Related papers: Finite Time Stability Analysis for Fractional Stoc…
One of the most popular methods of controlling dynamical systems is feedback. It can be used without acquiring detailed knowledge of the underlying system. In this work, we study the stability of fractional-order linear difference equations…
The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…
This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…
This technical report replies to the comments of [2] in detail, and corrects a possible mis-interpretation of [1] in terms of the conventional robust stability concept. After defining the robust stability and quadratic stability concepts,…
This paper addresses the problem of risk-aware fixed-time stabilization of a class of uncertain, output-feedback nonlinear systems modeled via stochastic differential equations. First, novel classes of certificate functions, namely…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
In this paper we study the controllability of fractional neutral stochastic functional differential equations with infinite delay driven by fractional Brownian motion in a real separable Hilbert space. The controllability results are…
This paper presents novel controllers that yield finite-time stability for linear systems. We first present a sufficient condition for the origin of a scalar system to be finite-time stable. Then we present novel finite-time controllers…
This article is concerned with the existence and uniqueness of solutions to some fractional order boundary value problems. Our results are based on some fixed point theorems. For the applicability of our results, we provide an example.
In this work stability results for systems described by coupled Retarded Functional Differential Equations (RFDEs) and Functional Difference Equations (FDEs) are presented. The results are based on the observation that the composite system…
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…
In this paper, the stability behaviors of stochastic differential equations (SDEs) driven by time-changed Brownian motions are discussed. Based on the generalized Lyapunov method and stochastic analysis, necessary conditions are provided…
We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…
We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…
The dynamics of the delay logistic equation with complex parameters and arbitrary complex initial conditions is investigated. The analysis of the local stability of this difference equation has been carried out. We further exhibit several…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…