In this paper, by using majorization inequalities, upper bounds on summations of eigenvalues (including the trace) of the solution for the Lyapunov matrix differential equation are obtained. In the limiting cases, the results reduce to bounds of the algebraic Lyapunov matrix equation. The effectiveness of the results are illustrated by numerical examples.

We consider strongly connected networks of input-to-state stable (ISS) systems. Provided a small gain condition holds it is shown how to construct an ISS Lyapunov function using ISS Lyapunov functions of the subsystems. The construction relies on two steps: The construction of a strictly increasing path in a region defined on the positive orthant in R by the gain matrix and the combination of t...

We perform numerical experiments to study the Lyapunov spectra of dynamical systems associated with the Navier–Stokes (NS) equation in two spatial dimensions truncated over the Fourier basis. Recently new equations, called GNS equations, have been introduced and conjectured to be equivalent to the NS equations at large Reynolds numbers. The Lyapunov spectra of the NS and of the corresponding GN...

In this paper we study the semi-global (approximate) state feedback stabilization of an infinite dimensional quantum stochastic system towards a target state. A discrete-time Markov chain on an infinite-dimensional Hilbert space is used to model the dynamics of a quantum optical cavity. We can choose an (unbounded) strict Lyapunov function that is minimized at each time-step in order to prove (...

Stability of an interconnected system consisting of two switched systems is investigated in the scenario where in both switched systems theremay exist some subsystems that are not input-to-state stable (nonISS). We show that, providing the switching signals neither switch too frequently nor activate non-ISS subsystems for too long, a small-gain theorem can be used to conclude global asymptotic ...

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...

In this paper we study the semi-global (approximate) state feedback stabilization of an infinite dimensional quantum stochastic system towards a target state. A discrete-time Markov chain on an infinite-dimensional Hilbert space is used to model the dynamics of a quantum optical cavity. We can choose an (unbounded) strict Lyapunov function that is minimized at each time-step in order to prove (...

In a previous paper [6] we suggested a numerical method for computing all Lyapunov exponents of a dynamical system by spatial integration with respect to an ergodic measure. The method extended an earlier approach of Aston and Dellnitz [2] for the largest Lyapunov exponent by integrating the diagonal entries from the QR-decomposition of the Jacobian for an iterated map. In this paper we provide...

— This paper presents an analysis approach to finite-time attraction in probability concerns with nonlinear systems described by nonlinear random differential equations (RDE). RDE provide meticulous physical interpreted models for some applications contain stochastic disturbance. The existence and the path-wise uniqueness of the finite-time solution are investigated through nonrestrictive assum...

Let {Tk}k=1 be a family of ∗–free identically distributed operators in a finite von Neumann algebra. In this work we prove a multiplicative version of the free central limit Theorem. More precisely, let Bn = T ∗ 1 T ∗ 2 . . . T ∗ nTn . . . T2T1 then Bn is a positive operator and B 1/2n n converges in distribution to an operator Λ. We completely determine the probability distribution ν of Λ from...