Related papers: Analysis of higher order time delay systems using …
This paper revisits a recently developed methodology based on the matrix Lambert W function for the stability analysis of linear time invariant, time delay systems. By studying a particular, yet common, second order system, we show that in…
This paper is a comprehensive study of a long observed phenomenon of increase in the stability margin and so the rate of convergence of a class of linear systems due to time delay. We use Lambert W function to determine (a) in what systems…
This brief note complements some results regarding a recently developed technique for the stability analysis of linear time-invariant, time delay systems using the matrix Lambert W function. By means of a numeric example, it is shown that…
In this work, we establish the response of scalar systems with multiple discrete delays based on the Laplace transform. The time response function is expressed as the sum of infinite series of exponentials acting on eigenvalues inside…
Eigenvalue assignment problem of a linear scalar system with a single discrete delay is analytically and exactly solved. The existence condition of the desired eigenvalue is established when the current and delay states are present in the…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
Time-delayed differential equations arise frequently in the study of nonlinear dynamics of lasers with optical feedback. Traditionally, one has resorted to numerical methods because the analytical solution of such equations are intractable.…
In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence…
A previously published algorithm for trajectory tracking control of tethered wings, i.e. kites, is updated in light of recent experimental evidence. The algorithm is, furthermore, analyzed in the framework of delay differential equations.…
Recently, we have studied a delay differential equation which has a coefficient that is a linear function of time. The equation has shown the oscillatory transient dynamics appear and disappear as the delay is increased between zero to…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
In this paper we address the problem of state observation of linear time-varying systems with delayed measurements, which has attracted the attention of many researchers|see [7] and references therein. We show that, adopting the parameter…
This paper investigates the problem of functional state estimation for linear time-delay systems in which the delay affecting the state evolution differs from the delay affecting the output measurements. While existing observer designs…
Wigner-Smith (WS) time delay concepts have been used extensively in quantum mechanics to characterize delays experienced by particles interacting with a potential well. This paper formally extends WS time delay theory to Maxwell's equations…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
We present a new approach to examine transient dynamics in a class of non-autonomous delay differential equations. Exact solutions for these equations are obtained using the Lambert W function alongside an appropriately chosen initial…
Time delay is ubiquitous in many experimental and real-world situations. It is often unclear whether time delay plays a significant role in observed phenomena, and if it does, how long the time lag really is. This would be invaluable…
Dynamical systems with long delay feedback can exhibit complicated temporal phenomena, which once re-organized in a two-dimensional space are reminiscent of spatio-temporal behavior. In this framework, normal forms description have been…
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…
We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…