector field X on a closed manifold which admits a Lyapunov one form. We assume X has Morse type zeros, satisfies the Morse– Smale transversality condition and has non-degenerate closed trajectories only. For a closed one form η, considered as flat connection on the trivial line bundle, the differential of the Morse complex formally associated to X and η is given by infinite serie...

In this paper, fundamental relationships are established between convergence of solutions, stability of equilibria, and arc length of orbits. More specifically, it is shown that a system is convergent if all of its orbits have finite arc length, while an equilibrium is Lyapunov stable if the arc length (considered as a function of the initial condition) is continuous at the equilibrium, and sem...

This paper addresses a linear finite-horizon robust optimal H∞ analysis problem, where the system matrices and the system initial conditions (ICs, x0) are concurrently uncertain, both in a polytopic manner. Current finite-horizon H∞ analysis practice assumes x0 ∈R ; that is, allows infinite ICs uncertainty. This assumption is unrealistically conservative, and incompatible with the prevalent rob...