Related papers: A Nonlinear Small-Gain Theorem for Large-Scale Tim…
A nonlinear inequality is formulated in the paper. An estimate of the rate of growth/decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can…
We present here the details of a backstepping transformation aiming at reformulating the dynamics of a nonlinear systems subject to unknown long input delay in a form which is suitable for Lyapunov stability analysis. The control law…
Non-ideal deterministic system "tank with liquid-electric motor" is studied. Two delay-approximation models are considered. Impact of the delay on the emergence, evolution and disappearance of regular and chaotic limit sets (attractors) of…
The fluctuation theorem characterizes the distribution of the dissipation in nonequilibrium systems and proves that the average dissipation will be positive. For a large system with no external source of fluctuation, fluctuations in…
The stability of interconnected linear time-invariant systems using singular values and the small gain theorem has been studied for many decades. The methods of mu-analysis and synthesis has been extensively developed to provide robustness…
These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…
This work provides an example that motivates and illustrates theoretical results related to a combination of small-gain and density propagation conditions. Namely, in case the small-gain fails to hold at certain points or intervals the…
We extend a law of the single logarithm for delayed sums by Lai to delayed sums of random fields. A law for subsequences, which also includes the one-dimensional case, is obtained in passing.
We propose here a method to estimate a delay from a time series taking advantage of analysis of random walks with delay. This method is applicable to a time series coming out of a system which is or can be approximated as a linear feedback…
We present the linear-stability analysis of synchronised states in coupled time-delay systems. There exists a synchronisation threshold, for which we derive upper bounds, which does not depend on the delay time. We prove that at least for…
This brief pedagogical note re-proves a simple theorem on the convergence, in $L_2$ and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances…
Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…
This paper addresses the problem of resilient state estimation and attack reconstruction for bounded-error nonlinear discrete-time systems with nonlinear observations/ constraints, where both sensors and actuators can be compromised by…
This paper is concerned with a linear quadratic stochastic Stackelberg differential game with time delay. The model is general, in which the state delay and the control delay both appear in the state equation, moreover, they both enter into…
It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to…
It is already well-understood that many delay differential equations with only a single constant delay exhibit a change in stability according to the value of the delay in relation to a critical delay value. Finding a formula for the…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare…
A delayed term in a differential equation reflects the fact that information takes significant time to travel from one place to another within a process being studied. Despite de apparent similarity with ordinary differential equations,…