an aggregate label setting policy for the multi objective shortest path problem we consider label setting algorithms for the multi objective shortest path problem with any number of sum and bottleneck objectives we propose a weighted sum aggregate ordering of the labels specifically tailored to combine sum and bottleneck objectives we show that the aggregate order leads to a consistent reduction of solution times up to two thirds with respect to the classical lexicographic order

on the stability of fuzzy systems studies the global asymptotic stability of a class of fuzzy systems it demonstrates the equivalence of stability properties of fuzzy systems and linear time invariant lti switching systems a necessary and sufficient condition for the stability of such systems are given and it is shown that under the sufficient condition a common lyapunov function exists for the lti subsystems a particular case when the system matrices can be simultaneously transformed to normal matrices is shown to correspond to the existence of a common quadratic lyapunov function a constructive procedure to check the possibility of simultaneous transformation to normal matrices is provided

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

an algorithm for ranking paths that may contain cycles abstract in this paper an algorithm is presented for determining the k best paths that may contain cycles in a directed network the basic idea behind the algorithm is quite simple once the best path has been determined it is excluded from the network in such a way that no new path is formed and no more paths are excluded this step leads to an enlarged network where all the paths but the best one can be determined the method is repeated until the desired paths have been computed the proposed algorithm can be used not only for the classical k shortest paths problem but also for ranking paths under a nonlinear objective function provided that an algorithm to determine the best path exists computational results are presented and comparisons with other approaches for the classical problem are made

optimal paths in bi attribute networks with fractional cost functions abstract an important routing problem is to determine an optimal path through a multi attribute network which minimizes a cost function of path attributes in this paper we study an optimal path problem in a bi attribute network where the cost function for path evaluation is fractional the problem can be equivalently formulated as the bi attribute rational path problem which is known to be np complete we develop an exact approach to find an optimal simple path through the network when arc attributes are non negative the approach uses some path preference structures and elimination techniques to discard from further consideration those partial paths that cannot be parts of an optimal path our extensive computational results demonstrate that the proposed method can find optimal paths for large networks in very attractive times

saturated finite interval iterative learning for tracking of dynamic systems with hnn structural output this brief investigates the interval iterative learning problem for dynamic systems with hierarchical neural network hnn structural output the first objective is to design the output of a dynamic system with hnn structure a sufficient condition is obtained to achieve the interval tracking in a finite interval by applying iterative learning control ilc then the saturated ilc is considered into the discussed system and a less conservative criterion is obtained to achieve the tracking in a finite interval using a network structure decomposition technique finally simulation results are given to illustrate the usefulness of the developed criteria

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

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

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

on the asymptotic stability of free fuzzy systems it has been shown by thathachar and viswanath ibid vol 5 p 145 51 1997 that the stability of takagi and sugeno s fuzzy system is equivalent to that of a corresponding switching system with finite number of characteristic matrices in this correspondence we shall correct a false proof of a result in thathachar and viswanath

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

sets of matrices all infinite products of which converge an infinite product iit lmi of matrices converges on the right if limi m mi exists a set z ai i l of n x n matrices is called an rcp set rightconvergent product set if all infinite products with each element drawn from z converge such sets of matrices arise in constructing self similar objects like von koch s snowflake curve in various interpolation schemes in constructing wavelets of compact support and in studying nonhomogeneous markov chains this paper gives necessary conditions and also some sufficient conditions for a set x to be an rcp set these are conditions on the eigenvalues and left eigenspaces of matrices in 2 and finite products of these matrices necessary and sufficient conditions are given for a finite set z to be an rcp set having a limit function m d rit lad where d d d which is a continuous function on the space of all sequences d with the sequence topology finite rcp sets of column stochastic matrices are completely characterized some results are given on the problem of algorithmically deciding if a given set x is an rcp set

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

iterative learning control for discrete time systems with event triggered transmission strategy and quantization this paper investigates the iterative learning problem for discrete time systems with event triggered scheme and quantization the event triggered scheme is firstly considered in the iterative learning controllers to reduce the number of iteration steps to be updated here the event triggered scheme is designed depending on time t and iterative learning step k quantization is then introduced in the event triggered controllers and some relaxed conditions are presented to guarantee the tracking problem by using some interval matrix properties finally simulation results are given to illustrate the usefulness of the developed criteria

on the stability of discrete time linear interval systems abstract a general contraction mapping based method is proposed for studying the stability of linear interval systems sufficient conditions for the system uniform asymptotic stability using the products of vertex matrices are provided

brief paper stability analysis of discrete time iterative learning control systems with interval uncertainty this paper presents a stability analysis of the iterative learning control ilc problem for discrete time systems when the plant markov parameters are subject to interval uncertainty using the so called super vector approach to ilc vertex impulse response matrices are employed to develop sufficient conditions for both asymptotic stability and monotonic convergence of the ilc process it is shown that the stability of such interval ilc systems can be determined by checking the stability of the system using only the vertex points of the interval markov parameters

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

polynomial identities in graded group rings restricted lie algebras and p adic analytic groups let g be any finitely generated group and let k be a field of characteristic p 0 it is shown that the graded group ring gr kg satisfies a nontrivial polynomial identity if and only if the pro p completion of g is p adic analytic i e can be given the structure of a lie group over the p adic field q p the proof applies theorems of lazard quillen and passman as well as results on engel lie algebras and on dimension subgroups in positive characteristic

a bicriterion shortest path algorithm abstract among the network models one of the more popular is the so called shortest path problem this model is used whenever it is intended to minimize a linear function which represents a distance between a predetermined pair of nodes in a given network often a single objective function is not sufficient to completely characterize some real world problems for instance in a road network two parameters as cost and time can be assigned to each arc clearly the fastest path may be too costly nevertheless the decision maker must choose one solution possibly not the best for both criteria in this paper we present an algorithm for this problem with this algorithm a special set of paths the set of pareto optimal paths is determined one objective for any pareto optimal path can not be improved without worsening the other one

dimension subgroups nilpotency indices and the number of generators of ideals in p group algebras abstract various problems in modular p group algebras are solved through extensive study of dimension subgroups as an application it is shown that if g is an infinite res p group p 2 and k is a field of characteristic p then the least upper bound on the numbers of generators of ideals in kg equals the minimal index of a cyclic subgroup of g

extreme point robust stability results for discrete time polynomials this paper provides some new extreme point robust stability results for discrete time polynomials with special uncertainties in the coefficient space the proofs obtained using the bilinear transformation are simple and the results specialize to existing robust stability results

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

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

exact maximum singular value of a complex interval matrix this paper shows that exact maximum singular value of a complex interval matrix can be found from a set of selected matrices the results include both square interval matrix and generalized non square interval matrix three illustrative examples are presented to verify the validity and utility of the proposed method

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

on a special class of bicriterion path problems abstract in this paper we are concerned with a special class of bicriterion path problems for the considered class of bicriterion problems at least one of the objectives is type maxmin for the other one besides an objective type maxmin also a minsum and a minratio type objective are considered two algorithms are presented for the considered class of bicriterion path problems the first one only determines the minimal complete set of nondominated paths and the second one determines the entire set of nondominated paths both algorithms can be used for any type of bicriterion path problems since one of the objectives is type maxmin and an algorithm exists to determine the best path for the other objective computational statistics for the three types of considered bicriterion path problems are also presented

the generalized spectral radius theorem an analytic geometric proof abstract let be a bounded set of complex matrices m a 1 a m a i the generalized spectral radius theorem states that where and are defined as follows lim sup m 1 m where m sup a a m with a the spectral radius lim sup m 1 m where m sup a a m with any matrix norm we give an elementary proof based on analytic and geometric tools which is in some ways simpler than the first proof by berger and wang

on the upper exponent of a finite p group abstract let p be a prime and for a finite p group g let 0 g g and i g 1 i 1 g for i n a theorem is proved stating that if exp g q and cl g c then the length of the i series cannot be bounded by a function of q alone an upper bound in terms of q and c is given which is shown to be attained in p groups of arbitrarily large class

the tricriterion shortest path problem with at least two bottleneck objective functions abstract the focus of this paper is on the tricriterion shortest path problem where two objective functions are of the bottleneck type for example minmax or maxmin the third objective function may be of the same kind or we may consider for example minsum or maxprod let p n be the complexity of a classical single objective algorithm responsible for this third function where n is the number of nodes and m be the number of arcs of the graph an o m 2 p n algorithm is presented that can generate the minimal complete set of pareto optimal solutions finding the maximal complete set is also possible optimality proofs are given and extensions for several special cases are presented computational experience for a set of randomly generated problems is reported

bounded semigroups of matrices in this note are proved two conjectures of daubechies and lagarias the first asserts that if z is a bounded set of matrices such that all left infinite products converge then 8 generates a bounded semigroup the second asserts the equality of two differently defined joint spectral radii for a bounded set of matrices one definition involves the conventional spectral radius and one involves the operator norm

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

asymptotic stability and generalized gelfand spectral radius formula let be a set of n n complex matrices for m 1 2 let m be the set of all products of matrices in of length m denote by the multiplicative semigroup generated by is said to be asymptotically stable in the sense of dynamical systems if there is 0 1 such that there are bounded neighborhoods u v cn of the origin for which av mu for all a m m 1 2 for a bounded set of n n complex matrices it is shown that the following conditions are mutually equivalent i is asymptotically stable ii g9 lim supm supa m a 1 m 1 iii lim supm supa m a 1 m 1 where a stands for the spectral radius of a and iv there exists a positive number such that a 1 for all a this fact answers an open question raised by brayton and tong the generalized gelfand spectral radius formula that is g9 conjectured by daubechies and lagarias and proved by berger and wang using advanced tools from ring theory and then by elsner using analytic geometric tools follows immediately form the above asymptotic stability theorem