mobius transformation and cauchy parameter estimation some properties of the ordinary two parameter cauchy family the circular or wrapped cauchy family and their connection via mobius transformation are discussed a key simplification is achieved by taking the parameter i to be a point in the complex plane rather than the real plane maximum likelihood estimation is studied in some detail it is shown that the density of any equivariant estimator is harmonic on the upper half plane in consequence the maximum likelihood estimator is unbiased for n 3 and every harmonic or analytic function of the maximum likelihood estimator is unbiased if its expectation is finite the joint density of the maximum likelihood estimator is obtained in exact closed form for samples of size n 4 and in approximate form for n 5 various marginal distributions including that of student s pivotal ratio are also obtained most results obtained in the context of the real cauchy family also apply to the wrapped cauchy family by mobius transformation

a new approach for designing a reduced order controller of linear singular systems an approach for designing a multivariable reduced order controller of a linear time invariant singular system is presented the approach is based on decomposing the original system into slow and fast subsystems using the drazin inverse technique the resulting subsystems are then used to obtain an observer of reduced order this in turn it used in designing a new reduced order controller which is capable of placing the dominant eigenvalues of the system in arbitrary locations the technique is shown to overcome some difficulties inherent in other treatments of reduced order controllers of singular systems and assures that the known corresponding controller of the regular state space systems is merely a special case of the present results

estimating the plant state from the compensator state for the system dot w sw where w x over z this note states and proves necessary and sufficient conditions under which a z is an estimate of a linear function of x i e z estimates tx or b a linear function of z is an estimate of x i e vz estimates x the mapping t has been used previously by the authors to compute the estimator controller form of a compensator whose state vector z had the same dimension as the plant state vector x

functional observer and state feedback in this paper relations between the designs of functional observers and state feedback in the state space and transfer function approaches are presented if the state space description of the plan can be written in a controllable canonical form we show that the state space approach of the functional observer and state feedback design can be transformed in the transfer function approach form once the equations in the transfer function approach are solved all unknown elements in the equations of the state space approach can be computed by an iterative algorithm thus the relationship between the two approaches is established we shall also show that the transfer function approach has fewer restrictions

a family of distributions on the circle with links to and applications arising from mobius transformation we propose a family of four parameter distributions on the circle that contains the von mises and wrapped cauchy distributions as special cases the family is derived by transforming the von mises distribution via a mobius transformation which maps the unit circle onto itself the densities in the family have a symmetric or asymmetric unimodal or bimodal shape depending on the values of the parameters conditions for unimodality are explored further properties of the proposed model are obtained many by applying the theory of mobius transformation properties of a three parameter symmetric submodel are investigated as well these include maximum likelihood estimation its asymptotics and a reparameterization that proves useful quite generally a three parameter asymmetric subfamily which often proves to be an adequate model is also discussed with emphasis on its mean direction and circular skewness the proposed family and subfamilies are used to model an asymmetrically distributed data set and ar

a new algorithm for the design of multifunctional observers this paper presents a general algorithm for low order multifunctional observer design with arbitrary eigenvalues the feature of this algorithm is that it can generate a functional observer with different orders which are no larger but usually much less than m v 1 where m is the number of functionals and v is the observability index of a c since the order needed for the observer varies with the functionals besides other system parameters this design approach should be practical the resulting observer system matrix is in its jordan form the key step of this algorithm is the generation of the basis for the transformation matrix which relates the system and observer states the computation of this algorithm is quite reliable it is based on the block observable lower hessenberg form of a c and all its initial and major computation involves only the orthogonal operations

function observer design for a class of linear time varying system this paper presents for the first time a reduced order linear function observer design algorithm for uniformly observable linear time varying systems the resulting observer will have a constant jordan form system matrix with arbitrarily given poles the order reduction of the function observer is also clarified and clearly explained

eigensensitivity based optimal damper location in variable geometry trusses in this paper two procedures are described to identify the optimal damping element locations in variable geometry trusses and to improve their behavior when dynamic loads are applied in simple structures subjected to well identified actions obtaining an optimal location for damping elements can be relatively easy however as the geometry of the structures becomes more complex the number of elements increases and the frequency range of external actions is wider finding the optimal location of dampers along the system becomes a difficult task furthermore if the structure varies its geometry in successive positions such as folding unfolding or any other movement another level of complexity is added to the problem the two procedures presented in this paper are based on calculating the effectiveness indices obtained from the derivatives of the eigenfrequencies of the dynamic eigenproblem with regard to parameters like stiffness or damping

a direct design procedure for linear state functional observers we propose a constructive procedure to design a luenberger observer to estimate a linear multiple linear state functional for a linear time invariant system among other features the proposed design algorithm is not based on the solution of a sylvester equation nor on the use of canonical state space forms the design is based on the solution set of a linear equation and a realization method the consistency of this equation and the stability of the observer can be used as a functional observability test

a tractable and interpretable four parameter family of unimodal distributions on the circle this article presents a class of four parameter distributions for circular data that are unimodal possess simple characteristic and density functions and a tractable distribution function can be interpretably parameterized directly in terms of their trigonometric moments afford a very wide range of skewness and kurtosis envelop numerous interesting submodels including the wrapped cauchy and cardioid distributions allow straightforward parameter estimation by both method of moments and maximum likelihood and are closed under convolution this class of distributions exhibits the widest range of attractive properties yet available while retaining unimodality

functional observer for linear parameter varying systems with application to diagnosis of pem fuel cell this paper is a contribution to the problem of functional observers for linear parameter varying systems the goal is twofold first we propose an extension of some results of literature on functional observers established originally for linear systems to systems the design of these observers are based on linear interpolation principle according to each parameter besides sufficient conditions for asymptotic convergence are expressed in terms of linear matrix inequalities easily tractable by convex optimisation techniques second we show how this new result can be used to investigate the problem of diagnosis for proton electrolyte membrane fuel cell more precisely we deal with the problem of flooding considered as an important issue for water management inside the fuel cell finally simulation results are given in order to highlight the performances of the proposed approach

eigensensitivity analysis in variable geometry trusses t he adaptive structures of variable geometry are light mechanical systems capable of modifying their geometry and mechanical properties to adapt to different operating conditions there are different kinds of mechanical variable geometry systems 1 amongwhich stand out the variable geometry trusses vgts 2 5 these structures are a subset of the former generally comprising a large number of biarticulated bars to form a complex truss some of these bars are active elements that is their length can vary in a controlled way to enable the actuation of the vgt one of the most important problems to be solved in vgts is vibration essentially due to two factors on the one hand they are generally slimline structures making them easily excitable at low frequencieswith large amplitudes whichmight interferewith correct vgt operation thereby harming its accuracy and even resulting in collisions with environmental obstacles 5 7 on the other hand as vgts may have highly different configurations throughout their operation the dynamic properties natural frequencies and vibration modes also change to a large extent there have been numerous contributions onvibratory dynamics of vgts there are a few works like those of keane and bright 8 keane 9 andnair andkeane 10 which opt for optimum redesign of the structure geometry using evolutionary methods to determine structural geometries presenting a better dynamic response the most widely accepted procedure for improving and or controlling dynamic properties is the inclusion of active semiactive or passive elements to control its dynamic response in this sense bilbao et al 11 carried out a detailed revision of the state of the art and proposed a new methodology for the optimal location of damping elements this note further contributes to vibratory dynamics of vgts describing a tool developed to efficiently estimate the dynamic properties of vgts frequencies and modes throughout their movement by responding to two needs first the information that frequencies and modes supply is often sufficient to foresee the dynamic behavior without having to perform costly direct dynamic analyses as verified in 12 second should said analyses be necessary they can be approached from the modal superposition viewpoint for which a tool that efficiently estimates natural frequencies and vibration modes is necessary a linear estimation is proposed tomodel the variation of these dynamic properties throughout the vgtevolution so that there is no need to calculate them per position but only for a fraction of these positions whichmay result in considerable computational saving thus a methodology estimating the value of natural frequencies and vibration modes in a new position from their value in the immediately prior position is employed this is done by differentiating natural frequencies and vibration modes with respect to nodal coordinates at the starting position and developing a first order series around the starting position to extrapolate the values of natural frequencies and vibration modes for a new position

passive vibration suppression of flexible space structures via optimal geometric redesign acomputationalframework is presented for the design of large flexible space structures with nonperiodicgeometries to achieve passive vibration suppression the present system combines an approximationmodel management framework ammf developed for evolutionary optimization algorithms eas with reduced basis approximate dynamic reanalysis techniques a coevolutionary genetic search strategy is employed to ensure that design changes during the optimization iterations lead to low rank perturbations of the structural system matrices for which thereduced basis methods give high quality approximations the k means algorithm is employed for cluster analysis of the population of designs to determine design points at which exact analysis should be carried out the fitness of the designs in an ea generation is then approximated using reduced basis models constructed around the points where exact analysis is carried out results are presented for the optimal design of a two dimensional cantilevered space structure to achieve passive vibration suppression it is shown that significant vibration isolation of the order of 50 db over a 100 hz bandwidth can be achieved further it is demonstrated that the ammf can potentially arrive at a better design compared to conventional approaches when a constraint is imposed on the computational budget available for optimization

partial state observers for nonlinear systems this note deals with the design of reduced order observers for a class of nonlinear systems the order reduction of the observer is achieved by only estimating a required partial set of the state vector necessary and sufficient conditions are derived for the existence of reduced order observers an observer design procedure based on linear matrix inequalities is given a numerical example is given to illustrate the design method

a new robust stability measure for state feedback systems abstract this brief paper proposes the use of sensitivities of each individual system pole to measure robust stability of state feedback systems compared with the existing measures of this kind m 1 and m 2 this measure is much easier to work with than m 1 while at least as accurate and is definitely more accurate than m 2 the upper and lower bounds of this measure are also derived and proved to be the same as those of m 1 this measure can be maximized numerically using existing explicit and systematic procedures some analytical guidelines which relate explicitly and directly the state feedback system s individual pole selection performance and decoupling to this new measure are also available and presented

inverse batschelet distributions for circular data we provide four parameter families of distributions on the circle which are unimodal and display the widest ranges of both skewness and peakedness yet available our approach is to transform the scale of a generating distribution such as the von mises using various nontrivial extensions of an approach first used in batschelet s 1981 circular statistics in biology book the key is to employ inverses of batschelet type transformations in certain ways these exhibit considerable advantages over direct batschelet transformations the skewness transformation is especially appealing as it has no effect on the normalizing constant as well as a variety of interesting theoretical properties when likelihood inference is explored these distributions display orthogonality between elements of a pairing of parameters into location skewness and concentration peakedness further the location parameter can sometimes be made approximately orthogonal to all the other parameters profile likelihoods come to the fore in practice two illustrative applications one concerning the locomotion of a drosophila fly larva the other analyzing a large set of sudden infant death syndrome data are investigated

conditional inference and cauchy models summary many computations associated with the two parameter cauchy model are shown to be greatly simplified if the parameter space is represented by the complex plane rather than the real plane with this convention we show that the family is closed under m6bius transformation of the sample space there is a similar induced transformation on the parameter space the chief raison d etre of the paper however is that the two parameter cauchy model provides an example of a nonunique configuration ancillary in the sense of fisher 1934 such that the maximum likelihood estimate together with either ancillary is minimal sufficient some consequences for bayesian inference and non bayesian conditional inference are explored in particular it is shown that conditional coverage probability assessments depend on the choice of ancillary for moderate deviations the effect occurs in the op n 1 term for large deviations the relative effect is op n2

design of scalar functional observers of order less than ν 1 this paper presents a new method of designing scalar functional observers of order less than the well known upper bound 1 a condition for the existence of observers of order p where 1 p 1 is given a simple and effective algorithm for solving the constrained generalized sylvester equation is proposed several numerical examples are given to illustrate the attractiveness of the design algorithm

new approach to robust observer design this paper shows that based on the recent development of observer design solution an observer pole selection method can be formulated to minimize the observer gain to the system input it is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems

control of a slow moving space crane as an adaptive structure if we assume that the space crane is a statically determinate truss with length adjustable bars and take as controls the length adjustments of these bars the computation of the incremental controls corresponding to the motion of a payload along a trajectory is given in terms of the inverse transpose of matrix b of the joint equilibrium equations bs p where s lists the bar forces and p the nodal loads an algorithm with 0 w2 computational complexity and 0 z storage demand is used for obtaining the inverse of the wth order sparse matrix b the compensation of the controls for elastic deformations and support movements is shown the crane is assumed to be moving sufficiently slowly so that no vibratory motion is created during its maneuver to simplify the computations a zero acceleration field is assumed in the workspace of the space crane it is shown that the computations may be done automatically and in real time by an attached processor once the characteristics of the crane s maneuver are keyed in

dynamic output feedback variable structure control for system stabilization simplex type dynamic output feedback variable structure control for stabilizing multivariable linear time invariant plants is analysed two types of controllers are considered a compensator type and an observer type it is shown that while the compensator type controller stabilizes the plant only if the plant is minimum phase the observer type controller does not face the same restriction the design of low order less than the order of the plant observer type controllers is also considered

a new design approach to unknown input observers this paper proposes a fundamentally new unknown input observer uio which has uniquely r decoupled modes provides r linearly independent combinations of plant system states and has zero gain to all p unknown inputs the parameter r is adjustable if the plant system satisfies the conditions of the existing uio then r n plant system order and there is no difference between our uio and the existing regular uio however if the plant system satisfies either of the following two significantly more general conditions m p m is the number of plant output measurements and at least one stable transmission zero then 1 n and our uio can still generate some constrained state feedback control signals hence this new uio can completely unify the regular uio r n and the static output feedback r m the two basic feedback structures of modern control theory far from being unified before

on the order reduction of linear function observers this note analyzes a new algorithm presented in 1 for designing a linear function observer with a minimum number of arbitrary poles it shows that the maximum order of the observer of 1 is nu nu p p for p leq q and n q for p geq q instead of p nu 1 1 as suggested in 1 where nu i i 1 to p are the descending ordered observability indexes of system a c and n p and q are the order of the system the number of the functions and the number of the system outputs respectively this note also shows the significance of this result for presentational purposes only a special case of 1 is considered here however the technical properties as proved in this note are general

a system decomposition approach to the design of functional observers this paper reports a system decomposition that allows the construction of a minimum order functional observer using a state observer design approach the system decomposition translates the functional observer design problem to that of a state observer for a smaller decomposed subsystem functional observability indices are introduced and a closed form expression for the minimum order required for a functional observer is derived in terms of those functional observability indices

levy flights and random searches in this work we discuss some recent contributions to the random search problem our analysis includes superdiffusive levy processes and correlated random walks in several regimes of target site density mobility and revisitability we present results in the context of mean field like and closed form average calculations as well as numerical simulations we then consider random searches performed in regular lattices and lattices with defects and we discuss a necessary criterion for distinguishing true superdiffusion from correlated random walk processes we invoke energy considerations in relation to critical survival states on the edge of extinction and we analyze the emergence of levy behavior in deterministic search walks finally we comment on the random search problem in the context of biological foraging

edgeworth series for lattice distributions and identically distributed lattice valued random variables we prove that the continuity corrected edgeworth series using sheppard adjusted cumulants is accurate to the same order in n as the usual edgeworth approximationfor continuous random variables finally as a partial justification of the sheppard adjustments it is shown that if a continuous random variable y is rounded into a discrete part d and a truncation error u such that y d u then under suitable limiting conditions the truncation error is approximately uniformly distributed and independent of y but not independent of d

on robust observer compensator design abstract this paper presents for the first time a unified explicit and restriction free set of design formulas for kalman type and luenberger type state observers and function observers with arbitrary poles in addition a new explicit and deterministic observer pole selection method for recovering the robustness of a direct state feedback system is also proposed two design examples are given in this paper these examples demonstrate the advantages of this robust recovery method the examples also show that both the luenberger type observers and the function observers generally have better stability margins this design methodology enables the design objectives of robustness order reduction and performance to be considered together in terms of observer pole selection

a complete analytical solution to the equation ta ft lc and its applications in this note a complete analytical and restriction free solution with complete and explicit freedom of the matrix equation ta ft lc is proposed here a c is given and is observable and f is in the jordan form with arbitrary given eigenvalues this solution appears to be new because it can be applied directly to obtain significantly better solutions to the following three basic design problems 1 2 d system eigenvalue assignment 2 function observer design and 3 state feedback eigenstructure design as shown in this note

mobius deconvolution on the hyperbolic plane with application to impedance density estimation in this paper we consider a novel statistical inverse problem on the poincare or lobachevsky upper complex half plane here the riemannian structure is hyperbolic and a transitive group action comes from the space of 2 x 2 real matrices of determinant one via mobius transformations our approach is based on a deconvolution technique which relies on the helgason fourier calculus adapted to this hyperbolic space this gives a minimax nonparametric density estimator of a hyperbolic density that is corrupted by a random mobius transform a motivation for this work comes from the reconstruction of impedances of capacitors where the above scenario on the poincare plane exactly describes the physical system that is of statistical interest

a family of symmetric distributions on the circle we propose a new family of symmetric unimodal distributions on the circle that contains the uniform von mises cardioid and wrapped cauchy distributions among others as special cases the basic form of the densities of this family is very simple although its normalization constant involves an associated legendre function the family of distributions can also be derived by conditioning and projecting certain bivariate spherically and elliptically symmetric distributions on to the circle trigonometric moments are available and a measure of variation is discussed aspects of maximum likelihood estimation are considered and likelihood is used to fit the family of distributions to an example set of data finally extension to a family of rotationally symmetric distributions on the sphere is briefly made

scaled von mises fisher distributions and regression models for paleomagnetic directional data we propose a new distribution for analyzing paleomagnetic directional data that is a novel transformation of the von mises fisher distribution the new distribution has ellipse like symmetry as

a markov process for circular data summary we propose a discrete time markov process which takes values on the unit circle some properties of the process including the limiting behaviour and ergodicity are investigated many computations associated with this process are shown to be greatly simplified if the variables and parameters of the model are represented in terms of complex numbers a further discussion is given on some submodels in particular on the stationary process the proposed model is compared with some existing markov processes for circular data some statistical issues of the model such as statistical inference model selection and diagnostic checks are considered finally an application of the model to wind direction data is provided

existence and design of functional observers for linear systems this paper presents straightforward derivations of the functional observers design for linear time invariant multivariable systems the order of these observers is equal to the dimension spl tau of the vector to be estimated necessary and sufficient conditions for the existence and stability of these observers are given illustrative examples are included

comments on parallel procedure for the design of observers in high order multivariable systems shafai 1988 proposed a state observer design algorithm which is very slightly different from an earlier algorithm of tsui 1985 furthermore the change made by shafai severely worsens the parallel computation property the only key property of his algorithm claimed by shafai it is important to mention that this comment is obviously valid for the dual version of shafai s algorithm state feedback design for pole assignment which has appeared elsewhere several times recently