continuous selections of trajectories of hybrid systems we present results on existence of continuous selections of trajectories of hybrid systems evolving according to lipschitz nonlinear inclusions first we utilize the skorohod metric to define both a family of pseudo metrics and a metric on the set of trajectories accepted by the hybrid automaton we show that under a non zeno condition the latter metric is complete second the existence of continuous selections with respect to the family of pseudo metrics is proved under a relatively mild assumption of transversality

an extension of lasalle s invariance principle for switched systems in this paper we address invariance principles for a certain class of switched nonlinear systems we provide an extension of lasalle s invariance principle for these systems and state asymptotic stability criteria we also present some related results on the compactness of the trajectories of these switched systems

existence and uniqueness theorems for periodic markov process and applications to stochastic functional differential equations abstract this work is devoted to an m valued markov process with a periodic transition probability function where m is a polish space sufficient conditions for the existence and uniqueness of the periodic markov process are given these existence theorems are rather general and the corresponding results in 1 11 15 23 are improved and generalized the uniqueness theorems for the periodic markov process are original as applications we study the existence uniqueness and global attractivity of periodic solution for the periodic stochastic n species lotka voltrra competitive model with bounded delays and the periodic stochastic neural networks with infinite delay respectively numerical simulations are presented to illustrate the main results

a common framework for complete and incomplete attitude synchronization in networks with switching topology in this paper we study attitude synchronization for elements in the unit sphere in mathbb r scriptscriptstyle scriptscriptstyle 3 and for elements in the three dimensional 3 d rotation group for a network with switching topology the agents angular velocities are assumed to be the control inputs and a switching control law for each agent is devised that guarantees synchronization provided that all elements are initially contained in a region which we identify later in the paper the control law is decentralized and it does not require a common orientation frame among all agents we refer to synchronization of unit vectors in mathbb r scriptscriptstyle 3 as incomplete synchronization and of 3 d rotation matrices as complete synchronization our main contribution lies in showing that these two problems can be analyzed under a common framework where all agents dynamics are transformed into unit vectors dynamics on a sphere of appropriate dimension

solutions to hybrid inclusions via set and graphical convergence with stability theory applications motivated by questions in stability theory for hybrid dynamical systems we establish some fundamental properties of the set of solutions to such systems using the notion of a hybrid time domain and general results on set and graphical convergence we establish under weak regularity and local boundedness assumptions that the set of solutions is sequentially compact and upper semicontinuous with respect to initial conditions and system perturbations the general facts are then used to establish several results for the behavior of hybrid systems that have asymptotically stable compact sets these results parallel what is already known for differential inclusions and difference inclusions for example the basin of attraction for a compact attractor is relatively open the attractivity is uniform from compact subsets of the basin of attraction and asymptotic stability is robust with respect to small perturbations

valuing finite lived russian options abstract this paper deals with the valuation of the russian option with finite time horizon in the framework of the black scholes merton model on the basis of the pde approach to a parabolic free boundary problem we derive laplace transforms of the option value the early exercise boundary and some hedging parameters using abelian theorems of laplace transforms we characterize the early exercise boundary at a time to close to expiration as well as the well known perpetual case in a unified way furthermore we obtain a symmetric relation in the perpetual early exercise boundary combining the gaver stehfest inversion method and the newton method we develop a fast algorithm for computing both the option value and the early exercise boundary in the finite time horizon

on path lifting mechanisms and unwinding in quaternion based attitude control the unit quaternion is a pervasive representation of rigid body attitude used for the design and analysis of feedback control laws because the space of unit quaternions constitutes a double cover of the rigid body attitude space quaternion based control laws are often by design inconsistent i e they do not have a unique value for each rigid body attitude inconsistent quaternion based control laws require an additional mechanism that uniquely converts an attitude estimate into its quaternion representation however conversion mechanisms that are memoryless e g selecting the quaternion having positive scalar component have a limited domain where they remain injective and when used globally introduce discontinuities into the closed loop system we show through an explicit construction and lyapunov analysis that such discontinuities can be hijacked by arbitrarily small measurement disturbances to stabilize attitudes far from the desired attitude to remedy this limitation we propose a hybrid dynamic algorithm for smoothly lifting an attitude path to the unit quaternion space we show that this hybrid dynamic mechanism allows us to directly translate quaternion based controllers and their asymptotic stability properties obtained in the unit quaternion space to the actual rigid body attitude space we also show that when quaternion based controllers are not designed to account for the double covering of the rigid body attitude space by a unit quaternion parameterization they can give rise to the unwinding phenomenon which we characterize in terms of the projection of asymptotically stable sets finally we employ the main results to show that certain hybrid feedbacks can globally asymptotically stabilize the attitude of a rigid body

invariance principles for hybrid systems with connections to detectability and asymptotic stability this paper shows several versions of the lasalle s invariance principle for general hybrid systems the broad framework allows for nonuniqueness of solutions zeno behaviors and does not insist on continuous dependence of solutions on initial conditions instead only a mild structural property involving graphical convergence of solutions is posed the general invariance results are then specified to hybrid systems given by set valued data further results involving invariance as well as observability detectability and asymptotic stability are given

razumikhin method and exponential stability of hybrid stochastic delay interval systems this paper deals with the exponential stability of hybrid stochastic delay interval systems also known as stochastic delay interval systems with markovian switching the known results in this area see e g x mao exponential stability of stochastic delay interval systems with markovian switching ieee trans automat control 47 10 2002 1604 1612 require the time delay to be a constant or a differentiable function and the main reason for such a restriction is due to the analysis of mathematics the main aim of this paper is to remove this restriction to allow the time delay to be a bounded variable only the razumikhin method is developed to cope with the difficulty arisen from the nondifferentiability of the time delay

a topological obstruction to continuous global stabilization of rotational motion and the unwinding phenomenon we show that a continuous dynamical system on a state space that has the structure of a vector bundle on a compact manifold possesses no globally asymptotically stable equilibrium this result is directly applicable to mechanical systems having rotational degrees of freedom in particular the result applies to the attitude motion of a rigid body in light of this result we explain how attitude stabilizing controllers obtained using local coordinates lead to unwinding instead of global asymptotic stability

brief paper spacecraft relative rotation tracking without angular velocity measurements we present a solution to the problem of tracking relative rotation in a leader follower spacecraft formation using feedback from relative attitude only the controller incorporates an approximate differentiation filter to account for the unmeasured angular velocity we show uniform practical asymptotic stability upas of the closed loop system for simplicity we assume that the leader is controlled and that we know orbital perturbations however this assumption can be easily relaxed to boundedness without degrading the stability property we also assume that angular velocities of spacecraft relative to an inertial frame are bounded simulation results of a leader follower spacecraft formation using the proposed controller structure are also presented

formation control and network localization via orientation alignment we propose a formation control strategy based on inter agent displacements for single integrator modeled agents in the plane since the orientations of the local reference frames of the agents are not aligned with each other due to the absence of a common sense of orientation the proposed strategy consists of an orientation alignment law and a formation control law under the proposed strategy if the interaction graph is uniformly connected and all the initial orientation angles belong to an interval with length less than the orientations are exponentially aligned and the formation exponentially converges to the desired formation we also show that the proposed strategy can be utilized for network localization as a dual problem

differential automata and their discrete simulators on presente la notion d automate differentiel pour la formulation d une classe de problemes aux valeurs initiales sur des champs vectoriels hysteretiques

cev asymptotics of american options abstract the constant elasticity of variance cev model is a practical approach to option pricing by fitting to the implied volatility smile its application to american style derivatives however poses analytical and numerical challenges by taking the laplace carson transform lct to the free boundary value problem characterizing the option value function and the early exercise boundary the analytical result involves confluent hyper geometric functions thus the numerical computation could be unstable and inefficient for certain set of parameter values we solve this problem by an asymptotic approach to the american option pricing problem under the cev model we demonstrate the use of the proposed approach using perpetual and finite time american puts

asymptotic option pricing under the cev diffusion abstract in finance many option pricing models generalizing the black scholes model do not have closed form analytic solutions so that it is hard to compute the solutions or at least it requires much time to compute the solutions therefore asymptotic representation of options prices of various type has important practical implications in finance this paper presents asymptotic expansions of option prices in the constant elasticity of variance model as the parameter appearing in the exponent of the diffusion coefficient tends to 2 which corresponds to the well known black scholes model we use perturbation theory for partial differential equations to obtain the relevant results for european vanilla barrier and lookback options we make our application of perturbation theory mathematically rigorous by supplying error bounds

a general stability criterion for time varying systems using a modified detectability condition uniform asymptotic stability for general nonlinear time varying systems is investigated from the output to state viewpoint a unified criterion is proposed using a modified detectability condition and certain integral inequalities the criterion extends the krasovskii lasalle theorem to nonperiodic time varying systems an example taken from the tracking control of mobile robots is given to illustrate that much as the invariance principle of lasalle is used in studying the stability of time invariant systems our results can be used to study the stability of nonperiodic time varying systems by checking the modified detectability condition

passivity based pose synchronization in three dimensions this paper addresses passivity based pose synchronization in the special euclidean group se 3 we first develop a passivity based distributed velocity input law to achieve pose synchronization we next show that the pose synchronizes exponentially fast under an assumption on the initial states of the bodies with an exponential convergence rate given by algebraic connectivity of interconnection graphs we also prove pose synchronization in the presence of communication delays and topology switches we moreover give further extensions of the present law where desirable velocities and collision avoidance are taken into account finally the effectiveness of the present inputs is demonstrated through numerical simulations and experiments on a planar 2d test bed

new criteria for mean square exponential stability of stochastic delay differential equations by a novel approach we present several new criteria for the mean square exponential stability of general non linear stochastic delay differential equations both delay independent and delay depend

nonpathological lyapunov functions and discontinuous caratheodory systems differential equations with discontinuous right hand side and solutions intended in caratheodory sense are considered for these equations sufficient conditions which guarantee both lyapunov stability and asymptotic stability in terms of nonsmooth lyapunov functions are given an invariance principle is also proven

unified cooperative control of multiple agents on a sphere for different spherical patterns in this technical note we consider the cooperative control of multiple agents on a sphere provide the appropriate attraction repulsion interactions between agents with introduction of the state dependent repulsive coefficients and design the unified control laws for agents to achieve three fundamental spherical configurations or patterns rendezvous uniform deployment and formation using both the first and second order models we present the analysis of the stability scaling and geometric patterns of the models on the sphere under different attraction repulsion parameters with illustration of the geometrical patterns and the geometrical isomerism by simulations the closed loop dynamics of agents are invariant with respect to group rotation actions on the sphere

singular perturbations in option pricing after the celebrated black scholes formula for pricing call options under constant volatility the need for more general nonconstant volatility models in financial mathematics motivated numerous works during the 1980s and 1990s in particular a lot of attention has been paid to stochastic volatility models in which the volatility is randomly fluctuating driven by an additional brownian motion we have shown in derivatives in financial markets with stochastic volatility cambridge university press cambridge uk 2000 internat j theoret appl finance 13 2000 pp 101 142 that in the presence of a separation of time scales between the main observed process and the volatility driving process asymptotic methods are very efficient in capturing the effects of random volatility in simple robust corrections to constant volatility formulas from the point of view of pdes this method corresponds to a singular perturbation analysis the aim of this paper is to deal with the nonsmoothness of the payoff

phase synchronization control of complex networks of lagrangian systems on adaptive digraphs this paper presents a formation control and synchronization method that utilizes adaptive network topologies for a class of complex dynamical networks comprised of a large number of highly nonlinear euler lagrange el systems a time varying and switching network topology constructed by the adaptive graph laplacian matrix relaxes the standard requirement of consensus stability even permitting exponential synchronization on an unbalanced digraph or a weakly connected digraph that can sporadically lose connectivity the time varying graph laplacian matrix is adapted by an adaptive control scheme based on relative positions and errors of synchronization and tracking the adaptive graph laplacian is integrated with a phase synchronization controller that synchronizes the relative motions of el systems moving in elliptical orbits thereby yielding a smaller synchronization error than an uncoupled tracking control law in the presence of bounded disturbances and modeling errors an example of reconfiguring hundreds of spacecraft in low earth orbit shows the effectiveness of the proposed phase synchronization controller for a large number of complex el systems moving in periodic elliptical orbits

stochastic volatility asymptotics of stock loans valuation and optimal stopping abstract a stock loan or equity security lending service is a loan which uses stocks as collateral the borrower has the right to repay the principal with interest and regain the stock or make no repayment and surrender the stock therefore the valuation of stock loan is an optimal stopping problem related to a perpetual american option with a negative effective interest rate the negative effective interest rate makes standard techniques for perpetual american option pricing failure using a fast mean reverting stochastic volatility model we applied a perturbation technique to the free boundary value problem for the stock loan price an analytical pricing formula and optimal exercise boundary are derived by means of asymptotic expansion

distributed attitude synchronization control of multi agent systems with switching topologies this paper addresses the attitude synchronization problem in multi agent systems with directed and switching interconnection topologies two cases for the synchronization problem are discussed under different assumptions about the measurable information in the first case the agents can measure their rotations relative to a global reference coordinate frame whilst in the second case they can only measure the relative rotations between each other two intuitive distributed control laws based on the axis angle representations of the rotations are proposed for the two cases respectively the invariance of convex balls in so 3 is guaranteed moreover attitude synchronization is ensured under the well known mild switching assumptions the joint strong connection for the first case and joint quasi strong connection for the second case to show the effectiveness of the proposed control schemes illustrative examples are provided

an integral invariance principle for differential inclusions with applications in adaptive control the byrnes martin integral invariance principle for ordinary differential equations is extended to differential inclusions on bbb r n the extended result is applied in demonstrating the existence of adaptive stabilizers and servomechanisms for a variety of nonlinear system classes

invariance principles for switching systems via hybrid systems techniques invariance principles and sufficient conditions for asymptotic stability for switching systems are given multiple lyapunov like functions are used and dwell time persistent dwell time and weak dwell time switching signals are considered the invariance principles are derived from general invariance principles for hybrid systems asymptotic stability is concluded under observability assumptions or common bounds on the lyapunov like functions

passivity as a design tool for group coordination we pursue a group coordination problem where the objective is to steer the differences between output variables of the group members to a prescribed compact set to stabilize this set we study a class of feedback rules that are implementable with local information available to each member when the information flow between neighboring members is bidirectional we show that the closed loop system exhibits a special interconnection structure which inherits the passivity properties of its components by exploiting this structure we develop a passivity based design framework which results in a broad class of feedback rules that encompass as special cases some of the existing formation stabilization and group agreement designs in the literature the passivity approach offers additional design flexibility compared to these special cases and systematically constructs a lurie type lyapunov function for the closed loop system we further study the robustness of these feedback laws in the presence of a time varying communication topology and present a persistency of excitation condition which allows the interconnection graph to lose connectivity pointwise in time as long as it is established in an integral sense

quaternion based hybrid feedback for robust global attitude synchronization we apply recent results on robust global asymptotic stabilization of the attitude of a single rigid body to the problem of globally synchronizing the attitude of a network of rigid bodies using a decentralized strategy the proposed hybrid feedback scheme relies on the communication of a binary logic variable between each pair of neighboring rigid bodies that determines the orientation of a torque component acting to reduce their relative error through a hysteretic switch of this logic variable the hybrid feedback achieves global synchronization under the assumption that the network is connected and acyclic the hysteresis eliminates chattering while preventing the unwinding phenomenon apparent in some quaternion based attitude control schemes the results are exercised in a numerical example

sparse iteration 4d cordic algorithms for multiplying quaternions novel 4d cordic algorithms and hardware architecture for multiplying quaternions are presented aimed at constant coefficient multipliers in our solution microrotations are multiplications by hypercomplex numbers with only one non zero imaginary part such transformations can be described using sparse matrices and implemented using less hardware resources than the iteration of the known quaternion cordic algorithm chip area can be saved because sparse microrotations can be computed using a permutation network and two operand adders without four operand additions which are necessary in the known solution the obtainable area savings depend on the implementation technology and the architectures of adders and bit shifters but can be as large as 45 and 25 percent for asic and fpga circuits respectively the circuitry simplifications come at the cost of slowing down computations our approach improves the area delay product and a single sparse iteration can be executed up to 15 percent faster than the conventional one but more microrotations are usually necessary to achieve the required accuracy on the other hand a sparse 4d iteration can be identified with microrotations of two 2d cordics which work in parallel this makes convergence analysis easier than in the previous 4d solution as it is sufficient to consider only two dimensions

an invariance principle for nonlinear hybrid and impulsive dynamical systems in this paper we develop an invariance principle for dynamical systems possessing left continuous flows specifically we show that left continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems as a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems namely state dependent impulsive dynamical systems these results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems

an artificial boundary method for american option pricing under the cev model the black scholes asset price dynamics is well known to be inadequate for capturing the volatility smile in the financial market therefore the constant elasticity of variance cev model has become a popular alternative to valuing options fitting to the smile american option pricing however is computationally intensive as there are no analytical formulas available this paper proposes an artificial boundary method for partial differential equations pdes to compute american option prices and greeks under the cev model the idea is to reduce the infinite computational domain to a finite one by introducing an artificial boundary on which an exact boundary condition is derived we then develop a crank nicolson scheme to solve the pde with the artificial boundary condition implemented with a numerical laplace inversion with a finite computational domain the optimal exercise boundary can be determined efficiently our numerical examples show that the proposed scheme is accurate robust with respect to

stochastic differential delay equation moment stability and application to hematopoietic stem cell regulation system we study the moment stability of the trivial solution of a linear differential delay equation in the presence of additive and multiplicative white noise the results established here are applied to examining the local stability of the hematopoietic stem cell hsc regulation system in the presence of noise the stability of the first moment for the solutions of a linear differential delay equation under stochastic perturbation is identical to that of the unperturbed system however the stability of the second moment is altered by the perturbation we obtain using laplace transform techniques necessary and sufficient conditions for the second moment to be bounded in applying the results to the hsc system we find that the system stability is sensitive to perturbations in the stem cell differentiation and death rates but insensitive to perturbations in the proliferation rate

smooth lyapunov functions for hybrid systems part i existence is equivalent to robustness hybrid systems are dynamical systems where the state is allowed to either evolve continuously flow on certain subsets of the state space or evolve discontinuously jump from other subsets of the state space for a broad class of such systems characterized by mild regularity conditions on the data we establish the equivalence between the robustness of stability with respect to two measures and a characterization of such stability in terms of a smooth lyapunov function this result unifies and generalizes previous results for differential and difference inclusions with outer semicontinuous and locally bounded right hand sides furthermore we give a description of forward completeness of a hybrid system in terms of a smooth lyapunov like function

asymptotic smooth stabilization of the inverted 3 d pendulum the 3 d pendulum consists of a rigid body supported at a fixed pivot with three rotational degrees of freedom it is acted on by gravity and it is fully actuated by control forces the 3 d pendulum has two disjoint equilibrium manifolds namely a hanging equilibrium manifold and an inverted equilibrium manifold the contribution of this paper is that two fundamental stabilization problems for the inverted 3 d pendulum are posed and solved the first problem asymptotic stabilization of a specified equilibrium in the inverted equilibrium manifold is solved using smooth and globally defined feedback of angular velocity and attitude of the 3 d pendulum the second problem asymptotic stabilization of the inverted equilibrium manifold is solved using smooth and globally defined feedback of angular velocity and a reduced attitude vector of the 3 d pendulum these control problems for the 3 d pendulum exemplify attitude stabilization problems on the configuration manifold so 3 in the presence of potential forces lyapunov analysis and nonlinear geometric methods are used to assess global closed loop properties yielding a characterization of the almost global domain of attraction for each case

improved razumikhin and krasovskii stability criteria for time varying stochastic time delay systems the problem of pth moment stability for time varying stochastic time delay systems with markovian switching is investigated in this paper some novel stability criteria are obtained by applying the generalized razumikhin and krasovskii stability approaches both pth moment asymptotic stability and integral input to state stability are considered based on the notion and properties of uniformly stable functions and the improved comparison lemmas the established results show that time derivatives of the constructed razumikhin functions and krasovskii functionals are allowed to be indefinite which improve the existing results on this topic by applying the obtained results for stochastic systems we also analyze briefly the stability of time varying deterministic time delay systems finally examples are provided to illustrate the effectiveness of the proposed results

stabilization of stochastic differential equations driven by g brownian motion with feedback control based on discrete time state observation abstract this paper mainly concerns the stability of the solutions for stochastic differential equations driven by g brownian motion g sdes via feedback control based on discrete time state observation more precisely the discrete time state feedback control is included in the drift coefficient of the g sdes by constructing an appropriate g lyapunov function a set of conditions is obtained for the h stability asymptotic stability and mean square exponential stability of the controlled systems finally an example with numerical simulation is presented to illustrate the effectiveness of the proposed control design technique

delay dependent stability of highly nonlinear hybrid stochastic systems abstract there are lots of papers on the delay dependent stability criteria for differential delay equations ddes stochastic differential delay equations sddes and hybrid sddes a common feature of these existing criteria is that they can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions namely satisfy the linear growth condition in other words there is so far no delay dependent stability criterion on nonlinear equations without the linear growth condition we will refer to such equations as highly nonlinear ones this paper is the first to establish delay dependent criteria for highly nonlinear hybrid sddes it is therefore a breakthrough in the stability study of highly nonlinear hybrid sddes

distributed geodesic control laws for flocking of nonholonomic agents we study the problem of flocking and velocity alignment in a group of kinematic nonholonomic agents in 2 and 3 dimensions by analyzing the velocity vectors of agents on a circle for planar motion or sphere for 3 d motion we develop a geodesic control law that minimizes a misalignment potential and results in velocity alignment and flocking the proposed control laws are distributed and will provably result in flocking when the underlying proximity graph which represents the neighborhood relation among agents is connected we further show that flocking is possible even when the topology of the proximity graph changes over time so long as a weaker notion of joint connectivity is preserved

local lyapunov functions for consensus in switching nonlinear systems this note presents two theorems on asymptotic state consensus of continuous time nonlinear multi agent systems the agents reside in mathbb r m and have switching interconnection topologies both the first theorem formulated in terms of the states of individual agents and the second theorem formulated in terms of the pairwise states for pairs of agents can be interpreted as variants of lyapunov s second method the two theorems complement each other the second provides stronger convergence results under weaker graph topology assumptions whereas the first often can be applied in a wider context in terms of the structure of the right hand sides of the systems the second theorem also sheds some new light on well known results for consensus of nonlinear systems where the right hand sides of the agents dynamics are convex combinations of directions to neighboring agents for such systems instead of proving consensus by using the theory of contracting convex sets a local quadratic lyapunov function can be used

an invariance principle for nonlinear switched systems abstract in this paper we address the problem of extending lasalle invariance principle to switched system we prove an extension of the invariance principle relative to dwell time switched solutions and a second one relative to constrained switched systems

hybrid feedback control and robust stabilization of nonlinear systems in this paper we show for any nonlinear system that is asymptotically controllable to a compact set that a logic based hybrid feedback can achieve asymptotic stabilization that is robust to small measurement noise actuator error and external disturbance the construction of such a feedback hinges upon recasting a stabilizing patchy feedback in a hybrid framework by making it dynamic with a discrete state while insisting on semicontinuity and closedness properties of the hybrid feedback and of the resulting closed loop hybrid system the robustness of stability is then shown as a generic property of hybrid systems having the said regularity properties auxiliary results give uniformity of convergence and of overshoots for hybrid systems and give a characterization of asymptotic stability of compact sets

matching asymptotics in path dependent option pricing abstract the valuation of path dependent options in finance creates many interesting mathematical challenges among them are a large delta and gamma near the expiry leading to a big error in pricing those exotic options as well as european vanilla options also the higher order corrections of the asymptotic prices of the derivatives in some stochastic volatility models are difficult to be evaluated in this paper we use the method of matched asymptotic expansions to obtain more practical values of lookback and barrier option prices near the expiry our results verify that matching asymptotics is a useful tool for pde methods in path dependent option pricing

consensus optimization on manifolds the present paper considers distributed consensus algorithms that involve n agents evolving on a connected compact homogeneous manifold the agents track no external reference and communicate their relative state according to a communication graph the consensus problem is formulated in terms of the extrema of a cost function this leads to efficient gradient algorithms to synchronize i e maximizing the consensus or balance i e minimizing the consensus the agents a convenient adaptation of the gradient algorithms is used when the communication graph is directed and time varying the cost function is linked to a specific centroid definition on manifolds introduced here as the induced arithmetic mean that is easily computable in closed form and may be of independent interest for a number of manifolds the special orthogonal group so n and the grassmann manifold text it grass p n are treated as original examples a link is also drawn with the many existing results on the circle

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