Related papers: Transportation-Inequalities, Lyapunov Stability an…
The Foster-Lyapunov theorem and its variants serve as the primary tools for studying the stability of queueing systems. In addition, it is well known that setting the drift of the Lyapunov function equal to zero in steady-state provides…
Reactivity, contractivity, and Lyapunov exponents are powerful tools for studying the stability properties of dynamical systems and have been extensively investigated in the literature for decades. In this paper, we review and extend the…
For complex nonlinear systems, it is challenging to design algorithms that are fast, scalable, and give an accurate approximation of the stability region. This paper proposes a sampling-based approach to address these challenges. By…
There are recent shifts in demand for design controllers from simplified to complex model-based. Although simplification approaches are successful in many areas of engineering control systems, high-fidelity simulation-based control design,…
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…
Using a nonlocal second-order traffic flow model we present an approach to control the dynamics towards a steady state. The system is controlled by the leading vehicle driving at a prescribed velocity and also determines the steady state.…
This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT system is certified.…
One dimensional intermittent maps with stretched exponential separation of nearby trajectories are considered. When time goes infinity the standard Lyapunov exponent is zero. We investigate the distribution of $\lambda_{\alpha}=…
Determination of stability and instability of singular points in nonlinear dynamical systems is an important issue that has attracted considerable attention in different fields of engineering and science. So far, different well-defined…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…
For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities, transportation inequalities…
We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…
This paper studies the stability of sampled and networked control systems with sampling and communication times governed by probabilistic clocks. The clock models have few restrictions, and can be used to model numerous phenomena such as…
We consider the problem of global stability of nonlinear sampled-data systems. Sampled-data systems are a form of hybrid model which arises when discrete measurements and updates are used to control continuous-time plants. In this paper, we…
This technical note studies Lyapunov-like conditions to ensure a class of dynamical systems to exhibit predefined-time stability. The origin of a dynamical system is predefined-time stable if it is fixed-time stable and an upper bound of…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We propose and analyze a new candidate Lyapunov function for relaxation towards general nonequilibrium steady states. The proposed functional is obtained from the large time asymptotics of time-symmetric fluctuations. For driven Markov jump…
Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of…
The focus of this article is on entropy and Markov processes. We study the properties of functionals which are invariant with respect to monotonic transformations and analyze two invariant "additivity" properties: (i) existence of a…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…