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The root locus is an important tool for analysing the stability and time constants of linear finite-dimensional systems as a parameter, often the gain, is varied. However, many systems are modelled by partial differential equations or delay…
A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
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, the notion of robust strict QSR-dissipativity is applied to solve the static output feedback control problem for a class of continuous-time nonlinear rational systems subject to input saturation and bounded parametric…
This paper is about the stabilization of a cascade system composed by an infinite-dimensional system, that we suppose to be exponentially stable, and an ordinary differential equation (ODE), that we suppose to be marginally stable. The…
We introduce the notions of semi-uniform input-to-state stability and its subclass, polynomial input-to-state stability, for infinite-dimensional systems. We establish a characterization of semi-uniform input-to-state stability based on…
This paper develops stability and stabilization results for systems of fully coupled jump diffusions. Such systems frequently arise in numerous applications where each subsystem (component) is operated under the influence of other…
The algebraic stability theorem for $\mathbb{R}$-persistence modules is a fundamental result in topological data analysis. We present a stability theorem for $n$-dimensional rectangle decomposable persistence modules up to a constant…
Power distribution systems are becoming much more active with increased penetration of distributed energy resources. Because of the intermittent nature of these resources, the stability of distribution systems under large disturbances and…
We study convective stability of a two-front superposition in a reaction-diffusion system. Due to the instability of the connecting equilibrium, long-range semi-strong interaction is expected between the two waves. When restricting to the…
This paper deals with transient stability in interconnected micro-grids. The main contribution involves i) robust classification of transient dynamics for different intervals of the micro-grid parameters (synchronization, inertia, and…
This paper focuses on using the first curvature $\kappa(t)$ of trajectory to describe the stability of linear time-invariant system. We extend the results for two and three-dimensional systems [Y. Wang, H. Sun, Y. Song et al.,…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions…
This note is devoted to study the output stabilizability of a simplified and a one-dimensional diffusion equation. Necessary and sufficient conditions for the system to be output stabilizable will be given. These conditions are given in…
The robust stability problem involves designing a controlled system which remains stable in the presence of modeling uncertainty. In this context, results known as small gain theorems are used to quantify the maximum amount of uncertainty…
In this paper, we will prove a very general result of stability for perturbations of linear integrable Hamiltonian systems, and we will construct an example of instability showing that both our result and our example are optimal. Moreover,…