information induced multimodel solutions in multiple decisionmaker problems this paper is concerned with modeling and control strategy interaction in a multimodel context the role of the observability structure in multiple decisionmaker dm problems is examined a procedure is developed for generating multimodel solutions based on certain deterministic information patterns this is achieved by first explicitly identifying the state space structure induced by the observation sets of the dm s and then overlapping appropriately the input space structure of each dm such a representation is used to identify the class of admissible strategies which generate multimodel solutions conditions which depend on the information pattern are obtained under which these multimodel solutions admit partial noninteraction among the dm s

a topological approach to periodic oscillations related to the liebau phenomenon abstract we give some sufficient conditions for existence non existence and localization of positive solutions for a periodic boundary value problem related to the liebau phenomenon our approach is of topological nature and relies on the krasnosel ski guo theorem on cone expansion and compression our results improve and complement earlier ones in the literature

existence of one signed periodic solutions of some second order differential equations via a krasnoselskii fixed point theorem this paper is devoted to study the existence of periodic solutions of the second order equation x 00 f t x where f is a caratheodory function by combining some new properties of green s function together with krasnoselskii fixed point theorem on compression and expansion of cones as applications we get new existence results for equations with jumping nonlinearities as well as equations with a repulsive or attractive singularity in this latter case our results cover equations with weak singularities and are compared with some recent results by i rachunkova m tvrdyand i vrkoc r 2002 elsevier science usa all rights reserved

on the semi convergence of interval matrices we derive a necessary and sufficient criterion for the convergence of powers of interval matrices a to a limit which may differ from o generalizing former results we allow now the absolute value a of a to be reducible with minor additional restrictions

positivity and lower and upper solutions for fourth order boundary value problems abstract this paper is devoted to the study the boundary value problem u 4 t f t u t for all t i 0 1 u 0 u 1 u 0 u 1 0 we prove the existence of at least one two or three solutions in the presence of a pair of not necessarily ordered lower and upper solutions the proof follows from maximum principles related to the operator u 4 m u and amann s three solutions theorem

on regular and singular interval systems we give a survey on interval linear systems discussing problems for regular systems as well as for singular ones we consider several solution sets and direct methods to enclose them moreover we study iterative methods particularly the total step method as the basis for other ones we also use this method for enclosing solutions of singular linear systems

on the convergence of the neumann series in interval analysis abstract let a be a real or complex n n interval matrix then it is shown that the neumann series k 0 a k is convergent iff the sequence a k converges to the null matrix o i e iff the spectral radius of the real comparison matrix b constructed in 2 is less than one

the method of lower and upper solutions for third order periodic boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem l n u t t u t u i 0 u i 2 i r i 0 n 1 with ln an nth order linear operator and a caratheodory function we obtain sufficient conditions to guarantee the validity of the monotone method for this problem for this we study the sign of the green function of the operator t 1n with tnu lnu mu m 0 furthermore existence results are obtained we show that the results obtained are optimal given a lower solution and an upper solution we obtain the existence of solution between and when either or this general study is applied to the third order problem u t pu t qu t t u t u i 0 u i 2 i r i 0 1 2 with p q r for this problem we obtain the best value on the constant m to guarantee that the green function of the operator t 13 is positive

convergence of max arithmetic mean powers of a fuzzy matrix fuzzy matrices provide convenient representations for fuzzy relations on finite universes in the literature the powers of a fuzzy matrix with max min max product max archimedean t norm compositions have been studied it turns out that the limiting behavior of the powers of a fuzzy matrix depends on the composition involved in this paper the max arithmetic mean composition is considered for the fuzzy relations we show that the max arithmetic mean powers of a fuzzy matrix always are convergent

controllability and observability of coordinated linear systems abstract this paper develops concepts of controllability and observability for the class of coordinated linear systems a special class of linear hierarchical systems with a top to bottom information structure the usual concepts of reachability and indistinguishability for linear systems are refined taking into account the decentralized nature of coordinated linear systems the corresponding controllability and observability decompositions are derived and several concepts of controllability and observability for coordinated linear systems are introduced and discussed these results are then combined to a definition and characterization of stabilizability via dynamic measurement feedback for this class of systems

survey generic properties and control of linear structured systems a survey in this survey paper we consider linear structured systems in state space form where a linear system is structured when each entry of its matrices like a b c and d is either a fixed zero or a free parameter the location of the fixed zeros in these matrices constitutes the structure of the system indeed a lot of man made physical systems which admit a linear model are structured a structured system is representative of a class of linear systems in the usual sense it is of interest to investigate properties of structured systems which are true for almost any value of the free parameters therefore also called generic properties interestingly a lot of classical properties of linear systems can be studied in terms of genericity moreover these generic properties can in general be checked by means of directed graphs that can be associated to a structured system in a natural way we review here a number of results concerning generic properties of structured systems expressed in graph theoretic terms by properties we mean here system specific properties like controllability the finite and infinite zero structure and so on as well as solvability issues of certain classical control problems like disturbance rejection input output decoupling and so on in this paper we do not try to be exhaustive but instead by a selection of results we would like to motivate the reader to appreciate what we consider as a wonderful modelling and analysis tool we emphasize the fact that this modelling technique allows us to get a number of important results based on poor information on the system only moreover the graph theoretic conditions are intuitive and are easy to check by hand for small systems and by means of well known polynomially bounded combinatorial techniques for larger systems

brief paper simultaneous schur stability of interval matrices interval matrix structures are ubiquitous in nature and engineering ordinarily in an uncertain system there is associated with a set of coupled interval matrices a basic issue of exploring its asymptotic stability here we introduce the notion of simultaneous schur stability by linking the concepts of the majorant and the joint spectral radius and prove the asymptotic stability of a set of interval matrices governed by simultaneous schur stability the present result may lead to the stability analysis of discrete dynamical interval systems

an inequality for the spectral radius of an interval matrix abstract for an n n interval matrix a aij we say that a is majorized by the point matrix a a ij if aij aij when the jth column of a has the property that there exists a power a m containing in the same jth column at least one interval not degenerated to a point interval and aij aij otherwise denoting the generalized spectral radius in the sense of daubechies and lagarias of a by a and the usual spectral radius of a by a it is proved that if a is majorized by a then a a this inequality sheds light on the asymptotic stability theory of discrete time linear interval systems

on power boundedness of interval matrices abstract in a recent paper by g mayer 8 the convergence of the sequence a k of the powers of an interval matrix a to the nullmatrix was investigated in this note we give some conditions for the boundedness of the sequence k a k where is a nonnegative number the connection to the stability of the set a is discussed

on the convergence of powers of interval matrices abstract we give a necessary and sufficient condition for the sequence a k of the powers of an interval matrix a to converge to the null matrix o we construct a point matrix b which has spectral radius b less than one if a k converges

on the convergence of powers of interval matrices 2 let mathfrak a be a real irreduciblen n interval matrix then a necessary and sufficient condition is given for the sequence mathfrak a k of the powers of an interval matrix mathfrak a to converge to a matrix mathfrak a infty which is not the null matrix in addition a criterion for mathfrak a is proved to decide whether the limit matrix mathfrak a infty satisfies the condition of symmetry mathfrak a infty mathfrak a infty

sufficient conditions for the stability of linear takagi sugeno free fuzzy systems in this paper we will study the stability issues of the linear takagi sugeno t s free fuzzy systems based on matrix norm we propose a new sufficient condition for the linear t s free fuzzy system to be globally asymptotically stable we then study the stability analysis in the case of systems with consequent parameter uncertainty based on mayer s convergent theorem we propose a sufficient condition which is easily implemented for the systems with consequent parameter uncertainty to be globally asymptotically stable

computation of green s functions for boundary value problems with mathematica abstract this paper is devoted to construct an algorithm that allows us to calculate the explicit expression of the green s function related to a n th order linear ordinary differential equation with constant coefficients coupled with two point linear boundary conditions we develop this algorithm by making a mathematica package

maximum and antimaximum principles for a second order differential operator with variable coefficients of indefinite sign new criteria for the existence of a maximum or antimaximum principle of a general second order operator with periodic conditions as well as conditions for nonresonance are provided and compared with the related literature

on the sign of the green s function associated to hill s equation with an indefinite potential abstract in this note we give a l p criterium for the positiveness of the green s function of the periodic boundary value problem x a t x 0 x 0 x t x 0 x t with and indefinite potential a t moreover we prove that such green s function is negative provided a t belongs to the image of a suitable periodic ricatti type operator

hierarchically consistent control systems large scale control systems typically possess a hierarchical architecture in order to manage complexity higher levels of the hierarchy utilize coarser models of the system resulting from aggregating the detailed lower level models in this layered control paradigm the notion of hierarchical consistency is important as it ensures the implementation of high level objectives by the lower level system in this paper we define a notion of modeling hierarchy for continuous control systems and obtain characterizations for hierarchically consistent linear systems with respect to controllability objectives as an interesting byproduct we obtain a hierarchical controllability criterion for linear systems from which we recover the best of the known controllability algorithms from numerical linear algebra

positive solutions of nonlinear fourth order boundary value problems with local and non local boundary conditions we establish new existence results for multiple positive solutions of fourth order nonlinear equations which model deflections of an elastic beam we consider the widely studied boundary conditions corresponding to clamped and hinged ends and many non local boundary conditions with a unified approach our method is to show that each boundary value problem can be written as the same type of perturbed integral equation in the space c 0 1 involving a linear functional u but although we seek positive solutions the functional is not assumed to be positive for all positive u the results are new even for the classic boundary conditions of clamped or hinged ends when u 0 because we obtain sharp results for the existence of one positive solution for multiple solutions we seek optimal values of some of the constants that occur in the theory which allows us to impose weaker assumptions on the nonlinear term than in previous works our non local boundary conditions contain multi point problems as special cases and for the first time in fourth order problems we allow coefficients of both signs

comparison results for first order linear operators with reflection and periodic boundary value conditions abstract this work is devoted to the study of the first order operator x t m x t coupled with periodic boundary value conditions we describe the eigenvalues of the operator and obtain the expression of its related green s function in the non resonant case we also obtain the range of the values of the real parameter m for which the integral kernel which provides the unique solution has constant sign in this way we automatically establish maximum and anti maximum principles for the equation some applications to the existence of nonlinear periodic boundary value problems are shown

a necessary and sufficient condition for robust asymptotic stability of time variant discrete systems a necessary and sufficient condition for the stability of time variant interval matrices is presented this condition allows stability to be tested by checking only products of vertex extreme matrices the implementation of the test in the form of an algorithm and two illustrative examples are provided

green s functions and spectral theory for the hill s equation the aim of this paper is to show certain properties of the green s functions related to the hill s equation coupled with various two point boundary value conditions we will obtain the expression of the green s function of neumann dirichlet mixed and anti periodic problems as a combination of the green s function related to periodic ones as a consequence we will prove suitable results in spectral theory and deduce some comparison results for the solutions of the hill s equation with various boundary value conditions

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

letter section a note about power boundedness of interval matrices in this note we simplify the main theorem on power boundedness of interval matrices of garloff 1986 in addition another new result about powers of interval matrices is given

on the stability of takagi sugeno fuzzy systems with time varying uncertainties this paper studies the problems of stability analysis of takagi sugeno free fuzzy systems with time varying uncertainties in our prior study we represented the time varying uncertainty incurred in characteristic interval matrices in terms of the stability of takagi sugeno free fuzzy systems with consequent parameter uncertainties based on mayer s convergent theorem for powers of single interval matrix and its generalization we further proposed some sufficient conditions for the takagi sugeno free fuzzy system with time varying uncertainties to be globally asymptotically stable in this paper we propose the notion of simultaneously nilpotent interval matrices to investigate the takagi sugeno free fuzzy system with time varying uncertainties to be strongly stable within steps where relates to the dimension of interval matrices moreover a unique situation for the deterministic takagi sugeno free fuzzy system to be strongly stable within steps is derived as well where relates to the dimension of characteristic matrices for the deterministic takagi sugeno free fuzzy system

lq control for coordinated linear systems coordinated linear systems are a special class of hierarchical linear systems with a strict top to bottom information structure the lq problem over all structure preserving static state feedbacks is discussed the overall control problem separates into conditionally independent subproblems a numerical approach to their solution is derived and the behavior and performance of the resulting control law are illustrated in examples

remarks on the lower and upper solutions method for second and third order periodic boundary value problems we study the solvability and the approximation of the solutions by monotone iteration of the second and third order periodic boundary value problems bvps u cu t u u 0 u email protected u 0 u email protected and email protected au bu t u u 0 u email protected u 0 u email protected u 0 u email protected in the presence of lower and upper solutions which may not satisfy the usual ordering condition to this end some maximum and antimaximum principles are stated and proved for certain linear differential operators naturally associated with the previously stated problems

maximum and anti maximum principles for the general operator of second order with variable coefficients this paper is devoted to the study of existence of solutions of the nonlinear second order differential equation u t p t u t f t u t 0 together with different types of linear boundary conditions to this end we assume the existence of a pair of ordered lower and upper solutions and deduce comparison results for the general linear operator l p q u t u t p t u t q t u t together with the condisered boundary conditions

on the solutions of the quaternion interval systems x a x b abstract it is known that linear matrix equations have been one of the main topics in matrix theory and its applications the primary work in the investigation of a matrix equation system is to give solvability conditions and general solutions to the equation s in the present paper for the quaternion interval system of the equations defined by x a x b where a is a quaternion interval matrix and b and x are quaternion interval vectors we derive a necessary and sufficient criterion for the existence of solutions x thus we reduce the existence of a solution of this system in quaternion interval arithmetic to the existence of a solution of a system in real interval arithmetic

construction and minimality of coordinated linear systems coordinated linear systems are a particular class of hierarchical systems with a top to bottom information structure consisting of a coordinator system and two or more subsystems this paper deals with the construction and minimality of coordinated linear systems construction procedures are given to transform unstructured or interconnected systems into coordinated linear systems using the geometric i e basis independent concepts of observability and controllability subspaces several concepts of minimality for coordinated linear systems are suggested and characterized in order to identify decompositions which are as decentralized as possible the extension of the developed methods and results to the broader class of hierarchical linear systems is discussed 2014 elsevier inc

the method of lower and upper solutions for second third fourth and higher order boundary value problems abstract in this paper we develop the monotone method in the presence of lower and upper solutions for the problem u n t t u t u i a u i b i r i 0 n 1 where is a caratheodory function we obtain necessary and sufficient conditions in to guarantee the existence of solutions between a lower solution and an upper solution for n 2 if n 3 either or and n 4 if furthermore we obtain sufficient conditions in for n 2 k 6 when