ripple free deadbeat control of siso discrete systems the ripple free deadbeat control problem for arbitrary not necessarily stable siso linear discrete plants and reference signals is treated it is established that a causal stabilizing ripple free deadbeat controller exists if and only if the zeros of the plant and the poles of the reference signal are disjoint and a complete characterization of all such controllers is obtained solutions to two illustrative problems are presented

a new search for skewsymmetric binary sequences with optimal merit factors previous results on skewsymmetric sequences with low autocorrelation obtained by making exhaustive searches for sequences with optimal merit factor are extended up to length 69 a sieve that required both the symmetric and antisymmetric components of a skewsymmetric sequence to have high merit factor to make limited searches up to length 117 was used and many sequences with merit factor greater than 9 were found

binary sequences with merit factor 6 3 a method is described for the construction of binary sequences of very long length and with asymptotic merit factor 6 3 the result is backed up by strong experimental evidence although no formal proof for the asymptote is known the sequences were found by kristiansen using a small deterministic search which we describe borwein choi and jedwab have independently identified a merit factor asymptote of 6 3421 after we became aware of their work we realized that the sequences we construct are more simply described as periodic extensions of periodically rotated legendre sequences

the merit factor of binary sequences related to difference sets long binary sequences related to cyclic difference sets are investigated among all known constructions of cyclic difference sets it is shown that only sequences constructed from hadamard difference sets can have an asymptotic nonzero merit factor maximal length shift register sequences legendre and twin prime sequences are all constructed from hadamard difference sets the authors prove that the asymptotic merit factor of any maximal length shift register sequence is three for twin prime sequences it is shown that the best asymptotic merit factor is six this value is obtained by shifting the twin prime sequence one quarter of its length it turns out that legendre sequences and twin prime sequences have similar behavior jacobi sequences are investigated on the basis of the jacobi symbol the best asymptotic merit factor is shown to be six through the introduction of product sequences it is argued that the maximal merit factor among all sequences of length n is at least six when n is large the authors also demonstrate that it is fairly easy to construct sequences of moderate composite length with a merit factor close to six

exact output control for a family of linear plants with parameter uncertainties a family of linear continuous time plants parametrized by a vector of unknown parameters taking values in a known finite set is considered the problem investigated consists in finding a linear discrete time compensator that independently of the actual value of the parameter vector guarantees zero continuous time steady state output error with respect to a given continuous time external reference it is shown that the problem admits a solution in the class of periodic controllers

an alternative to the luders generalization of the von neumann projection and its interpretation an alternative to the luders generalization of the von neumann projection is formulated allowing a generalization to measurements represented by positive operator valued measures this generalization is based on the notions of non orthogonal projections and bi orthonormal systems in hilbert schmidt space and is closely related to phase space representations of quantum mechanics a number of applications will be discussed it is demonstrated that the alternative projection has a natural interpretation as a representation of the information on the initial state to be obtained by the measurement

constructing binary sequences with good correlation properties an efficient analytical computational interplay binary sequence sets with asymptotically optimal auto cross correlation peak sidelobe level psl growth have been known in the literature for a long time and their construction has been studied both analytically and numerically in contrast it has been a long standing problem whether we can construct a family of binary sequences whose auto correlation psl grows in an optimal manner in this paper we devise a construction method of binary sequences with asymptotically optimal psl growth from the sequence sets with good correlation properties a key component of the design follows from the observation that if the psl of the sequence set grows optimally or nearly optimally then the psl of the constructed binary sequence will experience a similar growth as a consequence the proposed construction is simple to implement and is shown to be accomplished in polynomial time with such a construction we not only bridge the gap between analytical construction and computational search but also pave the way to settle the long standing design problem of binary sequences with an optimal growth of the auto correlation psl

entropic measures of joint uncertainty effects of lack of majorization we compute renyi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two dimensional quantum systems the relative amount of uncertainty between two states depends on the uncertainty measure used these results are not reproduced by a more standard duality relation we show that these behaviors are consistent with the lack of majorization relation between the corresponding statistics

simplified dynamic model for the motility of irregular echinoids inspired by the locomotion mechanism of sea urchins we study the locomotion of an irregular echinoid by means of a simplified dynamical model we prove that if two conjectures are assumed the geometrical arrangement of the five ambulacral petals of irregular echinoids should form a eutactic star in order to optimize motility we firstly propose an adequate measure of eutacticity that allows us to to verify the statistical tendency to such a property for a representative collection of fossil specimens next regarding dynamics the biological advantage of eutactic stars is addressed as a minimal path problem finally we study the stability of some eutactic stars under small perturbations

deadbeat error control of discrete multivariable systemsdagger abstract the main objective of this paper is to delineate conditions under which deadbeat error control can be achieved between a plant output and a discrete reference input signal all facets of this problem are considered in the linear multivariable case i e when the reference is any non diminishing signal whether the plant is truly discrete or a discretized continuous one and whether the initial conditions are zero or unknown the results presented can also be used to resolve the case of known non zero initial conditions on the state of the plant as well as the compensator

ripple free tracking problem in the deadbeat control of discrete plants originating from continuous ones it is important to have exact tracking not only at the sampling instants but also in between the instants this paper investigates such a problem in the general case of a reference signal that can vary within a pre specified class the design procedure proposed here is based on a polynomial algebra approach an internally stable closed loop system is derived by means of an algorithm where the transfer function of the controller originates from the solution of a set of linear equations algebraic conditions are given to determine the minimum time control scheme numerical examples are reported to show the feasibility of the method and the simplicity of including other specific requirements into the control law

ripple free deadbeat control for sampled data systems in this paper the ripple free deadbeat control problem for sampled data systems is considered this control objective is to settle the error to zero for all time after some finite settling time in other words to eliminate the ripples between the sampling instants in deadbeat control of sampled data systems the necessary and sufficient conditions to solve this problem are derived and related to the system type and a method of constructing the ripple free deadbeat control system is presented

concepts of conditional expectations in quantum theory a concept of conditional expectations in quantum theory is established with interrelations to previously introduced concepts of the cycon hellwig conditional expectations and a posteriori states which are analogous to the existing interrelations in the classical probability theory among conditional expectations related to random variables those related to subalgebras and conditional probability distributions these three concepts are shown to have satisfactory statistical interpretation in the quantum measuring processes for the above purpose we introduce an integration with respect to functions with values in the states of operator algebras and positive operator valued measures such that the resulting indefinite integrals are completely positive map valued measures eventually it is proved that in the von neumann algebraic formulation the cycon hellwig conditional expectations always exist as completely positive map valued measures

on the search for good aperiodic binary invertible sequences for an aperiodic invertible sequence of length l the optimality criterion is chosen to be the minimum noise enhancement factor of the corresponding aperiodic inverse filter the noise enhancement factor is defined as the ratio of the noise energies at the outputs of the aperiodic inverse and the normalized matched filters of the sequence due to white noise at the filter inputs optimal binary sequences of length l spl les 32 and optimal binary skew symmetric sequences of length 33 spl les l spl les 59 were found by exhaustive search the search for near optimal sequences is shown to have strong connections to the search for sequences with large products of golay 1977 merit factor times the minimum of the energy density spectrum based on legendre sequences and on kronecker product sequences long near optimal binary sequences are found that have associated noise enhancement factors close to 1 db

on deadbeat controllers the possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way a detailed analysis of the control sequence generated by any deadbeat controller is then presented

parametrized solution of the periodic dead beat control problem the dead beat control problem for linear periodic discrete time systems in presence of unmeasurable disturbances and external reference signals is considered using a polynomial method a parametrization of all causal output feedback controllers solving the problem is provided

measurement theory in local quantum physics in this paper we aim to establish foundations of measurement theory in local quantum physics for this purpose we discuss a representation theory of completely positive cp instruments on arbitrary von neumann algebras we introduce a condition called the normal extension property nep and establish a one to one correspondence between cp instruments with the nep and statistical equivalence classes of measuring processes we show that every cp instrument on an atomic von neumann algebra has the nep extending the well known result for type i factors moreover we show that every cp instrument on an injective von neumann algebra is approximated by cp instruments with the nep the concept of posterior states is also discussed to show that the nep is equivalent to the existence of a strongly measurable family of posterior states for every normal state two examples of cp instruments without the nep are obtained from this result it is thus concluded that in local quantum physics not every cp instrument represents a measuring process but in most of physically relevant cases every cp instrument can be realized by a measuring process within arbitrary error limits as every approximately finite dimensional von neumann algebra on a separable hilbert space is injective to conclude the paper the concept of local measurement in algebraic quantum field theory is examined in our framework in the setting of the doplicher haag roberts and doplicher roberts theory describing local excitations we show that an instrument on a local algebra can be extended to a local instrument on the global algebra if and only if it is a cp instrument with the nep provided that the split property holds for the net of local algebras

quantum measuring processes of continuous observables the purpose of this paper is to provide a basis of theory of measurements of continuous observables we generalize von neumann s description of measuring processes of discrete quantum observables in terms of interaction between the measured system and the apparatus to continuous observables and show how every such measuring process determines the state change caused by the measurement we establish a one to one correspondence between completely positive instruments in the sense of davies and lewis and the state changes determined by the measuring processes we also prove that there are no weakly repeatable completely positive instruments of nondiscrete observables in the standard formulation of quantum mechanics so that there are no measuring processes of nondiscrete observables whose state changes satisfy the repeatability hypothesis a proof of the wigner araki yanase theorem on the nonexistence of repeatable measurements of observables not commuting conserved quantities is given in our framework we also discuss the implication of these results for the recent results due to srinivas and due to mercer on measurements of continuous observables

binary sequences with merit factor greater than 6 34 the maximum known asymptotic merit factor for binary sequences has been stuck at a value of 6 since the 1980s several authors have suggested that this value cannot be improved in this paper we construct an infinite family of binary sequences whose asymptotic merit factor we conjecture to be greater than 6 34 we present what we believe to be compelling evidence in support of this conjecture the numerical experimentation that led to this construction is a significant part of the story

parameterization of all multivariable ripple free deadbeat tracking controllers this paper presents an explicit parameterization of all ripple free deadbeat tracking controllers for multi input multi output mimo sampled data control systems the advantages over the previous results are the following first a useful necessary and sufficient condition to obtain a ripple free deadbeat tracking response for mimo sampled data control systems is presented second not only all ripple free mimo deadbeat tracking controllers but also all achievable deadbeat sequences and all control input ones are characterized by completely free parameters in an explicit form third the design method is simple and straightforward the computation consists of simple polynomial matrix equations without involving troublesome calculation such as the reduction to smith mcmillan form fourth the class of the reference inputs for which ripple free deadbeat tracking responses are achieved is generalized finally a numerical example demonstrates that the proposed parameterization makes it easy to clarify the r

deadbeat ripple free tracking with disturbance rejection a polynomial approach the deadbeat ripple free tracking problem for sampled data systems is considered it is assumed that both the state and the output of the continuous time plant to be controlled are affected by external disturbances a polynomial approach is adopted and solvability conditions are given both in terms of the sampled system and of the original continuous time one

design of ripple free multivariable robust servomechanisms the application of standard robust servomechanism theory to sampled data systems guarantees asymptotic tracking at sampling instances and between sampling instants the output will normally contain ripple in this note the robust servomechanism theory is extended to sampled data systems and a technique is proposed for ripple free tracking of sinusoids and polynomials it is shown that a continuous internal model is necessary and sufficient to provide ripple free response

brief paper multivariable closed loop deadbeat control a polynomial matrix approach the closed loop deadbeat servo problem cdsp considered in this paper consists of the synthesis of a linear output feedback controller such that the control signal and tracking error both vanish after a finite period of time for every reference sequence from a prespecified class and for every initial state of a plant and the controller the closed loop structure is determined by studying necessary and sufficient conditions for deadbeat tracking performance a new theorem asserts that if an open loop deadbeat control strategy exists for every initial state of the plant and every reference function from a given class then cdsp is solvable and all desired control laws are found in an explicit parametric form by solving simple unilateral linear equations in polynomial matrices on the basis of this theorem a design algorithm is developed asymptotic stability of the closed loop system exhibiting deadbeat properties is demonstrated a numerical example is given to illustrate the usefulness and computational efficiency of the new design algorithm presented