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In this paper, we first give the definition of random almost periodic solutions of random dynamical systems and give some examples. Then, we prove the existence of such random almost periodic solutions. Further, we introduce the definition…

We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…

This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or…

Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…

A major limitation of the classical control theory is the assumption that the state space and its dimension do not change with time. This prevents analyzing and even formalizing the stability and control problems for open multi-agent…

Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…

The robustness of the stability properties of dynamical systems in the presence of unknown/adversarial perturbations to system parameters is a desirable property. In this paper, we present methods to efficiently compute and improve the…

This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…

This note introduces a new notion of random dynamical system with inputs and outputs, and sketches a small-gain theorem for monotone systems which generalizes a similar theorem known for deterministic systems.

We consider the problem of asymptotic convergence to invariant sets in interconnected nonlinear dynamic systems. Standard approaches often require that the invariant sets be uniformly attracting. e.g. stable in the Lyapunov sense. This,…

This paper addresses the problem of risk-aware fixed-time stabilization of a class of uncertain, output-feedback nonlinear systems modeled via stochastic differential equations. First, novel classes of certificate functions, namely…

We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…

Prediction of events is the challenge in many different disciplines, from meteorology to finance; the more this task is difficult, the more a system is {\it complex}. Nevertheless, even according to this restricted definition, a general…

We describe a new class of self-similar symmetric $\alpha$-stable processes with stationary increments arising as a large time scale limit in a situation where many users are earning random rewards or incurring random costs. The resulting…

A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…

The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…

We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on…

The question of biological stability (permanence) of a replicator reaction-diffusion system is considered. Sufficient conditions of biological stability are found. It is proved that there are situations when biologically unstable…

Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…

We demonstrate with a minimal example that in Filippov systems (dynamical systems governed by discontinuous but piecewise smooth vector fields) stable periodic motion with sliding is not robust with respect to stable singular perturbations.…