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Given a discrete-state continuous-time reactive system, like a digital circuit, the classical approach is to first model it as a state transition system and then prove its properties. Our contribution advocates a different approach: to…
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
This paper addresses, for the first time in the literature, optimal control problems for dynamic systems governed by a novel class of sweeping processes with time delay. We establish well-posedness of such processes, in the sense of the…
We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
Motivated by a real problem in steel production, we introduce and analyze a general class of singularly perturbed linear hybrid systems with both switches and impulses, in which the slow or fast nature of the variables can be…
Stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
This paper introduces new techniques for using convex optimization to fit input-output data to a class of stable nonlinear dynamical models. We present an algorithm that guarantees consistent estimates of models in this class when a small…
In this paper we provide conditions to ensure the existence, for $e>0$ sufficiently small, of periodic solutions of given period $T>0$ in a prescribed domain $U$ for a class of singularly perturbed first order differential systems. Here…
We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact…
This paper proposes a procedure to control an uncertain discrete-time networked control system through a limited stabilizing input information. The system is primarily affected by the time-varying, norm bounded, mismatched parametric…
In this work the stability of perturbed linear time-varying systems is studied. The main features of the problem are threefold. Firstly, the time-varying dynamics is not required to be continuous but allowed to have jumps. Also the system…
This paper investigates the stability of a class of differential systems time-changed by $E_{t}$ which is the inverse of a $\beta$-stable subordinator. In order to explore stability, a time-changed Gronwall's inequality and a generalized…
In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…
This paper deals with the exponential stabilization of a time-delay system with an average of the state as the output. A general stability theorem with a guaranteed exponential decay-rate based on a Wirtinger-based inequality is provided.…
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design. This research focuses on learning continuous linear models from data. Stability, a key feature of dynamic systems, is…
In this paper we introduce the notion of a patient first-mean stable system. Such systems are switched systems that are first-mean stable meaning that they converge to a globally attracting fixed point on average. They are also patient so…
A static non-linear homogeneous feedback for a fixed-time stabilization of a linear time-invariant (LTI) system is designed in such a way that the settling time is assigned exactly to a prescribed constant for all nonzero initial…