Related papers: Advancing Nonlinear System Stability Analysis with…
A faithful description of the state of a complex dynamical network would require, in principle, the measurement of all its $d$ variables, an infeasible task for systems with practical limited access and composed of many nodes with high…
Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
In this paper, a hybrid measurement and model-based method is proposed which can estimate the dynamic state Jacobian matrix in near real-time. The proposed method is computationally efficient and robust to the variation of network topology.…
Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize…
This paper considers the generalized continuation Newton method and thetrust-region updating strategy for the underdetermined system of nonlinear equations. Moreover, in order to improve its computational efficiency, the new method will not…
This paper propose new sufficient conditions for stability analysis for non autonomous systems.
This paper proposes a new approach to describe the stability of linear time-invariant systems via the torsion $\tau(t)$ of the state trajectory. For a system $\dot{r}(t)=Ar(t)$ where $A$ is invertible, we show that (1) if there exists a…
This article proposes a non-autonomous mathematical model with delay for confrontation between two countries, and examines the stability of its equilibrium state. Our criteria for stability take into account the influence of the factor of…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between the stability property of the exact discrete-time model for a given sequence of (aperiodic)…
Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these…
Recent work have shown how the optimal state-feedback, obtained as the solution to the Hamilton-Jacobi-Bellman equations, can be approximated for several nonlinear, deterministic systems by deep neural networks. When imitation (supervised)…
Despite extensive experimental evidence of turbulence in Hagen Poiseuille flow, linear stability analysis has not yet confirmed its instability. One challenge is the singularity introduced by the term 1/r in the center of the pipe, which…
This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
We present applications of the notion of isomorphic vector fields to the study of nonlinear stability of relative equilibria. Isomorphic vector fields were introduced by Hepworth [Theory Appl. Categ. 22 (2009), 542-587] in his study of…
This paper proposes a novel Gronwall inequality-based method for transient stability assessment for power systems. The challenges of applying such methods to power systems are how to construct the differential inequality and how to treat…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
This paper introduces a novel method for the stability analysis of positive feedback systems with a class of fully connected feedforward neural networks (FFNN) controllers. By establishing sector bounds for fully connected FFNNs without…