a general class of sliding surface for sliding mode control in the conventional sliding mode control the relative degree of the chosen sliding surface is usually one this paper addresses a general class of sliding surface whose relative degree is no longer restricted to one we show that when the relative degree is more than two it is inevitable that there will exist a limit cycle for the nonlinear sign function and for the case of relative degree two the system possesses poor phase margin however these disadvantages can be remedied remarkably by smoothing out the control nonlinearity in a suitable boundary layer with a saturation function that ensures asymptotic stability of the overall system

design of variable structure controllers with continuous switching control a modified variable structure controller is proposed to deal with the conirol chattering problem which is one of the major difficulties for implementing the variable structure control vsc the new control strategy is effective for a class of uncertain nonlinear dynamical systems based on a suitably designed sliding sector a continuous switching controller whose control structure is switched whereas the control signal at switching remains continuous is constructed the complete attractiveness and the stability properties of the sliding sector in the sense of lyapunov stability ensure the retention of benefits achieved with the conventional vsc some typical examples are also investigated which show the improvement of system performance

transition from circle packing to covering on a sphere the odd case of 13 circles how must n equal circles spherical caps of given angular radius r be arranged on the surface of a sphere so that the area covered by the circles will be as large as possible in this paper a con

identification of mixture models using support variations abstract we consider the issue of identifying nonparametrically continuous mixture models in these models all observed variables depend on a common and unobserved component but are mutually independent conditional on it such a structure applies for instance to measurement error matching and auction models traditional approaches rely on parametric assumptions or strong functional restrictions we show that these models are actually identified nonparametrically if the supports of the observed variables move with the value of the unobserved component moreover this assumption is testable nonparametrically using tools from extreme value theory we develop an appropriate test and derive its asymptotic properties

brief paper output feedback variable structure control design with an h2 performance bound constraint in this paper we give an lmi based method for designing an output feedback variable structure control vsc system with an h 2 constraint the uncertain system model under consideration may have nonmatching disturbance input signals nonmatching disturbance input signal reduction is performed via h 2 norm minimization in terms of a constrained riccati inequality we give a sufficient condition for the existence of a linear sliding surface and a compensator guaranteeing an h 2 constraint and we show that the control parameters can be characterized by using the solution to the given inequality condition we also give a simple lmi based design algorithm of an output feedback vsc law guaranteeing an h 2 constraint finally by using a design example we show that our method can supplement the existing results

variable structure model reference adaptive control using only input and output measurements abstract a variable structure model reference adaptive controller vs mrac using only the input and output measurements of the plant is proposed stability and transient properties are analysed and discussed remarkable transient behaviour is revealed in particular model following can be perfectly achieved in a finite time the effect of plant input disturbance is investigated and the performance of the vs controller is also shown to be qualitatively superior to that obtained with conventional integral adaptation algorithms a link between the vs mrac and the conventional mrac is suggested simulations are presented to highlight the theoretical results

a semiparametric bootstrap technique for simulating extreme order statistics abstract we propose a technique for simulating the joint distribution of the j largest order statistics of a very large sample we assume that the parent population is in the domain of attraction of the type 1 gumbel extreme value distribution the bootstrap variates are generated by resampling the normalized spacings of the k largest observed values in the original data where k is larger than j we compare the bootstrap distribution to the fitted extremal distribution of weissman both distributions have the same means conditional on the k largest observed values in the data set if k is large and the normalized spacings behave as independent and identically distributed exponential random variables then the bootstrap variates behave as though sampled from the extremal distribution we propose several procedures for estimating k and give a numerical example

brief paper output feedback variable structure control for linear systems with uncertainties and disturbances this paper proposes a dynamic output feedback variable structure controller for linear mimo systems with mismatched and matched norm bounded uncertainties and matched nonlinear disturbances the proposed controller consists of nonlinear and linear parts similar to the unit vector type of controller the nonlinear part of the new controller takes care only of matched uncertainties and disturbances and on the other hand the linear part with full dynamics completely handles mismatched uncertainties designing such a linear part leads to use a lyapunov function associated with the full states which achieves the global stability against the mismatched uncertainties the resulting criteria are furthermore converted into solvable ones by using the so called cone complementary linearization algorithm for bi convex problems

matrix analysis of statically and kinematically indeterminate frameworks abstract the paper is concerned with the structural mechanics of assemblies of bars and pinjoints particularly where they are simultaneously statically and kinematically indeterminate the physical significance of the four linear algebraic vector subspaces of the equilibrium matrix is examined and an algorithm is set up which determines the rank of the matrix and the bases for the four subspaces in particular this algorithm gives full details of any states of self stress and modes of inextensional deformation which an assembly may possess a scheme is devised for the segregation of inextensional modes into rigid body modes up to six of these may be allowed by the foundation constraints and internal mechanisms in some circumstances a state of self stress may impart first order stiffness to an inextensional mode a matrix method for detecting this effect is devised and it is shown that if there is no state of self stress which imparts first order stiffness to a given mode then that mode can undergo rather large distortion which involves either zero change in length of the bars or possibly changes in length of third or higher order in the displacements the significance of negative stiffness as indicated by the matrix method is discussed the paper contains simple examples which illustrate all of the main points of the work

output feedback control based on a high order sliding manifold approach in this note we address the problem of output feedback control of multiple input multiple output plants the proposed approach is based on a high order sliding manifold strategy the resulting controller exhibits strong robustness properties similar to high gain control laws but avoids peaking phenomena thanks to the adoption of a time varying sliding surface moreover the dynamic control law is continuous and differentiable thus avoiding chattering problems

estimating the extremal index summary the extremal index is an important parameter measuring the degree of clustering of process the extremal index a parameter in the interval 0 1 is the reciprocal of the mean cluster size apart from being of interest in its own right it is a crucial parameter for determining the limiting distribution of extreme values from the process in this paper we review current work on statistical estimation of the extremal index and consider an optimality criterion based on a bias variance trade off theoretical results are developed for a simple doubly stochastic process and it is argued that the main formula obtained is valid for a much wider class of processes the practical implications are examined through simulations and a real data example

analysis and design of variable structure systems using a geometric approach multivariable variable structure systems in the sliding mode are studies using a geometric approach the properties of system order reduction and disturbance rejection are proved using projector theory new design methods for the choice of switching hyperplanes are derived for the closed loop eigenvalue eigenvector assignment problem

a symmetry extension of maxwell s rule for rigidity of frames a symmetry extension of maxwell s rule for rigidity of frames is found this rule subsumes and strengthens maxwell s 1864 rule by requiring that the internal and external degrees of freedom of a pin jointed structure are not only numerically equal but are also equisymmetric a number of special cases of maxwell s original rule are studied to show the improved insight that the symmetry adapted version can give

packing of regular tetrahedral quartets of circles on a sphere how must 4n nonoverlapping equal circles forming n quartets be packed on a sphere so that the angular diameter of the circles will be as large as possible under the constraint that within each qua

estimation of extreme quantiles for functions of dependent random variables we propose a new method for estimating the extreme quantiles for a function of several dependent random variables in contrast with the conventional approach based on extreme value theory we do not impose the condition that the tail of the underlying distribution admits an approximate parametric form and furthermore our estimation makes use of the full observed data the method proposed is semiparametric as no parametric forms are assumed on the marginal distributions but we select appropriate bivariate copulas to model the joint dependence structure by taking advantage of the recent development in constructing large dimensional vine copulas consequently a sample quantile resulting from a large bootstrap sample drawn from the fitted joint distribution is taken as the estimator for the extreme quantile this estimator is proved to be consistent under the regularity conditions on the closeness between a quantile set and its truncated set and the empirical approximation for the truncated set the simulation results lend further support to the reliable and robust performance of the method proposed the method is further illustrated by a real world example in backtesting financial risk models

reconstructing sliding surfaces for siso variable structure output feedback control systems using inverse method there exists a dynamic mapping relationship between the sliding variable and the output variable in a linear time invariant lti single input single output siso system this relationship is invariant of the matched disturbances which lies in the control space in this note a continuous time dynamic inverse compensator is proposed to reconstruct the sliding variable from the system output this inverse compensator is stable and causal provided that the original siso system is minimum phase and that the input output relative degree is less than or equal to one in case the system relative degree is greater than one a digital approximation for the inverse compensator is introduced to track the sliding variable in discrete time to the accuracy of o t where t is the sampling period thus the discrete time variable structure control vsc law can be implemented without full state accessibility

unmodeled dynamics in adaptive control systems revisited an alternative approach to analyze the robustness of adaptive systems with respect to unmodeled dynamics and external disturbances is presented this approach shows that certain restrictive assumptions needed earlier can in fact be discarded it also shows that an adaptation algorithm based on a time varying factor equivalent to a constant factor together with projection can provide a globally asymptotically stable system with respect to a compact residual set under mild requirements

on the estimation of the extreme value index and large quantile estimation l article se constitue de deux parties on donne une preuve simple de la convergence faible de l estimation de pickand pour le parametre principal d une loi de valeurs extremes on donne d autres conditions naturelles pour la convergence forte et pour la normalite asymptotique de l estimation ensuite une grande quantile d une loi est estimee par une combinaison de statistiques d ordre intermediaires ou extremes ceci mene a un intervalle de confiance asymptotique

variable structure model reference adaptive control systems model reference adaptive controllers when only input and output measurements are available are designed using the theory of variable structure systems state variable filters are used in order to obtain differentiator free controllers the proposed design allows the error transient to be prescribed in advance the drawbacks deriving from the typical high frequency chattering of the control signal during the sliding motion can be partially eliminated by means of a little modification of the adaptation law that does not cause the error signal to deteriorate considerably

packing regular triplets of circles on a sphere this article examines how 3 n non overlapping equal circles forming n triplets must be packed on a sphere to ensure that the angular diameter of the circles will be as large as possible furthermore this problem is solved under the constraint that within each triplet the circle centres lie at the vertices of an equilateral triangle inscribed into a great circle of the sphere computer generated solutions to this optimization problem are presented for n 2 7 triplets the configurations obtained are characterized as compounds nolids of equilateral triangles

numerical methods to design the reaching phase of output feedback variable structure control abstract two numerical methods are developed to design a variable structure control that satisfies the reaching condition using static output feedback the design is formulated as a nonsmooth convex optimization problem for which existing algorithms are available it is shown how the resulting control law can be modified to be robust in the presence of parameter uncertainty or a disturbance numerical examples successfully demonstrate the developed techniques

the vss approach to the model reference control of nonminimum phase linear plants a nontrivial application of the discontinuous control system theory based on filippov s solution concept is presented the problem addressed is the model reference output feedback control of linear plants with non hurwitzian numerator in the transfer function a solution in the case of known systems is presented first an error state equation whose state is accessible is then derived for the case in which the plant parameters are unknown in the case in which some bounds on the plant characteristics are supposed known a pair of discontinuous signals acting on both the plant and the model is chosen causing the error state to vanish asymptotically

brief variable structure output feedback control design for a class of uncertain dynamic systems in this paper we consider the problem of designing a variable structure output feedback control vsofc law for a class of uncertain systems with mismatched uncertainty in the state matrix we derive existence conditions of linear sliding surfaces in terms of constrained linear matrix inequalities lmis and we give vsofc strategies we also give a simple design procedure and parameterizations of the linear switching surfaces together with solvability conditions for the given constrained lmis finally we give a design example in order to show the effectiveness of our method

using extreme value theory to estimate large percentiles weissman 1978 suggested percentile estimators based on the joint limiting distribution of the k largest order statistics the present work identifies situations where weissman s estimators are a significant improvement over the usual sample percentile estimators and gives practical advice on how to use these new estimators effectively in particular large reductions in mean squared error can be made when the tails of the distributions are approximately exponential and p 95

a symmetry treatment of danzerian rigidity for circle packing a symmetry extended mobility criterion that incorporates danzer s concept of bar and joint assemblies is derived and applied to the spherical circle packing problem the known scalar counting rule

on testing the extreme value index via the pot method n alternatives based on the point processes n of the exceedances among y n i over a sequence of thresholds t it turns out that the random number of n exceedances t n over t is the central sequence for the log likelihood n ratio d l n rd l n yielding its local asymptotic normality lan b n b n n 0 this result implies in particular that t n carries asymptotically all the information about the underlying parameter b which is contained in n n we establish sharp bounds for the rate at which t n becomes asymptoti cally sufficient which show however that this is quite a poor rate these results remain true if we add an unknown scale parameter 1 n a model assumption on the upper tail of the underlying d f such as m is for example indispensable if one is interested in extreme quantities of the underlying d f that is such quantities of f which are usually outside the range of the given data y y a typical example is inference about 1 n y1 4 extreme quantiles f p inf t g r f t g p with p being close to 1 this problem is typically tackled by hydrologists for the prediction of large w

adaptive control with discontinuous σ factor and saturation for improved robustness an adaptive control law is proposed to improve the robustness of the adaptive system with respect to fast unmodelled dynamics represented by a singular perturbation the new law is based on saturation of the regressor and control parameter vector with inclusion of a discontinuous factor the analysis of the resulting system is presented and the conclusions are illustrated by simulations the introduction of a discontinuous factor represents an extension of an earlier work the advantages of this extension include global stability with less restrictive assumptions and better transient behaviour

on some estimates based on sample behavior near high level excursions let j be a stationary sequence of weakly dependent random variables and letm n k be thek th largest value of j 1 j n the estimation of the parameters of the asymptotic distribution ofm n k is considered using a procedure motivated by a limit theorem pertaining to the point process sum nolimits j delta j n n bar f xi j a number of statistical issues concerning the procedure including how to select the tuning parameters are addressed the second problem that we consider is the estimation of the filter of a moving average process with heavy tails in particular the investigation covers the moving average stable process motivated by ideas in rootzen 1978 our estimator uses information contained in the sample behavior of the process near the largest excursion

stable robust tracking by sliding mode control sliding mode control is examined from the perspective of obtaining stable and robust tracking of an arbitrary time varying reference by a multi input output linear time invariant system driven by a certain class of bounded errors nonlinearities and disturbances most existing schemes for such systems are subsumed by the one presented here the results are developed via the use of inverse models and make clear the constraints imposed by the finite and infinite zero structure of the system in particular stable and robust tracking is shown to be obtained by the scheme in this paper if and only if the system is minimum phase

analysis and design of i o based variable structure adaptive control this paper presents an overview of a technique for the design of variable structure model reference adaptive control vs mrac systems using only input output data the main ideas underlying the design and the analysis as well as the main properties of the controller are described having as point of departure a well known parameter adaptive mrac scheme then asymptotic properties of the vs mrac system are established taking into account the effect of the averaging filters necessary to implement some equivalent control signals in particular global exponential stability of the associated error system with respect to a small residual set is demonstrated the effect of linear zones in the relay functions is assessed showing that they can alleviate the chattering phenomena this is related with the fact that the vs mrac has a high gain stability property a procedure for noise sensitivity reduction is also proposed simulations illustrate the very satisfactory performance of the vs mrac in adverse operating conditions

discrete time output feedback sliding mode control design for uncertain systems using linear matrix inequalities an output feedback based sliding mode control design methodology for discrete time systems is considered in this article in previous work it has been shown that by identifying a minimal set of current and past outputs an augmented system can be obtained which permits the design of a sliding surface based upon output information only if the invariant zeros of this augmented system are stable in this work a procedure for realising discrete time controllers via a particular set of extended outputs is presented for non square systems with uncertainties this method is applicable when unstable invariant zeros are present in the original system the conditions for existence of a sliding manifold guaranteeing a stable sliding motion are given a procedure to obtain a lyapunov matrix which simultaneously satisfies both a riccati inequality and a structural constraint is used to formulate the corresponding control to solve the reachability problem a numerical method using linear matrix inequalities is suggested to obtain the lyapunov matrix finally the design approach given in this article is applied to an aircraft problem and the use of the method as a reconfigurable control strategy in the presence of sensor failure is demonstrated

output feedback stabilization of uncertain fuzzy systems using variable structure system approach based on the variable structure system theory an output feedback fuzzy control design method is developed for a class of uncertain nonlinear systems that can be represented by a t s takagi sugeno fuzzy model the uncertain fuzzy systems under consideration may have mismatched uncertainties in the state matrix as the local controller a compensator based sliding mode output feedback controller with a nonlinear discontinuous term is used in terms of linear matrix inequalities lmis a sufficient condition is derived for the existence of the fuzzy controller guaranteeing a stable sliding motion it is shown that the compensator gain and the switching surface parameter matrix can be characterized in terms of the solution of the lmi existence condition finally an lmi based design algorithm and numerical design examples are given

extremal quantile treatment effects this paper establishes an asymptotic theory and inference method for quantile treatment effect estimators when the quantile index is close to or equal to zero such quantile treatment effects are of interest in many applications such as the effect of maternal smoking on an infant s adverse birth outcomes when the quantile index is close to zero the sparsity of data jeopardizes conventional asymptotic theory and bootstrap inference when the quantile index is zero there are no existing inference methods directly applicable in the treatment effect context this paper addresses both of these issues by proposing new inference methods that are shown to be asymptotically valid as well as having adequate finite sample properties

mobility of a class of perforated polyhedra a class of over braced but typically flexible body hinge frameworks is described they are based on polyhedra with rigid faces where an independent subset of faces has been replaced by a set of holes the contact polyhedron c describing the bodies vertices of c and their connecting joints edges of c is derived by subdivision of the edges of an underlying cubic polyhedron symmetry calculations detect flexibility not revealed by counting alone a generic symmetry extended version of the grubler kutzbach mobility counting rule accounts for the net mobilities of infinite families of this type based on subdivisions of prisms wedges barrels and some general inflations of a parent polyhedron the prisms with all faces even and all barrels are found to generate flexible perforated polyhedra under the subdivision construction the investigation was inspired by a question raised by walter whiteley about a perforated polyhedron with a unique mechanism reducing octahedral to tetrahedral symmetry it turns out that the perforated polyhedron with highest oh point group symmetry based on subdivision of the cube is mechanically equivalent to the hoberman switch pitch toy both objects exhibit an exactly similar mechanism that preserves td subgroup symmetry over a finite range this mechanism survives in two variants suggested by bob connelly and barbara heys that have the same contact graph but lower initial maximum symmetry

output feedback sliding mode control for sampled data systems we address the output feedback sliding mode control problem for a sampled data linear system with external disturbances of the matching type by taking into account the disturbance compensation a deadbeat high gain output feedback control strategy with additional dynamics is able to attenuate the disturbances in the framework of singular perturbation analysis it is shown that the closed loop system exhibits good robustness against exogenous disturbances

transition from spherical circle packing to covering geometrical analogues of chemical isomerization how must n equal circles spherical caps of given angular radius r be arranged on the surface of a sphere so that the area covered by the circles will be as large as possible in this paper conjectured solutions of this problem for n 5 7 8 9 10 11 are given when r varies from the maximum packing radius to the minimum covering radius the relation of the results of this problem to the extremal configurations of n mutually repulsive equal point charges on the surface of a sphere is discussed variation of the solution polyhedra with r gives an abstract model of chemical isomerization processes for example for n 5 where the packing covering transition models the berry pseudo rotation of a trigonal bipyramid

on variable structure output feedback controllers for uncertain dynamic systems a class of variable structure output feedback controllers for uncertain dynamic systems with bounded uncertainties is proposed no statistical information about the uncertain elements is assumed a variable structure systems approach and a geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed controllers

estimation of high conditional quantiles for heavy tailed distributions estimation of conditional quantiles at very high or low tails is of interest in numerous applications quantile regression provides a convenient and natural way of quantifying the impact of covariates at different quantiles of a response distribution however high tails are often associated with data sparsity so quantile regression estimation can suffer from high variability at tails especially for heavy tailed distributions in this article we develop new estimation methods for high conditional quantiles by first estimating the intermediate conditional quantiles in a conventional quantile regression framework and then extrapolating these estimates to the high tails based on reasonable assumptions on tail behaviors we establish the asymptotic properties of the proposed estimators and demonstrate through simulation studies that the proposed methods enjoy higher accuracy than the conventional quantile regression estimates in a real application involving statistical downscaling of daily precipitation in

output feedback stabilization of uncertain plants a variable structure systems approach the problem of output stabilization for uncertain s1so systems is considered using structural transformations uncertain systems can change to the form convenient for output feedback design synthesis of observer based variable structure control for asymptotical stabilization or uniform ultimate boundedness of the closed loop system is provided examples are considered and simulation results are given

the closest packing of equal circles on a sphere the closest packing of x circles on the surface of a sphere is examined with the use of techniques that have been developed to determine the stereochemical arrangement of atoms packed around a central atom the technique is based on the concept that the centres of the circles repel one another and minimizing the total repulsion energy leads to an approximate structure from which exact solutions can be determined a number of improved packings have been discovered for values of x in the range 20 40 many different types of structure are found that are of lower symmetries than those previously described the packing density p defined as the fraction of the spherical surface that is enclosed by the circles is found to increase as the number of circles increases in contrast to the conclusion from previous studies however this increase in p is very slight and the values remain substantially below that for an infinite number of circles or a close packed plane

comments and further results regarding on variable structure output feedback controllers this paper points out some misleading statements of the above mentioned paper kwan 1996 and shows that the proposed controller can be easily derived under less restrictive conditions from a previously proposed output feedback variable structure control scheme

packing of twinned circles on a sphere the twinned circle problem is to pack 2 n non overlapping equal circles forming n pairs of twins rigidly connected neighbours on a sphere so that the angular radius of the circles will be as large as possible in the case that the contact graph s of the unconstrained circle packing support s at least one perfect matching a complete solution to the twinned circles problem is found with the same angular radius as the unconstrained problem solutions for n 2 12 pairs of twins are counted and classified by symmetry for n 2 6 and 12 these are mathematically proven to be the best solutions for n 7 11 they are based on the best known conjectured solutions of the unconstrained problem where the contact graph of the unconstrained problem has one or more rattling circles the twinned problem is most easily solved by finding perfect matchings of an augmented graph in which each rattling circle is supposed to be simultaneously in contact with all its contactable neighbours the underlying contact graphs for the unconstrained packings for n 2 12 are all hamiltonian guaranteeing the existence of perfect matchings but hamiltonicity is not a necessary condition the first solution to the twins problem based on an example of a non hamiltonian contact graph occurs at n 16

on variable structure output feedback controllers in a recent work by zak hui 1993 a sliding mode controller for mimo systems using static output feedback was proposed very nice geometric conditions for how to design sliding surfaces were given however there are two restrictive assumptions in it one is that the uncertainties in the system must be bounded by a known function of outputs which excludes some possible uncertainties in the a matrix if the system is described by the triple a b c the other one requires a matrix equality to be held which may also be very difficult to satisfy in many systems in this paper we propose a modification of the sliding mode controller for a class of single input single output siso systems which can eliminate the above mentioned limitations and under certain conditions guarantee global closed loop stability hence the range of applicability of zak hui s method can be greatly broadened

extremal quantile regression quantile regression is an important tool for estimation of conditional quantiles of a response y given a vector of covariates x it can be used to measure the effect of covariates not only in the center of a distribution but also in the upper and lower tails this paper develops a theory of quantile regression in the tails specifically it obtains the large sample properties of extremal extreme order and intermediate order quantile regression estimators for the linear quantile regression model with the tails restricted to the domain of minimum attraction and closed under tail equivalence across regressor values this modeling setup combines restrictions of extreme value theory with leading homoscedastic and heteroscedastic linear specifications of regression analysis in large samples extreme order regression quantiles converge weakly to arg min functionals of stochastic integrals of poisson processes that depend on regressors while intermediate regression quantiles and their functionals converge to normal vectors with variance matrices dependent on the tail parameters and the regressor design

from circle packing to covering on a sphere with antipodal constraints the problem treated here is how must n antipodal pairs of equal circles spherical caps of given angular radius r be arranged on the surface of a sphere so that the area covered by the circles will be as large as possible conjectured solutions of this problem for n 4 5 7 are given where r varies from the maximum antipodal packing radius to the minimum antipodal covering radius these cases exhibit sequences of symmetry and edge number transitions in the contact polyhedra which in general differ from those of the unconstrained problem where centrosymmetry is not enforced new minimum antipodal covering arrangements are conjectured for 4 5 and 7 pairs they are a hexagonal bipyramid a d 2h deltahedron and the cube octahedron compound respectively

a transformed lure problem for sliding mode control and chattering reduction the sliding mode control problem is investigated with the frequency domain approach the authors show that the sliding mode control can be transformed into a lure problem with this formulation it is shown that the conventional sliding mode control with a nonlinear sign function can only guarantee to make the overall system stable but not asymptotically stable the authors also consider a practical situation where the sign nonlinearity may contain a hysteresis loop for this situation they show that even if the hysteresis loop is very small there still exists a limit cycle however chattering phenomenon caused by the limit cycle behavior can be eliminated by a certain class of nonlinearities

new approach to robust model reference adaptive control for a class of plants motivated by recent advances in designing robust adaptive controllers and in dealing with uncertain dynamical systems a new model reference adaptive control which is robust to a class of unmodelled dynamics and bounded output disturbances in the case of relative degree one is presented the implementation of the controllers includes a switching mechanism which plays a crucially important role in functions of stabilizing as well as tracking it is shown that global stability of the overall system is achieved under no assumption of persistency of excitation and tracking errors will converge to a residual set whose size can be directly related to the size of unmodelled dynamics and of output disturbances explicitly in the ideal case the residual set degenerates to a single null point and convergence can be achieved in finite time without any requirement of persistency of excitation

lmi based nonlinear fuzzy observer controller design for uncertain mimo nonlinear systems based on the variable structure system theory we develop a nonlinear fuzzy observer controller design method for a class of uncertain nonlinear systems that can be represented by a takagi sugeno fuzzy model we use a sliding mode observer and a sliding mode controller as the local state observer and the local controller in terms of linear matrix inequalities lmis we derive sufficient conditions for the existence of the fuzzy observer and the fuzzy controller we also derive lmi conditions for the existence of the fuzzy observer and the fuzzy controller guaranteeing the alpha stability or generalized h2 hinfin performance constraints we show that the observer and the controller can be independently designed i e the separation property holds finally we give simple lmi based design algorithms together with an example

arrangement of 23 points on a sphere on a conjecture of r m robinson the problem of determining the largest angular diameter d n of n equal circles which can be packed on the surface of a sphere without overlapping is investigated it is known that the best packing of 5 11 circles on a sphere is obtained if one circle is removed from the best packing of 6 12 circles robinson has suggested that perhaps there are some other cases also where this property holds possibly n 24 48 60 120 are the circle numbers for which d n 1 d n in this paper it is proved that this property does not hold for n 24 thus d 23 d 24 and it is conjectured that d n 1 d n for n 48 60 120 a new packing construction is presented for 23 circles on a sphere with circle diameter 43 709964 and for 29 circles with circle diameter 38 677079

further results on variable output feedback controllers zak and hui 1993 proposed a sliding mode controller for linear multiple input multiple output mimo systems using static output feedback the author s previous paper 1996 provides an improvement of the output feedback controller of zak hui for a class of linear single input single output siso systems that eliminated two important limitations 1 system uncertainties must be bounded by the system output and 2 a requirement of a matrix inequality the controller developed previously can guarantee global closed loop stability this paper extends the previous results to linear mimo systems it is emphasized that the proposed mimo controller yields global closed loop stability whereas the one in zak hui can only guarantee local stability an application of the proposed mimo controller to an aircraft model is included to show the effectiveness of the method

fixed k asymptotic inference about tail properties we consider inference about tail properties of a distribution from an iid sample based on extreme value theory all of the numerous previous suggestions rely on asymptotics where eventually an in

an ilmi approach to robust static output feedback sliding mode control this paper proposes a systematic methodology for designing robust static output feedback sliding mode control sofsmc for a class of systems with mismatched uncertainties this methodology consists of two parts one is a new sufficient and necessary condition for the existence problem in terms of two matrix inequalities the other is a direct solving method using the iterative linear matrix inequality ilmi technique the main advantages of this method are that only original system parameters are involved without any extra coordinate changes and that appealing to solving the static output feedback stabilization sofs problem is no longer required in addition the ilmi algorithm includes an optimal part to avoid high control efforts a numerical example also demonstrates the efficacy of the proposed approach

estimating heavy tail exponents through max self similarity in this paper a novel approach to the problem of estimating the heavy tail exponent 0 of a distribution is proposed it is based on the fact that block maxima of size m scale at a rate m1 for independent as well as for a number of dependent data this scaling rate can be captured well by the max spectrum plot of the data that leads to regression based estimators for consistency and asymptotic normality of these estimators is established for independent data under mild conditions on the behavior of the tail of the distribution the proposed estimators have an important computational advantage over existing methods namely they can be calculated and updated sequentially in an on line fashion without having to store the entire data set practical issues on the automatic selection of tuning parameters for the estimators and corresponding confidence intervals are also addressed extensive numerical simulations show that the proposed method is competitive for both small and large sample sizes robust to contaminants and continues to work under the presence of substantial amount of dependence the proposed estimators are used to illustrate the close connection between long range dependence and heavy tails over an internet traffic trace