Related papers: Stability Analysis of Continuous-Time Linear Time-…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
In this paper we present a direct adaptive control method for a class of uncertain nonlinear systems with a time-varying structure. We view the nonlinear systems as composed of a finite number of ``pieces,'' which are interpolated by…
This contribution is a follow-up of a recent paper by the authors on adaptive, non-linear time-frequency transforms, focusing on the STFT based transforms. The adaptivity is provided by a focus function, that depends on the analyzed…
Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…
In this paper, we mainly study the robust stability of linear continuous systems with parameter uncertainties, a more general kind of uncertainties for system matrices is considered, i.e., entries of system matrices are rational functions…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
The linear stability of stratified two-phase flows in rectangular ducts is studied numerically. The linear stability analysis takes into account all possible infinitesimal three-dimensional disturbances and is carried out by solution of the…
This paper reports a breakdown in linear stability theory under conditions of neutral stability that is deduced by an examination of exponential modes of the form $h\approx {{e}^{i(kx-\omega t)}}$, where $h$ is a response to a disturbance,…
We propose a principled method for projecting an arbitrary square matrix to the non-convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an…
In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible…
Higher-order time integration methods that unconditionally preserve the positivity and linear invariants of the underlying differential equation system cannot belong to the class of general linear methods. This poses a major challenge for…
We present a new application of Lagrangian Perturbation Theory (LPT): the stability analysis of fluid flows. As a test case that demonstrates the framework we focus on the plane Couette flow. The incompressible Navier-Stokes equation is…
We revisit the classical problem of absolute stability; assessing the robust stability of a given linear time-invariant (LTI) plant in feedback with a nonlinearity belonging to some given function class. Standard results typically take the…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
With an increasing share of renewable energy sources, accurate and efficient modeling of grid-forming inverters is becoming crucial for system stability. Linear methods are a powerful tool for understanding dynamics close to an operating…
We study the stability properties of a class of time-varying nonlinear systems. We assume that non-strict input-to-state stable (ISS) Lyapunov functions for our systems are given and posit a mild persistency of excitation condition on our…
Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a…
The topic of this manuscript is the stability analysis of continuous-time switched nonlinear systems with constraints on the admissible switching signals. Our particular focus lies in considering signals characterized by upper and lower…
This paper studies the finite-time stability and stabilization of linear discrete time-varying stochastic systems with multiplicative noise. Firstly, necessary and sufficient conditions for finite-time stability are presented via state…