Related papers: Gradient Formulation for the Stability of DC-Micro…
In this paper, by using a characterization of functions having fractional derivative, we propose a rigorous fractional Lyapunov function candidate method to analyze stability of fractional-order nonlinear systems. First, we prove an…
In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…
This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically sticks to the ground. The…
In this note we identify a class of underactuated mechanical systems whose desired constant equilibrium position can be globally stabilised with the ubiquitous PID controller. The class is characterised via some easily verifiable conditions…
Railway tracks rest on a foundation known for exhibiting nonlinear viscoelastic behavior. Railway track deflections are modeled by a semilinear partial differential equation. This paper studies the stability of solutions to this equation in…
There are two main challenges in control of hybrid systems which are to guarantee the closed-loop stability and reduce computational complexity. In this paper, we propose the exponential stability conditions of hybrid systems which are…
Representation of inductive coupling lines with conventional static phasors is the main reason of inadequacy of the existing phasors based simplified stability analysis methods for microgrids with inductive coupling lines. In the…
While stability analysis is a mainstay for control science, especially computing regions of attraction of equilibrium points, until recently most stability analysis tools always required explicit knowledge of the model or a high-fidelity…
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
We introduce a method for learning provably stable deep neural network based dynamic models from observed data. Specifically, we consider discrete-time stochastic dynamic models, as they are of particular interest in practical applications…
The dc grid became more popular, by emerging the distributed generations (DGs). Despite this popularity, the dc grid is not yet widely used because the majority of loads in a power system are ac, which means the ac grid is still the…
When electric vehicles (EVs) are integrated into standalone DC microgrids (DCMGs), stability issues arise due to their constant power load (CPL) behavior, which provides negative incremental impedance (NII). In addition, the microgrids…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
This paper considers discontinuous dynamical systems, i.e., systems whose associated vector field is a discontinuous function of the state. Discontinuous dynamical systems arise in a large number of applications, including optimal control,…
The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent…
Lyapunov's indirect method is an attractive method for analyzing stability of non-linear systems since only the stability of the corresponding linearized system needs to be determined. Unfortunately, the proof for finite-dimensional systems…
In this paper, we present an algorithm for stability analysis of systems described by coupled linear Partial Differential Equations (PDEs) with constant coefficients and mixed boundary conditions. Our approach uses positive matrices to…
This paper explores the stability of nonsynchronous hybrid ac/dc power grids under the grid-forming hybrid angle control strategy. We formulate dynamical models for the ac grids and transmission lines, interlinking converters, and dc…
We consider the problem of computing equilibria (steady-states) for droop-controlled, islanded, AC microgrids that are both economic-optimal and dynamically stable. This work is motivated by the observation that classical optimal power flow…
The paper presents an approach to the construction of stabilizing feedback for strongly nonlinear systems. The class of systems of interest includes systems with drift which are affine in control and which cannot be stabilized by continuous…