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This paper addresses stochastic stabilization in case where implementation of control policies is digital, i. e., when the dynamical system is treated continuous, whereas the control actions are held constant in predefined time steps. In…
We study equilibrium selection for invariant measures of stochastic dynamical systems with constant step size, under persistent noise and minimal moment assumptions, in a general quasi-Feller framework. Such dynamics arise in…
In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay…
Constructal Law states that a finite-size flow system that persists in time evolves its configuration so as to provide progressively easier access to the currents that flow through it. Classical Constructal theory derives hierarchical flow…
We present generalised Lyapunov-Razumikhin techniques for establishing global asymptotic stability of steady-state solutions of scalar delay differential equations. When global asymptotic stability cannot be established, the technique can…
There are recent shifts in demand for design controllers from simplified to complex model-based. Although simplification approaches are successful in many areas of engineering control systems, high-fidelity simulation-based control design,…
We study the existence of stationary solutions of the Vlasov-Poisson system with finite radius and finite mass in the stellar dynamics case. So far, the existence of such solutions is known only under the assumption of spherical symmetry.…
This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
We explicitly construct global strict Lyapunov functions for rapidly time-varying nonlinear control systems. The Lyapunov functions we construct are expressed in terms of oftentimes more readily available Lyapunov functions for the limiting…
Switch-like behaviour in dynamical systems may be modelled by highly nonlinear functions, such as Hill functions or sigmoid functions, or alternatively by piecewise-smooth functions, such as step functions. Consistent modelling requires…
Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
The natural trajectory tracking problem is studied for generic quantum states represented by density operators. A control design based on the Hilbert-Schmidt distance as a Lyapunov function is considered. The control dynamics is redefined…
We introduce a holistic framework for the analysis, approximation and control of the trajectories of hybrid dynamical systems which display event-triggered discrete jumps in the continuous state. We begin by demonstrating how to explicitly…
The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
A Lyapunov-Krasovskii functional with prescribed derivative whose construction does not require the stability of the system is introduced. It leads to the presentation of stability/instability theorems. By evaluating the functional at…
In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…