In this paper we propose a numerical method for computing all Lyapunov coefficients of a discrete time dynamical system by spatial integration. The method extends an approach of Aston and Dellnitz (1999) who use a box approximation of an underlying ergodic measure and compute the first Lyapunov exponent from a spatial average of the norms of the Jacobian for the iterated map. In the hybrid meth...

The problem of evaluation of Lyapunov exponent in queueing network analysis is considered based on models and methods of idempotent algebra. General existence conditions for Lyapunov exponent to exist in generalized linear stochastic dynamic systems are given, and examples of evaluation of the exponent for systems with matrices of particular types are presented. A method which allow one to get ...

In this paper, we establish a model reduction technique for periodic discrete-time descriptor systems exploiting the generalized inverses of the periodic singular matrix pairs associated with the systems. We compute the generalized inverses of periodic singular matrix pairs to implement a structure preserving iterative method for the solution of the periodic projected Lyapunov equations that ar...

Lyapunov drift is a powerful tool for optimizing stochastic queueing networks subject to stability. However, the most convenient drift conditions often provide results in terms of a time average expectation, rather than a pure time average. This paper provides an extended drift-plus-penalty result that ensures stability with desired time averages with probability 1. The analysis uses the law of...

The theory of Lyapunov exponents and methods from ergodic theory have been employed by several authors in order to study persistence properties of dynamical systems generated by ODEs or by maps. Here we derive sufficient conditions for uniform persistence, formulated in the language of Lyapunov exponents, for a large class of dissipative discrete-time dynamical systems on the positive orthant o...

We study new formulas based on Lyapunov exponents for entropy, mutual information, and capacity of finite state discrete time Markov channels. We also develop a method for directly computing mutual information and entropy using continuous state space Markov chains. Our methods allow for arbitrary input processes and channel dynamics, provided both have finite memory. We show that the entropy ra...

The measure of heart rate variability (HRV) has become a valuable metric for diagnosing cardiac health. The ECG is the representative signal containing information about the condition of this health metric. Analysis of this highly complex and irregular signal cannot always be addressed through linear statistics. Nonlinear methods are able to describe the processes generated by biological system...

Predictive control of nonlinear systems subject to output and input constraints is considered. A fuzzy model is used to predict the future behavior. Two new ideas are proposed here. First, an added constraint on the applied control action is used to ensure the decrease of a quadratic Lyapunov function, and so guarantee Lyapunov exponential stability of the closed-loop system. Second, the feasib...

It is well known that the bilinear transform, or first order diagonal Padé approximation to the matrix exponential, preserves quadratic Lyapunov functions between continuous-time and corresponding discrete-time linear time invariant (LTI) systems, regardless of the sampling time. It is also well known that this mapping preserves common quadratic Lyapunov functions between continuous-time and di...

This note presents a new approach to deriving stability conditions for continuous-time linear systems interconnected with a saturation. The method presented here can be extended to handle a deadzone, or in general, nonlinearities in the form of piecewise linear functions. By representing the saturation as a constrained optimization problem, the necessary (Kuhn–Tucker) conditions for optimality ...