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Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
In applications of nonlinear and complex dynamical systems, a common situation is that the system can be measured but its structure and the detailed rules of dynamical evolution are unknown. The inverse problem is to determine the system…
Basin stability (BS) is a measure of nonlinear stability in multi-stable dynamical systems. BS has previously been estimated using Monte-Carlo simulations, which requires the explicit knowledge of a dynamical model. We discuss the…
Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
Information in the time distribution of points in a state space reconstructed from observed data yields a test for ``nonstationarity''. Framed in terms of a statistical hypothesis test, this numerical algorithm can discern whether some…
Accurate knowledge of the state variables in a dynamical system is critical for effective control, diagnosis, and supervision, especially when direct measurements of all states are infeasible. This paper presents a novel approach to…
This survey paper deals with the stabilization of nonlinear systems by analyzing the controlling method in terms of state feedback and output feedback. A brief overview of some literature on how the feedback controller of some dynamic…
In theoretical studies, the most commonly used measure of ecological stability is resilience: ecosystems asymptotic rate of return to equilibrium after a pulse-perturbation $-$or shock. A complementary notion of growing popularity is…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
We consider a non-linear system modelling the dynamics of a linearly elastic body immersed in an incompressible viscous fluid, without damping on the elastic part. We prove local existence of strong solutions and global existence and…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
This paper presents a method that learns a regionally stable recurrent neural network model from a set of input-output data generated by an unknown dynamical system. Relying on generalized sector conditions on the deadzone activation…
This paper concerns the adaptive control problem for a class of nonlinear stochastic systems in which the state update is given by a nonlinear function of linear dynamics plus additive stochastic noise. Such systems arise in a wide range of…
Dynamic response of loads has a significant effect on system stability and directly determines the stability margin of the operating point. Inherent uncertainty and natural variability of load models make the stability assessment especially…