robust control with rejection of harmonic disturbances this paper considers a finite time output feedback control problem for a class of uncertain systems subject to harmonic disturbances of known frequencies the controller is required to minimize a quadratic cost functional subject to the given uncertainties and harmonic disturbances the main result gives a necessary and sufficient condition for the existence of a suitable controller the condition is given terms of a pair of riccati differential equations which arise in a corresponding h sup spl infin control problem

the analysis of dynamic instability on the large amplitude vibrations of a beam with transverse magnetic fields and thermal loads abstract the dynamic instability of a pinned beam subjected to an alternating magnetic field and thermal load with the nonlinear strain and made of physically nonlinear thermoelastic material has been studied applying the hamilton s principle the equation of motion with damping factor induced current and thermal load is derived using the galerkin s method the governing equation is reduced to a time dependent mathieu equation the incremental harmonic balance ihb method is applied to analyse the dynamic instability the effects of non dimensional parameters frequency ratio load factor amplitude a damping factor k1 and temperature increment t on the dynamic instability are obtained and discussed results show that the characteristics of magnetoelastic instability for the beam having the large deformation are distinctive from those of the beam having small deformation

convolutions and multiplier transformations of convex bodies rotation intertwining maps from the set of convex bodies in into itself that are continuous linear operators with respect to minkowski and blaschke addition are investigated the main focus is on blaschke minkowski homomorphisms we show that such maps are represented by a spherical convolution operator an application of this representation is a complete classification of all even blaschke minkowski homomorphisms which shows that these maps behave in many respects similar to the well known projection body operator among further applications is the following result if an even blaschke minkowski homomorphism maps a convex body to a polytope then it is a constant multiple of the projection body operator

frequency response of sampled data systems this paper introduces the concept of frequency response for sampled data systems and explores some basic properties as well as its computational procedures it is shown that 1 by making use of the lifting technique the notion of frequency response can be naturally introduced to sampled data systems in spite of their time varying characteristics 2 it represents a frequency domain steady state behaviour and 3 it is also closely related to the original transfer function representation via an integral formula it is shown that the computation of the frequency response can be reduced to a finite dimensional eigenvalue problem and some examples are presented to illustrate the results

what is known about unit cubes unit cubes from any point of view are among the simplest and the most important objects in n dimensional euclidean space in fact as one will see from this survey they are not simple at all on the one hand the known results about them have been achieved by employing complicated machineries from number theory group theory probability theory matrix theory hyperbolic geometry combinatorics etc on the other hand the answers for many basic problems about them are still missing in addition the geometry of unit cubes does serve as a meeting point for several applied subjects such as design theory coding theory etc the purpose of this article is to figure out what is known about the unit cubes and what do we want to know about them

inequalities for mixed projection bodies mixed projection bodies are related to ordinary projection bodies zonoids in the same way that mixed volumes are related to ordinary volume analogs of the classical inequalities from the brunn minkowski theory such as the minkowski brunn minkowski and aleksandrov fenchel inequalities are developed for projection and mixed projection bodies

frequency response of sampled data systems this paper develops a frequency domain theory that provides a method to analyze and design sampled data control systems including their intersample behaviors the key idea is to consider the signal space x x t x t n x xn exp j t jn st n x xn 2 where s is the sampling angular frequency it is shown that a stable sampled data system equipped with a strictly proper pre filter before the sampler maps x into x l2 in the steady state that mapping is denoted by q j and is referred to as an fr operator it is proved that the norm of the sampled data system as an operator from l2 to l2 is given by max q j 2 2 where 12 s 12 s a set of equations relating outputs of a closed loop system to its inputs in the frequency domain is derived and their solution is given in an explicit form based on that solution the sensitivity fr operator y j and the complementary sensitivity fr operator t j are defined for feedback control systems and it is shown that y j gives the improvement of the sensitivity of the transfer characteristics from the reference to the controlled output and also represents the ability of rejecting disturbances and that t j represents the degree of robust stability and at the same time gives the effect of detection noises it is also shown that y j t j i and thus a frequency domain paradigm for the design of sampled data control systems which is exactly parallel to the continuous time case is established

inherent design limitations for linear sampled data feedback systems there is a well developed theory describing inherent design limitations for linear time invariant feedback systems consisting of an analogue plant and analogue controller this theory describes limitations on achievable performance present when the plant has non minimum phase zeros unstable poles and or time delays the parallel theory for linear time invariant discrete time systems is less interesting because it describes system behaviour only at sampling instants this paper develops a theory of design limitations for sampled data feedback systems wherein the response of the analogue system output is considered this is done using the fact that the steady state response of a hybrid feedback system to a sinusoidal input consists of a fundamental component at the frequency of the input together with infinitely many harmonics at frequencies spaced integer multiples of the sampling frequency away from the fundamental this fact allows fundamental sensitivity and complementary sensitivity functions that re

brief damping of harmonic disturbances in sampled data systems parameterization of all optimal controllers optimal damping of harmonic disturbances of known frequencies is studied for sampled data systems a sampled data output feedback controller is designed to minimize the intersample variations of the controlled variable the set of all stabilizing optimal controllers is obtained in terms of the youla parameterization and a set of interpolation conditions at the disturbance frequencies which ensure that the stationary cost is minimized

projection bodies and valuations let be the projection operator which maps every polytope to its projection body it is well known that maps the set of polytopes pn in rn into pn that it is a valuation and that for every p pn p is affinely associated to p it is shown that these properties characterize the projection operator this proves a conjecture by lutwak

h sub infinity control and filtering for sampled data systems h sub infinity control and filtering problems for sampled data systems are studied necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified h sub infinity performance bound when these conditions hold explicit formulas for a controller and a filter satisfying the h sub infinity performance bound are also given

harmonic generation in adaptive feedforward cancellation schemes the paper investigates the generation of harmonics in adaptive feedforward cancellation schemes specifically it is shown that an algorithm designed to reject a certain number of frequency components may in fact be capable of reducing higher order harmonics as well this effect originates in the time variation of the adaptive parameters a consequence is that the adaptive system may perform better than the algorithm with the fixed ideal parameters surprisingly the response to higher order harmonics can be calculated precisely using a laplace transform analysis the origin of the numerical procedure is in the equivalence between the adaptive feedforward cancellation scheme and a control scheme based on the internal model principle the implication of the results on design and implementation issues is discussed

performance limitations for discrete time systems in the presence of multi sinusoidal disturbance performance limitations for single input single output siso linear discrete time systems perturbed by multi sinusoidal disturbance with additive gaussian white noise are considered a steady stat

projection problems for symmetric polytopes abstract let k r n be a convex body a compact convex subset with non empty interior k its projection body finding the least upper bound as k ranges over the class of origin symmetric convex bodies of the affine invariant ratio v k v k n 1 being called schneider s projection problem is a well known open problem in the convex geometry to study this problem lutwak yang and zhang recently introduced a new affine invariant functional for convex polytopes in r n for origin symmetric convex polytopes they posed a conjecture for the new functional u p in this paper we give an affirmative answer to the conjecture in r n thereby obtain a modified version of schneider s projection problem

optimal damping of forced oscillations in discrete time systems in this paper we consider a linear discrete time control system affected by an additive sinusoidal disturbance with known frequencies but unknown amplitudes and phases the problem is to damp this forced oscillation in an optimal fashion we show that the natural solution from the point of view of optimal control is neither robust with respect to errors in the frequencies and thus not optimal in practice nor independent of the unknown amplitudes and phases the main result of this paper concerns the existence and design of a realizable robust optimal regulator which is universal in the sense that it does not depend on the unknown amplitudes and phases and is optimal for all choices of such parameters the regulator allows for a considerable degree of design freedom to satisfy other design specifications finally it is shown that this regulator is optimal also for a wide class of stochastic control problems

a new affine invariant for polytopes and schneider s projection problem new affine invariant functionals for convex polytopes are introduced some sharp affine isoperimetric inequalities are established for the new functionals these new inequalities lead to fairly strong volume estimates for projection bodies two of the new affine isoperimetric inequalities are extensions of ball s reverse isoperimetric inequalities if k is a convex body i e a compact convex subset with nonempty interior in euclidean n space rn then on the unit sphere sn l its support function h k sn 1 r is defined for u e sn l by h k u max u y y e k where u y denotes the standard inner product of u and y the projection body hk of k can be defined as the convex body whose support function for u e sn 1 is given by h ihk u vol n1 klu1 where voln l denotes n 1 dimensional volume and klul denotes the image of the orthogonal projection of k onto the codimension 1 subspace orthogonal to u an important unsolved problem regarding projection bodies is schneider s projection problem what is the least upper bound as k ranges over the class of origin symmetric convex bodies in r of the affine invariant ratio v hnk v k n1 1 n1 where v is used to abbreviate vol see s1 s2 sw and le schneider s1 conjectured that this ratio is maximized by parallelotopes in s1 schneider also presented applications of such results in stochastic geometry however a counterexample was produced in br to show that this is not the case we will present a modified version of schneider s conjecture that has an affirmative answer in addition we will obtain an inequality that gives an upper bound for the affine ratio while our upper bound is not sharp for any n nevertheless it is asymptotically optimal to be more specific in this paper we introduce a new centro affine functional u defined on the class of polytopes which is closely related to the volume functional v while in general u k v k if k is a random polytope with many faces then u k is very close to v k we shall prove the following variation of schneider s projection conjecture received by the editors february 26 2000 1991 mathematics subject classification primary 52a40

general l_p affine isoperimetric inequalities sharp l p affine isoperimetric inequalities are established for the entire class of l p projection bodies and the entire class of l p centroid bodies these new inequalities strengthen the l p petty projection and the l p busemann petty centroid inequality

the surface measure and cone measure on the sphere of ell_p n we prove a concentration inequality for the l n p norm on the l n p sphere for p q 0 this inequality which generalizes results of schechtman and zinn 2000 is used to study the distance between the cone measure and surface measure on the sphere of l n p in particular we obtain a significant strengthening of the inequality derived by naor and romik 2003 and calculate the precise dependence of the constants that appeared there on p

extremum problems for the cone volume functional of convex polytopes abstract lutwak yang and zhang defined the cone volume functional u over convex polytopes in r n containing the origin in their interiors and conjectured that the greatest lower bound on the ratio of this centro affine invariant u to volume v is attained by parallelotopes in this paper we give affirmative answers to the conjecture in r 2 and r 3 some new sharp inequalities characterizing parallelotopes in r n are established moreover a simplified proof for the conjecture restricted to the class of origin symmetric convex polytopes in r n is provided