Related papers: Lyapunov Theorems for Systems Described by Retarde…
It is shown that the asymptotic spectra of finite-time Lyapunov exponents of a variety of fully chaotic dynamical systems can be understood in terms of a statistical analysis. Using random matrix theory we derive numerical and in particular…
The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…
The paper endeavours to solve the problem of the necessary and sufficient conditions for testing asymptotic stability of the equilibrium state without using a positive definite or semi-definite Lyapunov function for time-invariant nonlinear…
A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at…
We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
A robust controller is developed for uncertain, second-order nonlinear systems subject to simultaneous unknown, time-varying state delays and known, time-varying input delays in addition to additive, sufficiently smooth disturbances. An…
This book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
We consider nonautonomous cyclic systems of delay differential equations with variable delay. Under suitable feedback assumptions, we define an (integer valued) Lyapunov functional related to the number of sign changes of the coordinate…
This paper focuses on the fractional difference of Lyapunov functions related to Riemann-Liouville, Caputo and Grunwald-Letnikov definitions. A new way of building Lyapunov functions is introduced and then five inequalities are derived for…
Lyapunov functions are used to prove stability of equilibria, or to indicate a gradient-like structure of a dynamical system. Zelenyak (1968) and Matano (1988) constructed a Lyapunov function for quasilinear parabolic equations. We modify…
In this note, two generalized corollaries to the LaSalle-Yoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous right-hand sides. Lyapunov-based analysis methods are…
In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further…
In this work, we present the equivalent of many theorems available for continuous time systems. In particular, the theory is applied to Averaging Theory and Separation of time scales. In particular the proofs developed for Averaging Theory…
This paper considers the stability problem of a linear time invariant system in feedback with a string equation. A new Lyapunov functional candidate is proposed based on the use of augmented states which enriches and encompasses the…
We address the classic problem of stability and asymptotic stability in the sense of Lyapunov of the equilibrium point of autonomic differential equations using discrete approach. This new approach includes a consideration of a family of…
In this paper, a necessary and sufficient condition for the stability of Lyapunov exponents of linear differential system are proved in the sense that the equations satisfy the weaker form of integral separation instead of its classical…
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…
We introduce the notion of Lyapunov exponents for random dynamical systems, conditioned to trajectories that stay within a bounded domain for asymptotically long times. This is motivated by the desire to characterize local dynamical…