The Lyapunov stability method is the most popular and applicable stability analysis tool of nonlinear dynamic systems. However, there are some bottlenecks in the Lyapunov method, such as need for negative definiteness of the Lyapunov function derivative in the direction of the system’s solutions. In this paper, we develop a new theorem to dispense the need for negative definite-ness of Lyapunov...

Motivated by a recently developed backward error analysis for QR methods, we consider the error in the Lyapunov exponents of perturbed triangular systems. We consider the case of stable and distinct Lyapunov exponents as well as the case of stable but not necessarily distinct exponents. We illustrate our analytical results with a numerical example. 1. Introduction. Lyapunov exponents are often ...

The paper studies numerical methods that preserve a Lyapunov function of dynamical system, i.e., approximations whose energy decreases, just like in the original differential equation. With this aim, discrete gradient method is implemented for integration system ordinary equations. In principle, procedure yields first-order methods, but analysis paves way design higher-order methods. As case po...

Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Low-rank iterative methods of periodic projected Lyapunov equations and their application in model reduction of periodic descriptor systems Abstract We discuss the numerical solution of large-scale sparse projected discrete-time periodic Lyapunov equations ...