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International audience; Delays appear in the dynamics of many systems due to non-vanishing reaction times of control systems. In biochemical systems, long sequences of repeated steps, especially in biopolymerization processes, can be modeled by delays. However, modelling systems with delays is often complicated by physical constraints, such as the requirement that solutions representing concentrations of chemical species remain positive. In this work, we consider a model for a detoxifying enzyme whose synthesis is controlled by its substrate. The model includes bindingsite clearance delays, caused by the time required for an RNA polymerase or ribosome to clear its binding site before another such machine can bind. The existence of a positive equilibrium and the positivity and boundedness of solutions of the corresponding delay-differential equations are proven. In addition, the stability of the model is studied using the "small-gain" theorem.

WOS: 000391588600005, Sometimes a network of dynamical systems shows a form of incomplete synchronization, characterized by synchronization of some but not all of its component systems. This type of incomplete synchronization is called partial synchronization or cluster synchronization. Partial synchronization is associated with the existence of partial synchronization manifolds, which are linear invariant subspaces of C, the state space of the network of systems. We focus on partial synchronization manifolds in networks of identical systems, characterized by linear diffusive coupling described by a weighted graph, and allowing for time-delay in the coupling. We present equivalent existence criteria for partial synchronization manifolds in terms of invariant spaces, the block-structure of a reordered adjacency matrix, and the solvability of a Sylvester equation. We emphasize decomposable networks, according to the rational dependency structure of the coupling weights, and according to the delay values, respectively. It is obvious that if the existence conditions for partial synchronization manifolds are satisfied for all subnetworks simultaneously, they hold for the original network, yet the converse result is not always true, as we shall illustrate with an example. Furthermore, as our main results, we show that if the decomposition is according to the weights and the basis weights are rationally independent numbers, or if the decomposition is according to different delay values, then finding a partial synchronization manifold for the original network is equivalent to finding common partial synchronization manifolds for the subnetworks, i.e., restricting to the analysis of the subnetworks does not impose any conservatism, which simplifies the analysis significantly. For the case of decomposable networks according to the weights, with rationally independent basis weights, we provide a fourth existence criterion for partial synchronization manifolds in terms of a balanced coloring of an associated multigraph. In addition, we briefly describe publicly available software for detecting partial synchronization manifolds. Our equivalent existence criteria, which depend on the network and delay structure but not on the dynamics of the systems at the nodes, are sufficient for the presence of a partial synchronization manifold. We show that under a mild assumption on the systems at the nodes, namely, left-invertibility, these conditions are necessary as well. In all criteria it turns out that the distinction between noninvasive and invasive delayed coupling is important, i.e., whether or not a coupling term between two systems vanishes whenever the latter are synchronized., Programme of Interuniversity Attraction Poles of the Belgian Federal Science Policy Office (IAP P6-DYSCO); OPTEC, the Optimization in Engineering Center of KU Leuven; Research Foundation-Flanders (FWO) [G.0712.11N]; Odysseus grant from FWO, This research was supported by the Programme of Interuniversity Attraction Poles of the Belgian Federal Science Policy Office (IAP P6-DYSCO), by OPTEC, the Optimization in Engineering Center of KU Leuven, and by project G.0712.11N of the Research Foundation-Flanders (FWO). The third author was supported by an Odysseus grant from FWO.

20th Meeting of the International-Linear-Algebra-Society (ILAS) -- JUL 11-15, 2016 -- Univ Leuven, KU Leuven, Leuven, BELGIUM, WOS: 000425197500030, A question of ongoing interest for linear Time-delay systems is to determine conditions on the equation parameters that guarantee the exponential stability of solutions. In recent works a new interesting property of time-delay systems was emphasized. As a matter of fact, the multiple spectral values for time-delay systems was characterized by using a Birkhoff/Vandermonde-based approach. Then, a multiplicity induced stability criteria were exhibited for reduced order systems; scalar delay-equations and a special class of second order systems. This work, further explores such a criteria and shows their applicability to the control of a mechanical system, Int Linear Algebra Soc, Hubert Curien (PHC) BRANCUSI [38390ZL]; EU Operational Programme Research, Development and Education; Center of Advanced Aerospace Technology, Faculty of Mechanical Engineering, Czech Technical University in Prague [CZ.02.1.01/0.0/0.0/16 - 019/0000826], The authors would like to thank the reviewers for valuable suggestions. We warmly thank Professor Gabor Stepan (Budapest University of Technology and Economics, Hungary) for stimulating discussions on delay topics. Last but not least, we thank Karim L. Trabelsi (IPSA Paris, France) for careful reading of the manuscript and for valuable remarks. IB and SIN are partially financially supported by a grant from Hubert Curien (PHC) BRANCUSI 2017, project number 38390ZL. TV acknowledges support from the EU Operational Programme Research, Development and Education, and from the Center of Advanced Aerospace Technology (CZ.02.1.01/0.0/0.0/16 - 019/0000826), Faculty of Mechanical Engineering, Czech Technical University in Prague.

International audience; Belousov-Zhabotinskii reaction is a complicated chemical oscillator exhibits temporal and spatiotemporal behaviours that quantitatively match some rhythmic behaviours in biological systems. Its important features are covered by a simple irreversible mechanism, called the Oregonator. By taking into account the physical constraints and to describe the mechanism with a fewer variables, two-delays Oregonator based model is considered in order to investigate the delay effects in chemical reactions exhibiting sustained oscillations. It is shown that the solutions of the model, obtained by use of the delay-mass action kinetics, are positive and bounded. By utilizing the asymptotic stability properties of the model which exhibits positive and bounded solutions, a positive invariant set for the solutions is described. Numerical results are presented to compare with the existing solutions which are qualitatively matches with the experimental results.

et al.;IFAC TC 1.5. Networked Systems;IFAC TC 2.1. Control Design;IFAC TC 2.2. Linear Control Systems;IFAC TC 2.3. Non-Linear Control Systems;IFAC TC 2.5. Robust Control, 10th IFAC Workshop on Time Delay Systems, TDS-2012 -- 22 June 2012 through 24 June 2012 -- Boston, MA -- 92592, Stable controllers are required due to modelling imperfections and for better performance achievements. As is well known, a stable stabilizing controller for a given real-rational plant exists if and only if the plant staisfies the so-called parity interlacing property. In this paper, a recent result, which proves that this condition is also necessary for infinite-dimensional plants is first presented. The condition is also sufficient if the plant satisfies certain additional properties. This result is then applied to time-delay systems. Two examples are considered. For the first example it is shown that it is not possible to design a stable stabilizing controller. For the second example it is shown that there exists a stable controller which stabilizes the plant and the design of such a controller is demonstrated

Robust controller design for a flow control problem where uncertain multiple time-varying time-delays exist is considered. Although primarily data-communication networks are considered, the presented approach can also be applied to other flow control problems and can even be extended to other control problems where uncertain multiple time-varying time-delays exist. Besides robustness, tracking and fairness requirements are also considered. To solve this problem, an ℋ∞ optimization problem is set up and solved. Unlike previous approaches, where only a suboptimal solution could be found, the present approach allows to design an optimal controller. Simulation studies are carried out in order to illustrate the time-domain performance of the designed controllers. The obtained results are also compared to the results of a suboptimal controller obtained by an earlier approach. Copyright © 2009 John Wiley & Sons, Ltd.

WOS: 000320838600010, One of the major problems of communication networks is congestion. In order to address this problem in TCP/IP networks, Active Queue Management (AQM) scheme is recommended. AQM aims to minimize the congestion by regulating the average queue size at the routers. To improve upon AQM, recently, several feedback control approaches were proposed. Among these approaches, PI controllers are gaining attention because of their simplicity and ease of implementation. In this paper, by utilizing the fluid-flow model of TCP networks, we study the PI controllers designed for TCP/AQM. We compare these controllers by first analyzing their robustness and fragility. Then, we implement these controllers in ns-2 platform and conduct simulation experiments to compare their performances in terms of queue length. Taken together, our results provide a guideline for choosing a PI controller for AQM given specific performance requirements, French-Turkish PIA Bosphorus (TUBITAK) [109E127]; French-Turkish PIA Bosphorus (EGIDE) [22974WJ]; K.U. Leuven Research Council [STRT1-09/33]; DPT-HAMIT project; CONACYT [131587], The authors thank the Associate Editor and reviewers for their useful suggestions that helped us to improve the paper. This work is supported in part by the French-Turkish PIA Bosphorus (TUBITAK Grant No. 109E127 and EGIDE Project No. 22974WJ). The work of Hakki Ulas final is supported by the project STRT1-09/33 of the K.U. Leuven Research Council. The work of Hitay Ozbay is partially supported by DPT-HAMIT project. The work of Daniel Melchor-Aguilar is supported by CONACYT Grant 131587.

IFAC Technical Committee on Linear Control Systems, 4th IFAC Symposium on System, Structure and Control, SSSC 2010 -- 15 September 2010 through 17 September 2010 -- Ancona -- 94468, In this paper, ns-2 simulations and related comparisons of four different PI controllers designed for TCP/AQM networks will be presented. The simulations are performed for various scenarios

IFAC - Tech. Comm. Linear Control Syst.;IFAC - Tech. Comm. Nonlinear Syst.;IFAC - Tech. Comm. Robust Control;IFAC - Tech. Comm. Control Des.;IFAC - Tech. Comm. Networked Syst., 8th IFAC Workshop on Time-Delay Systems, TDS'09 -- 1 September 2009 through 3 September 2009 -- Sinaia -- 85994, Stable H? controller design, for a flow control problem which involves multiple time-delays, is considered. An algorithm, which produces a stable controller apart from the integral action, is developed utilizing a rational approximation of finite-impulse response filters. An example is also presented to show the performance of the stable H? flow controller obtained by the proposed approach. This controller robustly stabilizes the system and achieves all design requirements, whereas the H ?-optimal controller, which is unstable, fails to achieve the same requirements. Copyright © IFAC 2009.