a note on the power sequence of a fuzzy matrix abstract the properties of power sequence of an n n fuzzy matrix under some different pairs of fuzzy operations have been studied especially under min max composition the properties can be deduced from the results in this paper furthermore some results were established in the sense of max t composition when t is a commonly used product type triangular norm

convergence of the power sequence of a nearly monotone increasing fuzzy matrix abstract by introducing a new classification the essential role of the principal diagonal elements for the convergence of the power sequence of a fuzzy matrix a is exported at the level of a itself the established theorems cover those of monotone or nearly monotone increasing fuzzy matrices the convergence index of matrices of this type is always less than or equal to n the results can be considered to be a generalization of the results obtained by some authors on the one hand and on the other it is more important that the results have laid the foundation for studying the convergence and oscillation for power sequence of an arbitrary fuzzy matrix in general furthermore as a typical case which needs to be considered the necessary and sufficient conditions for an increasing fuzzy matrix a to have the property a n 1 a n a n 1 were established and the typical form was represented

robust hybrid control incorporating over saturation a switching controller aimed at dealing with a class of uncertain systems subject to input saturation is presented the switching strategy is such that a pre specified level of over saturation is allowed forcing the input deliberately into saturation the goal of this method is to use the full authority of the available control the proposed scheme allows for up to 100 over saturation under these conditions robust stability of the hybrid scheme is established

a switched server system of order n with all its trajectories converging to n 1 limit cycles abstract the paper analyzes an example of the discrete control of a continuous variable system we prove that the switched server system with one server and an arbitrary number of buffers has a finite set of periodic trajectories which attracts all other trajectories of the system

aggregation vs global diffusive behavior in the higher dimensional keller segel model abstract we consider the classical parabolic parabolic keller segel system u t u u v x t 0 v t v v u x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n it is proved that in space dimension n 3 for each q n 2 and p n one can find e 0 0 such that if the initial data u 0 v 0 satisfy u 0 l q e and v 0 l p e then the solution is global in time and bounded and asymptotically behaves like the solution of a discoupled system of linear parabolic equations in particular u v approaches the steady state m m as t where m is the total mass m u 0 of the population moreover we shall show that if is a ball then for arbitrary prescribed m 0 there exist unbounded solutions emanating from initial data u 0 v 0 having total mass u 0 m

on the power sequence of a fuzzy matrix iii a detailed study on the power sequence of matrices of commonly used types abstract focusing on the behavior of the principal diagonal elements of ak a new classification has been introduced which is called circularly k dominating in turns out that the convergence index or the oscillating index of the power sequence of an n n fuzzy matrix of the circularly k dominating type is bounded by nk n k from above and if it is oscillating then the period index pa is a factor of k the fuzzy matrices of the 2 dominating type were discussed in detail it was shown that the 2 dominating type is a more general class than those have been discussed before and the results established for matrices of 2 dominating type is as good as the results obtained for controllable matrices therefore most commonly used types of fuzzy matrices can be examined under the framework of 2 dominating matrices and the convergence index or oscillating index can be estimated based on the results

on simultaneously nilpotent fuzzy matrices abstract nilpotent fuzzy matrices play a crucial role in the study of fuzzy matrices in this paper we shall extend the nilpotence to the notion of simultaneous nilpotence for a finite set of fuzzy matrices the notion of simultaneous nilpotence relates to the infinite products of a finite number of fuzzy matrices which converge to the zero matrix properties of the simultaneous nilpotence will be established in the study of consecutive powers of a fuzzy matrix a controllable fuzzy matrix can be characterized by an associated nilpotent fuzzy matrix in this paper we propose the notion of simultaneously controllable fuzzy matrices which can be thought of as a generalization of the notion of controllable fuzzy matrices similar to the nilpotent characterization for a controllable fuzzy matrix the simultaneously controllable fuzzy matrices can be characterized by a finite set of associated simultaneously nilpotent fuzzy matrices

indices and periods of incline matrices abstract inclines are the additively idempotent semirings in which products are less than or equal to factors thus inclines generalize boolean algebra fuzzy algebra and distributive lattice and the boolean matrices the fuzzy matrices and the lattice matrices are the prototypical examples of the incline matrices i e the matrices over inclines this paper studies the power sequence of incline matrices in detail a necessary and sufficient condition for the incline matrix to have index is given and the indices of some incline matrices with indices are estimated it is proved that the period of n n incline matrix with index is a divisor of n and that the set of periods of n n incline matrices with indices is not bounded from above in the sense of a power of n for all n an equivalent condition and some sufficient conditions for the incline matrix to converge in finite steps are established the stability of the orbits of an incline matrix is considered and a theorem in fuzzy sets and systems 81 1996 227 is pointed out being false the results in the present paper include some previous results in the literatures which were obtained for the boolean matrices the fuzzy matrices and the lattice matrices among their special cases

global existence and boundedness of solutions to a chemotaxis system with singular sensitivity and logistic type source abstract we consider the fully parabolic keller segel system with singular sensitivity and logistic type source u t u u v v r u u k v t v v u under the non flux boundary conditions in a smooth bounded convex domain r n r 0 k 1 a global very weak solution for the system with n 2 is obtained under one of the following conditions i r 2 4 for 0 2 or r max 2 4 1 p 0 2 1 for 2 with p 0 4 k 1 4 2 k k 2 if k 2 1 n 2 ii 2 min 2 r r 2 k 4 k k 1 k 2 if k 2 furthermore this global very weak solution should be globally bounded in fact provided r and the initial data u 0 l 2 v l 4 suitably small for n 2 3 in addition if k 3 n 2 n 4 replaces k 2 in the condition ii the system admits globally bounded classical solutions all these describe the influence of the exponent k 1 in the logistic type source r u u k to the behavior of solutions for the considered fully parabolic keller segel system with singular sensitivity

existence of global bounded classical solution to a quasilinear attraction repulsion chemotaxis system with logistic source abstract this paper concerns the global existence of bounded classical solution to a quasilinear attraction repulsion chemotaxis system with logistic source u t d u u u v u w u u 2 in v t v u v in w t w u w in under homogeneous neumann boundary condition with positive parameters and d s c 0 s m 1 for s 0 d 0 0 we prove that in dimension three there exists a unique global bounded classical solution provided that m 6 5 and 0 with an additional assumption d s c 0 s m 1 1 for s 0 we prove that for any m 1 6 5 there exists a constant 0 0 m such that for all 0 the above problem admits a unique global bounded classical solution

on the sequence of consecutive powers of a fuzzy matrix with max archimedean t norms in the literature the limiting behavior of powers of a fuzzy matrix has been studied with max product composition pang and guu proposed a simple and effective characterization for the limiting behavior with the notion of asymptotic period in this paper we shall extend pang and guu s work to the realm with the max archimedean t norm composition to which the max product belongs moreover some sufficient conditions for the powers to converge in finitely many steps will be established

modifying the power method in max algebra in the max algebra system the eigenequation for an n n irreducible nonnegative matrix a aij is a x a x here a x i maxjaijxj and a is the maximum circuit geometric mean the complexity of the power method given in l elsner p van den driessche linear algebra appl to appear to compute a and x is considered under some assumptions on the critical matrix it is shown that the algorithm may have time complexity o n4 a modified power method based on karp s formula is presented for this new algorithm with no assumptions on the critical matrix a and x can be computed in o n3 time furthermore this algorithm can be used to compute all linearly independent eigenvectors corresponding to a

how strong a logistic damping can prevent blow up for the minimal keller segel chemotaxis system in this paper we study the minimal keller segel model with a logistic source and obtain quantitative and qualitative descriptions of the competition between logistic damping and other ingredient especially chemotactic aggregation to guarantee boundedness and convergence more specifically we establish how precisely strong a logistic source can prevent blow up and then we obtain an explicit relationship between logistic damping and other ingredient especially chemotactic aggregation so that convergences are ensured and their respective convergence rates are explicitly calculated out known results in the literature are completed and refined furthermore our findings provide clues on how to produce blowup solutions for ks chemotaxis models with logistic sources

explicit lower bound of blow up time for an attraction repulsion chemotaxis system abstract in this paper we study classical solutions to the zero flux attraction repulsion chemotaxis system u t u u v u w in 0 t 0 v u v in 0 t 0 w u w in 0 t where is a smooth and bounded domain of r 2 t is the blow up time and are positive real numbers from the literature it is known that under a proper interplay between the above parameters and suitable assumptions on the initial data u x 0 u 0 c 0 system has a unique classical solution which becomes unbounded as t t the main result of this investigation is to provide an explicit lower bound for t estimated in terms of u 0 2 d x and attained by means of well established techniques based on ordinary differential inequalities

an efficient algorithm for critical circuits and finite eigenvectors in the max plus algebra abstract we consider the eigenvalue problem in the max plus algebra for matrices in r n n but with eigenvectors in r n the problem is relaxed to a linear optimization lo problem of which the dual problem is solved by finding a maximal average weight circuit in the graph of the matrix the floyd warshall procedure is used to find such a circuit this procedure also provides an efficient algorithm for finding an eigenvector

global well posedness and asymptotic stabilization for chemotaxis system with signal dependent sensitivity abstract a fully parabolic chemotaxis system u t u u v v v t v v u in a smooth bounded domain r n n 2 with homogeneous neumann boundary conditions is considered where the non negative chemotactic sensitivity function satisfies v a v k for some a 0 and k 1 it is shown that a novel type of weight function can be applied to a weighted energy estimate for k 1 consequently the range of for the global existence and uniform boundedness of classical solutions established by mizukami and yokota 23 is enlarged moreover under a convexity assumption on an asymptotic lyapunov functional is obtained and used to establish the asymptotic stability of spatially homogeneous equilibrium solutions for k 1 under a smallness assumption on in particular when v v and n 8 it is shown that the spatially homogeneous steady state is a global attractor whenever 1 2

on the oscillating power sequence of a fuzzy matrix abstract the properties of an oscillating power sequence of an n n fuzzy matrix have been studied the necessary and sufficient conditions have been established for a power sequence to be oscillatory furthermore the oscillation index was detailed to some degree especially for some typical boolean matrices it is also shown that the period index set of the power sequences of fuzzy matrices of order n is not bounded from above by a power of n for all integers n

robust stabilizing control laws for a class of second order switched systems abstract for a class of second order switched systems consisting of two linear time invariant lti subsystems we show that the so called conic switching law proposed previously by the present authors is robust not only in the sense that the control law is flexible to be explained further but also in the sense that the lyapunov stability resp lagrange stability properties of the switched system are preserved in the presence of certain kinds of vanishing perturbations resp nonvanishing perturbations the analysis is possible since the conic switching laws always possess certain kinds of quasi periodic switching operations we also propose for a class of nonlinear second order switched systems with time invariant subsystems a switching control law which locally exponentially stabilizes the entire nonlinear switched system provided that the conic switching law exponentially stabilizes the linearized switched systems consisting of the linearization of each nonlinear subsystem this switched control law is robust in the sense mentioned above

global existence and boundedness in a fully parabolic attraction repulsion chemotaxis system with signal dependent sensitivities and logistic source abstract this paper deals with the fully parabolic attraction repulsion chemotaxis system with signal dependent sensitivities and logistic source u t u u v v u w w u 1 u x t 0 v t v v u x t 0 w t w w u x t 0 under homogeneous neumann boundary conditions and initial conditions where r n n 2 is a bounded domain with smooth boundary are functions satisfying some conditions and 0 is a constant when are constants it is known that the above system possesses a globally bounded classical solution in some cases however there has been no work in the case that are functions this paper develops global existence and boundedness of classical solutions to the above system in such case

on nilpotent fuzzy matrices abstract in this paper we study the issue of nilpotent fuzzy matrices we first provide some properties of nilpotent fuzzy matrices in terms of eigenvalues when a finite number of fuzzy matrices are simultaneously considered we establish some characterizations of the simultaneous nilpotence for a finite number of fuzzy matrices on the other hand it is well known that the max min algebra is one kind of lattice we shall extend the results on simultaneous nilpotence to matrices on a bounded distributive lattice

global asymptotic stability of constant equilibria in a fully parabolic chemotaxis system with strong logistic dampening abstract this paper deals with nonnegative solutions of the neumann initial boundary value problem for the parabolic chemotaxis system u t u u v u u 2 x t 0 v t v v u x t 0 in bounded convex domains r n n 1 with smooth boundary it is shown that if the ratio is sufficiently large then the unique nontrivial spatially homogeneous equilibrium given by u v 1 is globally asymptotically stable in the sense that for any choice of suitably regular nonnegative initial data u 0 v 0 such that u 0 0 the above problem possesses a uniquely determined global classical solution u v with u v t 0 u 0 v 0 which satisfies u t 1 l 0 and v t 1 l 0 as t

repulsion effects on boundedness in the higher dimensional fully parabolic attraction repulsion chemotaxis system abstract this paper deals with an attraction repulsion chemotaxis system u t d u u u v u w x t 0 1 v t v u v x t 0 2 w t w u w x t 0 under homogeneous neumann boundary conditions in a smooth bounded domain r n n 2 where parameters i i 1 2 and are positive and diffusion coefficient d u c 2 0 satisfies d u 0 for u 0 d u d u m 1 with d 0 and m 1 for all u 0 it is proved that the corresponding initial boundary value problem possesses a unique global bounded classical solution for m 2 2 n in particular in the case 1 2 and the solution is globally bounded if m 2 2 n n 2 n 2 n 2 therefore due to the inhibition of repulsion to the attraction the range of m 2 2 n of boundedness is enlarged and the results of 21 is thus extended to the higher dimensional attraction repulsion chemotaxis system with nonlinear diffusion

boundedness and global existence in the higher dimensional parabolic parabolic chemotaxis system with without growth source abstract in this paper we are concerned with a general class of quasilinear parabolic parabolic chemotaxis systems with without growth source under homogeneous neumann boundary conditions in a smooth bounded domain r n with n 2 it is recently known that blowup is possible even in the presence of superlinear growth restrictions here we derive new and interesting characterizations on the growth versus the boundedness we show that the hard task of proving the l boundedness of the cell density can be reduced to proving its l r boundedness in other words we show that the l r boundedness of the cell density can successfully guarantee its l boundedness and hence its global boundedness where r n or n 2 depending on whether the growth restriction is essentially linear including no growth or superlinear hence a blowup solution also blows up in l p norm for any suitably large p more detailed information on how the growth source affects the boundedness of the solution is derived these results reveal deep understandings of blowup mechanism for chemotaxis models then we use these criteria to establish uniform boundedness and hence global existence of the underlying models logistic source in 2 d cubic source as initially proposed by mimura and tsujikawa in 3 d n 1 st source in n d with n 4 as a consequence in a chemotaxis growth model blowup is impossible if the growth effect is suitably strong finally we underline that our results remove the commonly assumed convexity on the domain

a note on the sequence of consecutive powers of a nonnegative matrix in max algebra abstract in this note we shall consider the sequence of consecutive powers in max algebra of a nonnegative matrix with each element less than or equal to 1 the notion of asymptotic period is defined to study the limiting behavior of this sequence a simple and effective characterization for the asymptotic period of the sequence is given

eigenvectors in bottleneck algebra abstract let b be a nonempty linearly ordered set without maximum and minimum and max min a vector x is said to be an eigenvector of a square matrix a if a x x the aim of the present paper is to characterize the eigenvectors by means of the associated graph of the matrix and to give bounds for the set of all eigenvectors we define the lower and the upper basic eigenvectors and derive efficient methods for computing them

sub logistic source can prevent blow up in the 2d minimal keller segel chemotaxis system it is well known that the neumann initial boundary value problem for the minimal keller segel chemotaxis system in a 2d bounded smooth domain has no blow ups for any presence of logistic source of cell kinetics here for a large class of cell kinetics including sub logistic sources we find an explicit condition involving the chemotactic strength the asymptotic damping rate and the initial mass of cells to ensure the uniform in time boundedness for the corresponding 2d neumann initial boundary value problem our finding in particular shows that sub logistic source can prevent blow up in 2d indicating that logistic damping is not the weakest damping to guarantee boundedness for the 2d keller segel minimal chemotaxis model

boundedness in a fully parabolic chemotaxis system with singular sensitivity abstract this paper deals with a fully parabolic chemotaxis system u t u u v v v t v v u with singular sensitivity v 0 on a bounded domain r n n 2 the main result solves the open problem of uniform in time boundedness of solutions for 2 n which was conjectured by winkler 16

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

optimal persistent disturbance attenuation control for linear hybrid systems abstract in this paper the disturbance attenuation properties for a class of linear hybrid systems are investigated and a hybrid optimal persistent disturbance attenuation control problem is studied first a procedure is developed to determine the minimal l induced gain of linear hybrid systems however for general hybrid systems the termination of the procedure is not guaranteed then the decidability issues are discussed the termination of the procedure in a finite number of steps is shown for a subclass of hybrid systems with simplified discrete event dynamics called switched linear systems finally the optimal persistent disturbance attenuation controller synthesis problem is studied it is shown that the optimal performance level can be achieved by a piecewise linear state feedback control law and a systematic approach is proposed to design such feedback control

on the powers of matrices in bottleneck fuzzy algebra abstract powers of square matrices under the operations max and min are studied we show that the powers of a given matrix stabilize if and only if its orbits stabilize for each starting vector and prove a necessary and sufficient condition for this property using the associated graphs of the matrix applications of the obtained results to several special classes of matrices including circulants are given

stabilization in the logarithmic keller segel system abstract the keller segel system u t d u d u v v x t 0 v t d v v u x t 0 is considered in a bounded domain r n n 2 with smooth boundary where 0 and d 0 the main results identify a condition on the parameters 2 n and d 0 essentially reducing to the assumption that 2 d be suitably small under which for all reasonably regular and positive initial data the corresponding classical solution of an associated neumann initial boundary value problem known to exist globally according to previous findings approaches the homogeneous steady state u 0 u 0 at an exponential rate with respect to the norm in l 2 as t where u 0 1 u 0 as a particular consequence this entails a convergence statement of the above flavor in the normalized system with d 1 and fixed 2 n provided that satisfies a certain smallness condition

canonical form of a transitive fuzzy matrix some properties of a transitive fuzzy matrix are examined and the canonical form of the transitive matrix is given using the properties as a special case an open problem concerning idempotent matrices of kim and roush is solved in our results a nilpotent matrix and a symmetric matrix play an important role we decompose a transitive matrix into the sum of a nilpotent matrix and a symmetric matrix then we obtain a canonical form of the transitive matrix

on the asymptotic period of powers of a fuzzy matrix in our prior study we have examined in depth the notion of an asymptotic period of the power sequence of an nxn fuzzy matrix with max archimedean t norms and established a characterization for the power sequence of an nxn fuzzy matrix with an asymptotic period using analytical decomposition methods in this paper by using graph theoretical tools we further give an alternative proof for this characterization with the notion of an asymptotic period using graph theoretical tools we additionally show a new characterization for the limit behaviour and then derive some results for the power sequence of an nxn fuzzy matrix with an asymptotic period

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

max balancing weighted directed graphs and matrix scaling a weighted directed graph g is a triple v a g where v a is a directed graph and g is an arbitrary real valued function defined on the arc set a let g be a strongly connected simple weighted directed graph we say that g is max balanced if for every nontrivial subset of the vertices w the maximum weight over arcs leaving w equals the maximum weight over arcs entering w we show that there exists a up to an additive constant unique potential pv for v v such that v a gp is max balanced where gap pu ga pv for a u v a we describe an o v 2 a algorithm for computing p using an algorithm for computing the maximum cycle mean of g finally we apply our principal result to the similarity scaling of nonnegative matrices

a new approach to robust control of hybrid systems over infinite time the paper presents a new approach to output feedback robust control synthesis problems for hybrid dynamical systems the hybrid system under consideration is a composite of a continuous plant and a discrete event controller an output feedback h sup spl infin control problem on an infinite time interval is considered the main results are given in terms of the existence of suitable solutions to a dynamic programming equation and a riccati algebraic equation of the h sup spl infin filtering type these results show a connection between the theories of hybrid dynamical systems and robust and nonlinear control

powers of matrices over distributive lattices a review in this paper we review the results on powers of matrices over a distributive lattice we stress the significance of the graph theoretical approach and show how several previous results for matrices of special types can be obtained in a unified way

robust h sub spl infin output feedback control for nonlinear systems in this paper we present a new approach to the solution of the output feedback robust h sub spl infin control problem we employ the recently developed concept of information state for output feedback dynamic games and obtain necessary and sufficient conditions for the solution to the robust control problem expressed in terms of the information state the resulting controller is an information state feedback controller and is intrinsically infinite dimensional stability results are obtained using the theory of dissipative systems and our results are expressed in terms of dissipation inequalities

convergence of products of fuzzy matrices convergence of powers of a fuzzy matrix has been studied in the literature in this paper we shall extend the scope to the products of a finite number of fuzzy matrices we shall demonstrate that the outcomes of products of fuzzy matrices will be more complicated than the cases of powers of a fuzzy matrix two notions of convergence are established weak convergence and strong convergence the main results to guarantee the weak convergence of products of fuzzy matrices are due to the concepts of transitive and compact properties of fuzzy matrices which can be viewed as a generalization of the transitive and compact properties of a fuzzy matrix sufficient conditions similar to the pinching theorem in calculus are given as well for strong convergence

a connection between h control and the absolute stabilizability of uncertain systems abstract this paper considers a stabilization problem for a class of uncertain systems in which the uncertainty satisfies a certain integral quadratic constraint such uncertain systems have been previously studied in the theory of absolute stability with most publications in this area being in the russian literature the paper introduces a notion of absolute stabilizability and shows that an uncertain system is absolutely stabilizable if and only if there exists a solution to a corresponding h control problem the paper also shows that if an uncertain system can be absolutely stabilized via nonlinear output feedback control then it can be absolutely stabilized via linear output feedback control

a max version of the perron frobenius theorem abstract if a an n n nonnegative irreducible matrix then there exists a 0 and a positive vector x such that maxjaijxj a xi i 1 2 n furthermore a is the maximum geometric mean of a circuit in the weighted directed graph corresponding to a this theorem which we refer to as the max version of the perron frobenius theorem is well known in the context of matrices over the max algebra and also in the context of matrix scalings in the present work which is partly expository we bring out the intimate connection between this result and the perron frobenius theory we present several proofs of the result some of which use the perron frobenius theorem structure of max eigenvalues and max eigenvectors is described possible ways to unify the perron frobenius theorem and its max version are indicated some inequalities for a are proved

convergence of powers of s transitive fuzzy matrices abstract natural powers via max min multiplication of s transitive fuzzy matrices are considered it is shown that they oscillate with period equal to 2 this is an extension of the convergence property concerning max min transitive fuzzy matrices

on the max nilpotent t norm powers of a fuzzy matrix fuzzy matrices have been proposed to represent fuzzy relations in finite universes various studies have evaluated the powers of a fuzzy matrix with max min max product max archimedean t norm max t norm max arithmetic mean compositions indicating that the limiting behavior of the powers of a fuzzy matrix depends on its composition in this paper max nilpotent composition is considered for the fuzzy relations we demonstrate that the max nilpotent powers of a fuzzy matrix either converge or oscillate in a finite period moreover the max nilpotent t norm powers of a fuzzy matrix a are p periodic if and only if the powers of an associated boolean matrix a c are p periodic finally necessary and sufficient conditions are proposed for nilpotent fuzzy matrices that exhibit max nilpotent composition

convergence of powers of a fuzzy transitive matrix convergence of powers of a fuzzy transitive matrix is considered and some conditions for convergence are given under the max min operation on fuzzy matrices a fuzzy transitive matrix is a matrix which represents a fuzzy transitive relation and has many interesting properties the conditions for convergence of fuzzy matrices are examined under a special operation which is essential to reduction of fuzzy matrices or fuzzy systems given results show graph theoretic properties of fuzzy matrices and are useful when we consider convergence of systems represented by fuzzy matrices

h sub infinity state estimation for linear periodic systems this note deals with the h sub infinity state estimation problem for linear periodic systems the question addressed is the design of an unbiased linear periodic and asymptotically stable estimator that achieves a prescribed h sub infinity performance on an infinite horizon necessary and sufficient conditions for the existence of a periodic estimator have been derived asymptotic properties of the finite horizon estimation problem when the time horizon tends to infinity are also investigated

on the power method in max algebra abstract the eigenvalue problem for an irreducible nonnegative matrix a a ij in the max algebra system is a otimes x lambda x where a otimes x i mathop max j a ij x j and lambda turns out to be the maximum circuit geometric mean mu a a power method algorithm is given to compute mu a and eigenvector x the algorithm is developed by using results on the convergence of max powers of a which are proved using nonnegative matrix theory in contrast to an algorithm developed in 4 this new method works for any irreducible nonnegative a and calculates eigenvectors in a simpler and more efficient way some asymptotic formulas relating mu a the spectral radius and norms are also given

the power algorithm in max algebra abstract it is proved that under certain conditions an algorithm resembling the power algorithm in conventional linear algebra can be used to find the eigenvector and eigenvalue of a max algebra system if the conditions are not satisfied the eigenvector can be found using an extension of the power algorithm

boundedness of the attraction repulsion keller segel system a b s t r a c t this paper considers the initial boundary value problem of the attraction repulsion keller segel model describing aggregation of microglia in the central nervous system in alzheimer s disease due to the interaction of chemoattractant and chemorepellent if repulsion dominates over attraction we show the global existence of classical solution in two dimensions and weak solution in three dimensions with large initial data u x 0 u0 x v x 0 v 0 x w x 0 w 0 x x

global existence and boundedness in a chemotaxis haptotaxis system with signal dependent sensitivity abstract this paper deals with the chemotaxis haptotaxis system with signal dependent sensitivity u t u v u v u w u 1 u w x t 0 v t v v u x t 0 w t v w x t 0 under homogeneous neumann boundary conditions and initial conditions where r n n 3 is a bounded domain with smooth boundary 0 are constants and is a function satisfying some conditions in the case that is a constant it is known that the above system possesses a global classical solution under some conditions cao 4 tao 10 tao and winkler 11 however in the case that is a function the above system has not been studied the purpose of this paper is to establish global existence and boundedness in the above system