strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

strict lyapunov krasovskiĭ functionals for undirected networks of euler lagrange systems with time varying delays for an undirected network of nonidentical interconnected euler lagrange systems whose communication is affected by varying time delays that may not be differentiable we consider the problem of establishing leaderless and leader follower consensus via the simplest proportional plus damping decentralized controller the main contribution of this work is to prove that the agents positions and velocities converge uniformly globally and asymptotically to a common non specified position in the leaderless case and to a given reference in the leader follower case the main results are established via lyapunov s direct method a strict lyapunov krasovskii functional is constructed to the best of our knowledge for the first time in the literature it is shown that the resulting closed loop system is input to state stable with regards to external additive inputs perturbations in turn the separation principle applies to a certainty equivalence controller implemented with any globally convergent velocity estimator such as the immersion invariance observer

the restricted kirillov reshetikhin modules for the current and twisted current algebras we define a family of graded restricted modules for the polynomial current algebra associated to a simple lie algebra we study the graded character of these modules and show that they are the same as the graded characters of certain demazure modules in particular we see that the specialized characters are the same as those of the kirillov reshetikhin modules for quantum affine algebras

brief paper distributed containment control for lagrangian networks with parametric uncertainties under a directed graph in this paper we study the distributed containment control problem for networked lagrangian systems with multiple dynamic leaders in the presence of parametric uncertainties under a directed graph that characterizes the interaction among the leaders and the followers we propose a distributed adaptive control algorithm combined with distributed sliding mode estimators a necessary and sufficient condition on the directed graph is presented such that all followers converge to the dynamic convex hull spanned by the dynamic leaders asymptotically as a byproduct we show a necessary and sufficient condition on leaderless consensus for networked lagrangian systems under a directed graph numerical simulation results are given to show the effectiveness of the proposed control algorithms

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

spaces of quasi exponentials and representations of gln we consider the action of the bethe algebra on the weight subspace of weight of the tensor product of k polynomial irreducible modules with highest weights respectively the bethe algebra depends on n complex numbers under the assumption that k1 kn are distinct we prove that the image of in end is isomorphic to the algebra of functions on the intersection of suitable schubert cycles in the grassmannian of n dimensional spaces of quasi exponentials with exponents we also prove that the module is isomorphic to the coregular representation of that algebra of functions we present a bethe ansatz construction identifying the eigenvectors of the bethe algebra with points of that intersection of schubert cycles

minimax observers for linear differential algebraic equations in this note we construct minimax observers for linear stationary differential algebraic equations dae s with bounded uncertain inputs given noisy measurements we prove a new duality principle and show that a finite infinite horizon minimax observer exists if and only if the dae is ell impulse observable ell detectable remarkably the regularity of the dae is not required

observers for a class of nonlinear singular systems this technical note considers the observers design for a class of nonlinear singular systems the approach is based on the new parameterization of the generalized sylvester equations solutions the conditions for the existence of these observers are given and sufficient conditions for their stability are derived using linear matrix inequalities lmis formulation reduced order minimal order and full order observers are designed by a unified method a numerical example is presented to demonstrate the effectiveness of the developed method

an application of global weyl modules of sln 1 t to invariant theory abstract we identify the sl n 1 isotypical components of the global weyl modules w k 1 with certain natural subspaces of the polynomial ring in k variables we then apply the representation theory of current algebras to classical problems in invariant theory

observer design for descriptor systems two detectability notions are introduced for the most general class of linear descriptor systems necessary and sufficient conditions are derived for the detectabilities and for the existence of observers depending on existence conditions satisfied the observers can be either in the familiar luenberger form or in a generalized form i e in descriptor form as the original system itself is a unified procedure is provided for the design of observers in both forms

maximum entropy and conditional probability it is well known that maximum entropy distributions subject to appropriate moment constraints arise in physics and mathematics in an attempt to find a physical reason for the appearance of maximum entropy distributions the following theorem is offered the conditional distribution of x l given the empirical observation 1 n sum n i l h x i alpha where x 1 x 2 cdots are independent identically distributed random variables with common density g converges to f lambda x e lambda t h x g x suitably normalized where lambda is chosen to satisfy int f lambda x h x dx alpha thus the conditional distribution of a given random variable x is the normalized product of the maximum entropy distribution and the initial distribution this distribution is the maximum entropy distribution when g is uniform the proof of this and related results relies heavily on the work of zabell and lanford

observability of singular systems with commensurate time delays and neutral terms this paper deals with the observability problem of a sort of singular systems with commensurate time delays in the trajectories of the system in the time derivative of the trajectories neutral terms and in the output system by using a recursive algorithm sufficient conditions easy testable are proposed for guaranteeing the backward and the algebraic observability of the system this condition implies that the trajectories of the system can be reconstructed by using the actual and past values of the system output

a novel approach to the design of unknown input observers a novel state estimator design scheme for linear dynamical systems driven by partially unknown inputs is presented it is assumed that there is no information available about the unknown inputs and thus no prior assumption is made about the nature of these inputs a simple approach for designing a reduced order unknown input observer uio with pole placement capability is proposed by carefully examining the dynamic system involved and simple algebraic manipulations it is possible to rewrite equations eliminating the unknown inputs from part of the system and to put them into a form where it could be partitioned into two interconnected subsystems one of which is directly driven by known inputs only this makes it possible to use a conventional luenberger observer with a slight modification for the purpose of estimating the state of the system as a result it is also possible to state similar necessary and sufficient conditions to those of a conventional observer for the existence of a stable estimator and also arbitrary placement of the eigenvalues of the observer the design and computational complexities involved in designing uios are greatly reduced in the proposed approach

closed form line segment extraction using the hough transform this paper proposes a novel closed form solution to complete line segment extraction given a voting angle in image space the voting distribution is analyzed and two functional relationships are deduced regarding the corresponding column in hough space voting along the distance axis is considered as being a random variable and voting values in cells are considered as forming a probability distribution statistical characteristics of this distribution are used to fit a quadratic polynomial curve and a linear curve direction length and width of a line segment are simultaneously computed in a closed form based on coefficients of fitted quadratic polynomial curves the midpoint of a line segment is determined based on the fitted linear curve the method is tested on simulated and real world images results show that the proposed closed form solution is feasible in the presence of quantization errors or image noise highlightswe proposed a method for obtaining the complete set of line segment parameters the direction length and width of a line segment are extracted simul taneously in a closed form we provided a complete theoretical derivation of voting variance with respect to voting angle the midpoint of a line segment is determined by the coefficients of the fitted linear curve parallel crossing and aligned line segments are discussed by analysing events in image space and hough space

current algebras highest weight categories and quivers abstract we study the category of graded finite dimensional representations of the polynomial current algebra associated to a simple lie algebra we prove that the category has enough injectives and compute the graded character of the injective envelopes of the simple objects as well as extensions between simple objects the simple objects in the category are parametrized by the affine weight lattice we show that with respect to a suitable refinement of the standard ordering on the affine weight lattice the category is highest weight we compute the ext quiver of the algebra of endomorphisms of the injective cogenerator of the subcategory associated to an interval closed finite subset of the weight lattice finally we prove that there is a large number of interesting quivers of finite affine and star shaped type as well as tame quasi hereditary algebras that arise from our study

on existence optimality and asymptotic stability of the kalman filter with partially observed inputs for linear stochastic time varying systems we investigate the properties of the kalman filter with partially observed inputs we first establish the existence condition of a general linear filter when the unknown inputs are partially observed then we examine the optimality of the kalman filter with partially observed inputs finally on the basis of the established existence condition and optimality result we investigate asymptotic stability of the filter for the corresponding time invariant systems it is shown that the results on existence and asymptotic stability obtained in this paper provide a unified approach to accommodating a variety of filtering scenarios as its special cases including the classical kalman filter and state estimation with unknown inputs

line fitting in a noisy image the conventional least squared distance method of fitting a line to a set of data points is unreliable when the amount of random noise in the input such as an image is significant compared with the amount of data correlated to the line itself points which are far away from the line outliers are usually just noise but they contribute the most to the distance averaging skewing the line from its correct position the author presents a statistical method of separating the data of interest from random noise using a maximum likelihood principle

bgg reciprocity for current algebras abstract we study the category i gr of graded representations with finite dimensional graded pieces for the current algebra g c t where g is a simple lie algebra this category has many similarities with the category o of modules for g and in this paper we formulate and study an analogue of the famous bgg duality we recall the definition of the projective and simple objects in i gr which are indexed by dominant integral weights the role of the verma modules is played by a family of modules called the global weyl modules we show that in the case when g is of type s l 2 the projective module admits a flag in which the successive quotients are finite direct sums of global weyl modules the multiplicity with which a particular weyl module occurs in the flag is determined by the multiplicity of a jordan holder series for a closely associated family of modules called the local weyl modules we conjecture that the result remains true for arbitrary simple lie algebras we also prove some combinatorial product sum identities involving kostka polynomials which arise as a consequence of our theorem

a nonlinear luenberger like observer for nonlinear singular systems this paper investigates observer design problem for a large class of nonlinear singular systems with multiple outputs we firstly regularize the singular system by injecting the derivative of outputs into the system then differential geometric method is applied to transform the regularized system into a simple normal form for which a luenberger like observer is proposed

unknown input and state estimation for unobservable systems the concept of strong detectability and its relation with the concept of invariant zeros is reviewed for strongly detectable systems which includes the strongly observable systems it is proposed a hierarchical design of a robust observer whose trajectories converge to those of the original state vector furthermore it is shown that neither left invertibility is a sufficient condition nor strong detectability is a necessary condition to estimate the unknown inputs it is shown that the necessary and sufficient condition for estimating the unknown inputs is that the set of the invariant zeros that do not belong to the set of unobservable modes be within the interior of the left half plane of the complex space this shows that the unknown inputs could be estimated even if it is impossible to estimate the entire state vector of the system two numerical examples illustrate the effectiveness of the proposed estimation schemes

weyl demazure and fusion modules for the current algebra of sl r 1 we construct a poincare birkhoff witt type basis for the weyl modules v chari a pressley weyl modules for classical and quantum affine algebras represent theory 5 2001 191 223 math qa 0004174 of the current algebra of as a corollary we prove the conjecture made in v chari a pressley weyl modules for classical and quantum affine algebras represent theory 5 2001 191 223 math qa 0004174 v chari a pressley integrable and weyl modules for quantum affine in quantum groups and lie theory durham 1999 in london math soc lecture note ser vol 290 cambridge univ press cambridge 2001 pp 48 62 math qa 0007123 on the dimension of the weyl modules in this case further we relate the weyl modules to the fusion modules defined in b feigin s loktev on generalized kostka polynomials and the quantum verlinde rule in differential topology infinite dimensional lie algebras and applications in amer math soc transl ser 2 vol 194 1999 pp 61 79 math qa 9812093 of the current algebra and the demazure modules in level one representations of the corresponding affine algebra in particular this allows us to establish substantial cases of the conjectures in b feigin s loktev on generalized kostka polynomials and the quantum verlinde rule in differential topology infinite dimensional lie algebras and applications in amer math soc transl ser 2 vol 194 1999 pp 61 79 math qa 9812093 on the structure and graded character of the fusion modules

observability of singular time delay systems with unknown inputs in this manuscript we give sufficient conditions guaranteeing the observability of singular linear systems with commensurable delays affected by unknown inputs appearing in both the state equation and the output equation these conditions allow for the reconstruction of the entire state vector using past and actual values of the system output the obtained conditions coincide with known necessary and sufficient conditions of singular linear systems without delays

image normalization by complex moments the role of moments in image normalization and invariant pattern recognition is addressed the classical idea of the principal axes is analyzed and extended to a more general definition the relationship between moment based normalization moment invariants and circular harmonics is established invariance properties of moments as opposed to their recognition properties are identified using a new class of normalization procedures the application of moment based normalization in pattern recognition is demonstrated by experiment

analysis of descriptor systems using numerical algorithms in this paper we analyze numerical methods for the solution of the large scale dynamical system e dot y t ay t g t y t 0 y 0 where e and a are matrices possibly singular systems of this type have been referred to as implicit systems and more recently as descriptor systems since they arise from formulating system equations in physical variables special cases of such systems are algebraic differential systems we discuss the numerical advantages of this formulation and identify a class of numerical integration algorithms which have accuracy and stability properties appropriate to descriptor systems and which preserve structure detect nonsolvable systems resolve initial value consistency problems and are applicable to stiff descriptor systems we also present an algorithm for the control of the local truncation error on only the state variables

causal observability of descriptor systems observability analysis for descriptor systems by using a matrix pencil approach is presented systems under consideration are the most general class of linear continuous descriptor systems a few practically relevant notions of observability particularly the causal observability which corresponds to the existence of a luenberger observer and the corresponding necessary and sufficient test conditions are provided the interpretation of various observabilities in terms of matrix pencils offers insights into the physical meaning of these concepts

solvability controllability and observability of continuous descriptor systems in this paper we investigate the properties of the continuous descriptor system e dot x t ax t bu t 0 leqt leqb where e a and b are complex and possibly singular matrices and u t is a complex function differentiable sufficiently many times the traditional approach to such systems is to separate the state equations from the algebraic equations however such algorithms usually destroy the natural physically based sparsity and structure of the original system therefore we consider descriptor systems in their original form such systems possess numerous properties not shared by the well known state variable systems first we relate classical theories of matrix pencils to the solvability of descriptor systems then we extend the concepts of reachability controllability and observability of state variable systems to descriptor systems and describe the set of reachable states for descriptor systems

differentiation by integration with jacobi polynomials in this paper the numerical differentiation by integration method based on jacobi polynomials originally introduced by mboup et al 19 20 is revisited in the central case where the used integration window is centered such a method based on jacobi polynomials was introduced through an algebraic approach 19 20 and extends the numerical differentiation by integration method introduced by lanczos 1956 21 the method proposed here rooted in 19 20 is used to estimate the nth email protected n order derivative from noisy data of a smooth function belonging to at least c n 1 q email protected n in 19 20 where the causal and anti causal cases were investigated the mismodelling due to the truncation of the taylor expansion was investigated and improved allowing a small time delay in the derivative estimation here for the central case we show that the bias error is o h q 2 where h is the integration window length for email protected c n q 2 in the noise free case and the corresponding convergence rate is o d q 1 n 1 q where d is the noise level for a well chosen integration window length numerical examples show that this proposed method is stable and effective

character formulae and a realization of tilting modules for sl2 t abstract in this paper we study the category of graded modules for the current algebra associated to sl 2 the category enjoys many nice properties including a tilting theory which was established in 1 we show that the indecomposable tilting modules for sl 2 t are the exterior powers of the fundamental global weyl module and give the filtration multiplicities in the standard and costandard filtration an interesting consequence of our result which is far from obvious from the abstract definition is that an indecomposable tilting module admits a free right action of the ring of symmetric polynomials in finitely many variables moreover if we go modulo the augmentation ideal in this ring the resulting sl 2 t module is isomorphic to the dual of a local weyl module

comments on robust line fitting in a noisy image by the method of moments qjidaa and radouane 1999 presented a method for robust line fitting and experimentally compared it to other methods including a method suggested by us the results attributed by qjidaa and radouane to our algorithm are incorrect we apply our algorithm to the data used by qjidaa and radouane and demonstrate its robustness and accuracy

consensus of networked mechanical systems with communication delays a unified framework this technical note addresses the consensus problem of networked uncertain mechanical systems which interact on directed graphs containing a spanning tree and are subjected to nonuniform communication delays the challenge lies in the unclear input output property of a linear networked system containing communication delays and the unclear convergent property of this system under an external input we establish a new input output property of this linear networked system and moreover its convergent property under an external input upon which we establish a unified framework to resolve the consensus problem of multiple mechanical systems the proposed consensus framework unifies extends the existing results and in addition yields a fully cascaded closed loop system with lyapunov like analysis and frequency domain input output analysis we show that the proposed unified consensus control scheme ensures consensus without the integral action of the sliding vector and scaled weighted average consensus with the integral action of the sliding vector simulation results are provided to demonstrate the performance of the proposed consensus schemes

average consensus in networks of multi agents with both switching topology and coupling time delay abstract this paper is devoted to the study of the average consensus problem in directed networks of agents with both switching topology and time delay the stability analysis is performed based on a proposed lyapunov krasovskii function sufficient conditions in terms of linear matrix inequalities lmis are given to guarantee the average consensus under arbitrary switching of the network topology even if the time delay is time varying numerical simulations show the effectiveness of our theoretical results

unknown inputs functional observers designs for delay descriptor systems new time and frequency domain designs of unknown inputs functional observers uifo for a class of descriptor systems with a constant time delay are investigated in this paper the unknown inputs are present in both the state and the measurement equations the time procedure design is based on the unbiasedness of the estimation error and the lyapunov krasovskii stability theory after given the existence condition of such observers the gain implemented in the functional observer with internal delay design is obtained in terms of linear matrix inequalities the particular cases where the observer is independent of internal delay and where it is independent of delay are also investigated a design algorithm that summarises the different steps of the uifo design is proposed then the frequency procedure design is derived from time domain results by applying the factorisation approach where we define some useful matrix fraction descriptions note that the order of this unknown input observers is equal to

consensus protocol for multiple delta operator systems abstract this paper considers the consensus problem for multiple delta operator systems the delta operator system is used for describing continuous time processes at rapid rate sampling moreover it has been known to have a better model description than that of shift operator based approach in this work the consensus problem is first solved for multiple delta operator systems by using a distributed protocol to achieve consensus several important sufficient conditions are proposed for the fast sampling systems based on the parameters of sampling period and consensus strength in addition two distributed consensus protocols are constructed for both leaderless multiple delta operator systems and leader follower multiple delta operator systems finally the effectiveness of the theoretical analysis is illustrated by applying distributed consensus protocol to multi agent systems

synchronization of networks of nonidentical euler lagrange systems with uncertain parameters and communication delays this paper addresses the problem of synchronizing networks of nonidentical nonlinear dynamical systems described by euler lagrange equations which are assumed fully actuated with their states available for measurement but with unknown parameters the only assumption made on the communication graph is that it is connected moreover the communication is subject to constant time delays which are also unknown the main result of the paper is the construction of an adaptive controller that achieves global full state synchronization i e the difference between the agents positions and velocities asymptotically converges to zero if a desired trajectory for all systems is given a slight modification to the proposed scheme achieves also full state synchronization simulations using a ten robot manipulator network are used to illustrate the performance of the proposed schemes

high order sliding mode observer for linear systems with unbounded unknown inputs a global observer is designed for strongly detectable systems with unbounded unknown inputs the design of the observer is based on three steps first the system is extended taking the unknown inputs and possibly some of their derivatives as a new state then using a global high order sliding mode differentiator a new output of the system is generated in order to fulfil what we will call the hautus condition which finally allows decomposing the system in new coordinates into two subsystems the first one being unaffected directly by the unknown inputs and the state vector of the second subsystem is obtained directly from the original system output such decomposition permits designing of a luenberger observer for the first subsystem which satisfies the hautus condition i e all the outputs have relative degree one w r t the unknown inputs this procedure enables one to estimate the state and the unknown inputs using the least number of differentiations possible simulations are given in order to show the effectiveness of the proposed observer

unknown input proportional multiple integral observer design for linear descriptor systems application to state and fault estimation in this note the problem of observer design for linear descriptor systems with faults and unknown inputs is considered first it is considered that the fault vector function f is s times piecewise continuously differentiable if the s th time derivative of f is null then s integral actions are included into a luenberger observer which is designed such that it estimates simultaneously the state the fault and its finite derivatives face to unknown inputs second when the fault is not time piecewise continuously differentiable but bounded like actuator noise or s th time derivative of fault is not null but bounded too a high gain observer is derived to attenuate the fault impact in estimation errors the considered faults may be unbounded may not be determinist and faults and unknown inputs may affect the state dynamic and plant outputs sufficient conditions for the existence of such observer are given results are illustrated with a differential algebraic power system

design of observers for descriptor systems in this note simple and straightforward methods to design full and reduced order observers for linear time invariant descriptor systems are presented the approach for the reduced order observer design is based on the generalized sylvester equation sufficient conditions for the existence of the observers are given an illustrative example is included

observability and related structural results for linear hereditary systems new results on the theory of observability and deterministic observers for linear time invariant systems with delays are presented the results have been established only for the case of point delays which are commensurable however most of the results can be generalized to the situation with distributed delays and to the ease with non commensurate delays

observability of linear systems with commensurate delays and unknown inputs this paper investigates the observability analysis for linear time systems whose outputs are affected by unknown inputs three different definitions of observability are proposed by introducing the smith form and comparing the invariant factors a sufficient condition is deduced for each proposed definition observability several examples are given for the purpose of highlighting the effectiveness of the proposed approach

koszul duality patterns in representation theory the aim of this paper is to work out a concrete example as well as to provide the general pattern of applications of koszul duality to repre sentation theory the paper consists of three parts relatively independent of each other the first part gives a reasonably selfcontained introduction to koszul rings and koszul duality koszul rings are certain z graded rings with particularly nice homological properties which involve a kind of duality thus to a koszul ring one associates naturally the dual koszul ring the second part is devoted to an application to representation theory of semisimple lie algebras we show license or copyright restrictions may apply to redistribution see http www ams org journal terms of use koszul duality patterns 527 that the block of the bernstein gelfand gelfand category o that corresponds to any fixed central character is governed by the koszul ring moreover the dual of that ring governs a certain subcategory of the category o again this generalizes the selfduality theorem conjectured by beilinson and ginsburg in 1986 and proved by soergel in 1990 in the third part we study certain cate gories of mixed perverse sheaves on a variety stratified by affine linear spaces we provide a general criterion for such a category to be governed by a koszul ring in the flag variety case this reduces to the setup of part two in the more general case of affine flag manifolds and affine grassmannians the criterion should yield interesting results about representations of quantum groups and affine lie algebras department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address sasha math mit edu department of mathematics the university of chicago chicago illinois 60637 e mail address ginzburg math uchicago edu max planck institut fur mathematik gottfried claren strase 26 d 53 bonn 3 germany current address mathematisches institut universitat freiburg albertstrase 23b d 79104 freiburg germany e mail address soergel sun1 mathematik uni freiburg de license or copyright restrictions may apply to redistribution see http www ams org journal terms of use

disturbance decoupled observer design for descriptor systems in this paper we study the observer design problem for descriptor systems with partly unknown inputs we give necessary and sufficient conditions for the existence of a solution to the disturbance decoupled estimation problem with or without stable error spectrum requiring at the same time that the resulting combined system is regular and of index at most one all results are proved based on a condensed form that can be computed using orthogonal matrix transformations i e transformations that can be implemented in a numerically stable way

reduced order observer design for descriptor systems with unknown inputs a new method for the design of reduced order observers for descriptor systems with unknown inputs is presented the approach is based on the generalized constrained sylvester equation sufficient conditions for the existence of the observer are given

robust line fitting in a noisy image by the method of moments the standard least squared distance method of fitting a line to a set of data points is known to be unreliable when the random noise in the input is significant compared with the data correlated to the line itself here we present a new statistical clustering method based on legendre moment theory and maximum entropy principle for line fitting in a noisy image we propose a new approach for estimating the underlying probability density function p d f of the data set the p d f is expanded in terms of legendre polynomials by means of the legendre moments the order of the expansion is selected according to the maximum entropy principle then the points corresponding to the maxima of the p d f will be the true points of the line to be extracted by a chaining algorithm this approach is directly generalized to multidimensional data the proposed algorithm was successfully applied to real and simulated noisy line images with comparison to some well known methods

maximum entropy image reconstruction the authors justify the maximum entropy image reconstruction meir formulation proposed by zhuang et al 1987 solve an open problem of whether or not there exists a solution to the meir problem prove the fast convergence of the meir algorithm proposed by zhuang et al and show that the system of differential equations which is the basis of the meir algorithm is of the lyapunov type

state feedback impulse elimination for singular systems over a hermite domain we reduce the problem of impulse elimination via state feedback in singular differential equations to algebra our results are developed for systems over an arbitrary hermite domain we show that the established theories for the time invariant and the real analytic time varying settings can be unified in this way besides the constant and real analytic functions several other function rings are considered our algebraic theory is applied to these cases providing solutions to the impulse elimination problem for classes of systems not previously studied in particular our work allows the restriction of the feedback matrix to certain function rings

observability and detectability of singular linear systems with unknown inputs in this paper the strong observability and strong detectability of a general class of singular linear systems with unknown inputs are tackled the case when the matrix pencil is non regular is comprised i e more than one solution for the differential equation is allowed it is shown that under suitable assumptions the original problem can be studied by means of a regular non singular linear system with unknown inputs and algebraic constraints thus it is shown that for purposes of analysis the algebraic equations can be included as part of an extended system output based on this analysis we obtain necessary and sufficient conditions guaranteeing the observability or detectability of the system in terms of the zeros of the system matrix corresponding algebraic conditions are given in order to test the observability and detectability a formula is provided that expresses the state as high order derivative of a function of the output which allows for the reconstruction of the actual state vector it is shown that the unknown inputs may be reconstructed also

3 d moment forms their construction and application to object identification and positioning the 3 d moment method is applied to object identification and positioning a general theory of deriving 3 d moments invariants is proposed the notion of complex moments is introduced complex moments are defined as linear combinations of moments with complex coefficients and are collected into multiplets such that each multiplet transforms irreducibly under 3 d rotations the application of the 3 d moment method to motion estimation is also discussed using group theoretic techniques various invariant scalars are extracted from compounds of complex moments via clebsch gordon expansion twelve moment invariants consisting of the second order and third order moments are explicitly derived based on a perturbation formula it is shown that the second order moment invariants can be used to predict whether the estimation using noisy data is reliable or not the new derivation of vector forms also facilities the calculation of motion estimation in a tensor approach vectors consisting of the third order moments can be derived in a similar manner

brief paper state and input observability for structured linear systems a graph theoretic approach this paper deals with the state and input observability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure using a particular decomposition of the systems into two subsystems we express in simple graphic terms necessary and sufficient conditions for the generic state and input observability these conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph therefore our approach is suited to study large scale systems

solutions of differential algebraic equations as outputs of lti systems application to lq control problems abstract in this paper we propose a unified geometric framework for representing all solutions of a linear time invariant differential algebraic equation dae lti as outputs of classical linear time invariant ordinary differential equations ode lti the proposed framework is then used to solve an lq optimal control problem for dae ltis with rectangular matrices

robust clustering with applications in computer vision a clustering algorithm based on the minimum volume ellipsoid mve robust estimator is proposed the mve estimator identifies the least volume region containing h percent of the data points the clustering algorithm iteratively partitions the space into clusters without prior information about their number at each iteration the mve estimator is applied several times with values of h decreasing from 0 5 a cluster is hypothesized for each ellipsoid the shapes of these clusters are compared with shapes corresponding to a known unimodal distribution by the kolmogorov smirnov test the best fitting cluster is then removed from the space and a new iteration starts constrained random sampling keeps the computation low the clustering algorithm was successfully applied to several computer vision problems formulated in the feature space paradigm multithresholding of gray level images analysis of the hough space and range image segmentation

robust estimation for range image segmentation and reconstruction this correspondence presents a segmentation and fitting method using a new robust estimation technique we present a robust estimation method with high breakdown point which can tolerate more than 80 of outliers the method randomly samples appropriate range image points in the current processing region and solves equations determined by these points for parameters of selected primitive type from k samples we choose one set of sample points that determines a best fit equation for the largest homogeneous surface patch in the region this choice is made by measuring a residual consensus resc using a compressed histogram method which is effective at various noise levels after we get the best fit surface parameters the surface patch can be segmented from the region and the process is repeated until no pixel left the method segments the range image into planar and quadratic surfaces the resc method is a substantial improvement over the least median squares method by using histogram approach to inferring residual consensus a genetic algorithm is also incorporated to accelerate the random search

on image analysis by moments research has been performed investigating the use of moments for pattern recognition in recent years the basic problem of the influence of discretization and noise on moment accuracy as object descriptors has been barely investigated in this paper the detailed error analysis involved in the moment method is discussed several new techniques to increase the accuracy and efficiency of moment descriptor are proposed we utilize these results for the problem of image reconstruction from the orthogonal legendre moments computed from discrete and noisy data the automatic selection of an optimal number of moments is also discussed

observer design for linear singular time delay systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state and its derivatives the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantees the existence of a luenberger like observer for the general system

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

exact legendre moment computation for gray level images a novel method is proposed for exact legendre moment computation for gray level images a recurrence formula is used to compute exact values of moments by mathematically integrating the legendre polynomials over digital image pixels this method removes the numerical approximation errors involved in conventional methods a fast algorithm is proposed to accelerate the moment s computations a comparison with other conventional methods is performed the obtained results explain the superiority of the proposed method

a family of koszul algebras arising from finite dimensional representations of simple lie algebras abstract let g be a finite dimensional simple lie algebra and let s g be the locally finite part of the algebra of invariants end c v s g g where v is the direct sum of all simple finite dimensional modules for g and s g is the symmetric algebra of g given an integral weight let be the subset of roots which have maximal scalar product with given a dominant integral weight and such that is a subset of the positive roots we construct a finite dimensional subalgebra s g of s g and prove that the algebra is koszul of global dimension at most the cardinality of using this we construct naturally an infinite dimensional non commutative koszul algebra of global dimension equal to the cardinality of the results and the methods are motivated by the study of the category of finite dimensional representations of the affine and quantum affine algebras

unknown input functional observability of descriptor systems with neutral and distributed delay effects in this paper a general class of linear systems with time delays is considered which includes linear classical systems linear systems with commensurate delays neutral systems and singular systems with delays after given a formal definition of functional backward observability bo an easily testable condition is found the fulfillment of the obtained condition allows for the reconstruction of the trajectories of the system under consideration using the actual and past values of the system output and some of its derivatives the methodology we follow consists in an iterative algorithm based upon the classical silverman algorithm used for inversion of linear systems by using basic module theory we manage to prove that the proposed algorithm is convergent a direct application of studying functional observability is that a condition can be derived for systems with distributed delays also we do this as a case of study the obtained results are illustrated by two examples one is merely academic but illustrates clearly the kind of systems which the proposed methodology works for and the other is a practical system with distributed delays

on image analysis by the methods of moments various types of moments have been used to recognize image patterns in a number of applications a number of moments are evaluated and some fundamental questions are addressed such as image representation ability noise sensitivity and information redundancy moments considered include regular moments legendre moments zernike moments pseudo zernike moments rotational moments and complex moments properties of these moments are examined in detail and the interrelationships among them are discussed both theoretical and experimental results are presented

observers for singular systems the following three major aspects of the design of observers for linear time invariant singular systems are resolved the necessary and sufficient conditions for the problem to have a solution the order of the minimal observer and the properties of the closed loop system separation principle an algorithm is presented for the construction of the minimal order observer

on the strong observability in linear time varying singular systems abstract in this article the strong observability conditions necessary and sufficient conditions originally stated for the state reconstruction of linear systems with unknown inputs are extended to the class of linear time varying singular systems this novel local in a time interval of interest conditions are given under a constant rank assumption a method to reconstruct the state in finite time in linear time varying singular systems despite the presence of unknown inputs is presented the proposed observer consists of two parts one part that ensures the asymptotic convergence of the estimation errors to a bounded region around the origin and another one that ensures the finite time convergence of the state estimates to their actual values

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

interval observer for a class of uncertain nonlinear singular systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantee the existence of a luenberger like observer for the general system

translation and scale invariants of legendre moments abstract by convention the translation and scale invariant functions of legendre moments are achieved by using a combination of the corresponding invariants of geometric moments they can also be accomplished by normalizing the translated and or scaled images using complex or geometric moments however the derivation of these functions is not based on legendre polynomials this is mainly due to the fact that it is difficult to extract a common displacement or scale factor from legendre polynomials in this paper we introduce a new set of translation and scale invariants of legendre moments based on legendre polynomials the descriptors remain unchanged for translated elongated contracted and reflected non symmetrical as well as symmetrical images the problems associated with the vanishing of odd order legendre moments of symmetrical images are resolved the performance of the proposed descriptors is experimentally confirmed using a set of binary english chinese and latin characters in addition to this a comparison of computational speed between the proposed descriptors and the aforesaid geometric moments based method is also presented

observer design for generalized state space systems with unknown inputs abstract the following four major aspects for the observer design problem for generalized state space systems with unknown inputs are resolved necessary and sufficient conditions for the problem to have a solution the order of the minimal observer the properties of the closed loop system separation principle and general analytical expressions of the minimal order observer matrices all above results are first in the field

fully distributed flocking with a moving leader for lagrange networks with parametric uncertainties this paper addresses the leader follower flocking problem with a moving leader for networked lagrange systems with parametric uncertainties under a proximity graph here a group of followers move cohesively with the moving leader to maintain connectivity and avoid collisions for all time and also eventually achieve velocity matching in the proximity graph the neighbor relationship is defined according to the relative distance between each pair of agents each follower is able to obtain information from only the neighbors in its proximity involving only local interaction we consider two cases i the leader moves with a constant velocity and ii the leader moves with a varying velocity in the first case a distributed continuous adaptive control algorithm accounting for unknown parameters is proposed in combination with a distributed continuous estimator for each follower in the second case a distributed discontinuous adaptive control algorithm and estimator are proposed then the algorithm is extended to be fully distributed with the introduction of gain adaptation laws in all proposed algorithms only one hop neighbors information e g the relative position and velocity measurements between the neighbors and the absolute position and velocity measurements is required and flocking is achieved as long as the connectivity and collision avoidance are ensured at the initial time and the control gains are designed properly numerical simulations are presented to illustrate the theoretical results

what s in a set of points straight line fitting the problem of fitting a straight line to a planar set of points is reconsidered a parameter space computational approach capable of fitting one or more lines to a set of points is presented the suggested algorithm handles errors in both coordinates of the data points even when the error variances vary between coordinates and among points and can be readily made robust to outliers the algorithm is quite general and allows line fitting according to several useful optimality criteria to be performed within a single computational framework it is observed that certain extensions of the hough transform can be turned to be equivalent to well known m estimators thus allowing computationally efficient approximate m estimation

a least biased fuzzy clustering method a new operational definition of cluster is proposed and a fuzzy clustering algorithm with minimal biases is formulated by making use of the maximum entropy principle to maximize the entropy of the centroids with respect to the data points clustering entropy the authors make no assumptions on the number of clusters or their initial positions for each value of an adimensional scale parameter spl beta the clustering algorithm makes each data point iterate towards one of the cluster s centroids so that both hard and fuzzy partitions are obtained since the clustering algorithm can make a multiscale analysis of the given data set one can obtain both hierarchy and partitioning type clustering the relative stability with respect to spl beta of each cluster structure is defined as the measurement of cluster validity the authors determine the specific value of spl beta which corresponds to the optimal positions of cluster centroids by minimizing the entropy of the data points with respect to the centroids clustered entropy examples are given to show how this least biased method succeeds in getting perceptually correct clustering results

an efficient method for the computation of legendre moments legendre moments are continuous moments hence when applied to discrete space images numerical approximation is involved and error occurs this paper proposes a method to compute the exact values of the moments by mathematically integrating the legendre polynomials over the corresponding intervals of the image pixels experimental results show that the values obtained match those calculated theoretically and the image reconstructed from these moments have lower error than that of the conventional methods for the same order although the same set of exact legendre moments can be obtained indirectly from the set of geometric moments the computation time taken is much longer than the proposed method

delay robustness in consensus problems we investigate the robustness of consensus schemes for linear multi agent systems mas to feedback delays to achieve this we develop a unified framework that considers linear mas models with different feedback delays e g affecting only the neighbor s output or affecting both the agent s own and its neighbors output this framework has the advantage of providing scalable simple and accurate set valued conditions for consensus using these set valued conditions previous results on consensus in mas with delays can be recovered and generalized moreover we use them to derive conditions for the convergence rate of single integrator mas with feedback delays finally building on this framework we propose a scalable delay dependent design algorithm for consensus controllers for a large class of linear mas

category o for the schrodinger algebra we study category o for the centrally extended schrodinger algebra we determine the quivers for all blocks and relations for blocks of nonzero central charge we also describe the quiver and rel

quivers with relations arising from koszul algebras of g invariants abstract let g be a complex simple lie algebra and let be an extremal set of positive roots after chari and greenstein 2009 9 one associates with an infinite dimensional koszul algebra s g which is a graded subalgebra of the locally finite part of end v op s g g where v is the direct sum of all simple finite dimensional g modules we describe the structure of the algebra s g explicitly in terms of an infinite quiver with relations for g of types a and c we also describe several infinite families of quivers and finite dimensional associative algebras arising from this construction