In this paper, we give a necessary and sufficient condition for the existence of at least one Ψ-bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation. In addition, we give a result in connection with the asymptotic behavior of the Ψ-bounded solutions of this equation.

Assuming the existence of a general nonuniform dichotomy for the evolution operator of a non-autonomous ordinary linear differential equation in a Banach space, we establish the existence of invariant stable manifolds for the semiflow generated by sufficiently small nonlinear perturbations of the linear equation. The family of dichotomies considered satisfies a general growth rate given by some...

This paper deals with the problem of generating stable and robust oscillations in triangular nonlinear systems. The proposed method consists of two steps. First, a globally attractive oscillation is generated in a nominal second–order subsystem. Based on a partition of the state space and solving the Lyapunov equation on each part, a strict Lyapunov function is obtained that ensures exponential...

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given...

The one-dimensional wave equation describes many phenomena in physics [1]. In a periodic medium, the solution of the wave equation has a Floquet–Bloch structure. Very long waves propagate without attenuation and the medium can be viewed as homogeneous. However, for higher frequencies there are certain intervals (so-called gaps) where waves cannot propagate even though the system is perfectly co...

Two results are presented: First, we solve the problem of persistence of dissipation for reduction of kinetic models. Kinetic equations with thermodynamic Lyapunov functions are studied. Uniqueness of thermodynamic projector is proven: There exists only one projector which transforms the arbitrary vector field equipped with the given Lyapunov function into a vector field with the same Lyapunov ...

40 Impact of Varying Environmental Conditions Simulate switched extremum seeking controller for 1000 W/m2 to 500 W/m2 step change in incident solar irradiation at 200 ms Lyapunov-Based Switching Scheme • Use stability proof by Krstic and Wang, Automatica, 2000. • Compute the average system: xa = 1/T ∫T x(τ)dτ • Linearize the averaged system about the extremum point: A = [dfa/dxa]eq • Show the J...

Stability investigation of hereditary systems is connected often with construction of Lyapunov functionals. One general method of Lyapunov functionals construction was proposed and developed in [1-9] both for differential equations with aftereffect and for difference equations with discrete time. Here, some modification of Lyapunov-type stability theorem is proposed, which allows one to use thi...

A kinetic approach is adopted to describe the exponential growth of a small deviation of the initial phase space point, measured by the largest Lyapunov exponent, for a dilute system of hard disks, both in equilibrium and in a uniform shear flow. We derive a generalized Boltzmann equation for an extended one-particle distribution that includes deviations from the reference phase space point. Th...

The aim of this paper is to introduce a new hyperchaotic complex Lorenz system. This hyperchaotic complex system is constructed by adding a linear controller to the second equation of the chaotic complex Lorenz system. The new system is a 7-dimensional continuous real autonomous hyperchaotic system. This system has hyperchaotic attractors and quasi-periodic solutions with three zero Lyapunov ex...