the damped string problem revisited abstract we revisit the damped string equation on a compact interval with a variety of boundary conditions and derive an infinite sequence of trace formulas associated with it employing methods familiar from supersymmetric quantum mechanics we also derive completeness and riesz basis results with parentheses for the associated root functions under less smoothness assumptions on the coefficients than usual using operator theoretic methods rather than detailed eigenvalue and root function asymptotics only

grassmann invariants almost zeros and the determinantal zero pole assignment problems of linear multivariable systems the strucxpects of the rationxr spaces x c x fwhere x c is the columxof the transfer function matrix g s and x f is the space associated with right matrix fracxcriptions of g s are investigated for x f gcanonixqb s grassmgesentax g x c and g x f arxd and are shown xmplete basis free invariants for x c and x f respectively the almost zeros az and almost decoupling zeros adz of g s gdefinex local minima of a normgn defix g x c and g x f respectively the computation and certain aspects of the distribution in the complex plane of azs and adzs are examined the role of azs and adzs in the determinantal zero and pole assignment problems respectively is examined next two important families of systems are defined the strongly zero non assignable szna and the strongly pole non assignable spna systems for szna and spna systems minimal radius discs dem e z r em e z and dem f zb centred at an az and adz respectively are defined it is shown that dem e r em e z contains at least one zer

disturbance and input output decoupling of singular systems the disturbance decoupling and the simultaneous disturbance and input output decoupling problems for singular systems are considered in the context of the matrix fraction description mfd of the system solvability conditions are obtained in terms of the composite matrix of a column reduced mfd of the system a characterisation of the fixed poles of both problems is given and it is shown that the remaining poles can be arbitrarily assigned

proportional plus multiintegral stabilizing compensators for a class of mimo feedback systems with infinite dimensional plants a method is presented for designing proportional plus multiintegral stabilizing compensators for a class of feedback systems with exponentially stable infinite dimensional plants these compensators enable the feedback system to asymptotically track polynomial inputs and suppress polynomial disturbances of corresponding order when used in design the effectiveness of the construction procedure presented can be increased considerably by combining it with the computational stability criterion and semiinfinite optimization in this manner the coefficient matrices of a compensator designed by the method can be further modified to ensure better feedback system performance with respect to various performance requirements without destroying stability tracking and disturbance rejection properties

paper minimal representations of implicit linear systems definitions of external behaviour equivalence and minimality are given for a class of implicit non oriented linear dynamical systems of particular interest in computer aided analysis and design conditions for minimality are stated in terms of the rank properties of submatrices in the singular pencil realization and a geometric analysis is used in the proof a stable library quality numerical algorithm for minimization is included

projective equivalence of homogenous binary polynomials abstract an essential subproblem in the study of invariants of homogeneous matrix pencils sf g under bilinear strict equivalence is the study of complex projective equivalence pe p defined on the set k of complex homogeneous binary polynomials of fixed homogeneous degree k for an s k the study of invariants of the pe class p is reduced to a study of invariants of matrices of the set m 2 m 2 matrices with all 2 2 minors nonzero under extended hermite equivalence ehe eh for the equivalence class eh t t m 2 it is shown that if m 1 2 3 then eh m 2 for the case m 4 eh t is characterized by a complete set of invariants the set of plucker vectors t of t these results lead to the definition of new sets of invariants for the class p f which are the plucker vectors f and the list of degrees f of the elementary divisors of f s

application of prediction models using fuzzy sets a fuzzy inference framework based on fuzzy relations is developed adapted and applied to temperature and humidity measurements from a specific coffee crop site in brazil this framework consists of fuzzy relations over possibility distributions resulting in a model analogous to a bayesian inference process the application of this fuzzy model to a data set of experimental measurements and its correspondent forecasts of temperature and humidity resulted in a set of revised forecasts that incorporate information from a historical record of the problem each set of revised forecasts was compared with the correspondent set of experimental data using two different statistical measures mape mean absolute percentage error and willmott s d this comparison showed that the sets of forecasts revised by the fuzzy model exhibited better results than the original forecasts on both statistical measures for more than two thirds of the evaluated cases

well posedness of linear partial differential equations with unbounded delay operators in this paper we show the well posedness of the following constant delay equation u t au t bu t r t 0 u 0 x u f r 0 where a d a generates a strongly continuous semigroup t t t 0 on a banach space x and b d b is an unbounded and closed linear operator on x our approach is to transform the delay equation into an abstract cauchy problem in a special phase space and apply semigroup theory furthermore we show that the solution semigroup corresponding to the above delay equation is uniformly exponentially bounded finally we give an example to explain the well posedness of delay equations

decoupling and pole assignment of singular systems a frequency domain approach abstract a new approach to the row by row decoupling of singular systems via state feedback and regular input transformation is presented the proposed method is based on the matrix fraction description of the system and is an extension of the frequency domain method for strictly proper systems the solvability condition of the problem is readily obtained from the numerator matrix of a coprime and column reduced matrix fraction description of the given system pole placement and decoupling is also considered and the characterization of the fixed poles is given

on the computation of the fundamental subspaces for descriptor systems abstractin this paper we investigate several theoretical and computational aspects of fundamental subspaces for linear time invariant descriptor systems which appear in the solution of many control and estimation problems different types of reachability and controllability for descriptor systems are described and discussed the rosenbrock system matrix pencil is employed for the computation of supremal output nulling subspaces and supremal output nulling reachability subspaces for descriptor systems

on the structure of strongly controllable systems an important problem in the structure theory of linear systems is the construction of a canonical form for strongly controllable systems i e surjective systems without finite zeros the problem has been solved in principle morse 1973 kronecker 1890 but without a clear identification of the system theoretic meaning of the construction steps this paper proposes the concept of a train basis in order to give this interpretation the second main idea of the paper is the system associated with a sub space through which concept it is possible to translate problems concerning a b invariance etc of subspaces in terms of input output systems in this way we make contact with results of willems 1980 on almost invariance

simultaneous decoupling and disturbance rejection a structural approach abstract the combined problem of disturbance rejection and decoupling for linear systems is considered new necessary and sufficient conditions are derived for the existence of a state feedback controller that rejects the disturbances and simultaneously decouples the closed loop system these conditions are simple intuitively appealing and are expressed in terms of system structural invariants such as infinite zero orders then we consider the disturbance rejection with simultaneous decoupling problem for structured linear systems necessary and sufficient conditions for the generic solvability of this problem are provided they are expressed in terms of input output path length comparisons on the system associated graph

geometric theory for the singular roesser model a e b invariant and e a b invariant subspaces for the two dimensional singular roesser model are investigated these subspaces are related to the existence of the solutions when the boundary conditions are in these subspaces also the existence of a solution sequence in certain subspaces derived from the invariant subspaces is shown the boundary conditions that appear in the solution when some semistates in the solution are restricted to zero are also investigated

a new method for computing a column reduced polynomial matrix a new algorithm is presented for computing a column reduced form of a given full column rank polynomial matrix the method is based on reformulating the problem as a problem of constructing a minimal polynomial basis for the right nullspace of a polynomial matrix closely related to the original one the latter problem can easily be solved in a numerically reliable way three examples illustrating the method are included

a control theory for cartesian flexible robot arms in this article we first use a fourth order partial differential equation with boundary conditions to model a flexible robot arm on a moving base with a payload at the tip end through the state space formulation we show that such a system is both controllable and observable in an infinite dimensional hilbert space we also show that the system is stabilizable via a feedback control

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

algebraic characterizations of almost invariance this paper stresses the algebraic as opposed to analytic nature of the concept of almost invarianoe which has been introduced by willems 1980 as a means of studying asymptotic aspects of linear systems based on an interpretation in terms of difference equations it is shown that the basic properties and a number of characterizations of tho four fundamental classes of subspaces can be derived in a relatively simple and purely algebraic fashion among other things this paper also extends the results of hautus on the frequency domain interpretation of ordinary a b invariant subspaces re derives the pencil characterization of jaffe and karcanias 1981 and obtains a new hybrid type of characterization the last result also loads to a rank test for almost invariance

revision of possibility distributions a bayesian inference pattern abstract in probability theory the bayes rule of inference plays a central role as corroborated by the ever increasing number of applications in various fields the rule allows to revise a prior probability distribution when new information becomes available the posterior probability distribution takes the form of a conditional distribution although several similarities between the possibilistic and probabilistic frameworks have already been reported very few studies in possibility theory have dealt with bayesian inference the objective of this work is to thoroughly study this type of inference and to develop the counterpart of the bayes rule in the possibilistic framework with the use of conditional possibility distributions application of possibility theory wherever bayes theory has already been applied can now be envisaged as a new perspective to uncertainty modeling and processing in the last part of this paper the suitability of the proposed framework for the problem of forecast processing is discussed and an example illustrates the application of various rules of inference corresponding to different aggregation operators

order and the index of singular time invariant linar systems various concepts of order have been proposed in the literature it is shown that many of these are directly related to the index of a system

algebraic characterization of controllability subspaces in the current base and its practical computation from the concepts of input chain and controllability chain introduced by heymann and in view of the generalized eigenvector assignment a new algebraic characterization of controllability subspaces css is developed compared with the previous ones based on matrix pencil theory it presents both the advantages of being stated in the current base and of being derived without resorting to use of canonical forms a practical algebraic algorithm is provided in order to compute the controllable structure of a given pair a b this approach is then applied to characterize css contained in a given subspace and span css via eigenvector assignment

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

galerkin approximation in modeling of controlled distributed parameter flexible systems abstract numerical study of control problems for linear distributed parameter flexible mechanical systems requires finite dimensional modeling of the system we study the conditions for h covergence of the transfer functions of finite dimensional galerkin approximations this convergence ensures that control problems can be solved by using a galerkin model a stabilization problem for the angular position of a bernoulli euler beam illustrates the theoretical consideration the beam with an inertial drive represents a flexible manipulator link

matrix pencil characterization of almost a z invariant subspaces a classification of geometric concepts the equivalence between the algebraic matrix pencil characterization of the sub spaces of the extended geometric theory and their dynamic characterization 13 established as a result a complete classification of almost a b invariant a b invariant almost controllability and controllability subspaces is derived in terms of matrix pencil invariants the frequency propagation aspects of infinite spectrum a b invariant subspaces are investigated and it is shown that they are limits of closed loop eigenspaces with arbitrarily largo eigenvalues finally the importance of the infinite frequency subspaces in the study of the asymptotic behaviour of the closed loop eigenspaces and eigenvalues under scalar gain output feedback is discussed

the disturbance decoupling problem for implicit linear discrete time systems the disturbance decoupling problem for implicit linear discrete time systems is studied in detail necessary and sufficient conditions for the problem to be solved are given the results are obtained with the aid of the concepts of almost invariant sliding and coasting subspaces for implicit systems

proportional and proportional derivative canonical forms for descriptor systems with outputs we construct a new canonical form for descriptor systems e a b c under proportional state feedback proportional output injection and changes of bases in the input space the output space the state space domain and the state equation space codomain geometric characterizations of the invariants are given four pencils are introduced in order to point out the relationships with kronecker s theory of matrix pencils this finally allows us to define canonical forms under proportional plus derivative action

proper and stable minimal macmillan degrees bases of rational vector spaces the structure of proper and stable bases of rational vector spaces is investigated we prove that if t s is a rational vector space then among the proper bases of 3 s there is a subfamily of proper bases which are 1 stable 2 have no zeros in c bigcup infty and therefore are column row reduced at infinity and 3 their macmillan degree is minimum among the macmillan degrees of all other proper bases of 3 s and it is given by the sum of the macmillan degrees of their columns taken separately it is shown that this notion is the counterpart of forney s concept of a minimal polynomial basis for the family of proper and stable bases of 3 s

controllability of second order infinite dimensional systems in the paper the approximate controllability of linear abstract second order infinite dimensional dynamical systems is considered it is proved using the frequency domain method that approximate controllability of second order system can be verified by the approximate controllability conditions for the corresponding simplified first order system general results are then applied for approximate controllability investigation of a vibratory dynamical system modeling flexible mechanical structure some special cases are also considered moreover remarks and comments on the relationships between different concepts of controllability are given the paper extends earlier results on approximate controllability of second order abstract dynamical systems

markovian forecast processes abstract a sequential forecast process arises when forecasts of a fixed but uncertain state are prepared with decreasing lead times each subsequent forecast incorporating additional information and therefore updating the previous forecast bayesian markov models of such a process are investigated for purposes of rational decision making the markov structure although not universally valid seems plausible leads to tractable models and implies sequential sufficiency of forecasts roughly speaking each subsequent forecast is less uncertain than the previous one sequential sufficiency in turn has implications on modeling markov stopping control processes the normal model for point categorical forecasts is studied in detail

on the design of finite dimensional stabilizing compensators for infinite dimensional feedback systems via semiinfinite optimization the computational stability criterion presented by e polak and t l wuu see ibid vol 34 p 196 200 feb 1989 is extended to a form that can be used in the design of finite dimensional stabilizing compensators for a class of feedback systems with infinite dimensional plants since in this case the characteristic function is not a polynomial there is no simple way to define a normalizing polynomial hence approximation theory has to be used the new stability test guarantees not only input output stability but also internal stability of the feedback system furthermore since the numerical implementation of the test does not depend on the use of a reduced plant model the test does not lead to spillover effects because the compensator is parametrized in the state space form the order of the compensator can be assigned by the designer

on the regularizability of singular systems the property of regularity of singular systems is not a feedback invariant to correct this deficiency a new property of regularizability is defined and geometric tests are given for it in terms of system matrices regularizability is shown to be the natural extension of regularity which is a condition on the homogeneous system to controlled singular systems definitions of controllability and reachability are modified depending on regularizability rather than regularity a brief comparison of proportional and proportional plus derivative feedback laws in the context of making the closed loop system regular regular and reachable and regular and controllable is also given dynamical interpretations of these properties are also presented

block decoupling and pole assignment of singular systems a frequency domain approach the problem of block decoupling of singular systems via state feedback and regular input transformation is solved by following an approach based on the matrix fraction description mfd of the system the solvability condition is obtained from the numerator matrix of a coprime and column reduced mfd of the given system the characterization of the fixed poles is given and it is shown that all the non fixed poles can be arbitrarily assigned

generalized reachability subspaces for singular systems one of the most important concepts of the geometric theory for proper linear systems is that of the controllability subspaces of a b in an attempt to extend this concept to singular systems it became clear that the nonequivalence of reachability and controllability for singular systems makes it necessary to define both controllability and reachability subspaces of e a b as different though naturally related entities a subspace bf r respectively bf c is defined to be a generalized reachability subspace respectively generalized controllability subspace if there exist linear maps f and g such that bf r respectively bf c is the reachable respectively controllable subspace of a regular singular system e dot x a bf x bgv it is proved that 1 bf r is a generalized reachability subspace if and only if it is a generalized a e bf b invariant almost reachability subspace 2 every subspace bf k contains a unique supremal generalized reachabi

on disturbance decoupling in descriptor systems the disturbance decoupling problem for a linear multivariable control system is to determine when and how a state feedback may be chosen so that some class of disturbances has no effect on the system output the development of necessary and sufficient conditions for the solvability of this problem for state space systems by wonham and his co workers has profoundly influenced geometric control theory particularly by means of the concept of an a b invariant subspace this paper develops necessary and sufficient conditions for solvability of this problem for linear systems described by a mixture of algebraic and differential equations although the argument presented has the same structure as in the state space case and incorporates a generalisation of a b invariant subspaces to descriptor systems there are some additional issues demanding particularly careful attention is the ensuring of existence and uniqueness of classical solutions of the underlying differential equations which cannot be tak

input output decoupling by output feedback with disturbance attenuation of h control for any square system the combined problem of diagonal decoupling by output feedback with disturbance attenuation performance for any square system is formulated a sufficient condition which is more general than the necessary and sufficient one of static state feedback for the existence of the controller is determined the necessary and sufficient conditions for the controller and decoupled system that are both stable are presented an analytical form and a numerical computable method for the controller are obtained for the first time when the condition is satisfied the correctness of our method is tested by simulations for an example

spectrum and stability for elastic systems with global or local kelvin voigt damping in this paper we study the mathematical properties of a variational second order evolution equation which includes the equations modelling vibrations of the euler bernoulli and rayleigh beams with the global or local kelvin voigt k v damping in particular our results describe the semigroup setting the strong asymptotic stability and exponential stability of the semigroup the analyticity of the semigroup as well as characteristics of the spectrum of the semigroup generator under various conditions on the damping we also give an example to show that the energy of a vibrating string does not decay exponentially when the k v damping is distributed only on a subinterval which has one end coincident with one end of the string

technical communique fixed poles of simultaneous disturbance rejection and decoupling a geometric approach when the simultaneous disturbance rejection and regular block decoupling problem by static state feedback is solvable and under some unrestrictive minimality assumption all the poles of the closed loop system can be placed except the so called fixed poles which are present for any solution we present here a geometric characterization for this set of fixed poles as well as a constructive procedure based on geometric tools for designing a feedback solution of the problem which assigns the remaining poles to arbitrary prespecified locations

frequency domain conditions for disturbance rejection and decoupling with stability or pole placement the problem of disturbance rejection and disturbance rejection while decoupling with stability or pole placement is studied using a polynomial matrix approach necessary and sufficient conditions for the solvability of the problem of disturbance rejection as well as for the problem of disturbance rejection with input output decoupling are derived a number of poles of the closed loop system are proved to be fixed for both of the above problems and a procedure for placing all the remaining poles of the closed loop system is presented

analyticity and differentiability of semigroups associated with elastic systems with damping and gyroscopic forces abstract in this paper we consider a second order variational evolution equation in a hilbert space which can model an elastic system with damping and gyroscopic forces a new form of the corresponding first order evolution equation is introduced and its well posedness is proved by means of the semigroup theory we give sufficient conditions for analyticity and differentiablity of the associated semigroup the results are applied to several pdes with discontinuous coefficients and mechanical boundary conditions it is proved that russell s spacial hysteresis model of a vibrating beam 22 is associated with an exponentially stable analytic semigroup

coercive forms associated with elastic systems with damping abstract we consider the evolution equation u t au t 2ab u t 0 where b is comparable to a for some 1 2 1 this is a model for an elastic system with structural damping and it is known that the system operator associated with this model is the infinitesimal generator of an analytic semigroup on the natural energy space however except for the case of so called kelvin voigt damping 1 this operator is neither sectorial nor associated with a coercive sesquilinear form we show that these properties can be obtained via a different inner product on the energy space

grassmann invariants matrix pencils and linear system properties abstract the paper deals with the establishment of relationships between two different types of invariants defined on matrix pencils and polynomial matrices and highlights their significance in the context of linear systems for general singular matrix pencil sf g the grassmann invariants of the pencil are introduced as the column row grassmann representatives g c f g g r f g t and their corresponding plucker matrices p c f g p r f g the properties of these new invariants of matrix pencils are established these results provide alternative means for classifying the different families of matrix pencils which are important for the characterization of properties in linear systems finally the relationship between the grassmann plucker invariants of a general rational transfer function matrix and the system matrix pencil of a minimal realization is derived the latter results provide means for the computation of transfer function plucker matrices from state space descriptions as well as enable the linking of state space kronecker invariants to the plucker invariants of transfer functions

on the fixed poles for disturbance rejection we propose a geometric characterization of the fixed poles for the disturbance rejection problem by static state feedback and in the particular case when the system is controllable a structural characterization in terms of finite invariant zeros of certain open loop subsystems we propose solutions through which all the other poles can be freely assigned

canonical forms for descriptor systems under restricted system equivalence abstract the problem of canonical forms of implicit descriptor systems under restricted system equivalence is considered it is shown that the canonical form is directly related to the echelon form of the autoregressive matrix inducing the external behavior of the system the proposed canonical form is a generalization of the popov form and is also valid for singular systems under transfer equivalence

disturbance decoupling with stability and impulse free response in singular systems abstract the problem of disturbance decoupling with stability and impulse free response in square singular systems e x ax bu gq with output y dx by applying a state feedback u fx is considered by employing van dooren s recursive algorithm for the computation of the subspace supremal a b invariant subspace in kernel d and using kalman s decomposition theorem the paper s approach presents a complete solution to the underlying problem regarding state space systems it is shown that the solution to the underlying problem is obtained almost directly from van dooren s recursive algorithm

geometric and algebraic properties of minimal bases of singular systems for a general singular system with an associated pencil t s a complete classification of the right polynomial vector pairs connected with the rational vector space is given according to the proper nonproper property characterising the relationship of the degrees of those two vectors an integral part of the classification of right pairs is the development of the notions of canonical and normal minimal bases for and rational vector spaces where r s is the state restriction pencil of it is shown that the notions of canonical and normal minimal bases are equivalent the first notion characterises the pure algebraic aspect of the classification whereas the second is intimately connected to the real geometry properties and the underlying generation mechanism of the proper and nonproper state vectors the results describe the algebraic and geometric dimensions of the invariant partitioning of the set of reachability indices of singular systems the classification of all proper and nonproper polynomi

minimal bases of matrix pencils algebraic toeplitz structure and geometric properties abstract for a singular matrix pencil sf g the structure of the right rational null space h r is studied and new algebraic and geometric properties and invariants are established the results highlight the nature of the isomorphism between polynomial vectors of h r and real vectors in the right spaces n k r k 0 defined as null spaces of toeplitz matrices of f g the algebraic structure of l r is described by the properties of ordered minimal bases as well as those of new invariants the prime r s modules m i i the geometric structure of h r is defined by the properties of new invariant spaces p i p i r i associated with m i i m the high low and prime spaces as well as some additional invariant spaces defined through the toeplitz representation of ordered minimal bases these new invariant spaces and modules are shown to be naturally defined also on the right spaces n kr and this provides an alternative geometric definition of them which is independent of the original algebraic one it is shown that the construction of an ordered minimal basis is equivalent to a standard linear algebra problem the selection of a right system of generators for n k r k 0 finally certain parametrization issues for the polynomial vectors of h r are considered

simplified conditions of initial observability for infinite dimensional second order damped dynamical systems abstract in the paper the initial observability of abstract second order infinite dimensional dynamical systems is considered two cases of observation operator are explored first the observation operator is assumed to be bounded then results are extended to more general class of observations related to the observation operators that are assumed to be bounded with respect to square root of elasticity operator which covers the case of some unboundedness in observation using the frequency domain method it is proved that initial observability of second order system under discussion can be verified by the initial observability conditions for the corresponding simplified first order system general results are then applied for initial observability investigation of infinite dimensional systems described by partial differential equations modelling flexible mechanical structures some special cases are also discussed and practical comments and remarks are given the paper extends earlier results on initial observability for a class of infinite dimensional second order abstract dynamical systems

analyticity and exponential stability of semigroups for the elastic systems with structural damping in banach spaces abstract in this paper we consider a second order evolution equation in a banach space which can model an elastic system with structural damping new forms of the corresponding first order evolution equation are introduced and their well posed property is proved by means of the operator semigroup theory we give sufficient conditions for analyticity and exponential stability of the associated semigroups

to protect or not to protect bayes decisions with forecasts abstract a complete model structural characterization and analytic representation of the bayes solution is presented for a protection problem it is a sequential stationary finite horizon markov decision process involving at each stage a dichotomous action a binary state and a one period ahead forecast of an independent over time bernoulli input process two types of forecasts categorical and probabilistic are considered along with their limiting cases the naive and perfect forecasts the concept of sufficiency is introduced and operationalized so that consistent comparisons of forecasts can be made with respect to both statistical and economic criteria mappings between the sufficiency ordering and the optimal decision strategy are proven or illustrated numerically

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

necessary conditions for exact controllability with a finite dimensional input space we derive necessary conditions for exact controllability of infinite dimensional systems described by x ax bu where the generator a has a riesz basis of eigenvectors and the input space is finite dimensional these conditions are in terms of the eigenvalues of a and the degree of unboundedness of b but no further information about b is needed our results easily imply lack of exact controllability for a wide range of distributed parameter systems it is known from partial differential equation pde examples that the addition of damping into an exactly controllable second order system can destroy exact controllability we discuss the effect of damping on such systems using our general conditions we also give simple new proofs for results about the lack of exact controllability of hyperbolic systems in more than one space dimension

regularity analysis for an abstract system of coupled hyperbolic and parabolic equations abstract in this paper we provide a complete regularity analysis for the following abstract system of coupled hyperbolic and parabolic equations u t t a u a w w t a u t k a w u 0 u 0 u t 0 v 0 w 0 w 0 where a is a self adjoint positive definite operator on a complex hilbert space h and 0 1 0 1 we are able to decompose the unit square of the parameter into three parts where the semigroup associated with the system is analytic of specific order gevrey classes and non smoothing respectively moreover we will show that the orders of gevrey class is sharp under proper conditions

a solution to the disturbance decoupling problem in singular systems via analogy with state space systems abstract this paper presents an approach for solving the disturbance decoupling problem in a square linear time invariant singular system a simple criterion and an efficient algorithm for solving the underlying problem by applying a state feedback which preserves the uniqueness property of the closed loop singular system has been established the present algorithm is based on a well established approach borrowed from state space system theory

norm continuity fort 0 of propagators of arbitrary order abstract differential equations in hilbert spaces let acpn u n t n 1k 0aku k t 0 t 0 u k 0 uk 0 k n 1 be strongly wellposed where theak 0 k n 1 are densely defined closed linear operators in a hilbert space letsk t 0 k n 1 be the propagators of acpn andp ni n 1k 0 kak it is shown thats k k t 0 k n 1 is norm continuous fort 0 if and only if lim omega to infty left tau 0 i omega n 1 p tau 0 i omega 1 right 0 lim omega to infty left tau 0 i omega k 1 overline p tau 0 i omega 1 a k right 0 qquad 1 le k n le n 1 for a suitable real number 0

a complete classification of minimal realizations of nonsingular and strictly proper transfers under similarity transformations we consider minimal realizations of square nonsingular and strictly proper transfer matrices equivalence classes of all such realizations under similarity transformations are characterized via a canonical form

existence results for some damped second order volterra integro differential equations abstract in this paper we make a subtle use of operator theory techniques and the well known schauder fixed point principle to establish the existence of pseudo almost automorphic solutions to some second order damped integro differential equations with pseudo almost automorphic coefficients in order to illustrate our main results we will study the existence of pseudo almost automorphic solutions to a structurally damped plate like boundary value problem

a characterization of norm continuity of propagators for second order abstract differential equations abstract in this paper we obtain a concise characterization of norm continuity for t 0 of propagators for the complete second order abstract differential equation on a banach space e u t bu t au t 0 t 0 where b l e as a consequence we discover that a strongly continuous cosine operator function or operator group is norm continuous for t 0 if and only if its generator is bounded

some geometric considerations about the kronecker normal form abstract in the first part of this paper we develop general algorithms from the kronecker normal form of any matrix pencil and give some of their properties in the second part these results are applied to the so called restricted matrix pencil associated with a given c a b system and introduced by jaffe and karcanias 1981 this allows us to make a link with well known algorithms of the geometric approach particularly the a b invariant subspace algorithm and the almost a b controllability subspace algorithm finally relationships between morse s invariants morse 1973 and the invariants of the restricted matrix pencil are exhibited

reachability and controllability indices for linear descriptor systems abstract it is now well understood that reachability and controllability are different properties of descriptor systems these properties can be studied through some lists of integers namely the reachability and controllability indices the aim of this note is to recall the geometric definition and to give two polynomial characterizations of these indices

right left characteristic sequences and column row minimal indices of a singular pencil for a general singular pencil sf g m n s the right left characteristic sequences r f g l f g are defined and they are shown to be of the piecewise arithmetic progression type the sets of column row minimal indices c f g r f g are defined by a singular points analysis of r f g l f g respectively thus c f g r f g emerge as numerical invariants of the ordered pair f g and they may be computed by rank tests on toeplitz matrices defined on f g

numerical computation of a coprime factorization of a transfer function matrix abstract a new algorithm is presented for computing a coprime factorization of a transfer function matrix the method is based on reformulating the problem as a problem of constructing a minimal basis of the right nullspace of a matrix pencil b a due to the special structure and rank properties of the pencil obtained after transforming b a to generalized schur form the original problem can be easily solved in a numerically reliable way

proper invariant realizations of singular system problems the notion of proper invariant realization of a triple for a specially defined linear space is introduced and its properties and construction are investigated this notion of realization allows the reduction of the study of dynamic characterization of subspaces of singular systems to standard problems of linear systems theory the proof of the results is given

characterization of domains of fractional powers of certain operators arising in elastic systems and applications with x a hilbert space where a the elastic operator and b the damping operator are closed operators in x with dense domains q a and 9 b respectively moreover a is throughout assumed to be self adjoint and strictly positive stimulated by two conjectures raised in crl the most general of which referred to the case lx f described below we have already studied the operators and sb defined respectively by

further theoretical results on direct strain feedback control of flexible robot arms this paper is concerned with stability analyses for some nonstandard second order partial differential equations arising from direct strain feedback control of flexible robot arms exponential stability issues are addressed for three types of differential equations one of which is in general abstract evolution equation form and the other two are in partial differential equation form the obtained results are of especially theoretical interest because they reveal the essence of direct strain feedback control and demonstrate its power in control of flexible arms

inner and outer geometry for singular systems with computation of subspaces abstract output nulling and unknown input subspaces are defined for singular systems with recursions given for their computation inner i e domain subspaces are distinguished from outer i e codomain subspaces a general duality theory is presented and the composite image composite pre image and composite subspaces are introduced it is shown how output nulling and unknown input subspaces may be computed via the singular system structure algorithm and a new square root algorithm the latter algorithm is shown to be related to the solution of a riccati equation for singular systems a simplified riccati solution procedure is introduced that only requires the solution of a non square lyapunov equation and also applies in the state variable case

numerical computation of minimal polynomial bases a generalized resultant approach we propose a new algorithm for the computation of a minimal polynomial basis of the left kernel of a given polynomial matrix f s the proposed method exploits the structure of the left null space of generalized wolovich or sylvester resultants to compute row polynomial vectors that form a minimal polynomial basis of left kernel of the given polynomial matrix the entire procedure can be implemented using only orthogonal transformations of constant matrices and results to a minimal basis with orthonormal coefficients

exponential stability of solutions for higher order abstract cauchy problems abstract this paper investigates the condition ensuring the exponential stability of solutions for the following higher order abstract cauchy problem formula where a 0 a n 1 are linear operators in a complex banach space e new concise criteria are obtained

on the mathematical model for linear elastic systems with analytic damping in the present paper we investigate linear elastic systems with damping ddot y b dot y ay 0 in hilbert spaces where a is a positive definite unbounded linear operator and b is a closed linear operator related in various ways to a alpha frac 1 2 leqq alpha leqq 1 we discuss the spectral property of these systems and obtain some fundamental results for the holomorphic property and the exponential stability of the semigroups associated with these systems

generalized linear systems geometric and structural approaches abstract this paper presents a new way of introducing invariant subspaces for generalized systems this comes from somewhat known geometric algorithms but in most cases with initial conditions different from those usually seen in this context these definitions are shown to be consistent with other ones directly deduced from classical approaches like matrix pencil tools or discrete algebraic formalism the key starting point for their introduction is the extension of structural descriptions for these generalized systems such as have been available for proper systems many results from the proper case can thus be extended for instance the geometric definition for controllability indices and something similar to the famous morse canonical decomposition of the strictly proper case some links with the inversion algorithm are also sketched

calibration sufficiency and domination considerations for bayesian probability assessors abstract degroot and fienberg 1982a recently considered various aspects of the problem of evaluating the performance of probability appraisers after briefly reviewing their notions of calibration and sufficiency we introduce related ideas of semicalibration and domination and consider their relationship to the earlier concepts we then discuss some simple bayesian mechanisms for making probability assessments and study their calibration semicalibration sufficiency and domination properties finally several results concerning the comparison of finite dichotomous experiments relevant to the present work are collected in an appendix

a transfer matrix approach to feedback invariants of linear systems application to decoupling abstract the transfer matrix approach allows one to exhibit fairly easily fundamental invariants of multivariable systems under the action of transformation groups these transformation groups include the classical state feedback state and input changes of coordinates then the solvability of numerous classical control problems e g decouplability disturbance rejection model following can be expressed directly in terms of these invariants in this expository paper we present in a unified way three lists of feedback invariants related to the infinite behavior of linear systems these invariants turn out to be crucial in studying feedback decoupling problems the main tools for this study are factorization of transfer matrices over the p i d of proper rational functions when dealing with stability we factor transfer matrices over the p i d of proper rational stable functions we illustrate the use of these invariants by studying some decoupling problems

monotone iterative technique for the elastic systems with structural damping in banach spaces in this paper we use a monotone iterative technique in the presence of lower and upper solutions to discuss the existence of mild solutions to a second order evolution equation initial value problem in an ordered banach space which can model an elastic system with structural damping under monotone condition and the noncompactness measure condition on nonlinearity we obtain the existence of extremal mild solutions and positive mild solutions moreover some applications are given to illustrate our theoretical results

condensed forms of linear control system under output feedback abstract we present two complementary condensed forms of linear control system with output x a x b u x r n u r m y c x y r r under transformation of the state coordinates from them we derive two complementary condensed forms under output feedback as an application of the condensed forms we show that the output feedback control of the linear control systems generically reduces to a matrix completion problem and we provide a partial solution of that problem based on existing methods

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

semigroups arising from elastic systems with dissipation abstract in this paper we investigate the properties norm continuity differentiability analyticity and exponential stability of semigroups arising from elastic systems with dissipation the resulting theorems are complete in a sense extensions of 1 theorem 1 1 and 2 theorem 1 1

integrated semigroups and higher order abstract equations abstract let e be a banach space b 0 b n 1 closed linear operators on e and f 0 e this paper is devoted to the study of well posedness of the cauchy problem for higher order abstract differential equations formula using the theory of integrated semigroups we obtain some concise and useful criteria

numerical approach to the non linear diofantic equations with applications to the controllability of infinite dimensional dynamical systems the article is devoted to the analysis of the approximate controllability of a given type of second order infinite dimensional system defined by the hyperbolic type partial differential equation with dirichlet like type zero boundary conditions defined in the n dimensional rectangular prism following this aim spectral theory for linear unbounded operators is involved new numerical algorithms for solving some kind of non linear diofantic equations corresponding with the spectral properties of the unbounded operators are presented and proved an algorithm is optimized for eliminating the symmetrical solutions not interesting in the scope of verification of the controllability next the limit which shows that the direct application of the analytical methods of verifying the controllability in the numerical approach is impossible is proved finally so called partial approximate controllability is defined and the numerical algorithm for its verification is presented finally proven theorems are applied

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

controllability of dynamical systems with constraints abstract the article is devoted to analysing the approximate controllability without constrains and constrained controllability with non negative controls of a given type second order infinite dimensional system the considered dynamical system is governed by evolution equation with three damping terms and three terms without derivatives following this aim spectral theory for linear unbounded operators is involved at first remind the representation of considered infinite dimensional dynamical system by the infinite series of finite dimensional systems next two theorems on necessary and sufficient conditions of unconstrained and constrained approximate controllability of considered system are formulated and proved finally proven theorems are applied to two particular dynamical systems including one infinite dimensional