Minimal Lagrangian 2-Tori in CP2 Come in Real Families of Every Dimension

It is shown that for every non-negative integer n, there isa real n-dimensional family of minimal Lagrangian tori in CP²,and hence of special Lagrangian cones in C³ whose link is atorus. The proof utilises the fact that such tori arise fromintegrable systems, and can be described using algebro-geometric(spectral curve) data.     

Approximate controllability of non-linear evolution systems with time-varying delays

^** Email: balachandran_k{at}lycos.com In this paper, the approximate controllability of non-linearevolution time-varying delay systems with preassigned responsesis studied. These controllability results are for non-linearsystems that are not associated with linear systems and no compactnessassumption is imposed.     

Linear Systems and Quotients of Projective Space

A complete characterization of the categorical quotients of(P¹)ⁿ by the diagonal action of SL(2, C) with respect to anypolarization is given by M. Polito, in ‘SL(2, C)-quotientsde (P¹)ⁿ’, C. R. Acad. Sci. Paris Sér. I 321 (1995)1577–1582. In this paper, these categorical quotientsare obtained by certain linear systems on P^n–3, dependingon the given polarization. 2000 Mathematics Subject Classification14L24, 14L30     

Cubic Splines on Curved Spaces

We consider a second-order problem in the calculus of variations,with an application to robotics in mind. The analysis is carriedout on a general Riemannian manifold M and then specializedto the case where M is the Lie group SO(3) of rotations in R³.For SO(3), the Euler-Lagrange equations reduce to interestingnonlinear systems of ordinary differential equations in R³.     

Finite Time Equipartition for Second-order Hyperbolic Systems

A sufficient condition for equipartition of energy for secondorder hyperbolic systems in three space variables is given.The condition states that the system should evolve in such away that the time derivative of a solution of the form (u₁,0)^T is connected with the space derivatives of a solution ofthe form (0, u₂)^T and the time derivative of (0, u₂)^T is connectedwith the space derivatives of (u₁, 0)^T.     

On Central Cantor Sets with Self-Arithmetic Difference of Positive Lebesgue Measure

We prove the existence of C^r - (but not C^r+1-) regular centralCantor sets with zero Lebesgue measure such that their selfarithmetic difference is a Cantor set with positive Lebesguemeasure. This is motivated by a conjecture in the field of bifurcationsof dynamical systems posed by Jacob Palis.     

Explicit stability conditions for time-discrete vector Lur'e-type systems

^** Email: gilmi{at}cs.bgu.ac.il^*** Email: rmedina{at}ulagos.cl Non-linear discrete-time Lur'e-type systems are considered.Explicit stability conditions are suggested. They are formulatedin terms of the determinants of characteristic polynomials.Moreover, an estimate for the region of attraction of the zerosolution is derived.     

Mixed block elimination for linear systems with wider borders

The paper is about the stable solution of possibly ill-conditionedbordered linear systems. Given stable solvers for matrix A andfor A^T, we prove that the Govaerts Mixed Block Elimination (BEM)method constitutes a stable solver for the matrix consistingof A or A^T with a border of width 1, and hence by recursionfor a border of any width. We express the algorithm in an efficient,iterative, form. We analyse its operation count, and verifythe theory by extensive numerical experiments. ^*Senior Research Associate of the Belgian National Fund of ScientificResearch NFWO.     

BREAKDOWN OF CLASSICAL SOLUTION TO A KIND OF QUASILINEAR NON-STRICTLY HYPERBOLIC SYSTEMS

In this article, the author considers the Cauchy problem for quasilinear non-strictly hyperbolic systems and obtain a blow-up result for the C¹ solution to the Cauchy problem with weaker decaying initial data.     

Distributed control for cooperative systems involving parabolic operators with an infinite number of variables

^** Email: serraghm{at}yahoo.com The optimal control for cooperative systems involving parabolicoperators with an infinite number of variables is considered.First the existence and uniqueness of the states are proved;then the necessary and sufficient condition for the controlto be optimal is obtained by a set of inequalities. The controlin our problems is of distributed type and is allowed to bein the Hilbert space (L²(0, T, L²()))ⁿ.     

Controllability and quadratic stability quadratic stabilization of discrete-time interval systems--an LMI approach

^** Email: qlzhang{at}mail.neu.edu.cn This paper presents necessary and sufficient conditions fordiscrete-time interval systems to be quadratically stable orquadratically stabilizable, and sufficient conditions for discrete-timeinterval systems to be controllable. All the results are obtainedin terms of linear matrix inequality (LMI). With the LMI toolbox,the problems can be conveniently solved. Illustrative numericalexamples show that the results are effective and less conservativeto check the robust controllability and stability and to designthe stabilizing controller for discrete-time interval systems.     

A unified framework for the numerical solution of general quadratic matrix equations

^** Email: vassilios.tsachouridis{at}ieee.org^*** Email: N.karcanias{at}city.ac.uk^**** Email: ixp{at}le.ac.uk Algebraic quadratic equations are special cases of a singlegeneralized algebraic quadratic matrix equation (GQME). Thispaper focuses on the numerical solution of the GQME using probability-1homotopy methods. A synoptic review of these methods and theirapplication to algebraic matrix equations is provided as background.A large variety of analysis and design problems in systems andcontrol are reported as special cases of the presented frameworkand some of them are illustrated via numerical examples fromthe literature.     

Controllability and observability of impulsive hybrid dynamic systems

Corresponding author, Email: cbsoh{at}auto.eee.ntu.ac.sg This paper considers the controllability and observability ofhybrid dynamic systems with impulsive switching of the otherwisecontinuously evolving state. It derives necessary and sufficientconditions for impulsive hybrid dynamic systems to be controllableand observable.     

An Information Theoretic Approach to Regulation Systems

Based on the work of Enegell(1985), a novel approach to theanalaysis of control systems by means of information-theoreticalconcepts is presented. Using results from rate-distortion theory,the requisite variety of the regulator necessary for a certianperformance is derived. This theory is used to analyse feedbackregulation systems, in particular, the Minimum Variance Controllaw for linear systems with a quadratic performance criterion.The main result of this paper has implications for the evaluationof L-bounds on analytic functions.     

Differentiated service delivery in cooperative IP-based broadcast and mobile telecommunications networks

Email: angelo.centonza{at}brunel.ac.uk Corresponding author. Email: thomas.owens{at}brunel.ac.uk Email: john.cosmas{at}brunel.ac.uk^¶ Email: y.h.song{at}brunel.ac.uk Received on 26 November 2005. Accepted on 20 March 2007. The evolution of wireless systems has led recently to the deploymentof cooperative network infrastructures where networks basedon different technologies cooperate together to offer innovativeservices which the networks individually could not offer. Cooperativenetwork infrastructures are hybrid systems. Examples of hybridsystems are already in use in areas as diverse power systemsand locomotion systems. It is very important to apply efficientsystem management techniques to hybrid systems that produceadvantageous business case scenarios for each participatingsystem and efficient use of the available resources. In thispaper, scenarios are investigated where cooperation betweenan integrated project (IP)-based broadcast network and an IP-basedmobile telecommunications network has the potential to allowservices to be provided to mobile users which would not be economicalto offer over either an IP-based broadcast network or an IP-basedmobile telecommunications network alone. The paper presentsa novel technique for determining which network to use to deliversuch services at a given point in time. The application of thistechnique in appropriate scenarios has the potential to generateadditional income for both the IP-based broadcast network operatorand the IP-based mobile telecommunications network operatorin an infrastructure where the operators cooperate to offerinnovative services. The paper explains the construction ofutility functions for cooperative IP-based broadcast and mobiletelecommunications networks. These utility functions are thenused to provide results that enable the efficiency of the managementof the network to be assessed in terms of the utility volumegenerated by the innovative services provided.     

Stability analysis of multirate sampled-data control systems

The paper considers the stability of finite-dimensional linearmultirate sampled-data control systems. A notion of internalstability is defined, based on continous-time singals. A completeproof is given for the equivalence between continuous-time internalstability and discrete-time internal stability. An input-outputproperty called L^v(1v ) hybrid stability is investigated formulatirate systems having exogenous continuous-time inputs andoutput, and hybrid stability is shown to be equivalent to internalstability, which is fundamental to a true development of multiratesampled-data L^v control design. The relationship between internalstability and input-output stability is also discussed in continuoustime.     

Local-global double algebras for slow H{infty} adaptation; the case of l2 disturbances

In this paper, a common algebraic framework is described forthe frozen-time analysis of stability and H optimization inslowly time-varying systems, based on the notion of a normedalgebra on which local and global products are defined. Relationsbetween local stability, local (near) optimality. local coprimefactorization, and global versions of these properties are sought.The framework is valid for time-domain disturbances in l² (Z)^R. The first part of the paper elaborates the double-algebra conceptfor Volterra operators which approximately commute with theshift. The main algebraic properties and norm inequalities aresummarized. Local conditions for global inveribility are obtained.Classical frozen-time stability conditions are incorporatedin relations between local and global spectra. The paper continuesby establishing an explicit formula linking global and localsensitivity for systems with stable plants, where local sensitivityis a Lipschitz continuous function of data. Frequency-domainestimates of time-domain sensitivity norms. which become accurateas rates of time-variation approach zero, are obtained. Notionsof adaptive versus nonadaptive (robust) control are introduced.It is shown that adaptive control can achieve better sensitivitythan optimal nonadaptive control. It is demonstrated by an examplethat, in general, H-optimal interpolants do not depend Lipschitz-continuouslyon data. However, -suboptimal interpolants of the AAK central(maximal entropy) type are shown to satisfy a tractable Lipschitzcondition.     

CALIBRATED SUBMANIFOLDS OF R7 AND R8 WITH SYMMETRIES

The principal theory of this paper comprises a technique forconstructing associative, coassociative and Cayley submanifoldsof Euclidean space with symmetries, using first-order ordinarydifferential equations. Explicit examples of U(1)-invariantassociative cones in ⁷ and SU(2)-invariant Cayley 4-folds in⁸ are then produced using this method. Further examples of associative3-folds are presented, which are ruled, and other systems ofdifferential equations defining calibrated submanifolds in ⁷and ⁸ are given.     

The regulator problem for linear systems with constrained control: an LMI approach

^** Email: benzaouia{at}ucam.ac.ma A new methodology of the partial eigenstructure assignment bystate feedback via linear matrix inequality (LMI) is extendedto obtain a solution of the constrained regulator problem forlinear continuous-time and discrete-time systems by using theLMI formulation.     

A Fourth-order Tridiagonal Finite Difference Method for General Non-linear Two-point Boundary Value Problems with Mixed Boundary Conditions

We present a new fourth-order finite difference method for thegeneral second-order non-linear differential equation y^N = f(x,y, y') subject to mixed two-point boundary conditions. An interestingfeature of our method is that each discretization of the differentialequation at an interior grid point is based on just three evaluationsof f. We establish, under appropriate conditions, O(h⁴)-convergenceof the finite difference scheme. In the case of linear differentialequations, our finite difference scheme leads to tridiagonallinear systems. Numerical examples are considered to demonstratecomputationally the fourth order of the method.