Authors: J. E. Velázquez Velázquez; Vladimir L. Kharitonov

Abstract: In this paper a new form of the Lyapunov-Krasovskii functionals is proposed. It is shown that these functionals admits lower and upper quadratic bounds. Exponential estimates for solutions of the scalar neutral type time delay equations based on the Lyapunov-Krasovskii functionals are presented.

Keywords: neutral time delay equation,exponential estimate,Lyapunov-Krasovskii functional

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00004

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 18-23

Authors: J. Sieber; P. Kowalczyk

Abstract: We study dynamical systems that switch between two different vector fields depending on a discrete variable. If the two vector fields have linearly unstable fixed points and the switch is subject to a hysteresis and to a delay one expects the system to switch periodically back and forth between the two vector fields, always switching at certain submanifolds of the state space. This is true as long as the delay is sufficiently small. When the delay reaches a problem-dependent critical value so-called event collisions occur. We show that at these event collisions the switching manifolds can increase their dimension, giving rise to higher-dimensional dynamics near the periodic orbit than expected. In many practical applications such as control engineering the dynamical system has additional symmetry, which adds difficulty in the analysis because event collisions generically occur at several points along the periodic orbit simultaneously.

Keywords: hybrid dynamical system,delayed switch,non-smooth map

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00012

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 66-71

Authors: L. Zaccarian; P. Pepe; D. Nesic

Abstract: In this paper we show the effectiveness of a novel control scheme for dead-time systems recently proposed in (Zaccarian and Nešić, 2006 American Control Conference). In that paper, the prediction problem is formally stated and shown to be achievable for any type of dead-time system, as long as it is possible to determine a stabilizing control law. We propose here the employment of an LMI-based control strategy for this stabilization task and show the advantages of the novel modified Smith predictor scheme on a MIMO example. In particular, satisfactory simulation results are given both for the linearized model and for the nonlinear model of an inverted pendulum subject to disturbances.

Keywords:

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00045

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 270-275

Authors: Lisa Katrin Poppe

Abstract: This paper deals with an index concept for linear delay differential algebraic equations (DDAEs) of retarded type with constant coefficients. These systems can be transformed to a nondelayed system by a standard approach of introducing additional state variabels. The index of the DDAE is usually defined to be the index of the nondelayed part of the DDAE, but in this paper it is shown that it is possible, under certain conditions, to construct an augmented nondelayed system that has a lower index by using a different approach in the construction of the nondelayed system.

Keywords: differential-algebraic equations,time-delays,strangeness index,strangeness free,retarded type

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00053

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 320-324

Authors: Lotfi Belkoura; Jean-Pierre Richard

Abstract: This paper deals with on line identification of delay systems. The work is based on the approach initiated in (Fliess M., 2003) and extended to delays identification.

Keywords: delay systems,identification

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00023

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 132-137

Authors: Lucio Torelli

Abstract: This paper is devoted to stability analysis of Delay Differential Equations of Neutral type. In particular we present two reformulations of the problem, for which the neutral system is transformed into an ordinary differential equation coupled to an algebraic recursion. Hypotheses on the original equation allow to study contractivity and asymptotic stability of the true solution and of the numerical schemes by the theory of stability with respect to a forcing term.

Keywords: delay differential equations of neutral type,contractivity,asymptotic stability,Hale's form,numerical methods

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00037

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 223-228

Authors: M. Di Loreto

Abstract: This papers addresses an approximative version of the exact model matching problem for time-delay systems. The problem is the following: let be given a plant T(s) and a model Tm(s), two stable and realizable time-delay transfer functions. Find a realizable precompensator R(s) such that the matching error E(s) = Tm(s) - T(s)R(s) is the Laplace transform of an operator with bounded support. A parametrization of all precompensators that achieve this objective is done, and a constructive procedure to compute them is detailed. Then, a relationship with an optimization problem in the sense of the L∞-induced norm is described.

Keywords: model matching,finite impulse response,time-delay systems,feedforward control,pseudopolynomial,realizable fraction,stability,optimization

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00019

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 108-113

Authors: M.-N. Alpaslan Parlakçi

Abstract: In this paper a new class of augmented quasi full size Lypunov-Krasovskii functional is introduced for the robust stability of linear uncertain neutral systems. The nonlinear parameter perturbations and norm bounded uncertainties are taken into consideration separately. Delay-dependent robust stability criteria are derived in the form of linear matrix inequalities. Numerical examples are presented to illustrate the significant improvement on the conservativeness of the delay bound over some reported results in the literature.

Keywords: neutral systems,nonlinear parameter perturbations,norm-bounded uncertainty,delay-dependent stability,augmented quasi full size Lyapunov functional

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00047

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 284-289

Authors: M.-N. Alpaslan Parlakçi

Abstract: In this paper the robust H∞ output feedback control of uncertain neutral time-delay systems with norm-bounded type uncertainties is investigated. The control input is utilized as the augmenting state term and the system is represented in augmented dynamics form which enables to handle the design of the H∞ output feedback controller in terms of convex linear matrix inequalities (LMI) form which can be solved via interiorpoint algorithms. A novel augmented Lyapunov-Krasovskii functional is selected to obtain sufficient LMI conditions for the existence of delay-dependent H∞ output feedback control. Any model transformation and bounding for cross terms are strictly avoided to overcome the conservativeness of the results. A delay-dependent bounded real lemma is also presented in LMI form. Finally, several numerical examples are given to illustrate the effectiveness of the proposed method.

Keywords: neutral systems,static output-feedback,augmented dynamics,HÝ control problem,augmented Lyapunov functional,norm-bounded uncertainty

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00018

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 102-107

Authors: Mauro Boccadoro; Francesco Martinelli; Paolo Valigi

Abstract: In this paper we develop a dynamical model of a distributed production system taking into account the lead times of each site and the transportation among different sites, which introduce a delay on the effect of control actions on the inventory levels of the sites. We linearize about typical operative conditions, and show the intuitive result that it is not possible to decouple the buffer levels from the external (unknown) demand. Structural properties of this model are presented and different policies are defined in order to prevent undesired phenomena and to guarantee the optimal management of the overall system.

Keywords:

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00050

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 302-307

Authors: Nejat Olgac; Tomáš Vyhlídal; Rifat Sipahi

Abstract: The stability of neutral systems with two cross-talking delays is investigated using the method of cluster treatment of characteristic roots (CTCR). here are two main outcomes of this study: (a) Generation of the well-known delay stabilizability condition as a by-product of the CTCR procedure. This is achieved by a small delay stability treatment over the system. We also demonstrate for the delay-stabilizable systems the exact bounds of the stability regions in the domain of the delays. (b) Validation of these stability regions using an alternative point-wise algorithm, which computes the right-most roots of the characteristic quasi-polynomial.

Keywords: time-delay system,neutral system,delay-dependent stability

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00029

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 175-180

Authors: Nikolai Dyomin; Svetlana Rozhkova

Abstract: The joint synthesis of mean square optimal (MSO) unbiased filter-interpolator-extrapolator (FIE) is performed. It is supposed that these processes depend not only on the current values of an unobserved process but on an arbitrary number of its preceding values, and anomalous noise occurs in discrete observations. The properties of MSO FIE are investigated.

Keywords: stochastic systems,filtering,interpolation,extrapolation,time-delay,memory

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00013

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 72-77

Authors: O. Sename; C. Briat

Abstract: We propose here a new LMI solution to H∞ observer-controller design that ensures a disturbance attenuation level for the controlled output and for the state estimation error, which is an open problem. This will be compared with a well-known solution. An application to a wind tunnel model is provided.

Keywords: time-delay,delay-independent,HÝ,observer-based controller,LMI

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00020

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 114-119

Authors: Omar Santos; S. Mondié; V. L. Kharitonov

Abstract: In this contribution we propose an iterative method for the synthesis of suboptimal control laws for systems with pointwise and distributed delays. The method is based on the concepts of dynamic programming along with the Lyapunov second method.The Bellman functional is constructed using Lyapunov Krasovskii functionals of complete type.

Keywords: time delay systems,Lyapunov Krasovskii functional,suboptimal control,dynamic programming

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00017

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 96-101

Authors: P. Palumbo; S. Panunzi; A. De Gaetano

Abstract: A discrete delay-differential model of the glucose-insulin system is presented, representing the Intra-Venous Glucose Tolerance Test and allied experimental procedures of diabetological interest. The model ensures unique positive bounded solutions for any positive initial condition, and provides a unique equilibrium point. Conditions are given on the physical parameters in order to ensure the local asymptotic stability of the equilibrium point. These conditions are always satisfied, given the actual parameter estimates obtained experimentally. A study of the global stability properties is also performed.

Keywords: delay-differential systems,glucose-insulin homeostasis,stability analysis

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00038

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 229-234

Authors: Pavel Ettler; Ivan Puchr

Abstract: An interesting control problem was to be solved for an array of annealing furnaces with a simple construction. Temperature of the heated material should follow a prescribed diagram while no enforced cooling is available, furnace heating output is limited and a load-dependent time delay is present. The solution combines several control techniques including feedback using predicted values of temperature.

Keywords: time delay,prediction,industry automation,on-off control,annealing furnace

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00039

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 235-239

Authors: R. Gabasov; F. M. Kirillova; O. P. Yarmosh

Abstract: An optimal terminal control problem of one class of linear time-delay systems is under consideration. The fast realization of dual method for optimal controls calculation is proposed. It is based on the procedure of quasireduction of the fundamental matrices of solutions of the considered systems. As a result, on iterations of proposed method it is sufficient to integrate auxiliary system of ordinary differential equations on small time intervals. An algorithm of calculating current values of optimal feedbacks in real-time is described. The results are illustrated on the optimal control problem for stationary systems of the third order.

Keywords: on-line control,open-loop control,time-delay systems

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00016

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 90-95

Authors: R. Gabasov; F. M. Kirillova; P. V. Makevich

Abstract: A linear optimal observation problem for one type of time-delay systems with unknown but bounded initial state is under consideration. A fast version of the dual method of linear programming is developed to compute current estimates of it's states. Principal part of this algorithm is a quasireduction of the fundamental matrix of the system. It is shown that to fulfil an iteration, it is sufficient to integrate an auxiliary ordinary system over not large intervals of time. An algorithm of online calculation of current estimates of system's states is also described. The results are illustrated by the example.

Keywords: optimal estimation,time delay,algorithms,on-line control

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00022

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 126-131

Authors: Rifat Sipahi; Silviu-Iulian Niculescu

Abstract: Analytical stability study of some deterministic car following models under time-delay influences is presented and various case studies are demonstrated. Interestingly, for some control law deployed by human drivers, more than one stability interval in the domain of time delay is revealed. Physical interpretations along with comparisons conclude the study.

Keywords: car following model,delay,crossing curves,stability,sensitivity

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00031

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 187-192

Authors: Silviu-Iulian Niculescu; Peilin Fu; Jie Chen

Abstract: In this paper we study the stability properties of a class of lossless propagation systems. Roughly speaking, a lossless propagation model is defined by a system of semiexplicit delay differential algebraic equations, that is a system of differential equations coupled with a system of (continuous-time) difference equations. We show that the stability analysis in the commensurate delay case can be performed by computing the generalized eigenvalues of certain matrix pencils, which can be executed efficiently and with high precision. The results extend previously known work on retarded, and neutral systems, and demonstrate that similar stability tests can be derived for such systems.

Keywords: propagation,delay,stability,switches,matrix pencil

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00030

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 181-186

Authors: Tomáš Vyhlídal; Pavel Zítek

Abstract: An original method for computing the spectrum of a retarded time delay system over a large region in the complex plane is presented. The method is based on mapping the quasi-polynomial characteristic function and on utilizing asymptotic properties of the root chains. First, asymptotic exponentials of the root chains are assessed and large areas free of the roots are determined. These areas are then omitted in systematic mapping of the roots location. The roots are located as the intersection points of the contours determined by real and imaginary parts of the characteristic function. The theoretical explanation of the method is supplemented ith a discussion of implementation issues and an application example is added.

Keywords: retarded system, quasi-polynomial,spectrum distribution,root-finding techniques

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00028

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 169-174

Authors: Toshiki Oguchi; Henk Nijmeijer

Abstract: This paper considers the state prediction of chaotic behaviour using a master-slave synchronization scheme. In this paper, we consider the robust convergency of the prediction error of anticipating synchronization of nonlinear systems with model uncertainties and sufficient conditions for anticipatory synchronization are derived. The effectiveness of the obtained result is illustrated by a simulation example.

Keywords: nonlinear systems,time-delay,synchronization,state predictor

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00048

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 290-295

Authors: Tsuneo Yoshikawa

Abstract: Several works we have completed in coping with time delay problems in robotic systems and haptic interfaces are presented: ground-space teleoperation of a robot arm on a space satellite, passivity-based adaptive control of flexible robot arms and power assist devices, and partially continuous-time impedance display for haptic interface systems. For each topic, background, overview, the approach taken, and experimental results are discussed. Passivity is utilized directly or indirectly in all these works.

Keywords: time delay,robot,teleoperation,interface,virtual reality,passivity,PD-control

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00046

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 276-283

Authors: Vladimir L. Kharitonov

Abstract: A class of neutral type time delay systems is presented for which computation of Lyapunov matrices is reduced to solution of an auxiliary two point boundary problem for a delay free system of matrix equations.

Keywords: neutral type time delay systems,Lyapunov matrices

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00005

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 24-29

Authors: Vladimir Răsvan

Abstract: Starting from various models in control and electrical engineering, there is obtained a rather general model of an IBVP(Initial Boundary Value Problem) for hyperbolic PDE(Partial Differential Equations) with the boundary conditions connected in feedback to some systems described by ODE(Ordinary Differential Equations - lumped parameter systems). To this model it is associated a special class of FDE(Functional Differential Equations) - delay equations coupled to continuous time difference equations. This survey examines stability and oscillation problems for such systems within the framework underlined by the dialectics Liapunov function/Popov frequency domain inequalities. Several open problems are equally mentioned.

Keywords: lossless propagation,functional differential equations,stability,oscillations

Digital Object Identifier (DOI): 10.3182/20060710-3-IT-4901.00024

Conference: 6th IFAC Workshop on Time Delay Systems (2006)

Location: Hotel Duca degli Abruzzi, L’Aquila, Italy

Start Date: Mon Jul 10 2006 - End Date: Wed Jul 12 2006

Page Numbers: 138-150