Related papers: Dynamic Physical Systems: Energy Balances and Stab…
The paper is devoted to the analysis of relationships between principal objects of the spectral theory of dynamical systems (transfer and weighted shift operators) and basic characteristics of information theory and thermodynamic formalism…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from…
Several concepts on the measure of observability, reachability, and robustness are defined and illustrated for both linear and nonlinear control systems. Defined by using computational dynamic optimization, these concepts are applicable to…
We argue that statistical mechanics of systems with relaxation implies breaking the energy function of systems into two having different transformation rules. With this duality the energy approach incorporates the generalized vortex forces.…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
The presence of losses in nonlinear photonic structures is a crucial issue for modern applications. Active parts are introduced for wave power compensation resulting in unbalanced gain and loss landscapes where localized beam propagation…
Some unusual relations between stress tensors, conservation and equations of motion are briefly reviewed.
Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…
A system is called positive if the set of non-negative states is left invariant by the dynamics. Stability analysis and controller optimization are greatly simplified for such systems. For example, linear Lyapunov functions and storage…
Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stability criteria focusing on the interplay of network structures and the local dynamics of synchronous…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
Differential passivity is a property that allows to check with a pointwise criterion that a system is incrementally passive, a property that is relevant to study interconnected systems in the context of regulation, synchronization, and…
For linear control systems, the usual state feedback stabilizability has two components: one is a continuous observation mode (i.e., to observe solutions continuously in time), and the other is a class of feedback laws (which is usually the…
This is an expository-survey on weak stability of bounded linear operators acting on normed spaces in general and, in particular, on Hilbert spaces. The paper gives a comprehensive account of the problem of weak operator stability,…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…
This report investigates the dynamical stability conjectures of Palis and Smale, and Pugh and Shub from the standpoint of numerical observation and lays the foundation for a stability conjecture. As the dimension of a dissipative dynamical…
Symmetry properties of stochastic dynamical systems described by stochastic differential equation of Stratonovich type and related conserved quantities are discussed, extending previous results by Misawa. New conserved quantities are given…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…