Related papers: A Core Theory of Delay Systems
In this paper, we discuss delayed periodic dynamical systems, compare capability of criteria of global exponential stability in terms of various $L^{p}$ ($1\le p<\infty$) norms. A general approach to investigate global exponential stability…
In this paper, a global stability analysis is given for a rate-based congestion control system modeled by a nonlinear delayed differential equation. The model determines the dynamics of a single-source single-link network, with a…
This work studies the problem of distributed optimization in heterogeneous linear multi-agent systems. Instead of relying on a perfect communication network as in many existing distributed optimization approaches, we considered two…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
In this paper, we investigate the rapid stabilizability of linear infinite-dimensional control systems with constant delays. Under the assumptions that the state operator generates an immediately compact semigroup and that the delay…
In this paper, the stability of $\theta$-methods for delay differential equations is studied based on the test equation $y'(t)=-A y(t) + B y(t-\tau)$, where $\tau$ is a constant delay and $A$ is a positive definite matrix. It is mainly…
Assessing the boundedness and stability of vector nonlinear systems with variable delays and coefficients remains a challenging problem with broad applications in science and engineering. Existing methods tend to produce overly conservative…
Delayed feedback control is an easy realizable control method which generates control force by comparing the current and the delayed version of the system states. In this paper, a new form of the delayed feedback structure is introduced.…
Here we deal with the stabilization problem of non-diagonal systems by boundary control. In the studied setting, the boundary control input is subject to a constant delay. We use the spectral decomposition method and split the system into…
Delay coordinates are a widely used technique to pass from observations of a dynamical system to a representation of the dynamical system as an embedding in Euclidean space. Current proofs show that delay coordinates of a given dynamical…
This paper studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open loop system might…
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…
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…
Computer network tends to be subjected to the proliferation of mobile demands and increasingly multifarious, therefore it poses a great challenge to guarantee the quality of network service. By designing the model according to different…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. This paper considers linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic…
This paper presents a new method for dynamic output feedback stabilizing controller design for decomposable systems with switching topology and delay. Our approach consists of two steps. In the first step, we model the decomposable systems…
This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting…
A general theory is developed for the evolution of the cell order (CO) distribution in planar granular systems. Dynamic equations are constructed and solved in closed form for several examples: systems under compression; dilation of very…
In this paper, we consider a transmission problem in a bounded domain with a viscoelastic term and a delay term. Under appropriate hypothesis on the relaxation function and the relationship between the weight of the damping and the weight…
Limitations of the delayed feedback control and of its extended versions have been fully treated in the literature. The oscillating delayed feedback control appears as a promising scheme to overcome this problem. In this work, two methods…