synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

convergence criteria of iterative methods based on landweber iteration for solving nonlinear problems abstract landweber iteration xk 1 xk f xk f xk y for the solution of a nonlinear operator equation f x0 y0 can be viewed as a fixed point iteration with fixed point operator x f x f x y especially for nonlinear ill posed problems it seems impossible to verify that this fixed point operator is of contractive type which is a typical assumption for proving weak convergence of fixed point iteration schemes however for specific examples of nonlinear ill posed problems it is possible to verify conditions of quasi contractive type weak convergence of landweber iteration can be proven by application of general results for fixed point iterations based on quasi contractive type conditions in a recent paper by hanke et al a condition on the operator f has been investigated which guarantees convergence of the landweber s method a geometrical interpretation of this condition is given and is compared with well known conditions in the theory of fixed point iterations

stability of discrete time delayed impulsive linear systems with application to multi tracking this paper studies the stability issue for discrete time delayed impulsive systems ddis the ddis model is formulated from a discrete time delayed system with impulses by using the matrix spectrum theory the estimates of solution with growth exponent are derived for delayed difference inequalities based on these results two types of criteria on exponential stability with an estimated convergence rate have been established for ddis the first type investigates the effect of destabilising impulses while the second is for the case in which the impulses stabilise the unstable discrete time delayed systems as the application the stability results are used to solve the multi tracking issue for discrete time dynamical networks by mixed impulsive networked control minc in which the impulsive control signals are transmitted via a communication network the effect of data dropout of impulsive control signals is also investigated and the maximal allowable dropout rate is estimated for the designed minc

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

second order consensus of multi agent systems in the cooperation competition network with switching topologies a time delayed impulsive control approach abstract this paper investigates the consensus problem of second order multi agent systems with switching topologies by designing a time delayed impulsive consensus control scheme all the agents are governed by the same nonlinear intrinsic dynamics in this study agents can cooperate or compete with each other i e the elements in the weight matrix of the coupling graph can be either positive or negative by establishing a comparison system a new comparison principle method is successfully applied to study such consensus problem then several effective sufficient conditions are attained without assuming that the interaction topology is strongly connected or contains a directed spanning tree meanwhile the exponential consensus rate is also obtained finally simulation results are presented to validate the effectiveness of the theoretical analysis

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

weak convergence theorems for a finite family of strict pseudocontractions let e be a uniformly smooth real banach space which is also uniformly convex and k be a nonempty closed convex subset of e let t k k be a strict pseudocontraction for some 0 1 with x f t x k t x x 0 combining long solidus overlay for a fixed x0 k define a sequence xn by xn 1 1 n xn n t xn where n is a sequence in 0 1 satisfying the following conditions i n 0 n ii n 0 n2 then xn converges weakly to a fixed point of t furthermore weak convergence theorems are proved for a common fixed point for a finite family of strict pseudocontractions 2009 elsevier ltd all rights reserved

novel adaptive strategies for synchronization of linearly coupled neural networks with reaction diffusion terms in this paper two types of linearly coupled neural networks with reaction diffusion terms are proposed we respectively investigate the adaptive synchronization of these two types of complex network models with local information of node dynamics some novel adaptive strategies to tune the coupling strengths among network nodes are designed by constructing appropriate lyapunov functionals and using inequality techniques several sufficient conditions are given for reaching synchronization by using the designed adaptive laws finally two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results

leader following consensus of a class of stochastic delayed multi agent systems with partial mixed impulses in this paper the exponential leader following consensus problem is investigated for a class of nonlinear stochastic networked multi agent systems with partial mixed impulses and unknown time varying but bounded delays the main feature of partial mixed impulses is that time varying impulses are not only composed of synchronizing and desynchronizing impulses simultaneously but they are also injected into a fraction of nodes in multi agent systems three kinds of partial mixed impulses are proposed fixed partial mixed impulses periodic partial mixed impulses and try once discard like partial mixed impulses by means of the lyapunov function theory and the comparison principle conditions are derived for ensuring global exponential leader following consensus under the presented three kinds of partial mixed impulses simulations of leader following consensus of robotic systems are provided to validate the effectiveness of the proposed results and to show the advantages of the proposed partial mixed impulses

stability via hybrid event time lyapunov function and impulsive stabilization for discrete time delayed switched systems this paper proposes a new stability analysis method called the hybrid event time lyapunov function htlf approach for discrete time delayed switched systems ddss two types of stability notions guas and event guas are proposed to reflect the effects on stability from events a basic stability result is derived a ddss has event guas if and only if there exists an htlf which is strictly decreasing and converges to zero moreover some sufficient conditions expressed by htlf razumikhin type stability theorems are established the issue of impulsive stabilization for ddss is studied it is proved that an unstable ddss can be stabilized by impulsive control and the impulsive stabilization to input to state stability of ddss is also achieved

quasi exponential input to state stability for discrete time impulsive hybrid systems this paper investigates the problem of input to state stability iss for the general discrete time impulsive hybrid systems quasi exponential input to state stability criteria are established for non linear discrete time impulsive hybrid systems based on the lyapunov function the results are then specialized to the linear discrete time impulsive hybrid systems and fairly simple algebraic conditions are derived moreover iss small gain properties are also investigated for a class of interconnected discrete time impulsive systems several examples are given to illustrate results

input to state stability of nonlinear impulsive systems we prove that impulsive systems which possess an input to state stable iss lyapunov function are iss for time sequences satisfying the fixed dwell time condition if an iss lyapunov function is the exponential one we provide a stronger result which guarantees uniform iss of the whole system over sequences satisfying the generalized average dwell time condition then we prove two small gain theorems that provide a construction of an iss lyapunov function for an interconnection of impulsive systems if the iss lyapunov functions for subsystems are known the construction of local iss lyapunov functions via the linearization method is provided relations between small gain and dwell time conditions as well as between different types of dwell time conditions are also investigated although our results are novel already in the context of finite dimensional systems we prove them for systems based on differential equations in banach spaces that makes obtained results considerably more general

solving variational inequalities involving nonexpansive type mappings abstract the purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities v i d c i f involving nonexpansive type mappings in smooth banach spaces we study the existence of solutions of variational inequalities v i d c i f when d is the set of solutions of zeros of accretive operators or the set of fixed points of nonexpansive mappings or the set of fixed points of pseudocontractive mappings our convergence analysis covers proximal point algorithm for finding zeros of accretive operators as well as functional halpern algorithm for finding fixed points of nonexpansive mappings in banach spaces our results improve a number of results concerned with viscosity approximation methods in the context of weakly contraction mappings

quasi synchronization of heterogeneous dynamic networks via distributed impulsive control this paper studies leader follower synchronization in heterogeneous dynamic networks via distributed impulsive control the goal is to drive the followers to approximately synchronize with the leader within a nonzero error bound referred to as quasi synchronization some fundamental and yet challenging problems are addressed 1 how to obtain a tight quasi synchronization error bound 2 how many and which nodes should be controlled 3 how to design the coupling strength to select the pinned nodes and to determine the impulse intervals to optimize the error bound or to achieve quasi synchronization within a prescribed error bound first some general quasi synchronization conditions are derived with explicit expressions of the error bound second the pinning strategy and the coupling strength in achieving quasi synchronization are explored and expressed in term of impulse intervals it is interesting to find that a large coupling strength will destroy synchrony in contrast to continuous pinning control furthermore the common requirement that the leader has a directed path to every node is needed only in the case that the impulse intervals can be arbitrarily small a new concept referred to as impulse pinning controllability is introduced to the case that impulses cannot take place too frequently third an optimization of the error bound is discussed and formulated under a prescribed error bound the design problem of the coupling strength pinned nodes and impulse intervals is solved finally three examples are given to verify the theoretical results

an approximation method for strictly pseudocontractive mappings let k be a closed convex subset of a q uniformly smooth separable banach space t k k a strictly pseudocontractive mapping and f k k an l lispschitzian strongly pseudocontractive mapping for any t 0 1 let xt be the unique fixed point of t f 1 t t we prove that if t has a fixed point then xt converges to a fixed point of t as t approaches to 0

characterizations of input to state stability for hybrid systems abstract we study input to state stability iss for a broad class of hybrid systems which are combinations of a differential equation on a constraint set and a difference equation on another constraint set for this class of hybrid systems we establish the equivalence of iss nonuniform iss and the existence of a smooth iss lyapunov function by additionally assuming that the right hand side of the differential equation has a convex property with respect to inputs moreover we demonstrate by examples that the equivalence may fail when such a convexity assumption is removed

impulsive consensus for complex dynamical networks with nonidentical nodes and coupling time delays this paper investigates the problem of global consensus between a complex dynamical network cdn and a known goal signal by designing an impulsive consensus control scheme the dynamical network is complex with respect to the uncertainties nonidentical nodes and coupling time delays the goal signal can be a measurable vector function or a solution of a dynamical system by utilizing the lyapunov function and lyapunov krasovskii functional methods robust global exponential stability criteria are derived for the error system under which global exponential impulsive consensus is achieved for the cdn these criteria are expressed in terms of linear matrix inequalities lmis and algebraic inequalities thus the impulsive controller can be easily designed by solving the derived inequalities meanwhile the estimations of the consensus rate for global exponential consensus are also obtained two examples with numerical simulations are worked out for illustration

input to state stability of impulsive and switching hybrid systems with time delay this paper investigates input to state stability iss and integral input to state stability iiss of impulsive and switching hybrid systems with time delay using the method of multiple lyapunov krasovskii functionals it is shown that even if all the subsystems governing the continuous dynamics in the absence of impulses are not iss iiss impulses can successfully stabilize the system in the iss iiss sense provided that there are no overly long intervals between impulses i e the impulsive and switching signal satisfies a dwell time upper bound condition moreover these impulsive iss iiss stabilization results can be applied to systems with arbitrarily large time delays conversely in the case when all the subsystems governing the continuous dynamics are iss iiss in the absence of impulses the iss iiss properties can be retained if the impulses and switching do not occur too frequently i e the impulsive and switching signal satisfies a dwell time lower bound condition several illustrative examples are presented with their numerical simulations to demonstrate the main results

strong convergence of iterative methods by strictly pseudocontractive mappings in banach spaces abstract in this paper we deal with fixed point computational problems by strongly convergent methods involving strictly pseudocontractive mappings in smooth banach spaces first we prove that the s iteration process recently introduced by sahu in 14 converges strongly to a unique fixed point of a mapping t where t is strongly pseudocontractive mapping from a nonempty closed and convex subset c of a smooth banach space into itself it is also shown that the hybrid steepest descent method converges strongly to a unique solution of a variational inequality problem with respect to a finite family of i strictly pseudocontractive mappings from c into itself our results extend and improve some very recent theorems in fixed point theory and variational inequality problems particularly the results presented here extend some theorems of reich 1980 1 and yamada 2001 15 to a general class of strictly pseudocontractive mappings in uniformly smooth banach spaces

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

on reich s strong convergence theorems for resolvents of accretive operators let e be a real banach space with norm i then an operator a c e x e with domain d a and range r a is said to be accretive if xi xz 0 an accretive operator a c e x e is m accretive if r i ra e for all r 0 where z is the identity if a is accretive we can define for each positive r a singlevalued mapping j r z ra d a by j z ra it is called the resolvent of a in 6 reich proved the following theorem let e be a uniformly smooth banach space and let a c e x e be m accretive if 0 e r a then for each x in e the strong lim z x exists and belongs to a io he remarked also that the assumption that a is m accretive can be replaced with the assumption that cl a the closure of d a is convex and that a satisfies the range condition r z ra 1 cl d a for all r 0 in this paper we first prove a theorem that generalizes simultaneously the above results furthermore we generalize another reich strong convergence theorem asserting that the strong lim z x exists in uniformly convex and uniformly smooth banach spaces though our proofs are similar to those in 6 they are slightly simple on account of using banach limits

a new method for stabilization of networked control systems with random delays we consider the stabilization problem for a class of networked control systems in the discrete time domain with random delays the sensor to controller and controller to actuator delays are modeled as two markov chains and the resulting closed loop systems are jump linear systems with two modes the necessary and sufficient conditions on the existence of stabilizing controllers are established it is shown that state feedback gains are mode dependent an iterative linear matrix inequality lmi approach is employed to calculate the state feedback gains

pinning consensus in networks of multiagents via a single impulsive controller in this paper we discuss pinning consensus in networks of multiagents via impulsive controllers in particular we consider the case of using only one impulsive controller we provide a sufficient condition to pin the network to a prescribed value it is rigorously proven that in case the underlying graph of the network has spanning trees the network can reach consensus on the prescribed value when the impulsive controller is imposed on the root with appropriate impulsive strength and impulse intervals interestingly we find that the permissible range of the impulsive strength completely depends on the left eigenvector of the graph laplacian corresponding to the zero eigenvalue and the pinning node we choose the impulses can be very sparse with the impulsive intervals being lower bounded examples with numerical simulations are also provided to illustrate the theoretical results

semigroups of left quotients existence straightness and locality abstract a subsemigroup s of a semigroup q is a local left order in q if for every group h class h of q s h is a left order in h in the sense of group theory that is every q h can be written as a b for some a b s h where a denotes the group inverse of a in h on the other hand s is a left order in q and q is a semigroup of left quotients of s if every element of q can be written as c d where c d s and if in addition every element of s that is square cancellable lies in a subgroup of q if one also insists that c and d can be chosen such that c r d in q then s is said to be a straight left order in q this paper investigates the close relation between local left orders and straight left orders in a semigroup q and gives some quite general conditions for a left order s in q to be straight in the light of the connection between locality and straightness we give a complete description of straight left orders that improves upon that in our earlier paper

convergence theorems for λ strict pseudo contractions in 2 uniformly smooth banach spaces abstract in this paper we discuss some properties of iterates generated by a strict pseudo contraction or a finite family of strict pseudo contractions in a real 2 uniformly smooth banach space the results presented in this paper are interesting extensions and improvements upon those known ones of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 324 2007 336 349 in order to get a strong convergence theorem we modify the normal mann s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in c this result extends a recent result of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 both from nonexpansive mappings to strict pseudo contractions and from hilbert spaces to 2 uniformly smooth banach spaces

brief paper exponential stability of nonlinear time delay systems with delayed impulse effects the problem of exponential stability for nonlinear time delay systems with delayed impulses is addressed in this paper lyapunov based sufficient conditions for exponential stability are derived respectively for two kinds of delayed impulses i e destabilizing delayed impulses and stabilizing delayed impulses it is shown that if a nonlinear impulsive time delay system without impulse input delays is exponentially stable then under some conditions its stability is robust with respect to small impulse input delays moreover it is also shown that for a stable nonlinear impulsive time delay system if the magnitude of the delayed impulses is sufficiently small then under some conditions the delayed impulses do not destroy the stability irrespective of the sizes of the impulse input delays the efficiency of the proposed results is illustrated by three numerical examples

on the error estimation and t stability of the mann iteration abstract a formula of error estimation of mann iteration is given in the case of strongly demicontractive mappings based on this estimation a condition of strong convergence is obtained for the same class of mappings t stability for a particular case of strongly demicontractive mappings is proved some numerical examples showing the accuracy of the proposed estimations are also given

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network