Related papers: A Core Theory of Delay Systems
Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of characteristic equation and the argument principle, an algorithm is generated which is shown to outperform…
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…
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…
This article is the third in a series the aim of which is to use Lie group theory to obtain exact analytic solutions of Delay Ordinary Differential Systems (DODSs). Such a system consists of two equations involving one independent variable…
The input/output stability of an interconnected system composed of an ordinary differential equation and a damped string equation is studied. Issued from the literature on time-delay systems, an exact stability result is firstly derived…
The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
The propagation of primary discontinuities in initial value problems for linear delay differential-algebraic equations (DDAEs) is discussed. Based on the (quasi-) Weierstra{\ss} form for regular matrix pencil, a complete characterization of…
Hybrid systems with memory refer to dynamical systems exhibiting both hybrid and delay phenomena. While systems of this type are frequently encountered in many physical and engineering systems, particularly in control applications, various…
We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a…
Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant…
This work is devoted to the study of the relationships between graph theory and the qualitative analysis of ordinary differential equations, with a special focus on two-dimensional systems. In particular, we reinterpret classical results…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
Meeting the diverse delay requirements of emerging wireless applications is one of the most critical goals for the design of ultradense networks. Though the delay of point-to-point communications has been well investigated using classical…
There is a tendency to write the equations of general relativity as a first order symmetric system of time dependent partial differential equations. However, for numerical reasons, it might be advantageous to use a second order formulation…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…
In this paper we prove well-posedness and stabibility of a class of stochastic delay differential equations with singular drift. Moreover, we show local well-posedness under localized assumptions.
We prove that characteristic equations of certain types of delay differential systems, under some mild conditions on their coefficients, can possess infinitely many complex roots.
Stability of retarded differential equations is closely related to the existence of Lyapunov-Krasovskii functionals. Even if a number of converse results have been reported regarding the existence of such functionals, there is a lack of…