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

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

observability of structured linear systems in descriptor form a graph theoretic approach this paper deals with the right hand side observability of structured linear systems in descriptor form the method we propose is based on a graph theoretic approach it is applicable to a large class of descriptor systems including regular and nonregular systems even if they are square underdetermined or overdetermined after defining digraphs which represent such systems we express in graphic terms necessary and sufficient conditions to achieve the observability of the whole or of a given part of the state these conditions are easy to check because they are based on comparison of integers and on finding edges and subgraphs in a digraph therefore our approach is suited to study large scale and or uncertain systems

an operator valued t1 theory for symmetric czos abstract we provide a natural bmo criterion for the l 2 boundedness of calderon zygmund operators with operator valued kernels satisfying a symmetric property our arguments involve both classical and quantum probability theory in the appendix we give a proof of the l 2 boundedness of the commutators r j b whenever b belongs to the bourgain s vector valued bmo space where r j is the j th riesz transform a common ingredient is the operator valued haar multiplier studied by blasco and pott

a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

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

pseudo localization of singular integrals and noncommutative calderon zygmund theory abstract the weak type 1 1 boundedness of singular integrals acting on matrix valued functions has remained open since the 1980s mainly because the methods provided by the vector valued theory are not strong enough in fact we can also consider the action of generalized calderon zygmund operators on functions taking values in any other von neumann algebra our main tools for its solution are two first the lack of some classical inequalities in the noncommutative setting forces to have a deeper knowledge of how fast a singular integral decreases l 2 sense outside of the support of the function on which it acts this gives rise to a pseudo localization principle which is of independent interest even in the classical theory second we construct a noncommutative form of calderon zygmund decomposition by means of the recent theory of noncommutative martingales this is a corner stone in the theory as application we obtain the sharp asymptotic behavior of the constants for the strong l p inequalities also unknown up to now our methods settle some basics for a systematic study of a noncommutative calderon zygmund theory

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

an operator valued tb theorem we establish conditions similar to the tb theorem of david journe and semmes which guarantee the boundedness of an integral transformation t with l x valued kernel on lxp rn where 1 p and x is a banach space with the unconditionality property of martingale differences umd

pole assignment and observer design for continuous descriptor systems the problem of pole assignment and asymptotic observer design for multi input multi output continuous descriptor generalized state space systems is studied the problem is solved by introducing a new canonical form for controllable descriptor systems the internal stability of the descriptor variable feedback and observer configuration is also considered i e the extension of the separation principle to descriptor systems is given

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

multilinear singular integrals on non commutative l p spaces we prove l p bounds for the extensions of standard multilinear calderon zygmund operators to tuples of text umd spaces tied by a natural product structure the product can for instance mean the pointwise product in text umd function lattices or the composition of operators in the schatten von neumann subclass of the algebra of bounded operators on a hilbert space we do not require additional assumptions beyond text umd on each space in contrast to previous results we e g show that the rademacher maximal function property is not necessary the obtained generality allows for novel applications for instance we prove new versions of fractional leibniz rules via our results concerning the boundedness of multilinear singular integrals in non commutative l p spaces our proof techniques combine a novel scheme of induction on the multilinearity index with dyadic probabilistic techniques in the text umd space setting

solvability conditions consistency and weak consistency for linear differential algebraic equations and time invariant singular systems the general case we present several solvability concepts for linear differential algebraic equations daes with constant coefficients on the positive time axis as well as for the associated singular systems and investigate under which conditions these concepts are met next we derive necessary and sufficient conditions for global consistency of initial conditions for the dae as well as for the system and generalize these conditions with respect to our concept of weak consistency our distributional approach enables us to generalize results in an earlier paper where singular systems are assumed to have a regular pencil in the sense of gantmacher in particular we establish that global weak consistency in the system sense is equivalent to impulse controllability

γ bounded representations of amenable groups let g be an amenable group let x be a banach space and let g b x be a bounded representation we show that if the set t t g is bounded then extends to a bounded homomorphism w c g b x on the group c algebra of g moreover w is necessarily bounded this extends to the banach space setting a theorem of day and dixmier saying that any bounded representation of an amenable group on hilbert space is unitarizable we obtain additional results and complements when g z r or t and or when x has property

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

two graphs and skew two graphs in finite geometries abstract we describe the use of two graphs and skew oriented two graphs as isomorphism invariants for translation planes and m systems including ovoids and spreads of polar spaces in odd characteristic

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

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

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

twisted tensor product group embeddings and complete partial ovoids on quadrics in pg 2t 1 q abstract we study the geometry of the groups sl 2 qt and sp 2m qt m t 2 q even in their twisted tensor product representation we construct families of complete partial ovoids of hyperbolic quadrics in pg 2t 1 q all attaining the blokhuis moorhouse bound we identify the stabilizers of the complete partial ovoids

singular integral operators on triebel lizorkin spaces of para accretive type abstract in this article we study the boundedness of singular integral operators acting on triebel lizorkin spaces of para accretive type and show a tb theorem on these spaces which extends previous results in david journe and semmes 1985 3 han 1994 9 han lee and lin 2004 10 han and sawyer 1990 12 lin and wang 2009 15 wang 1999 22

impulsive modes and causality in singular systems the concepts of impulsive modes and causality in singular systems are considered their properties relations and applications are studied matrix rank criteria are presented thus all controllabilities and observabilities and related concepts have matrix rank criteria based on the original system coefficient matrices

on the design of observers for generalized state space systems using singular value decomposition in this paper a method is developed for the design of luenberger type observers for linear time invariant control systems whose state equation is of the form ex ax bu where e is a singular square matrix the method is based on the singular value decomposition of the matrix e and on the reduction of the equation ex ax bu to a system consisting of a differential equation of the form w1 f1w1 f2 w2 g1u and an algebraic equation of the form h1w1 h2w2 g1u 0 if w2 can be eliminated from the differential equation by the aid of the algebraic equation and the original output equation of the system the method yields a reduced order observer for the generalized state space system

on semi r boundedness and its applications abstract r boundedness is a randomized boundedness condition for sets of operators which in recent years has found many applications in the maximal regularity theory of evolution equations stochastic evolution equations spectral theory and vector valued harmonic analysis however in some situations additional geometric properties such as pisier s property are required to guaranty the r boundedness of a relevant set of operators in this paper we show that a weaker property called semi r boundedness can be used to avoid these geometric assumptions in the context of schauder decompositions and the h calculus furthermore we give weaker conditions for stochastic integrability of certain convolutions

brief paper jump modes analysis and observer design for discrete singular systems this paper is concerned with the reconstructability and detectability of the jump modes of discrete singular systems the notion of jump modes can be considered as the discrete counterpart of the impulsive modes of continuous singular systems which has been extensively studied the effect of jump modes on the existence of reduced order normal luenberger observers for discrete singular systems is investigated necessary and sufficient conditions for the existence of normal luenberger observers and the corresponding observer design procedure are obtained

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

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

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

operator valued fourier multiplier theorems on lp x and geometry of banach spaces abstract this paper gives the optimal order l of smoothness in the mihlin and hormander conditions for operator valued fourier multiplier theorems this optimal order l is determined by the geometry of the underlying banach spaces e g fourier type this requires a new approach to such multiplier theorems which in turn leads to rather weak assumptions formulated in terms of besov norms

operator valued fourier multiplier theorems and maximal l_p regularity we prove a mihlin type multiplier theorem for operator valued multiplier functions on umd spaces the essential assumption is r boundedness of the multiplier function as an application we give a characterization of maximal l p regularity for the generator of an analytic semigroup t t in terms of the r boundedness of the resolvent of a or the semigroup t t

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

design of observers for time varying discrete time descriptor systems in this note linear discrete time time varying descriptor systems i e control systems of the form ek 1 xk 1 akxk bkuk yk ckxk are considered where ek 1 and ak 1 are constant not necessarily square matrices the problem is to design a reduced order observer for the system using matrix generalized inverses and singular value decomposition a procedure is developed which either leads to a routine observer design problem involving an ordinary discrete time state equation or proves that no observer exists for the given descriptor system the method of this note is partly based on an earlier paper of the authors on observer design for continuous time time invariant systems of the form e dx dt ax bu y cx where e and a are square matrices el tohami et al 1983 and makes use of some results of luenberger on discrete time time varying descriptor systems luenberger 1977

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

the operator valued marcinkiewicz multiplier theorem and maximal regularity given a closed linear operator on a umd space we characterize maximal regularity of the non homogeneous problem

some generalized notions of observability generalized state space systems are a more natural way of describing dynamical behavior than standard state space systems such systems exhibit a much richer observability structure than standard state space systems three notions of observability are defined for generalized state space systems in contrast to previous work regularity is not assumed geometric characterization of each type of observability and matrix rank tests for each type of observability are derived

disturbance impulse controllability in descriptor system the descriptor system ex ax gu hv with external disturbance v is considered to characterize the possibility to cancel the impulses produced by external disturbance v through using control u the concept of disturbance impulse controllability is introduced

a t1 theorem for integral transformations with operator valued kernel we consider generalized calderon zygmund operators whose kernel k x y takes values in l x continuous linear operators on the banach space x and satis es variants of the classical standard estimates involving rboundedness which has recently become a crucial notion in connection with operator valued singular integrals boundedness criteria in the spirit of the t1 theorem of david and journe are proved for such operators on the bochner spaces lp rn x where 1 p and x is a umd space for some results x is also required to have pisier s property in the special case t1 t 1 0 we obtain an essentially complete analogue of the scalar valued theorem we also provide su cient conditions for the general case but they are stronger in general than the necessary t1 t 1 bmo type conditions although they reduce to them in the classical situation a counterexample is given to show that the natural necessary conditions are not su cient in general

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

kato s square root problem in banach spaces abstract let l be an elliptic differential operator with bounded measurable coefficients acting in bochner spaces l p r n x of x valued functions on r n we characterize kato s square root estimates l u p u p and the h functional calculus of l in terms of r boundedness properties of the resolvent of l when x is a banach function lattice with the umd property or a noncommutative l p space to do so we develop various vector valued analogues of classical objects in harmonic analysis including a maximal function for bochner spaces in the special case x c we get a new approach to the l p theory of square roots of elliptic operators as well as an l p version of carleson s inequality

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

design of observers for descriptor systems using a descriptor standard form methods are developed for constructing luenberger type observers for linear time invariant descriptor systems based on the descriptor standard form derived here by means of a simple matrix calculus full order observers reduced order observers and function observers of a general type are proposed some necessary and sufficient conditions for the function observers to estimate linear functions of the state are discussed then the so called separation property of combined observer controller systems is established

the 2 transitive ovoids an ovoid 0 in a classical polar space is a set of singular points such that every maximal totally singular subspace contains just one point in lo ovoids are intimately connected with other combinatorial objects including translation planes spreads partial geometries codes generalized hexagons and kerdock sets see s 9 163 for example interestingly enough many of the known ovoids are in fact 2 transitive that is they admit a 2 transitive automorphism group the notion of the automorphism group is made precise in 2 3 for example the suzuki groups sz q and the ree groups g q act 2 transitively on ovoids in 4 dimensional symplectic geometry and 7 dimensional orthogonal geometry respectively furthermore the unitary groups psu q for suitable prime powers q and the linear groups psl q3 with q even act 2 transitively on ovoids in 7or 8 dimensional orthogonal geometry the occurrence of such a large number of 2 transitive ovoids suggests that a classification of them is worthwhile much in the same spirit as kantor s classification of the finite linear spaces whose automorphism group acts 2 transitively on points lo the classification of the 2 transitive ovoids appears as our main theorem in section 2 we discover no new ovoids however we obtain some new results concerning the number of isomorphism classes of 2 transitive ovoids see section 2 our proof relies on the classification of the finite 2 transitive permutation groups which in turn relies on the recent classification of finite simple groups wc also draw upon several facts from the modular representation theory of finite groups

analysis of impulsive modes and luenberger observers for descriptor systems abstract in this paper the distinction between impulsive modes that can be generated by inputs and impulsive modes that can only be generated by initial conditions is investigated for linear time invariant descriptor systems it reveals that the input generatable impulsive modes are very crucial to the existence of normal luenberger observers of the systems based on this observation an earlier known concept called strongly detectability for regular descriptor systems is extended to irregular case that is shown to be of much clearer physical meanings in classical sense than a recently proposed equivalent notion of causal detectability does thus similar to the regular case strong detectability is also a sufficient and necessary condition for the existence of normal luenberger observers of irregular descriptor systems

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

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

design of a minimal order observer for singular systems this paper considers the design of an observer for generalized state space systems using the concept of generalized inverses in contrast to the luenberger observer theory a new method is proposed which does not presuppose the observer structure it is shown that under certain conditions it is possible to construct a minimal order observer for this class of systems illustrative examples are included

multilinear operator valued calderon zygmund theory abstract we develop a general theory of multilinear singular integrals with operator valued kernels acting on tuples of umd banach spaces this in particular involves investigating multilinear variants of the r boundedness condition naturally arising in operator valued theory we proceed by establishing a suitable representation of multilinear operator valued singular integrals in terms of operator valued dyadic shifts and paraproducts and studying the boundedness of these model operators via dyadic probabilistic banach space valued analysis in the bilinear case we obtain a t 1 type theorem without any additional assumptions on the banach spaces other than the necessary umd higher degrees of multilinearity are tackled via a new formulation of the rademacher maximal function rmf condition in addition to the natural umd lattice cases our rmf condition covers suitable tuples of non commutative l p spaces we employ our operator valued theory to obtain new multilinear multi parameter operator valued theorems in the natural setting of umd spaces with property

on observers for nonlinear differential algebraic systems we extend a recent approach to observer design for linear differential algebraic systems to systems with lipschitz nonlinearities the observer design further extends the standard luenberger type observer design we show that the design parameters for the observer can be obtained by the solution of a riccati type inequality the solutions of the latter can in turn be obtained by solving a set of linear matrix inequalities lmis and bilinear matrix inequalities bmis which provides a computational procedure a feature of the presented observer design is the possibility of reformulation as an ordinary differential equation