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We study the stability of switched systems where the dynamic modes are described by systems of higher-order linear differential equations not necessarily sharing the same state space. Concatenability of trajectories at the switching…
A general framework is presented for analyzing the stability and performance of nonlinear and linear parameter varying (LPV) time delayed systems. First, the input/output behavior of the time delay operator is bounded in the frequency…
We establish a logarithmic stability inequality for the inverse problem of determining the non linear term, appearing in a semilinear BVP, from the corresponding Dirichlet-to-Neumann map (abbreviated to DtN map in the rest of this text).…
It is shown that impulsive systems of nonlinear, time-varying and/or switched form that allow a stable global state weak linearization are jointly input-to-state stable (ISS) under small inputs and integral ISS (iISS). The system is said to…
Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or data assimilation. In many such problems, the dominant…
This paper is concerned with the state estimation problem for genetic regulatory networks with time-varying delays and reaction-diffusion terms under Dirichlet boundary conditions. It is assumed that the nonlinear regulation function is of…
In the present paper, a novel result for inferring uniform global, not semi-global, exponential stability in the sense of Lyapunov with respect to input-affine systems from global uniform exponential stability properties with respect to…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
Implicit models such as Deep Equilibrium Models (DEQs) have garnered significant attention in the community for their ability to train infinite layer models with elegant solution-finding procedures and constant memory footprint. However,…
This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some…
This study investigates the absolute stability criteria based on the framework of integral quadratic constraint (IQC) for feedback systems with slope-restricted nonlinearities. In existing works, well-known absolute stability certificates…
In this work we consider linear non-autonomous systems of Wazewski type on Hilbert spaces and provide a new approach to study their stability properties by means of a decomposition into subsystems and conditions implied on the…
An extensive overview of existing criteria, as well as some new uniform exponential stability tests are included for a scalar delay equation $$ \dot{x}(t)+ \sum_{j=1}^n a_j(t)x(h_j(t))=0. $$ Both cases of continuous and measurable…
In this work, we study the stabilization of the wave equation using an internal delayed potential. Interestingly, the stabilization mechanism is entirely induced by the delay, since exponential stabilization cannot be achieved in its…
In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and…
In this paper, we give explicit exponential estimates $\displaystyle |x(t)|\leq M e^{ -\gamma (t-t_0) }$, where $t\geq t_0$, $M>0$, for solutions of a linear scalar delay differential equation $$ \dot{x}(t)+\sum_{k=1}^m…
We propose two new classes of time integrators for stiff DEs: the implicit-explicit exponential (IMEXP) and the hybrid exponential methods. In contrast to the existing exponential schemes, the new methods offer significant computational…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
This paper presents a novel methodology for evaluating the boundedness, stability, and instability of some vector nonlinear systems with multiple time-varying delays and variable coefficients. The proposed technique develops two scalar…
In this paper, we present a new method for the dissipativity and stability analysis of a linear coupled differential-difference system (CDDS) with general distributed delays at both state and output. More precisely, the distributed delay…