Related papers: Stability radius for infinite-dimensional intercon…
This paper presents the analysis of the stability properties of PID controllers for dynamical systems with multiple state delays, focusing on the mathematical characterization of the potential sensitivity of stability with respect to…
This paper investigates the stability of switched linear systems whose switching signal is modeled as a stochastic process called a regenerative process. We show that the mean stability of such a switched system is characterized by the…
We report conditions on a switching signal that guarantee that solutions of a switched linear systems converge asymptotically to zero. These conditions are apply to continuous, discrete-time and hybrid switched linear systems, both those…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution. In particular, for the $n$ dimensional case, the zero solution is globally…
This paper proposes several definitions of robust stability for logic dynamical systems (LDSs) with uncertain switching, including robust/uniform robust set stability and asymptotical (or infinitely convergent)/finite-time set stability…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
The existence of instabilities, for example in the form of adversarial examples, has given rise to a highly active area of research concerning itself with understanding and enhancing the stability of neural networks. We focus on a popular…
The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…
We prove stability bounds for Stokes-like virtual element spaces in two and three dimensions. Such bounds are also instrumental in deriving optimal interpolation estimates. Furthermore, we develop some numerical tests in order to…
Motivated by networked systems, stochastic control, optimization, and a wide variety of applications, this work is devoted to systems of switching jump diffusions. Treating such nonlinear systems, we focus on stability issues. First…
This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…
Robust output regulation for linear time-varying systems has remained an open problem for decades. To address this, we propose the trajectory-matching system immersion framework, by reformulating the regulator equation into a more…
It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of…
In this letter, a new notion of stability is introduced, which is called triangular stability. A system is called triangularly stable if the norm of its state vector is bounded by a decreasing linear function of time such that its…
We study a two-state quantum system with a non linearity intended to describe interactions with a complex environment, arising through a non local coupling term. We study the stability of particular solutions, obtained as constrained…
In this paper, we study the problem of stabilizing switched linear systems when only limited information about the state and the mode of the system is available, which occurs in many applications involving networked switched systems (such…
Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…
We prove a superposition theorem for input-to-output stability (IOS) of a broad class of nonlinear infinite-dimensional systems with outputs including both continuous-time and discrete-time systems. It contains, as a special case, the…