EDelay Systems letter Updated on 22 June 2009 Greetings Colleagues, After a long delay, the third issue of the edelay systems letter is now available. What is different in this issue is that the editors decided to continuously update the eletter as information arrives instead of accumulating and posting this information in a new issue. We have two new contributions: (1) "Control of DelayODE, DelayPDE, and PDEODE Cascades," by Miroslav Krstic. (2) "A timedelay approach for the modeling and control of plasma instabilities in thermonuclear fusion," by Emmanuel Witrant, Erik OLOFSSON, SilviuIulian NICULESCU. We hope you will enjoy this new section and reading about a summary of our colleagues' recent work on time delay systems. Should you wish to participate in sharing your work with us, please do not hesitate to email to Rifat Sipahi at rifat AT coe DOT neu DOT edu with your documents, and we will be happy to post them and distribute them among the 1500 members we have in the emailing list. Regarding the emailing list. If you wish to be removed from the emailing list, please follow the simple instructions in the link below http://lists.coe.neu.edu/mailman/listinfo/edelay This link is also the main page we shall maintain the emailing list, to which new colleagues can subscribe simply by submitting their email addresses. If you have colleagues who might have interest in joining the emailing list, we will appreciate your help in spreading the news. Best regards, Rifat Sipahi & SilviuIulian Niculescu 
Invited Contributions 
Control of DelayODE, DelayPDE, and PDEODE Cascades Miroslav Krstic Several extensions of the `predictor' (or `finite spectrum assignment') feedback are introduced, including a generalization to nonlinear ODE plants, a delayadaptive design for LTI plants, predictor feedback for PDEs, and `predictorlike' feedback for ODEs with PDE actuator dynamics (such as reactiondiffusion or wave/string dynamics). The emphasis is on explicit construction of feedback laws and LyapunovKrasovskii functionals.. Click to continue (PDF) 
A timedelay approach for the modeling and control of plasma instabilities in thermonuclear fusion Emmanuel Witrant, Erik OLOFSSON, SilviuIulian NICULESCU This letter presents a summary of [1], where we investigated the stability problems and control issues that occur in a reversedfield pinch (RFP) device, EXTRAPT2R, used for research in fusion plasma physics and general plasma (ionized gas) dynamics. The plant exhibits, among other things, magnetohydrodynamic instabilities known as resistivewall modes (RWMs), growing on a timescale set by a surrounding nonperfectly conducting shell. We propose a new modeling approach that takes into account experimental constraints, such as the actuators dynamics and control latencies leading to a multivariable timedelay model of the system. The openloop fielderror characteristics are estimated and a stability analysis of the resulting closedloop delay differential equation (DDE) emphasizes the importance of the delay effects. We then design an optimal PID controller (its structure being constrained by the intelligentshell (IS) control architecture) that achieves a direct eigenvalue optimization of the corresponding DDE. The presented results are substantially based on and compared with experimental data. Click to continue (PDF) 
Announcements

December 1st, 2009: Submission of draft papers and invited sessions  Click for the announcement

Contributed by MayWin Thein 2010 American Control Conference: Call for PapersThe 2010 American Control Conference (ACC) will be held Wednesday through Friday, June 30 – July 2, 2010 at the Baltimore Marriott Waterfront in Baltimore, Maryland. The ACC is the annual conference of the American Automatic Control Council (AACC). The 2010 ACC, held in cooperation with IFAC, will present a technical program consisting of new developments in theory and practice in the area of automatic control. The technical program will consist of papers in regular technical sessions, invited sessions, special sessions, education/tutorial session, and preconference workshops. Special themes for the 2010 ACC include: Control in Medicine, Control of Robotic Systems, and Control of Green Energy Systems. Baltimore, home of the Orioles and Ravens, has a beautiful Inner Harbor with a scenic and popular waterfront. Baltimore is also rich with history, as the place where Francis Scott Key wrote the lyrics to “The StarSpangled Banner” as he watched soldiers of Fort McHenry defend Baltimore from the Royal Navy in the War of 1812. Other attractions include the Baltimore Aquarium, the Maryland Science Center, and a wide variety of other museums. Baltimore also hosts a wealth of famous restaurants and outdoor entertainment such as street entertainers, fireworks, cruise boats, and openair theatres. Submissions for the 2010 ACC program are invited. Contributors are encouraged to consult the conference website and contact appropriate organizing committee members for more information. Contributed papers can be submitted in regular or short paper categories. Regular papers are intended to be complete descriptions of finished work. Short papers are intended to present novel ideas or preliminary results. Invited session proposals should present topics from multiple viewpoints with unifying themes. Each proposal should consist of a summary statement and six regular papers. Special session proposals should address emerging research areas, industry and government initiatives, and other topics of broad interest. Education/Tutorial session proposals should address stateoftheart control theory and industrial applications. Tutorials are encouraged to have panel discussions. Preconference workshop proposals addressing topics of current interest to the controls community are invited. We also invite exhibit proposals related to control theory, practice, and education. The ACC exhibit area typically features booths by book publishers, local and national organizations, and suppliers of software and hardware systems. Please visit http://www.a2c2.org/conferences/acc2010/ for complete conference information. You may also contact the General Chair, Glenn Masada (masada@austin.utexas.edu), or the Program Chair, Richard Braatz (braatz@illinois.edu). Glenn Masada, General Chair 2010 ACC Key Dates:

Contributed by Vladimir Rasvan 
Contributed by Miroslav Krstic Miroslav Krstic, Delay Compensation in Nonlinear, Adaptive, and PDE Systems, Birkhauser, 2009 Click to see the Table of Contents 
Contributed by Pierdomenico Pepe Papers presented at the 6th IFAC Workshop on Time Delay Systems, held in L'Aquila, Italy, have been published: C. Manes & P. Pepe (Eds), Proceedings of the 6th IFAC Workshop on TimeDelay Systems, L’Aquila, Italy, 2006, IFACPapersOnline (www.ifacpapersonline.net), Vol. 6, Part 1, ISBN 9783902661111. 
Contributed by Rifat Sipahi http://www.elec.qmul.ac.uk/chaos09/ Plenary Talk: Wim Michiels, "Delay effects in dynamical systems and networks: analysis and control interpretations" Sessions relevant to "delay systems"

Contributed by Dimitri Breda Some upcoming conferences and workshops WORKSHOP ON DELAY DIFFERENTIAL EQUATIONS: FROM THEORY TO APPLICATIONS, Bristol, UK, 7th9th September 2009; International Workshop on Delayed Complex Systems, Dresden, Germany, 5th9th October 2009; Workshop on State Dependent Delay Equations, Dresden, Germany, 12th16th October 2009. 
Theses 
The spectrum of delaydifferential equations: numerical methods, stability and perturbation Elias Jarlebring, T.U. Braunschweig (now at K.U. Leuven) Supervisor: Abstract: Three types of problems related to timedelay systems are treated in this thesis. In our context, a timedelay system, or sometimes delaydifferential equation (DDE), is a generalization of an ordinary differential equation (ODE) with constant coefficients. For DDEs, unlike ODEs, the derivative of the state at some timepoint is not only dependent on the state at that timepoint, but also on one or more previous states. The second part of this thesis is related to exact stability conditions of the DDE. We find exact conditions on the delays such that the DDE has a purely imaginary eigenvalue. All those combinations of the delays such that there is a purely imaginary eigenvalue (called critical delays) are parameterized. That is, we construct a mapping consisting of computable expressions, from a simple mathematical object onto the set of all subsets of the critical delays. The mapping can be expressed explicitly with trigonometric functions for scalar DDEs. We find some new formulas and verify some formulas in the literature. In general, an evaluation of the map consists of solving a quadratic eigenvalue problem of squared dimension for nonscalar problems. The constructed eigenvalue problem is large, even for DDEs of moderate size. For that reason, we show how the computational cost for one evaluation of the map can be reduced. In particular we show that the matrixvector product corresponding to the companion linearization of the quadratic eigenvalue problem can be computed by solving a Lyapunov equation. Most of the results in the chapter on critical delays are derived for retarded DDEs as well as neutral DDEs with an arbitrary number of delays. The third and last part of this thesis is about perturbation results for nonlinear eigenvalue problems. We discuss some results in eigenvalue perturbation theory which can be generalized to nonlinear eigenvalue problems. A sensitivity formula for the movement of the eigenvalues extends nicely to nonlinear eigenvalue problems. We introduce a fixed point form for the nonlinear eigenvalue problem, and show that some methods in the literature can be interpreted as setvalued fixed point iterations. The convergence order of these types of iterations can be determined from an expression containing the left and right eigenvectors. We also use some results from fixed point theory. The famous result in perturbation theory referred to as the BauerFike theorem, can be generalized to the nonlinear eigenvalue problem if we assume that the setvalued fixed point problem has a certain contraction property. 
Robust control and observation of LPV TimeDelay Systems Corentin Briat (corentin.briat@gipsalab.inpg.fr / corentin@briat.info) Abstract: At the difference of finite dimensional systems, the derivation of design tools from stability results is more difficult in the framework of timedelay systems due to a larger number of decision matrices involved in the LMI conditions. This thesis is based on a particular LyapunovKrasovskii functional which leads to nonconvex conditions when used for design purposes. Several types of relaxations are discussed and a relaxation based on the introduction of 'slack' variables is considered. This 'oriented' relaxation has the benefit of simplifying the design problem at the expense of increasing (slightly) the conservatism and the computational complexity. Another advantage of this approach is the possibility of generalization to more complex functional such as discretized functionals, leading then to an efficient reduction of conservatism. Using these results, both memory and memoryless controllers/observers are developed and, more precisely, controllers implementing inexact delay are studied. A new type of controllers referred to as 'delayscheduled controllers' are also introduced. In such controllers, the matrix gains are scheduled by the delayvalue (as done in the LPV framework) and a robust synthesis with respect to delay uncertainty is performed. The interest of such an approach is to embed an information on the delay in the controller without any necessity of storing past values of the state (as done for controller with memory). The design of such controllers is a difficult problem which relies on several techniques that need to be improved in future works. 
Prepared by Rifat Sipahi, May 2009.