on the observer design for descriptor systems for the descriptor system ex ax bu y cx du an observer of the order p rank e p sub 1 0

eta invariants torsion forms and flat vector bundles we present a new proof as well as a c q extension and also certain c z extension of the riemann roch grothendieck theorem of bismut lott for flat vector bundles the main techniques used are the computations of the adiabatic limits of invariants associated to the so called sub signature operators we further show that the bismut lott analytic torsion form can be derived naturally from transgressions of forms appearing in the adiabatic limit computations

algebraic cycles and higher k theory here g x is the grothendieck group of coherent sheaves on x 13 gr refers to the graded group defined by the y filtration on g x cf kratzer 14 soult 20 and ch x is the chow group of codimension i algebraic cycles defined by fulton 9 the left hand isomorphism is a formal consequence of the existence of a i structure on g x while the existence of r is the central theme of the b f m rr theorem the main purpose of this paper is to define a theory of higher chow groups ch x n n 2 0 so as to obtain isomorphisms

periods for irregular singular connections on surfaces given an integrable connection on a smooth quasi projective algebraic surface u over a subfield k of the complex numbers we define rapid decay homology groups with respect to the associated analytic connection which pair with the algebraic de rham cohomology in terms of period integrals these homology groups generalize the analogous groups in the same situation over curves defined by bloch and esnault in dimension two however new features appear in this context which we explain in detail assuming a conjecture of sabbah on the formal classification of meromorphic connections on surfaces known to be true if the rank is lower than or equal to 5 we prove perfectness of the period pairing in dimension two

controllability analysis and eigenvalue assignment for generalized state space systems abstract an extended hessenberg triangular form is introduced as a tool for the controllability analysis of linear descriptor generalized state space systems the extended hessenberg triangular form may be applied to the multiple input eigenvalue placement via state feedback with the advantage that the number of eigenvalues that have to be assigned with each input may be decided only unitary transformations that lead to numerical stability are applied to the systems the assignment of the eigenvalues to both finite or infinite positions is considered

an improved algorithm for the computation of kronecker s canonical form of a singular pencil we give an 0 t algorithm for computing the kronecker structure of an arbitrary m x n pencil xe a the algorithm is shown to he numerically stable because only unitary transformations are used the improved speed over earlier unitary methods is due to the efficient use of condensed forms which are maintained throughout the recursions of the algorithm

design of a class of luenberger observers for descriptor systems a new approach to the design of a class of luenberger observers for descriptor systems is presented the design is performed in a straightforward manner the conditions required in the design are given in terms of the original system matrices the relationship among these and other well known conditions is highlighted

period determinant of an irregular connection over an elliptic curve abstract in this article we calculate the period of an irregular singular connection d d y on the legendre curve u y 2 x x 1 x we calculate its de rham cohomology and the cycles in the homology of the dual connection and describe the period matrix terasoma s work is introduced to approximate the direct image connection by a sequence of regular connections as an intermediate step where u a 1 spec k y x y y finally we will make the comparison of the period obtained by this approximation and that over u

geometric structure and feedback in singular systems the output nulling a e r b invariant subspaces are defined for singular systems rigorously justifying the name and demonstrating that special cases of these geometric objects are the familiar subspace of admissible conditions and the supremal a e r b invariant subspace a novel singular system structure algorithm is used to compute them by numerically efficient means their importance for describing the possible closed loop geometric structure in terms of the open loop geometric structure is shown an approach to spectrum assignment in singular systems that is based on a generalized lyapunov equation is introduced the equation is used to compute feedback gains to place poles and assign various closed loop invariant subspaces while guaranteeing closed loop regularity

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

a riemann roch theorem for flat bundles with values in the algebraic chern simons theory our purpose in this paper is to continue the algebraic study of complex local systems on complex algebraic varieties we prove a riemann roch theorem for these objects using algebraic chern simons characteristic classes a complex local system e on a smooth projective complex variety x gives rise to a locally free analytic sheaf ean e c oan x which using gaga admits a canonical algebraic structure e the tautological analytic connection on e co x induces an integrable algebraic connection e e x combining gaga with the poincare lemma we see that the analytic cohomology of the local system can be identified with the hypercohomology of the algebraic de rham complex

periods of hodge structures and special values of the gamma function at the end of the 1970s gross and deligne conjectured that periods of geometric hodge structures with multiplication by an abelian number field are products of values of the gamma function at rational arguments with exponents determined by the hodge decomposition we prove an alternating variant of this conjecture for smooth projective varieties acted upon by an automorphism of finite order thus improving previous results of maillot and rossler the proof relies on a product formula for periods of regular singular connections due to saito and terasoma

perfect observers for singular 2 d fornasini marchesini models a concept of the perfect observer for singular two dimensional 2 d fornasini marchesini models is proposed sufficient conditions are established for the existence of the perfect observer a procedure for design of the perfect observer is also derived and illustrated by a numerical example

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

transmission zero assignment using semistate descriptions the problem of finite infinite transmission zero assignment is examined by squaring a system from the outputs to the inputs in particular this problem is studied in two cases state accessible systems and partially state accessible systems it is shown that the problem of transmission zero assignment for state accessible state variable systems is equivalent to a pole placement problem with state feedback for a generalized system which always has a solution in the case of partially state accessible systems it is shown that the transmission zero assignment problem is equivalent to a pole placement problem with output feedback for a generalized system in both cases the block hessenberg form of the system and the extended lower triangular hessenberg form are exploited to formulate the problem

a geometric theory for derivative feedback the authors use a singular system setting to provide a geometric theory for dynamical systems under derivative feedback they define the relevant subspace and provide computational design techniques in terms of a generalized sylvester or lyapunov equation for which efficient solution techniques are well known the authors provide both geometric and algebraic characterizations of the effects of derivative feedback drawing connections with previous work in state variable systems as well as extending that work to singular systems

periods for flat algebraic connections in previous work hien math ann 337 631 669 2007 we established a duality between the algebraic de rham cohomology of a flat algebraic connection on a smooth quasi projective surface over the complex numbers and the rapid decay homology of the dual connection relying on a conjecture by c sabbah in the present article we generalize this result to arbitrary dimensions unconditionally using recent results of t mochizuki

deligne s conjecture on 1 motives we reformulate a conjecture of deligne on 1 motives by using the integral weight filtration of gillet and soule on cohomology and prove it this implies the original conjecture up to isogeny if the degree of cohomology is at most two we can prove the conjecture for the hodge realization without isogeny and even for 1 motives with torsion

gersten s conjecture for thek theory with torsion coefficients of a discrete valuation ring between quillen k groups induced by the obvious inclusion functors are all zero in 6 quillen proved this conjecture if r is essentially of finite type over a field in the case of discrete valuation rings this conjecture reduces to conjecture let r be a discrete valuation ring with residue field k and field of fractions f then for all q z 0 the transfer map which is defined since every k vector space is of finite projective dimension as an r module k k k r is zero equivalently the map r ec f induced by the ring homomorphism r p f is injective a third equivalent formulation is that the boundary map

on the reduced order causal observer for generalized control systems abstract this paper considers the problem of a causal state observer for a square singular system necessary and sufficient conditions for solvability of the problem have been established the approach of this study leads to a new insight concerning synthesis of a causal observer and establishes new results with regard to the structure and the dimension of a reduced order observer for singular systems

gauss manin determinants for rank 1 irregular connections on curves let f u to rm spec k be a smooth open curve over a field k supset k where k is an algebraically closed field of characteristic 0 let nabla l to l otimes omega 1 u k be a possibly irregular absolutely integrable connection on a line bundle l a formula is given for the determinant of de rham cohomology with its gaus manin connection big det rf l otimes omega 1 u k det nabla gm big the formula is expressed as a norm from the curve of a cocycle with values in a complex defining algebraic differential characters 7 and this cocycle is shown to exist for connections of arbitrary rank

adelic chern forms and applications let x be a variety over a field of characteristic 0 given a vector bundle e on x we construct chern forms c v t x ax here a x is the sheaf of beilinson adeles and v is an adelic connection when x is smooth wt x a x h r x the algebraic de rham cohomology and c q v are the usual chern classes we include three applications of the construction 1 existence of adelic secondary chern simons characteristic classes on any smooth x and any vector bundle e 2 proof of the bott residue formula for a vector field action and 3 proof of a gauss bonnet formula on the level of differential forms namely in the de rham residue complex 0 introduction let x be a scheme of finite type over a field k according to beilinson be given any quasi coherent x module m and an integer q9 there is a flasque ox module a dcm called the sheaf of adeles this is a gen eralization of the classical adeles of number theory cf example 2 3 moreover there are homomorphisms d aj ed m a m which make ared m into a complex and m ared m is quasi isomorphism now let qx be the algebra of kahler differential forms on x in hy we proved that the sheaf

boundedness of completely additive measures with application to 2 local triple derivations we prove a jordan version of dorofeev s boundedness theorem for completely additive measures and use it to show that every not necessarily linear nor continuous 2 local triple derivation on a continuous jbw triple is a triple derivation 2 local triple derivations are well understood on von neumann algebras jbw triples which are properly defined in section i are intimately related to infinite dimensional holomorphy and include von neumann algebras as special cases in particular continuous jbw triples can be realized as subspaces of continuous von neumann algebras which are stable for the triple product xy z zy x and closed in the weak operator topology

state feedback design using reduced order nonsquare descriptions a pole placement technique is proposed for computing state feedback in multi input linear systems the algorithm has good numerical behavior and utilizes nonsquare pencils and the notion of decomposability the fact that the method deals with reduced order pencils and exploits the schur hessenberg form improves the conditioning of the problem

a new proof of the existence of traces on jordan operator algebras and real von neumann algebras abstract in this paper we show that a jw algebra is modular if and only if it admits a separating family of finite normal traces the proof does not follow the von neumann algebras case but is based on the finiteness of the enveloping von neumann algebra for a reversible modular jw algebra for a locally modular jw algebra the existence of a faithful semifinite normal trace is proved similar results are obtained for respectively finite and semifinite real von neumann algebras

observers for descriptor systems for a singular non causal descriptor system of order n a p k lh order observer is proposed where p n q q is the number of infinite non dynamic modes of the system and k is the rank of a matrix obtained from a transformed system derived by using the singular value decomposition some useful results are given which establish the existence of this observer and which resolve problems encountered with pth order observers proposed in the literature robustness is achieved by choosing optimum gain matrices which reduce the sensitivity of observer performance to perturbations

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

the geisser levine method revisited and algebraic cycles over a finite field we reformulate part of the arguments of t geisser and m levine relating motivic cohomology with finite coefficients to truncated etale cohomology with finite coefficients 9 10 this reformulation amounts to a uniqueness theorem for motivic cohomology and shows that the geisser levine method can be applied generally to compare motivic cohomology with other types of cohomology theories we apply this to prove an equivalence between conjectures of tate and beilinson on cycles in characteristic p and a vanishing conjecture for continuous etale cohomology

design of proportional integral observer for unknown input descriptor systems this note presents simple methods to design full and reduced order proportional integral observer for unknown inputs ui descriptor systems sufficient conditions for the existence of the observer are given and proven the observer is solvable by any pole placement algorithm it achieves a posteriori robustness state and ui estimation versus to time varying parameters and bounded nonlinear ui an illustrative example is included

duality via cycle complexes we show that bloch s complex of relative zero cycles can be used as a dualizing complex over perfect fields and number rings this leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields finite fields local fields of mixed characteristic and rings of integers in number rings generalizing results which so far have only been known for smooth schemes or in low dimensions and unifying the p adic and l adic theory as an application we generalize rojtman s theorem to normal projective schemes

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

on the solution to the sylvester matrix equation av bw evf a simple direct complete and explicit parametric solution of the generalized sylvester matrix equation av bw evf is proposed for matrix f in the jordan form with arbitrary eigenvalues using the smith canonical form of the matrix a se b the obtained solution is in a clear neat form and may have important applications in descriptor linear system theory

solution to matrix equation av bw evf and eigenstructure assignment for descriptor systems a simple complete analytical restriction free parametric solution with complete and explicit freedom of matrix equation av bw evf is presented based on the presented solution of this equation an approach for eigenstructure assignment for continuous descriptor system ex ax bu via descriptor variable feedback u kx is proposed parametric forms of the gain matrix and the eigenvectors associated with the assigned finite closed loop eigenvalues are given the approach is shown to be better than that of fahmy and o reilly 1989 int j contr 49 129 143 in the sense that it not only possesses the functions of the approach of fahmy and o reilly 1989 int j contr 49 129 143 but also has the following three advantages 1 it eliminates the requirements on the assigned finite closed loop poles 2 it provides more design parameters and 3 it needs less computational work

geometric design techniques for observers in singular systems abstract we present geometric design techniques for observer design in generalized state space or singular systems the unknown input conditioned invariant subspaces are defined for singular systems and are related to the solution of a generalized lyapunov equation the approach emphasizes solution procedures based on the lyapunov equation and a singular system structure algorithm this paper extends the singular system observer theory both by providing a geometric basis for it and showing the best that may be accomplished if the system is not observable

a relation between the parabolic chern characters of the de rham bundles in this paper we consider the weight i de rham gauss manin bundles on a smooth variety arising from a smooth projective morphism f x u longrightarrow u for i geq 0 we associate to each weight i de rham bundle a certain parabolic bundle on s and consider their parabolic chern characters in the rational chow groups for a good compactification s of u we show the triviality of the alternating sum of these parabolic bundles in the positive degree rational chow groups this removes the hypothesis of semistable reduction in the original result of this kind due to esnault and viehweg

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

chained aggregation of singular systems extends the notion of aggregation to singular systems se a necessary and sufficient conditions for complete aggregability are given which reduce in the state space case e i to aoki s conditions a geometric quotient space analysis is given which uses a new result on the pencil induced in the quotient space by a regular matrix pencil a generalized chained aggregation algorithm is used to put the system into a hessenberg form which provides a reduced order model for the output dynamics it is shown that as in the state space situation chained aggregation corresponds to removal of the unobservable subspace it is also pointed out that the usual state space chained aggregation algorithm is very efficient and numerically unstable specializing the singular system chained aggregation algorithm to the state space case yields a better and more streamlined approach

observers for descriptor systems abstract the design of observers is investigated for the estimation of the descriptor vector x t of descriptor systems of the form ex t ax t bu t y t cx t such systems are divided into two categories non causal impulsive systems and causal impulse free systems for non causal systems an observer of order rank e is proposed and termed a full order observer since the dynamical order of a descriptor system is regarded as rank e for causal systems it is shown that the number of independent outputs m does not exceed rank e and an observer of order rank e m is introduced and termed a minimal order observer the approach is based on the transformation of the system into particular design coordinates via a singular value decomposition of the matrix e illustrative examples are included

riemann roch for equivariant k theory abstract we show that for a linear algebraic group g acting on a smooth quasi projective scheme x over a field there is a chern character map k i g x r g r g c h x g ch g x i s g s g with rational coefficients which is an isomorphism this establishes the equivariant version of the riemann roch isomorphism between the higher algebraic k theory and the higher chow groups of smooth quasi projective schemes

a simple procedure for the stabilization of a class of uncontrollable generalized systems this paper gives a simple procedure for the stabilization with a prescribed rate of convergence of the free motions of a class of possibly single input uncontrollable generalized continuous time time invariant linear systems preserving the impulse free property if any

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

remarks on observability of implicit linear discrete time systems abstract some results concerning the observability of implicit linear discrete time systems of the form exk 1 fxk yk hxk are presented it is not assumed that the corresponding pencil se f is regular the concept of reachability with pulse introduced in this paper is shown to be dual to the notion of observability

reduced order observers a new algorithm and proof this paper gives a new recursive algorithm to construct a reduced order observer with prescribed spectrum of a given observable system the method is based on the staircase form and implicitly gives a new proof for the existence of such reduced order observers

voevodsky s motives and weil reciprocity we describe somekawa s k group associated to a finite collection of semiabelian varieties or more general sheaves in terms of the tensor product in voevodsky s category of motives while somekawa s definition is based on weil reciprocity voevodsky s category is based on homotopy invariance we apply this to explicit descriptions of certain algebraic cycles

properties of numerical algorithms related to computing controllability the numerical properties of some methods for computing controllability are used in an expository way to motivate a wider understanding of numerical computations in particular the numerical rank of a matrix the numerical stability of algorithms the sensitivity of problems and the scaling of problems are discussed a numerically stable algorithm is given for computing controllability but it is pointed out that a measure of the distance of the given system from the nearest uncontrollable system would be more useful and this appears to be an open computational problem

design of reduced order interval observers for lti systems with bounded time varying disturbances a parametric approach this paper investigates the design problem of reduced order interval observers for linear time invariant systems with bounded time varying disturbances although there are many excellent design met

generalized functional observer a functional observer and state feedback are proposed for singular systems in the polynomial fraction form that requires no impulsive mode elimination the order of the compensator is determined by the newly defined generalized observability index that is associated with the mcmillan degree of the system a new generalized lyapunov equation is also proposed through a realization scheme that can be applied to both ordinary and singular systems the solution to the equation provides an algebraic approach to the observer of singular systems in the generalized state space form

a reduced order observer for descriptor systems abstract in this paper a reducer order observer is analyzed for so called generalized state space or descriptor systems based on the staircase form for generalized state space models a recursive algorithm is presented to construct a reduced order observer for a given observable descriptor system in the algorithm only the eigenfrequencies of the observer have to be specified

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

motives of reductive groups our aim is to prove that the geometric motive with rational coefficients of a split reductive group g over a perfect field decomposes as the symmetric co algebra object of certain split mixed tate motives which are computable in terms of the root data of g moreover the isomorphism respects the hopf algebra structures in a weight graded sense we will also provide explicit decompositions in the case of classical groups

on the solution of a sylvester equation appearing in descriptor systems control theory the solution of a generalized sylvester equation associated to a linear descriptor system and subject to some rank and regional pole placement constraints is studied in this paper under the hypothesis of strong detectability of the descriptor system a sequence of coordinate transformations is proposed such that the considered problem can be solved through a sylvester equation associated to a detectable reduced order normal system thus solutions to this equation can be found either by eigenstructure assignment or by regional pole placement in lmi type regions of the complex plane the proposed results are motivated from its use for designing minimal order observers and for computing output feedback control laws by a particular technique some numerical results are reported and possible extensions for the proposed approach are commented

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

character sums associated to finite coxeter groups we prove a character sum identity for coxeter arrangements which is a finite field analogue of macdonald s conjecture proved by opdam

observers for discrete singular systems the author considers the design of observers for the discrete singular system ex k 1 ax k bu k y k cx k placing special emphasis on the problems of state reconstruction and minimal time state reconstruction it is shown that for a singular system finite poles can be moved to infinity by state feedback and the state can be reconstructed by causal observers

comments on on the robust popov criterion for interval lur e systems this paper supplements the remarks made in a paper by dahleh et al ieee trans automat contr vol 38 p 1400 5 1993 regarding the popov sector of lur e systems with interval plants a numerical example is provided to show that strict inequalities hold among three sectors those obtained by the theorem of the paper by applying popov theorem to each member system and by applying that to each of the systems with kharitonov plants this counterexample negates a tempting conjecture on strong robust popov criterion

a geometric approach to proportional plus derivative feedback using quotient and partitioned subspaces abstract in this paper a new characterization of invariant subspaces is presented using the notions of partitioned and quotient subspaces this classification is based on a feedback approach that exhibits the importance of these subspaces for the problem of proportional plus derivative feedback it also provides the ability to decompose the closed loop system into two subsystems that completely characterize the closed loop behavior a feedback free formulation is also considered which opens new horizons for the problem of general semistate feedback by utilizing nonsquare pencils for spectrum assignability the importance of this technique arises from the fact that we deal with reduced order pencils therefore the computational methods are more stable in order to accomplish this we use two generalized lyapunov equations and exploit the generalized hessenberg form

algebraic chern simons theory a theory of secondary characteristic classes analogous to the classical chern simons theory is developed for algebraic vector bundles applications are made to questions involving finer charcterisitic classes for bundles with connection and to the griffiths group of algebraic cycles

noether lefschetz locus for beilinson hodge cycles i we discuss the noether lefschetz locus for beilinson s hodge cycles here beilinson s hodge cycles mean the cohomology class of bloch s higher chow cycles on smooth varieties the main result is to give an estimate of the dimension of the maximal component of the noether lefschetz locus for the universal family of open complete intersections