sampled data consensus over random networks this paper considers the consensus problem for a network of nodes with random interactions and sampled data control actions we first show that consensus in expectation in mean square and almost surely are equivalent for a general random network model when the inter sampling interval and maximum node degree satisfy a simple relation the three types of consensus are shown to be simultaneously achieved over an independent or a markovian random network defined on an underlying graph with a directed spanning tree for both independent and markovian random network models necessary and sufficient conditions for mean square consensus are derived in terms of the spectral radius of the corresponding state transition matrix these conditions are then interpreted as the existence of critical value on the intersampling interval below which a global mean square consensus is achieved and above which the system diverges in a mean square sense for some initial states finally we establish an upper bound on the intersampling interval below which almost sure consensus is reached and a lower bound on the intersampling interval above which almost sure divergence is reached some numerical simulations are given to validate the theoretical results and some discussions on the critical value of the inter sampling intervals for the mean square consensus are provided

consensus of multi agent networks with aperiodic sampled communication via impulsive algorithms using position only measurements in this technical note an impulsive consensus algorithm is proposed for second order continuous time multi agent networks with switching topology the communication among agents occurs at sampling instants based on position only measurements by using the property of stochastic matrices and algebraic graph theory some sufficient conditions are obtained to ensure the consensus of the controlled multi agent network if the communication graph has a spanning tree jointly a numerical example is given to illustrate the effectiveness of the proposed algorithm

a quantum computing primer for operator theorists this is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory after a brief introduction we discuss quantum algorithms we outline basic properties of quantum channels or equivalently completely positive trace preserving maps the main theorems for quantum error detection and correction are presented and we conclude with a description of a particular passive method of quantum error correction

on impulsive control of a periodically forced chaotic pendulum system we consider impulsive control of a periodically forced pendulum system which has rich chaos and bifurcation phenomena a new impulsive control method for chaos suppression of this pendulum system is developed some simple sufficient conditions for driving the chaotic state to its zero equilibrium are presented and some criteria for eventually exponentially asymptotical stability are established this work provides a rigorous theoretical analysis to support some early experimental observations on controlling chaos in the periodically forced pendulum system

outer unipotent classes in automorphism groups of simple algebraic groups we study the unipotent elements of disconnected algebraic groups of the formg whereg is a simple algebraic group in characterisctic p possessing a graph automorphism of order p we classify the unipotent classes in the coset g and determine the corresponding centralizers showing that these bear a close relation to classes in a certain natural connected overgroup of g we also obtain a formula for the total number of outer unipotent elements in the finite group g where is a frobenius morphism analogous to the well known steinberg formula for the number of inner unipotent elements

a second order multi agent network for bound constrained distributed optimization this technical note presents a second order multi agent network for distributed optimization with a sum of convex objective functions subject to bound constraints in the multi agent network the agents connect each others locally as an undirected graph and know only their own objectives and constraints the multi agent network is proved to be able to reach consensus to the optimal solution under mild assumptions moreover the consensus of the multi agent network is converted to the convergence of a dynamical system which is proved using the lyapunov method compared with existing multi agent networks for optimization the second order multi agent network herein is capable of solving more general constrained distributed optimization problems simulation results on two numerical examples are presented to substantiate the performance and characteristics of the multi agent network

a collective neurodynamic approach to distributed constrained optimization this paper presents a collective neurodynamic approach with multiple interconnected recurrent neural networks rnns for distributed constrained optimization the objective function of the distributed optimization problems to be solved is a sum of local convex objective functions which may be nonsmooth subject to its local constraints each local objective function is minimized individually by using an rnn with consensus among others in contrast to existing continuous time distributed optimization methods the proposed collective neurodynamic approach is capable of solving more general distributed optimization problems simulation results on three numerical examples are discussed to substantiate the effectiveness and characteristics of the proposed approach in addition an application to the optimal placement problem is delineated to demonstrate the viability of the approach

unital affine semigroups abstract affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable they were introduced by cohen and collins in 1959 we look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups most notably we improve a result of wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups

weighted consensus protocols design based on network centrality for multi agent systems with sampled data this technical note aims at constructing and analyzing an efficient framework for the leader following consensus protocol in multi agent systems mass we propose two novel consensus protocols weighted by calculating the betweenness and eigenvector centralities for agent and link which are determined by the interconnection structure of mass the concepts of centrality were introduced in the field of social science ultimately the use of the proposed protocols can be described with regard to not only the number of each agent s neighbors which was utilized in the existing works but also more information about agents through considering two such centralities by utilizing the lyapunov method and some mathematical techniques the leader following guaranteed cost consensus conditions for mass with the proposed protocols and sampled data will be established in terms of linear matrix inequalities lmis based on the result of consensus criteria two new protocol design methods which utilize the betweenness and eigenvector centralities will be proposed finally some simulation results are given to illustrate the advantages of the proposed protocols in point of the robustness on sampling interval and the transient consensus performance

stabilization of switched systems with nonlinear impulse effects and disturbances in this note we investigate the stabilization of switched systems with nonlinear impulse effects and disturbances based on the estimate on transition matrices and gronwall inequality feedback laws are designed to achieve the exponential stability of the closed loop system with arbitrary switching frequency

consensus of multi agent systems based on sampled data control this article studies the consensus problem in directed networks assuming that each agent is with double integrator dynamics and only obtains the measurements of its positions relative to its neighbours at sampling instants we propose a protocol based on sampled data control and derive an equivalent characterisation of the solvability of the consensus problem under this protocol in virtue of this equivalent characterisation we further consider two cases fixed topology and switching topology for the first case we present a set of sampling periods and feedback coefficients which ensure that the protocol can solve a consensus problem for the second case we derive sufficient conditions for the protocol to solve a consensus problem under arbitrary switching signals and under a class of switching signals respectively finally simulations are provided to illustrate the effectiveness of the theoretical results

subgroups of maximal rank in finite exceptional groups of lie type the purpose of this paper is to investigate a large and natural class of maximal subgroups of the finite exceptional groups of lie type which we call subgroups of maximal rank these subgroups play a prominent role both in the classification of local maximal subgroups in 9 theorem 1 and in the reduction theorem for subgroups in 28 theorem 2 in 9 it is shown that any local maximal subgroup of a finite exceptional group of lie type is either a subgroup of maximal rank or one of a small list of exceptions and in 28 using this result it is proved that any maximal subgroup is either of maximal rank or almost simple or in a known list to describe these subgroups we require the following notation let g be a simple adjoint algebraic group over an algebraically closed field k of characteristic p 0 and let o be an endomorphism of g such that l ga is a finite exceptional simple group of lie type over fq where q p let a be a group such that f x l the group aut l is generated by ga together with field and graph automorphisms see 5 38 all of which extend to morphisms of the abstract group g commuting with o thus there is a subgroup x of caut c a such that x x o and so x acts on the set of a stable subsets of g for a a stable subset y we write nx y for the stabilizer in x of y if d is a a stable closed connected reductive subgroup of g containing a maximal torus t of g and m nx d we call m a subgroup of maximal rank in x in this paper we determine the structure and conjugacy classes of those subgroups of maximal rank which are maximal in x

observer design for tracking consensus in second order multi agent systems fractional order less than two this technical note studies the leader following tracking consensus problem of a class of multi agent systems where the dynamics of the leader is described by second order systems in order to track the states of the leader observers for the followers are designed by fractional order multi agent systems where the relative velocity information is unavailable it is interestingly found that the followers can track the leader with second order dynamics even if the fractional order is less than two by only using the position information of the local neighbors which is different from the existing results a novel fractional order observer is first proposed whose order is surprisingly less than the original leader system it is also shown that leader following consensus can be ensured if some carefully selected followers are informed and the relative position based protocols are appropriately designed with fractional order being between one and two a necessary and sufficient condition for the leader following consensus in multi agent systems without control input delay is proposed the results are then extended to the case with constant control input delay it is found that in both cases the real and imaginary parts of the eigenvalues of the augmented laplacian matrix of the topology play an important role in achieving consensus

sampled data based consensus of continuous time multi agent systems with time varying topology this technical note studies consensus problems of multiple agents with continuous time second order dynamics where each agent can obtain its positions and velocities relative to its neighbors only at sampling instants it is assumed that the sampling period of each agent is independent of the others and the interaction topology among agents is time varying where the associated direct graphs may not have spanning trees if the union graph of all direct graphs has a spanning tree then there exist controller gains and sampling periods such that consensus is reached moreover two approaches are presented to design such controller gains and sampling periods simulations are performed to validate the theoretical results

sampled measurement output feedback control of multi agent systems with jointly connected topologies this note studies the consensus problem of a class of multi agent systems mass with linear dynamics where each agent is able to use the specified measurement output e g position relative to its neighbors at certain sampling instants it is assumed that the network has switching but jointly connected topologies in the sense that the union of the associated graphs over a certain time interval always has a spanning tree under this assumption a linear sampled measurement output feedback controller is proposed to achieve full state consensus for a sufficiently small sampling period

distributed averaging with linear objective maps a distributed averaging system is a linear multi agent system in which agents communicate to reach an agreement or a consensus state defined as the average of the initial states of the agents consider a more generalized situation in which each agent is given a nonnegative weight and the agreement state is defined as the weighted average of the initial conditions we characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph specifically we introduce a linear function called the objective map that defines the desired final state as a function of the initial states of the agents we then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map in particular we characterize not only the set of objective maps that are feasible for a given digraph but also the consensus dynamics that implements the objective map in addition we present a decentralized algorithm to design the consensus dynamics

impulsive multiconsensus of second order multiagent networks using sampled position data a multiconsensus problem of multiagent networks is solved in this paper where multiconsensus refers to that the states of multiple agents in each subnetwork asymptotically converge to an individual consistent value when there exist information exchanges among subnetworks a distributed impulsive protocol is proposed to achieve multiconsensus of second order multiagent networks in terms of three categories 1 stationary multiconsensus 2 the first dynamic multiconsensus and 3 the second dynamic multiconsensus this impulsive protocol utilizes only sampled position data and is implemented at sampling instants for those three categories of multiconsensus the control parameters in the impulsive protocol are designed respectively moreover necessary and sufficient conditions are derived under which each multiconsensus can be reached asymptotically several simulations are finally provided to demonstrate the effectiveness of the obtained theoretical results

multi consensus of multi agent networks via a rectangular impulsive approach abstract a multi consensus problem is studied in multi agent networks the interaction mechanism of competition abstention cooperation among agents is introduced three rectangular impulsive protocols are proposed to solve multi consensus of second order multi agent networks with a directed topology these algorithms have the performance of dirac impulsive control and discrete time control necessary and sufficient conditions are obtained for the stationary multi consensus and the dynamic multi consensus numerical examples are provided to illustrate the effectiveness of the obtained criteria

disconnected synchronized regions of complex dynamical networks this technical note addresses the synchronized region problem which is converted to a more convenient matrix stability problem for complex dynamical networks for any natural number n the existence of a network with n disconnected synchronized regions is theoretically proved and numerically demonstrated this shows the intrinsic complexity of the network synchronization problem convexity characteristic of stability for relevant matrix pencils is further discussed a smooth chua s circuit network is finally discussed as an example for illustration

impulsive stabilization of high order hopfield type neural networks with time varying delays this paper studies the problems of global exponential stability for impulsive high order hopfield type neural networks nns with time varying delays by employing the lyapunov razumikhin technique some criteria ensuring global exponential stability are derived our results are then used to obtain some sufficient conditions under which some nns can be forced to converge by impulsive control numerical examples are also discussed to illustrate our results

signalizer functors proper 2 generated cores and nonconnected groups as has been well understood since its inception the signalizer functor method works most smoothly in finite groups satisfying some connectedness condition in particular in groups with a connected sylow 2 subgroup the original approach to nonconnectivity disposed of the problem once and for all by completely classifying all groups of sectional 2 rank at most 4 and then determining those with a nonconnected sylow 2 subgroup as a corollary by a theorem of macwilliams 141 every section of a nonconnected 2group can be generated by at most four elements even though this approach was very effective it was extremely elaborate for the actual proof of the classification of such groups runs to 464 pages l 11 and in addition depends upon a number of other classification theorems concerning groups with specified types of sylow 2 subgroups moreover although the sectional 2 rank 4 theorem has been invoked at many other points in the classification of finite simple groups the analysis of nonconnected groups has remained its primary application hence in attempting to simplify the existing classification of the finite simple groups one of the first natural questions to consider is whether there exists a shorter more direct way of treating nonconnectivity indeed harada has recently achieved just such a direct approach by a short elementary fusion argument 121 his result can be stated as follows here a k group is any finite group whose composition factors are among the known simple groups

distributed adaptive consensus control of lipschitz nonlinear multi agent systems using output feedback abstractthis paper addresses output feedback based distributed adaptive consensus control of multi agent systems having lipschitz nonlinear dynamics distributed dynamic protocols are designed base

coordination and consensus of networked agents with noisy measurements stochastic algorithms and asymptotic behavior this paper considers the coordination and consensus of networked agents where each agent has noisy measurements of its neighbors states for consensus seeking we propose stochastic approximation type algorithms with a decreasing step size and introduce the notions of mean square and strong consensus although the decreasing step size reduces the detrimental effect of the noise it also reduces the ability of the algorithm to drive the individual states towards each other the key technique is to ensure a trade off for the decreasing rate of the step size by following this strategy we first develop a stochastic double array analysis in a two agent model which leads to both mean square and strong consensus and extend the analysis to a class of well studied symmetric models subsequently we consider a general network topology and introduce stochastic lyapunov functions together with the so called direction of invariance to establish mean square consensus finally we apply the stochastic lyapunov analysis to a leader following scenario

on hybrid impulsive and switching systems and application to nonlinear control in this note a new class of hybrid impulsive and switching models is introduced and their asymptotic stability properties are investigated using switched lyapunov functions some new general criteria for exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching are established in addition a new hybrid impulsive and switching control strategy for nonlinear systems is developed a typical example the unified chaotic system is given to illustrate the theoretical results

products of conjugacy classes in finite and algebraic simple groups abstract we prove the arad herzog conjecture for various families of finite simple groups if a and b are nontrivial conjugacy classes then a b is not a conjugacy class we also prove that if g is a finite simple group of lie type and a and b are nontrivial conjugacy classes either both semisimple or both unipotent then a b is not a conjugacy class we also prove a strong version of the arad herzog conjecture for simple algebraic groups and in particular show that almost always the product of two conjugacy classes in a simple algebraic group consists of infinitely many conjugacy classes as a consequence we obtain a complete classification of pairs of centralizers in a simple algebraic group which have dense product a special case of this has been used by prasad to prove a uniqueness result for tits systems in quasi reductive groups our final result is a generalization of the baer suzuki theorem for p elements with p 5

bounds on the number and sizes of conjugacy classes in finite chevalley groups with applications to derangements we present explicit upper bounds for the number and size of conjugacy classes in finite chevalley groups and their variations these results have been used by many authors to study zeta functions associated to representations of finite simple groups random walks on chevalley groups the final solution to the ore conjecture about commutators in finite simple groups and other similar problems in this paper we solve a strong version of the boston shalev conjecture on derangements in simple groups for most of the families of primitive permutation group representations of finite simple groups the remaining cases are settled in two other papers of the authors and applications are given in a third

impulsive consensus algorithms for second order multi agent networks with sampled information in this paper the distributed consensus problem for second order continuous time multi agent networks with sampled data communication is investigated motivated by impulsive control strategy two kinds of impulsive distributed consensus algorithm are proposed these algorithms only utilize the sampled information and are implemented at sampled times by using the stability theory of impulsive systems and properties of the laplacian matrix necessary and sufficient conditions are obtained to ensure the consensus of the controlled networks it is shown that the control gains the sampling period and the eigenvalues of the laplacian matrix of the communication graph play key roles in achieving the consensus a numerical example is given to illustrate the results

unfaithful minimal heilbronn characters of finite groups abstract we obtain necessary and sufficient conditions for a finite group g to possess an unfaithful minimal heilbronn character a virtual character but not a character of g whose inner product with every monomial character is nonnegative whose restriction to every proper subgroup and quotient is a character and whose restriction to some proper subgroup is unfaithful we give an application constraining hypothetical minimal counterexamples to artin s conjecture on the holomorphy of l series

brief paper second order consensus in multi agent dynamical systems with sampled position data this paper studies second order consensus in multi agent dynamical systems with sampled position data a distributed linear consensus protocol with second order dynamics is designed where both the current and some sampled past position data are utilized it is found that second order consensus in such a multi agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period a necessary and sufficient condition for reaching consensus of the system in this setting is established based on which consensus regions are then characterized it is shown that if all the eigenvalues of the laplacian matrix are real then second order consensus in the multi agent system can be reached for any sampling period except at some critical points depending on the spectrum of the laplacian matrix however if there exists at least one eigenvalue of the laplacian matrix with a nonzero imaginary part second order consensus cannot be reached for sufficiently small or sufficiently large sampling periods in such cases one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods finally simulation examples are given to verify and illustrate the theoretical analysis

perron eigenvectors and the symmetric transportation polytope abstract let x and y be positive vectors in r n the set of all n n nonnegative matrices having x and y t as their right and left perron eigenvectors is a polyhedral convex cone a cross section of this cone is the polytope p x y consisting of all n n nonnegative matrices c such that cx x and y t c y t the set of doubly stochastic matrices is obtained as a special case when x y 1 1 1 t our purpose is to investigate the structure of p x y and especially its extreme points this is done by transforming the problem into a symmetric transportation polytope which contains all n n nonnegative matrices having the same vector z as their row and column sum vector using graph theoretic methods we investigate the number of extreme points of this polytope in particular we study vectors z that yield the maximum number of extreme points

row stochastic matrices with a common left fixed vector abstract we consider the convex polytope s n x that consist of those n n row stochastic matrices having a common nonnegative left fixed vector xt we examine the 1 skeleton of s n x and show how to construct all extreme points adjacent to a given one as vertices of the 1 skeleton connections with transportation polytopes are discussed further we give a formula for the degree of an extreme point in the 1 skeleton of s n x find its maximum and minimum values and determine when all degrees are equal an explicit description of the 1 skeleton is given for n 3

unipotent subgroups of groups of lie type let g g be either a simple algebraic group over an algebraically closed field k or a finite chevalley group normal or twisted over k f with q 4 for the case of an algebraic group all groups discussed are taken to be closed subgroups of g in this paper we prove results that parallel those in 141 where we deterined those subgroups of g containing a maximal torus given restrictions on k here we study the overgroups of a certain type of unipotent subgroup of g which like the maximal tori are of particular importance to the understanding of the subgroup structure of g as applications we establish results about overgroups of local subgroups of g and results concerning generation by centralizers of unipotent elements a unipotent group i g is said to be full provided i contains each unipotent element of its centralizer such subgroups occur quite often for example let v be an arbitrary unipotent subgroup of g and v a maximal unipotent subgroup of either ng v or v c v then v v and v is full before stating the results we introduce the following notation and terminology let p char k a subgroup x of g is quasisimple if it is a perfect central extension of a simple group connected in case g is an algebraic group x is semisimple if it is a commuting product of quasisimple groups let r x denote the unipotent radical of x which we interpret as o x in case g is finite if k if or f4 let o x denote the group generated by all unipotent elements i e p elements of x

stability analysis of swarms in this note we specify an individual based continuous time model for swarm aggregation in n dimensional space and study its stability properties we show that the individuals autonomous agents or biological creatures will form a cohesive swarm in a finite time moreover we obtain an explicit bound on the swarm size which depends only on the parameters of the swarm model

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

analyzing and controlling the network synchronization regions abstract in this paper the commonly concerned issue of synchronization regions of complex dynamical networks is investigated for the case when the synchronous state is an equilibrium point some simple sufficient conditions for a network to have or have no unbounded synchronization regions of the form 1 are established where 1 is a constant in addition a sufficient condition for the existence of a bounded synchronization region of the form 2 3 is derived where 2 and 3 are constants by using the parameter dependent lyapunov function method furthermore some effective controller design methods are presented that can change the synchronization regions thereby managing the synchronizability of the network finally some numerical examples are given to show that a dynamical network may have disconnected synchronization regions particularly it may have the coexistence of unbounded and bounded synchronization regions in the form of 1 2 3

a geometric study of cores of idempotent stochastic matrices abstract for each idempotent e in the compact affine semigroup st n of n n stochastic matrices the core of e denoted by q e is defined as the maximal subsemigroup of st n with zero element e in this paper we study the algebraic and geometric structures of cores and describe how they are put together inside of st n in the process lattice structures of the idempotents and their cores inside a larger core are revealed and then employed to initiate a possible classification

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

a geometric description of the maximal monoids of some matrix semigroups abstract the maximal monoids of the form f s f are studied where f is a nonnegative idempotent matrix and s is one of the following matrix semigroups n n the nonnegative square matrices st n the stochastic matrices and d n the doubly stochastic matrices for the cases of n n and st n it is shown that these maximal monoids are affinely isomorphic to the full semigroups of lower order and for f d n f that it is a compact affine semigroup with zero here called the core of a primitive idempotent

reaching a consensus in a dynamically changing environment a graphical approach this paper presents new graph theoretic results appropriate for the analysis of a variety of consensus problems cast in dynamically changing environments the concepts of rooted strongly rooted and neighbor shared are defined and conditions are derived for compositions of sequences of directed graphs to be of these types the graph of a stochastic matrix is defined and it is shown that under certain conditions the graph of a sarymsakov matrix and a rooted graph are one and the same as an illustration of the use of the concepts developed in this paper graph theoretic conditions are obtained which address the convergence question for the leaderless version of the widely studied vicsek consensus problem

observer based distributed consensus for general nonlinear multi agent systems with interval control inputs in this paper observer based distributed consensus for general nonlinear multi agent systems with interval control inputs under strongly connected balanced topology is encountered when the relative states of agents are unavailable or undesirable theoretical analysis method is further extended to the case of general nonlinear multi agent systems under switching setting moreover tracking problem on the leader follower scenario is also explicitly investigated under a mutual assumption that the communication graph which represents the interaction among agents contains a directed spanning tree with the leader as its root it is shown that the consensus for underlying considered multi agent systems can be desirable as long as the data missing rate does not exceed a certain threshold finally simulation examples are presented to effectively corroborate the analytical findings

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

consensus of fractional order multi agent systems with uncertain topological structure a takagi sugeno fuzzy event triggered control strategy abstract in this paper the consensus problem of fractional order multi agent systems fomass with uncertain topological structure via designed takagi sugeno fuzzy event triggered control is investigated first takagi sugeno fuzzy event triggered control for fomass is designed to effectively alleviate the congestion of communication capacity then by utilizing the tools including lyapunov function method the fractional inequality technique and laplace transform some sufficient conditions for the consensus of fomass with uncertain topological structure are obtained and a rigorous proof is given to exclude zeno behavior for the designed takagi sugeno fuzzy event triggered control finally two examples are given to not only illustrate the availability of the proposed approach but also show that the designed takagi sugeno fuzzy event triggered control in this paper is more effective than the previous methods

consensus of second order multi agent systems via impulsive control using sampled hetero information in this paper the consensus problem for second order multi agent systems using impulsive control with sampled hetero information is investigated necessary and sufficient conditions for sampling interval to achieve consensus for the second order multi agent systems are obtained analysis for the upper bound of sampling interval convergence performance and communication cost of the proposed control protocols are also discussed some numerical examples are given to demonstrate the effectiveness of the proposed control protocols

leader following formation control of multi agent systems under fixed and switching topologies in this article two kinds of leader following formation control problems for second order nonlinear multi agent systems are investigated that is the cases with fixed topology and with switching topology for the former by constructing an appropriate lyapunov functional and utilising linear matrix inequality lmi method we propose a formation control algorithm which makes the nonlinear multi agent systems converge to a desired formation in addition a formation control algorithm is also developed for coupled double integrators with a constant reference velocity then we extend these results to the case when the interaction topology is switching numerical simulations are presented finally to demonstrate the effectiveness of the proposed results

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper