Related papers: Positive Invariance Condition for Continuous Dynam…
We introduce the concept of a control contraction metric, extending contraction analysis to constructive nonlinear control design. We derive sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control…
We present simple general conditions on the acceptance sets under which their induced monetary risk and deviation measures are comonotonic additive. We show that acceptance sets induce comonotonic additive risk measures if and only if the…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
We present a stability analysis for two different rotational pressure correction schemes with open and traction boundary conditions. First, we provide a stability analysis for a rotational version of the grad-div stabilized scheme of [A.…
Starting from the classic contraction mapping principle, we establish a general, flexible, variational setting that turns out to be applicable to many situations of existence in Differential Equations. We show its potentiality with some…
In this paper we consider sufficient conditions for the existence of uniform compact global attractor for non-autonomous dynamical systems in special classes of infinite-dimensional phase spaces. The obtained generalizations allow us to…
The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…
Natural dynamos such as planets and stars generate global scale magnetic field despite the inferred presence of small scale turbulence. Such systems are known as large scale dynamos and are typically driven by convection and influenced by…
We study the existence and uniqueness of equilibrium states for continuous flows on a compact, locally maximal invariant set under weak, non-uniform versions of specification, expansivity, and the Bowen property, further improving the…
There has been a long-standing and at times fractious debate whether complex and large systems can be stable. In ecology, the so-called `diversity-stability debate' arose because mathematical analyses of ecosystem stability were either…
Recently, sufficient conditions of stability or instability for time-delay systems have been proven to be necessary. In this way, a remarkable necessary and sufficient condition has then been developed by Gomez et al. It is presented as a…
We study stability criteria for discrete-time switched systems and provide a meta-theorem that characterizes all Lyapunov theorems of a certain canonical type. For this purpose, we investigate the structure of sets of LMIs that provide a…
We consider dissipative strongly competitive systems $\dot{x}_{i}=x_{i}f_{i}(x)$ of ordinary differential equations. It is known that for a wide class of such systems there exists an invariant attracting hypersurface $\Sigma$, called the…
We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system has a dissipative structure, we proved that a random…
Several recent works in online optimization and game dynamics have established strong negative complexity results including the formal emergence of instability and chaos even in small such settings, e.g., $2\times 2$ games. These results…
In this paper, we derive several new sufficient conditions of non-breakdown of strong solutions for for both the 3D heat-conducting compressible Navier-Stokes system and nonhomogeneous incompressible Navier-Stokes equations. First, it is…
A key idea in convex optimization theory is to use well-structured affine functions to approximate general functions, leading to impactful developments in conjugate functions and convex duality theory. This raises the question: what are the…
We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching…
We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with…
We consider a non-autonomous ordinary differential equation on a smooth manifold, with right-hand side that randomly switches between the elements of a finite family of smooth vector fields. For the resulting random dynamical system, we…