Necessary and sufficient conditions for parameter insensitive disturbance-rejection problems with dynamic output feedback

Email: otsuka{at}j.dendai.ac.jp Received on November 11, 2005; Accepted on December 16, 2006 In this paper, necessary and sufficient conditions for the parameterinsensitive disturbance-rejection problem with dynamic outputfeedback which was studied in Otsuka (1999) to be solvable aregiven for the structured uncertain linear systems. Further,necessary and sufficient conditions for the solvability of theproblems with static output feedback and state feedback arealso studied as special cases. The obtained results containsome extensions of the previous results to the structured uncertainlinear systems.     

Error estimates for the finite-element solution of an elliptic singularly perturbed problem

e-mail:ang{at}am.uni-erlangen.de The paper deals with an upwind discretization of finite-volume-typefor singularly perturbed elliptic boundary value problems. Stability,inverse monotonicity and convergence are considered. The mainobjective is to pursue the dependence of the error estimateon the perturbation parameter.     

A multiple-criteria decision model with ranked inputs

Address for correspondence: G. Gregory, Laburnum Cottage, 10 Main Street, Milnthorpe, Cumbria, LA7 7PN. A model for multiple-criteria decision analysis is proposedwhere the input data consist of rankings of criteria and ofalternatives within each criterion. The analysis uses the approachof data-envelopment analysis, summing over the scores obtainedby this method. Examples of further assessment of the best alternativesare presented.     

Post-processing with computable error bounds for the finite element approximation of a nonlinear heat conduction problem

Email: ain{at}mcs.le.ac.uk Email: D.Kelly{at}unsw.edu.au^* Email: I.Sloan{at}unsw.edu.au^** Email: swang{at}cs.curtin.edu.au It is shown how the finite element approximation of a nonlinearheat conduction problem may be post-processed to yield enhancedapproximations to the solution and the flux at any point inthe domain. Sharp computable bounds on the accuracy of the post-processedapproximations are derived. A criterion is identified for guidingadaptive refinements of the finite element discretization. Anumerical example is given illustrating the theoretical results.     

Therapy burden, drug resistance, and optimal treatment regimen for cancer chemotherapy

Email: boldrini{at}ime.unicamp.brAuthor to whom correspondence should be addressed. Email: michel{at}Incc.br Three nonlinear models of tumour cell growth under continuousdelivery of cycle nonspecific anticancer agents are studied.A dynamical optimization problem with the objective of minimizingthe final level of tumour cells is posed for these mathematicalsetups. The simplest setup does not possess toxicity constraints,whereas the other setups contain a dynamical equation describingthe therapy burden as a toxicity criterion. In addition, thethird setting contains the dynamics of drug resistant cells.A discussion conceming the optimal strategies of the respectivemodels is performed.     

The Convergence of Operator Approximations at Turning Points

Present address: Department of Mathematics, University of Reading, Reading RG6 2AX. We consider the convergence of solution curves of approximationsto parameter-dependent operator equations of the form G(, x)= 0. Provided G_x(, x) remains non-singular this problem is cateredfor by a simple extension to standard theory. In this paper,however, attention is concentrated on solution curves throughcertain singular points (⁰, x⁰), and the main result is thatconvergence depends on consistency and stability results forthe linear eigenvalue problem G_x(⁰, x⁰)0 = 0.     

Dual-based optimization of cyclic four-day workweek scheduling

Email: hesham{at}ccse.kfupm.edu.sa An optimization method is presented for the cyclic labour days-offscheduling problem, in which workers are given three consecutivedays off per week. This method does not include linear or integerprogramming, and it does not assume that the costs of differentdays-off work patterns are equal. The dual problem is firstsolved to determine the minimum workforce size. Then, the dualsolution is used to determine days-off assignments that minimizethe total labour cost. By requiring only simple manual calculations,the new method eliminates the need for linear or integer programmingsoftware.     

Estimation and decomposition of cost efficiency in the health care food service sector: an extended stochastic frontier approach

K. M. Matawie School of Computing and Mathematics, University of Western Sydney, Locked Bag 1797, Penrith South DC NSW 1797, Australia Email: a.assaf{at}uws.edu.au Corresponding author. Email: k.matawie{at}uws.edu.au Received on 11 February 2007. Accepted on 14 September 2007. This paper introduces and implements an extended stochasticfrontier model to estimate and decompose cost efficiency (CE)in the health care foodservice sector. The interesting featureof this model is that it allows differentiation between thethree different types of efficiency: technical efficiency (TE),allocative efficiency (AE) and their associated CE. A completeillustration of these efficiencies is presented using a cross-sectionalsample of 101 hospital foodservice operations. Results showedthat the model and all its parameter coefficients were plausible,significant and satisfy all theoretical requirements. It wasalso clear that the average efficiency scores were lower forTE (80%) than AE (88%), indicating that TE is the main sourceof CE and requires further attention.     

Delay-dependent conditions for guaranteed cost observer-based control of uncertain neutral systems with time-varying delays

Email: chlien{at}mail.nkmu.edu.tw Received on August 10, 2006; Accepted on September 6, 2006 In this paper, delay-dependent guaranteed cost observer-basedcontrol for neutral systems with time-varying delays is considered.Control and observer gains will be given from the linear matrixinequality feasible solutions. Optimal guaranteed cost observer-basedcontrol which will minimize the guaranteed cost of the systemis provided.     

Numerical stabilization of polynomial and matrix

Email: jdhan{at}sia.cn Email: zhjiang{at}sia.cn Corresponding author Email: nyy{at}sia.cn Received on March 6, 2006; Accepted on September 4, 2006 In this paper, the conception of numerical stabilization, whichis related to mantissa digits of computer and dimensions ofsystem, is described; and several strategies for the numericalstabilization of polynomial and matrix are presented.     

New conditions on absolute stability of uncertain Lur'e systems and the maximum admissible perturbed bound

Email: fhao{at}buaa.edu.cn Received on April 5, 2006; Accepted on September 10, 2006 The robust absolute stability problem for structured uncertainLur'e systems is considered in this paper by using Popov criterionand extended strictly positive real lemma. The conditions onrobust absolute stability for Lur'e systems with structureduncertainties are established in terms of multilinear matrixinequalities. An estimate of the maximum bound of all admissibleperturbations is given by a generalized eigenvalue problem.Finally, a numerical example is worked out to illustrate theefficiency of the main results.     

On the Stability Analysis of Nonlinear Systems

The stability of nonautonomous delay differential equationsis studied via a combination of the global linerization andnonlinear variation of parameter techniques. Permanent address: Department of Mathematics, University ofElectronics Science & Technology of China, Chengdu, China.     

Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. II: convection-diffusion-type problems

e-mail address: stynes{at}bureau.ucc.ie We consider singularly perturbed high-order elliptic two-pointboundary value problems of convection-diffusion type. Undersuitable hypotheses, the coercivity of the associated bilinearform is proved and a representation result for the solutionsof such problems is given. A family of Galerkin finite-elementmethods based on piecewise polynomial test/trial functions ona Shishkin mesh is constructed and proved to be convergent,uniformly in the perturbation parameter, in energy and Wnorms. Numerical results are presentedfor a second-order problem and fourth-order problems.     

Realistic a Priori and a Posteriori Error Bounds for Computed Eigenvalues

Permanent address: Department of Engineering Mathematics, Cairo University, Giza, Egypt. A priori and a posteriori error bounds are given for the computedeigenpair (, ) of the eigenvalue problem Ax = x, which are shownto be more realistic than some of the available ones. A simplemethod is also presented for computing the backward error. Finallya scaling procedure is explained for reducing the residual error.     

An LMI-based approach for robust stabilization of time delay systems containing saturating actuators

Email: elhaous_fati{at}yahoo.fr Corresponding author. Email: elh_tissir{at}yahoo.fr Received on September 8, 2005; Accepted on July 24, 2006 This paper deals with the problem of robust stabilization foruncertain systems with input saturation and time delay in thestate. The parameter uncertainties are time-varying and unknownbut are norm bounded. Sufficient conditions obtained via a linearmatrix inequality formulation are stated to guarantee the localstabilization. The method of synthesis consists in determiningsimultaneously a state feedback control law and an associateddomain of safe admissible states for which the stability ofthe closed-loop system is guaranteed when control saturationseffectively occur. Numerical examples are used to demonstratethe effectiveness of the proposed design technique.     

On Chebyshev Solution of Parabolic Partial Differential Equations

Now at Mathemarics Department, Assiut University Egypt A method is presented to transform parabolic equations to asystem of ordinary differential equations for the solution atthe Chebyshev points. The system may be solved analyticallyor by numerical methods and the Chebyshev coefficients are computed.We have the exact solution of a perturbed problem.     

Time optimal control of retarded parabolic systems

Email: skrakowi{at}usk.pk.edu.pl Received on June 15, 2005; Accepted on July 12, 2006 In this paper, the time-optimal control problem for parabolicsystems in which time lags appear in the integral form bothin the state equation and in the Neumann boundary conditionis presented. The particular properties of the optimal controlare discussed.     

Optimal boundary feedback stabilization of a string with moving boundary

Email: gugat{at}am.uni-erlangen.de Received on April 30, 2006; We consider a finite string that is fixed at one end and subjectto a feedback control at the other end which is allowed to move.We show that the behaviour is similar to the situation whereboth ends are fixed: As long as the movement is not too fast,the energy decays exponentially and for a certain parameterin the feedback law it vanishes in finite time. We considermovements of the boundary that are continuously differentiablewith a derivative whose absolute value is smaller than the wavespeed. We solve a problem of worst-case optimal feedback control,where the parameter in the feedback law is chosen such thatthe worst-case L^p-norm of the space derivative at the fixedend of the string is minimized (p [1, )). We consider the worstcase both with respect to the initial conditions and with respectto the boundary movement. It turns out that the parameter forwhich the energy vanishes in finite time is optimal in thissense for all p.     

Time integration of the non-linear Galerkin method

e-mail: bosco{at}mac.cie.uva.es, frutos@mac.cie.uva.es Numerical tests are presented that, for the Kuramoto-Sivashinskyand a reaction-diffusion equation, compare the non-linear Galerkinmethod with standard pseudospectral and pure spectral Galerkindiscretizations. The results show that, for these problems,the non-linear Galerkin method is not competitive with eitherpure spectral Galerkin or pseudospectral discretizations.     

Delay-dependent dissipativity of singular time-delay systems

Email: msmahmoud{at}kfupm.edu.sa Received on September 21, 2007; Revision received March 10, 2008. Accepted on April 30, 2008 In this paper, new results are established for the delay-dependentproblems of dissipative analysis and state-feedback synthesisof singular time-delay (STD) systems with polytopic uncertainties.The developed results for the nominal singular system encompassavailable results on approach, passivity and positive realnessfor STD systems as special cases. All the sufficient stabilityconditions are cast as linear matrix inequality-based feasibilitytests. Robust dissipativity results are also derived. Numericalexamples are provided.