Related papers: On the Lyapunov Matrix of Linear Delay Difference …
This paper provides a self-contained ordinary differential equation solver approach for separable convex optimization problems. A novel primal-dual dynamical system with built-in time rescaling factors is introduced, and the exponential…
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
This is the continuation of previous article. For subspaces $M^n(t)$ and $M^{n-m}(t)$ which are invariant manifolds of the differential equation under consideration we build a change of variables which splits this equation into a system of…
We consider linear delay differential equations at the verge of Hopf instability, i.e. a pair of roots of the characteristic equation are on the imaginary axis of the complex plane and all other roots have negative real parts. When…
The stability and convergence of the neural networks are the fundamental characteristics in the Hopfield type networks. Since time delay is ubiquitous in most physical and biological systems, more attention is being made for the delayed…
We study the dynamics of perturbations in time delayed dynamical systems. Using a suitable space-time coordinate transformation, we find that the time evolution of the linearized perturbations (Lyapunov vector) can be mapped to the linear…
We introduce a new class of quadratic functions based on a hierarchy of linear time-varying (LTV) dynamical systems. These quadratic functions in the higher order space can be also seen as a non-homogeneous polynomial Lyapunov functions for…
Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.
Time bounded reachability is a fundamental problem in model checking continuous-time Markov chains (CTMCs) and Markov decision processes (CTMDPs) for specifications in continuous stochastic logics. It can be computed by numerically solving…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two…
Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…
This paper develops an explicit spectral representation for solutions of a one-dimensional linear wave equation with a constant time delay. The model is considered on a bounded interval with non-homogeneous Dirichlet boundary data and a…
This work focuses on the well-posedness of McKean-Vlasov stochastic differential delay equations. Under suitable lipschitz conditions on the drift and diffusion terms, along with a distribution dependent Lyapunov condition, this paper shows…
It is already well-understood that many delay differential equations with only a single constant delay exhibit a change in stability according to the value of the delay in relation to a critical delay value. Finding a formula for the…
This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state…
This work is dedicated to the stability analysis of time-delay systems with a single constant delay using the Lyapunov-Krasovskii theorem. This approach has been widely used in the literature and numerous sufficient conditions of stability…
The $\mu$-neutral linear fractional multi-delayed differential nonhomogeneous system with noncommutative coefficient matrices is introduced. The novel $\mu$-neutral multi-delayed perturbation of Mittag-Leffler type matrix function is…
This paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints. Specifically, the nonlinear distributed kernel includes functions such as polynomials,…