This monograph is devoted to the effect of delays on the stability properties of dynamical systems. Stability regions with respect to the delay parameters are considered, and some sufficient characterizations are proposed. The text addresses general delay problems and offers solutions in some cases. In other cases, approximations of the stability regions can be proposed. The interpretation of delays as uncertainty allows the authors to use the advances in robust control and robust convex optimization to solve or to approximate the solutions of the corresponding problems.
This monograph is devoted to the effect of delays on the stability properties of dynamical systems. Stability regions with respect to the delay parame...
In the mathematical description of a physical or biological process, it is a common practice assume that the future behavior of Ihe process considered depends only on the present slate, and therefore can be described by a finite sct of ordinary diffe rential equations. This is satisfactory for a large class of practical systems. However. the existence of lime-delay elements, such as material or infonnation transport, of tcn renders such description unsatisfactory in accounting for important behaviors of many practical systems. Indeed. due largely to the current lack of effective metho...
In the mathematical description of a physical or biological process, it is a common practice assume that the future behavior of Ihe process consider...
Time delays are present in many physical processes due to the period of time it takes for the events to occur. Delays are particularly more pronounced in networks of interconnected systems, such as supply chains and systems controlled over c- munication networks. In these control problems, taking the delays into account is particularly important for performance evaluation and control system's design. It has been shown, indeed, that delays in a controlled system (for instance, a c- munication delay for data acquisition) may have an "ambiguous" nature: they may stabilize the system, or, in the...
Time delays are present in many physical processes due to the period of time it takes for the events to occur. Delays are particularly more pronounced...
Rifat Sipahi Tomas Vyhlidal Silviu-Iulian Niculescu
This book covers the control and dynamics of time delay systems, from its six-decade history to new texhniques designed to meet the many new challenges that are emerging from engineering, physics, mathematics, and economics.
This book covers the control and dynamics of time delay systems, from its six-decade history to new texhniques designed to meet the many new challenge...
Mehmet Eren Ahsen Hitay Ozbay Silviu-Iulian Niculescu
This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a...
This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback....
In this brief the authors establish a new frequency-sweeping framework to solve the complete stability problem for time-delay systems with commensurate delays. The text describes an analytic curve perspective which allows a deeper understanding of spectral properties focusing on the asymptotic behavior of the characteristic roots located on the imaginary axis as well as on properties invariant with respect to the delay parameters. This asymptotic behavior is shown to be related by another novel concept, the dual Puiseux series which helps make frequency-sweeping curves useful in the study...
In this brief the authors establish a new frequency-sweeping framework to solve the complete stability problem for time-delay systems with commensu...
