where is the nearest non regular pencil abstract this is a first step toward the goal of finding a way to calculate a smallest norm deregularizing perturbation of a given square matrix pencil minimal de regularizing perturbations have geometric characterizations that include a variable projection linear least squares problem and a minimax characterization reminiscent of the courant fischer theorem the characterizations lead to new computationally attractive upper and lower bounds we give a brief survey and illustrate strengths and weaknesses of several upper and lower bounds some of which are well known and some of which are new the ultimate goal remains elusive

near optimal control of nonstandard singularly perturbed systems abstract near optimal control of nonstandard multiparameter multitime scale singularly perturbed systems is studied using the descriptor variable approach in particular the slow models of the considered systems are allowed to exhibit impulses in the case of multiparameter singular perturbations the near optimal control is a cascade connection of separately designed slow and fast subregulators in the case of multitime scale singular perturbations the near optimal control is hierarchically composed of n 1 subregulators a parallel algorithm is provided for designing the subregulators separately the knowledge of the small singular perturbation parameters is not required in the overall design furthermore the frequency responses of the near optimal systems are analyzed and several design examples are given

strongly self absorbing c algebras say that a separable unital c algebra v c is strongly self absorbing if there exists an isomorphism v such that lx ai e approximately unitarily equivalent homomorphisms we study this class of algebras which includes the cuntz algebras 2 ooo the uhf algebras of infinite type the jiang su algebra z and tensor products of 00 with uhf algebras of infinite type given a strongly self absorbing c algebra v we characterise when a separable c algebra absorbs v tensorially i e is p stable and prove closure properties for the class of separable testable c algebras finally we compute the possible if groups and prove a number of classification results which suggest that the examples listed above are the only strongly self absorbing c algebras

a closed form solution for regular descriptor systems using the moore penrose generalized inverse abstract a new procedure to compute non impulsive solutions of regular continuous descriptor systems is presented the procedure is based on a closed form solution derived by applying the moore penrose generalized inverse concept

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

technical communique an algorithm for the computation of the transfer function matrix for singular systems for singular systems i e for systems of the form ex ax bu with e singular the problem of computing the transfer function matrix has been solved an algorithm is developed which uses the souriau frame faddeev algorithm for regular systems the final expression is suitable for computer use

improved algorithm for optimal state regulation of generalized systems abstract generalized systems with the form e x ax bu where e is singular are considered an efficient algorithm for designing optimal state regulators of such systems is developed

an efficient tabu search approach for the 0 1 multidimensional knapsack problem abstract in this paper we describe a new approach to tabu search ts based on strategic oscillation and surrogate constraint information that provides a balance between intensification and diversification strategies new rules needed to control the oscillation process are given for the 0 1 multidimensional knapsack 0 1 mkp based on a portfolio of test problems from the literature our method obtains solutions whose quality is at least as good as the best solutions obtained by previous methods especially with large scale instances these encouraging results confirm the efficiency of the tunneling concept coupled with surrogate information when resource constraints are present

abelian mathrm c ast subalgebras of mathrm c ast algebras of real rank zero and inductive limit mathrm c ast algebras

graph c algebras with real rank zero given a row finite directed graph e a universal c algebra c e generated by a family of partial isometries and projections subject to the relations determined by e is associated to the graph e the cuntz krieger algebras are those graph c algebras associated to some finite graphs we prove that a graph c algebra c e has real rank zero in the sense that the set of invertible self adjoint elements is dense in the set of all self adjoint elements in c e or in the unitization of c e if c e is nonunital if and only if e satisfies a loop condition k that is analogous to the condition for a finite 0 1 matrix a under which cuntz analyzed the ideal structure of the cuntz krieger algebra oa

a frequency domain approach to control of singular systems in this paper singular control systems are studied from the frequency domain point of view the proper stable factorization of a singular system is derived the stability of the closed loop system consisting of a singular system and controller is addressed most significantly all proper stabilizing controllers are parameterized for a given singular system

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

the nuclear dimension of graph c algebras abstract consider a graph c algebra c e with a purely infinite ideal i possibly all of c e such that i has only finitely many ideals and c e i is approximately finite dimensional we prove that the nuclear dimension of c e is 1 if i has infinitely many ideals then the nuclear dimension of c e is either 1 or 2

topological aspects of controllability and observability on the manifold of singular and regular systems abstract in a previous article j d cobb j math anal appl nov 1986 we considered the class of all singular and regular linear time invariant systems and proved some basic topological properties of that set in this paper we examine specific implications of those results to control theory and demonstrate among other things that controllability and observability are generic properties even when singular systems are included in the construction we also derive related results for other important subclasses of systems proving that only some of the remaining fundamental system properties are generic finally we extend existing results on connectedness and show that the number of connected components of the controllable and observable sets is diminished whenever singular systems are brought into the picture

robust pole assignment in singular control systems abstract necessary conditions are given for the problem of pole assignment by state feedback in singular linear systems descriptor systems to have a solution which is regular and nondefective for a robust solution such that the assigned closed loop poles are insensitive to perturbations in the system data the same conditions must hold it can be shown that these conditions are also sufficient for the existence of a feedback which assigns the maximum possible number of finite poles with regularity these results provide the basis of a procedure for constructing closed loop semistate systems with given poles guaranteed regularity and maximum robustness

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

graphs groupoids and cuntz krieger algebras we associate to each locally finite directed graphgtwo locally compact groupoidsgandg the unit space ofgis the space of one sided infinite paths ing andg is the reduction ofgto the space of paths emanating from a distinguished vertex we show that under certain conditions theirc algebras are morita equivalent the groupoidc algebrac g is the cuntz krieger algebra of an infinite 0 1 matrix defined byg and that the algebrasc g contain thec algebras used by doplicher and roberts in their duality theory for compact groups we then analyse the ideal structure of these groupoidc algebras using the general theory of renault and calculate theirk theory

open loop optimal control of linear time invariant systems containing the first derivative of the input abstract linear time invariant systems of the form are considered the problem is to find a control vector u t that will drive the state of this system from a given z 0 to some not necessarily fixed final state z t f in some not necessarily fixed time t f while minimizing a cost functional of the form the original system is re written in the form of a descriptor variable system consisting of the equations diag it is shown that there is a matrix such that thus the original optimal control problem is equivalent to the following problem find a control vector u t that drives the descriptor vector x t from a given x 0 to some x t f while minimizing using the results of an earlier paper on optimal control of descriptor systems ibrahim et al 1988 necessary conditions are derived for the existence of minima of the problem of finding sufficient conditions for the existence of minima of is not considered various formulae are obtained for designing open loop controls corresponding to three diffe

computation of transfer function matrices of generalized state space models a reliable computational algorithm is proposed for the evaluation of the transfer function matrices of linear multivariable systems described by generalized state space models the algorithm is based on a new efficient and numerically stable procedure for computing irreducible state space realizations of generalized state space models for each input output channel the proposed algorithm computes an irreducible realization using this procedure then the parameters of the corresponding transfer function gain poles zeros are determined from the resulting irreducible model

stationary lqg control of singular systems the stationary linear quadratic gaussian control problem is formulated and solved for single input single output singular systems the control system is required to be internally proper and stable in order to avoid both impulsive and unstable exponential behavior the set of all controllers resulting in such a control system is specified in parametric form all controllers that yield finite cost are identified once again in parametric form within this set necessary and sufficient conditions are then established for an optimal controller to exist all optimal controllers are shown to possess the same transfer function the problem is analyzed in the complex domain the transfer functions are expressed as quotients of proper strict hurwitz rational functions by means of this maneuver the powerful tools of algebra are made available the synthesis of the optimal controller is reduced to the solution of two linear diophantine equations whose coefficients are obtained by spectral factorization

robust stabilization of discrete generalized systems the robust stabilization problem for generalized discrete time systems described by polynomial or improper transfer function matrices subject to perturbations acting on the normalized coprime factors is solved the maximum achievable stability margin and the robust stabilizing controller are given in terms of realizations and solutions to appropriate riccati equations

boundary value descriptor systems well posedness reachability and observability in this paper we introduce the class of two point boundary value descriptor systems tpbvds discrete time systems described by possibly linear dynamics and a set of boundary conditions constraining the values of the system state at the two endpoints of the system s interval of definition by introducing a standard form for regular pencils we obtain a new and simple generalized cayley hamilton theorem that simplifies our investigation of well posedness green s function solutions and reachability and observability for tpbvds there are two distinct notions of reachability and observability that one can define for tpbvds associated with processes that propagate inward from and outward toward the boundaries we investigate each of these in detail obtaining among other things far simpler forms for the reachability and observability results than found previously in the literature in addition we describe several methods for the efficient solution of tpbvds one involving recursions from each end of t

solutions to the output regulation problem of linear singular systems in this paper we revisit the output regulation problem for linear singular systems and identify an important case of the general regulation problem where the measurement output is identical to the vector to be regulated we derive a necessary and sufficient condition for the regulation problem to be solvable via either full information feedback or error feedback then we show how full information feedback and error feedback controllers can be constructed explicitly

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

inner outer factorization for strictly proper functions with j w axis zeros abstract this paper discussed the inner outer factorization for square real rational matrices which may have zeros on the j axis including infinity a factorization method is given in terms of the descriptor form representation of the rational matrix this method uses the solution of a generalized riccati equation we also propose an efficient computation algorithm for solving the generalized riccati equation

a framework for the solution of the generalized realization problem in this paper we present a novel way of constructing generalized state space representations e a b c d of interpolants matching tangential interpolation data the loewner and shifted loewner matrices are the key tools in this approach

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

robust s regularity of matrix pencils applied to the analysis of descriptor models abstract this paper deals with the robust s regularity of an uncertain linear matrix pencil e a and its applicability to the analysis of uncertain linear descriptor models of the form e x ax for the continuous case or ex k 1 ax k for the discrete case lmi linear matrix inequality based conditions for the robust s regularity of e a are established when both a and e are affected by lft linear fractional transform based uncertainties these conditions though sufficient are also necessary in numerous cases of practical interest moreover the relevance of the conditions for the analysis of the d admissibility of descriptor models d stability and impulse freeness or causality is also discussed

a note on the solution of regular pmds a new resolvent decomposition of a regular polynomial matrix is derived which is a refinement of the results given by gohberg et al and vardulakis based on this a complete solution of the regular polynomial matrix descriptions pmds is presented that reflects precisely the zero input response and the zero state response and takes into account the impulsive properties of the system an algorithm for the computation of this resolvent decomposition is provided

descriptor variable systems and optimal state regulation linear systems of the form e dot x ax bu with e singular are treated it is desired to find a control which drives the system asymptotically to the origin minimizing a quadratic cost functional no restrictions are placed on initial conditions the cost associated with the impulsive behavior of the system is examined as well as existence and uniqueness of the optimal control through a sequence of coordinate transformations it is proven that the optimal control can be found by solving a reduced order riccati equation

state feedback and transfer matrix in singular systems abstract the influence of state feedback on the transfer matrix in singular systems is considered we first discuss the problem for siso systems then by utilizing the time scale transformation the same problem is solved for mimo systems we also consider realizations of the feedback control strategies given here it is pointed out that the singular system is distinguished from the normal one by an important feature we can design a pure input prediction system for it finally the results are applied to the model matching problem

robustness of regional pole placement for uncertain continuous time implicit systems in this note under assumptions that the nominal linear implicit system is regular impulse free with all its generalized eigenvalues lying inside some specified regions sufficient conditions are proposed to preserve the assumed properties when structured perturbations are added into the nominal system explicit bounds on perturbations with different structures are given in terms of the spectral radii of some nonnegative matrices

the cuntz toeplitz algebras have nuclear dimension one abstract we prove that unital extensions of kirchberg algebras by separable stable af algebras have nuclear dimension one the title follows

controllability and observability of second order descriptor systems we analyze controllability and observability conditions for second order descriptor systems and show how the classical conditions for first order systems can be generalized to this case we show that performing a classical transformation to first order form may destroy some controllability and observability properties as an example we demonstrate that the loss of impulse controllability in constrained multibody systems is due to the representation as a first order system to avoid this problem we will derive a canonical form and new first order formulations that do not destroy the controllability and observability properties

fundamental properties of the manifold of singular and regular linear systems abstract we construct a real analytic manifold l of systems of the form e x ax bu y cx and show that l is the completion with respect to solutions of the set of regular state space systems i e those systems with nonsingular e other geometric and analytic properties of l are established including genericity of the regular systems

robustness analysis of uncertain linear singular systems with output feedback control the robustness analysis for a linear singular system with uncertain parameters and static output feedback control is considered the problem is transformed into a robust nonsingularity problem based on the linear fractional transformation lft approach the robustness bounds to preserve regularity impulse immunity and stability are found in terms of the structured singular value spl mu with respect to parametric uncertainties the lft approach provides a unified framework for robustness analysis of both uncertain linear continuous discrete time singular systems

on minimal order inverses of discrete time descriptor systems in this paper linear discrete time control systems of the form e k x k 1 a k x k b k u k y k c k x k d k u k are considered where e k and a k are not necessarily square matrices the problem to be solved is this find a system of the form e k v k 1 k v k bcirc k k u k kvk dcirc k k where k is a partitioned column vector whose blocks are linear combinations of some of the output vectors of the original system and which possesses either or both of the following properties i if the outputs of the original system are known then the output equation of the second system uniquely specifies the same inputs that generated the known outputs of the original system ii if the output vectors of the original system are desired outputs then the equation uk kvk dcirc k k yields one or more sequences of inputs for the original system that can generate the desired outputs we shall furthermore seek the system which among all systems having property i or ii or both has the sm

c algebras of real rank zero abstract the concept of real rank of a c algebra is introduced as a non commutative analogue of dimension it is shown that real rank zero is equivalent to the previously defined conditions fs and hp and that it is invariant under strong morita equivalence in particular under stable isomorphism real rank zero is also invariant under inductive limits and split extensions and the class may well be regarded as the conceptual completion of the af algebras in some cases notably when the algebra is matroid it is shown that the multiplier algebra also has real rank zero although that is not true in general by a result of g j murphy this implies a weyl von neumann type result for self adjoint multiplier elements in these cases

on the solutions of linear differential equations with singular coefficients abstract equations of the form e ax u with e and a square matrices and e singular are considered the controversy that exists in the literature concerning the solutions of such equations is investigated solutions are arrived at through an application of singular perturbation theory

j factorizations of a general discrete time system abstract the problems of extending the j lossless conjugation the j j spectral factorization and the j j lossless factorization to a completely general discrete time system are considered existence conditions together with a numerically sound prototype algorithm for computing the factors are provided for a system having any type of singularity including arbitrary normal rank poles and zeros at infinity at zero or on the unit circle

realization of singular systems via markov parameters and moments an algorithm is developed via the markov parameters and moments for the construction of minimal realizations for linear finite dimensional time invariant discrete time singular systems the algorithm presented is an exact one and needs only simple numerical operations

convergence in the boundary layer for singularly perturbed equations a singularly perturbed linear finite dimensional ordinary differential equation is considered on the half line 0 the reduced system is assumed to have a unique solution in the sense of distributions it is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense and the order of the limiting distribution is computed an application to the optimal linear quadratic regulator with cheap control is described

on the nuclear dimension of certain uct kirchberg algebras abstract we give a partial answer to the question for the precise value of the nuclear dimension of uct kirchberg algebras raised by w winter and j zacharias in 12 it is shown that every kirchberg algebra in the uct class with torsion free k 1 group has nuclear dimension 1

classical and generalized solutions of time dependent linear differential algebraic equations abstract a coordinate free reduction procedure is developed for linear time dependent differential algebraic equations that transforms their solutions into solutions of smaller systems of ordinary differential equations the procedure applies to classical as well as distribution solutions in the case of analytic coefficients the hypotheses required for the reduction not only are necessary for the validity of the existence and uniqueness results but even allow for the presence of singularities straightforward extensions including undetermined systems and systems with nonanalytic coefficients are also discussed

dimension and stable rank in the k theory of c algebras in topological k theory which can be viewed as the algebraic side of the theory of vector bundles some of the interesting properties which one investigates are for example the conditions under which bundles must possess trivial direct summands or the extent to which the cancellation property for direct whitney sums of bundles holds such properties turn out to be controlled in part by the dimension of the base space and results describing the nature of this control are among what are frequently called stability results 17 during the past few years there has been a sudden flowering of a theory for c algebras see surveys 35 36 37 since c algebras are profitably thought of as non commutative locally compact spaces with the finitely generated projective modules being the appropriate generalization of vector bundles according to swan s theorem 40 it would be natural to look for stability results for c algebras but until now the theory has been focussed on the c groups of c algebras and there has been little discussion of stability properties presumably in part for lack of an appropriate concept of dimension for c algebras one of the main objectives of this paper is to introduce a concept of dimension for c algebras which directly generalizes the classical concept of dimension for compact spaces 16 20 22 and to develop some techniques for calculating it notably for c algebras which are obtained as crossed product algebras for an action of the group of integers in algebraic k theory which is the generalization of topological c theory to rings a substantial number of stability properties have been discovered 2 39 42 48 within that theory the concept which has played a role most analogous to that of dimension is the bass stable rank but despite its many successes the bass stable rank has often been difficult to calculate even for relatively uncomplicated rings another main objective of the present paper is to make accessible for application to c algebras some of the stability results from algebraic c theory this comes about from the fact that the concept of dimension which we introduce dominates the bass stable rank i was led to seek stability results for c algebras by my desire to determine whether the cancellation property for projective modules holds for the irrational rotation c algebras discussed in 30 which as elliott 11 has suggested can appropriately be called 2 dimensional non commutative tori in more concrete terms the question is whether two projections in such an algebra which have the same trace must be unitarily equivalent the present paper provides the general theory which is needed for the affirmative answer which i obtained in a subsequent paper i will derive the

on regularizing descriptor systems by output feedback in this paper linear time invariant descriptor variable systems are considered which are either nonregular or if they are regular they have impulsive modes it is shown that if a certain necessary and sufficient condition is satisfied then both regularity can be established and impulsive modes can be eliminated by output feedback we have also considered the problem of achieving structural properties of the regularized system

uct kirchberg algebras have nuclear dimension one we prove that every kirchberg algebra in the uct class has nuclear dimension 1 we first show that kirchberg 2 graph algebras with trivial k0 and finite k1 have nuclear dimension 1 by adapting a technique developed by winter and zacharias for cuntz algebras we then prove that every kirchberg algebra in the uct class is a direct limit of 2 graph algebras to obtain our main theorem

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

the k theoretical range of cuntz krieger algebras abstract we augment restorff s classification of purely infinite cuntz krieger algebras by describing the range of his invariant on purely infinite cuntz krieger algebras we also describe its range on purely infinite graph c algebras with finitely many ideals and provide unital range results for purely infinite cuntz krieger algebras and unital purely infinite graph c algebras

simple c algebras with locally finite decomposition rank abstract we introduce the notion of locally finite decomposition rank a structural property shared by many stably finite nuclear c algebras the concept is particularly relevant for elliott s program to classify nuclear c algebras by k theory data we study some of its properties and show that a simple unital c algebra which has locally finite decomposition rank real rank zero and which absorbs the jiang su algebra z tensorially has tracial rank zero in the sense of lin as a consequence of our result and of a theorem of elliott and gong any such c algebra if it additionally satisfies the universal coefficients theorem is approximately homogeneous of topological dimension at most 3 our result in particular confirms the elliott conjecture for the class of simple unital z stable ash algebras with real rank zero moreover it implies that simple unital z stable ah algebras with real rank zero not only have slow dimension growth in the ash sense but even in the ah sense

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

computation of inner outer factorization of rational matrices we propose a new numerically reliable computational approach to determine the inner outer factorization of a rational transfer matrix g of a linear descriptor system in contrast to existing computationally involved one shot methods which require the solution of riccati or generalized riccati equations the new approach relies on an efficient recursive zeros dislocation technique the resulting inner and outer factors always have minimal order descriptor representations the approach proposed is completely general being applicable whenever g is proper strictly proper or not or of full column row rank or not

the nuclear dimension of c algebras abstract we introduce the nuclear dimension of a c algebra this is a noncommutative version of topological covering dimension based on a modification of the earlier concept of decomposition rank our notion behaves well with respect to inductive limits tensor products hereditary subalgebras hence ideals quotients and even extensions it can be computed for many examples in particular it is finite for all uct kirchberg algebras in fact all classes of nuclear c algebras which have so far been successfully classified consist of examples with finite nuclear dimension and it turns out that finite nuclear dimension implies many properties relevant for the classification program surprisingly the concept is also linked to coarse geometry since for a discrete metric space of bounded geometry the nuclear dimension of the associated uniform roe algebra is dominated by the asymptotic dimension of the underlying space

controllability and observability at infinity of multivariable linear second order models in this note we give in the spirit of 4 numerically attractive tests of controllability and observability of linear multivariable second order systems in which the leading matrix is singular

efficient algorithms for solving multiconstraint zero one knapsack problems to optimality the multiconstraint 0 1 knapsack problem is encountered when one has to decide how to use a knapsack with multiple resource constraints even though the single constraint version of this problem has received a lot of attention the multiconstraint knapsack problem has been seldom addressed

the algorithm for computing nonmonic second order multivariable systems abstract an efficient method for computing impulse response matrices of nonmonic multivariable second order systems is proposed a procedure has been developed which uses some properties of regular matrix polynomials p s s 2 a 2 sa 1 a 0 with a 2 identically singular an algorithm suitable for computer use is established and its applications can be effectively controlled via the newly introduced special graphical scheme it produces simultaneously the adjoint and determinant of the matrix polynomial p s and avoids the inversion of any matrix moreover all computations can be performed on constant matrices and coefficients only it is shown that substantial economy may be achieved in computation time and storage when solving large order problems characteristic of many physical plants and engineering structures

h infinity kalman estimation for rectangular descriptor systems with unknown inputs this note considers h filtering and prediction for rectangular descriptor systems with unknown inputs that affect both the system and the output an optimal h descriptor kalman estimator hdke which can simultaneously solve the h filtering and prediction problems for rectangular descriptor systems with unknown inputs is developed based on the maximum likelihood descriptor kalman filtering method the hdke serves as a unified solution to solve h and kalman filtering for descriptor systems and standard systems with or without unknown inputs to reduce the computational complexity problem some efficient alternatives to the developed hdke are further proposed the relationship between the hdke and the existing literature results is also addressed an illustrative example is given to show the usefulness of the proposed results

on input function observers for generalized state space systems abstract linear control systems of the form e dx dt ax bu y cx du are considered where e and a are not necessarily square matrices and no assumption is made on the rank of the matrix pencil se a the problem to be solved is this find a system of the form edz dt z bcirc u z dcirc where is some linear combination of y the output of the original system and its derivatives and u is the input of the original system for the solution of this problem a method based on the use of matrix generalized inverses is developed that can be applied both to time invariant and time varying systems a numerical procedure is elaborated for the time invariant case that either yields a system e dz dt z bcirc u z dcirc in which the coefficient matrices are of the smallest possible dimensions or it shows that there is no such system this procedure makes use of a recent paper of wilkinson on singular systems of linear differential equations in the special case where e

sufficient conditions for impulse uncontrollability and impulse unobservability of singular systems simple sufficient conditions for impulse uncontrollability and impulse unobservability of completely singular systems are established it is well know that a singular linear system can be decomposed into a regular subsystem and a completely singular subsystem from previously published results it follows that a singular system is impulse uncontrollable unobservable if its singular subsystem is impulse uncontrollable unobservable it is shown that in a particular case the results can be also applied to the controllability and observability of regular linear systems

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

a new polynomial time algorithm for 0 1 multiple knapsack problem based on dominant principles abstract this paper presents a heuristic to solve the 0 1 multi constrained knapsack problem 01mkp which is np hard in this heuristic the dominance property of the constraints is exploited to reduce the search space to find near optimal solutions of 01mkp this heuristic is tested for 10 benchmark problems of sizes up to 105 and for seven classical problems of sizes up to 500 taken from the literature and the results are compared with optimum solutions space and computational complexity of solving 01mkp using this approach are also presented the encouraging results especially for relatively large size test problems indicate that this heuristic can successfully be used for finding good solutions for highly constrained np hard problems

diophantine equations in control a survey abstract this survey is also a tutorial whose aim is to explain the role of diophantine equations in the synthesis of feedback control systems these are linear equations in a ring and result from a fractional representation of the systems involved the cornerstone of the exposition is a simple parametrization of all stabilizing controllers for a given plant one can then choose in principle the best controllers for various applications these ideas evolved from early attempts to use polynomial equations in the design of discrete time linear systems by now they have been extended to continuous time infinite dimensional time varying and non linear systems

singular systems a new approach in the time domain a new approach in the time domain is developed for the study of singular linear systems of the form e dot x ax bu y cx with e singular central to the approach is the fundamental triple alpha e a 1 e alphae a 1 b c with a real number satisfying det alpha e a neq 0 controllability and observability matrices are expressed in terms of the fundamental triple new tests for impulse controllability and impulse observability are also established feedback control problems including pole placement decoupling and disturbance localization are studied by use of a modified proportional and derivative feedback of the state in the form of u f alpha x dot x v

a geometric approach to eigenstructure assignment for singular systems moore s well known result on the feedback assignment of eigenstructure in linear state space systems 5 was generalized to descriptor systems in 9 in this note we make some useful extensions to fill out the theory to begin with we do not assume controllability of the plant it is shown that the maximum number of finite closed loop eigenvalues is equal to dim el where l is the supremal a e r b invariant subspace in order to relate the possible closed loop structure to the open loop plant structure we define a set of indexes for descriptor systems which are in many respects similar to the controllability indexes of state space systems in terms of these controllability indexes we give a systematic approach to selecting the closed loop eigenvectors a major contribution of this note is the fact that it is geometric in nature and hence avoids any decomposition of the system matrices into a special form e g weierstrass form 1 the geometric setting introduced here should constitute a basis for further research in generalizing the well known results in geometric system theory disturbance decoupling input output decoupling etc to singular systems

computation of structural invariants of generalized state space systems in this paper we develop an algorithm for computing the zeros of a generalized state space model described by the matrix 5 tuple e a b c d where e may be a singular matrix but det a he 0 the characterization of these zeros is based on the system matrix of the corresponding 5 tuple both the characterization and the computational algorithm are extensions of equivalent results for state space models described by the 4 tuples a b c d we also extend these results to the computation of infinite zeros and left and right minimal indices of the system matrix several non trivial numerical examples are included to illustrate the proposed results

nuclear dimension and mathcal z stability of pure c algebras in this article i study a number of topological and algebraic dimension type properties of simple c algebras and their interplay in particular a simple c algebra is defined to be tracially m bar m pure if it has strong tracial m comparison and is tracially bar m almost divisible these notions are related to each other and to nuclear dimension

linear transformations which leave controllable multiinput descriptor systems controllable abstract a general linear descriptor system e itx ax bu where e a c n n b c n m x c n u c m e singular is called controllable if rank e a b n for all 0 0 c let f c n n m c n n m be a linear transformation form f x cxd we characterize all such linear transformations that leave the set c e a b rank e a b n 0 0 c invariant and show that only the well known transformations that leave controllability invariant can occur

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

exact pole assignment with regularity by output feedback in descriptor systems part 2 in this paper the first of two we examine the problem of modal control of linear time invariant multivariable descriptor systems in particular for systems satisfying a certain inequality we will give necessary and sufficient conditions for the existence of an output feedback matrix possibly complex which exactly assigns an arbitrary set of r the number of independent semi state variables of the system distinct complex numbers to a generalized eigenspectrum of the closed loop system while ensuring that the resulting system has a unique smooth solution for each admissible initial condition furthermore it is shown that if the set of proposed poles contains only real elements the assignment can be carried out using real feedback next we present conditions that are necessary and sufficient for pole assignability by real feedback of a self conjugate set of complex numbers provided that the system satisfies a further inequality

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

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

dynamical order assignment for linear descriptor systems this paper considers the problem of dynamical order assignment for linear descriptor systems by derivative feedback control the approach is based on an ability to adjust the number of infinite non dynamical modes of the system within a permissible range increasing the dynamical order enables the designer to implement specific otherwise unrealizable control strategies on the other hand dynamical order reduction simplifies the design procedures for a large scale system the solution is obtained by imbedding the descriptor space problem in an equivalent state space problem where a zero value eigenvalue with a prescribed geometric multiplicity is assigned to a linear state system by proportional feedback control

convergence of singular perturbations in singular linear systems abstract a convergence criterion for singular perturbations in linear systems is established the criterion is useful for regular and singular systems it is assumed that the matrices of the system depend analytically on e it is proved that if the real parts of the divergent eigenvalues tend to the solution of the system converges to the solution for e 0 uniformly in compact subsets of 0 on the other hand if there is a divergent eigenvalue whose real part does not tend to then there are initial values such that the solution does not converge at some points the criterion is valid both for the homogeneous equation and for the nonhomogeneous equation if functions are sufficiently smooth the use of distributions allows the analysis with inconsistent initial conditions

preview control for impulse free continuous time descriptor systems this paper studies the preview control problem of impulse free linear continuous time descriptor systems the system is first decomposed into a normal system i e slow subsystem and an algebraic equation set by restricted equivalent linear transformation then applying the method of preview control theory to the slow subsystem by taking derivatives on both the error vector and the state function and with the error vector being a part of the new state vector the augmented system is constructed and the tracking problem is transformed into a regulation problem according to preview control theory the controller of the augmented system can be obtained and the control input of the original descriptor system with preview function can be acquired by integrating on the controller of the augmented system both the stabilisability and detectability of the augmented system are discussed numerical simulation verifies the presented results

singular perturbations and time scale methods in control theory survey 1976 1983 recent progress in the use of singular perturbation and two time scale methods of modeling and design for control systems is reviewed over 350 references are organized into major problem areas representative issues and results are discussed with a view to outlining research directions and indicating potential areas of application the survey is aimed at engineers and applied mathematicians interested in model order reduction separation of time scales and allied simplified methods of control system analysis and design the exposition does not assume prior knowledge of singular perturbation methods