In this paper Kharitonov's t h e o m for the robust stability of interval polynomials is proved using the second method of Lyapunov. The Hermite matrix is taken as the matrix of the quadratic form which is used as a Lyapunov function to prove Hurwitz stability. It is shown that if the four Hemite matrices correspondii to the four Kharitonov extreme polynomials are positive definite, the Hermite...

We consider a class of nonlinear control systems for which stabilizing feedbacks and corresponding Lyapunov functions for the closed loop systems are available. In the presence of feedback delays and actuator errors, we explicitly construct input-tostate stability (ISS) Lyapunov-Krasovskii functionals for the resulting feedback delayed dynamics, in terms of the available Lyapunov functions for ...

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matri...

Abstract—In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known res...

We explain why the maximal positive Lyapunov exponent of classical SU(N) gauge theory coincides with (twice) the damping rate of a plasmon at rest in the leading order of thermal gauge theory. Typeset using REVTEX 1

In this report the Krylov subspace methods are reviewed and some applications in linear system theory and modern control theory are introduced. A modiication to the Arnoldi-based method to solve the Lyapunov matrix equation is also proposed.

We generalize the definition of quantum Anosov properties and the related Lyapunov exponents to the case of quantum systems driven by a classical flow, i.e. skew-product systems. We show that the skew Anosov properties can be interpreted as regular Anosov properties in an enlarged Hilbert space, in the framework of a generalized Floquet theory. This extension allows us to describe the hyperboli...

This brief addresses the problem of synchronization of two Lü chaotic systems. As opposed to nonlinear Lyapunov-based controllers, which are designed with the aim of rendering the derivative of a Lyapunov function negative along trajectories of the closed-loop system, control design exploits the natural stability properties of the system. The proof relies not only on basic Lyapunov stability th...

We study the positive recurrence of piecewise Ornstein–Uhlenbeck (OU) diffusion processes, which arise from many-server queueing systems with phase-type service requirements. These diffusion processes exhibit different behavior in two regions of the state space, corresponding to “overload” (service demand exceeds capacity) and “underload” (service capacity exceeds demand). The two regimes cause...

We consider the relationship between stationary distributions for stochastic models of chemical reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well known Lyapunov function of chemical reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced syst...