a rigorous formalism of information transfer between dynamical system components ii continuous flow the transfer of information between dynamical system components is formalized with causality faithfully represented in a continuous system with many components information transfer is a mechanism controlling the marginal entropy evolution of the target component it is measured by the rate of entropy thus transferred which is obtained through freezing the source component instantaneously and comparing the entropy increases between the original system and the so modified system the resulting transfer measure is consistent with our earlier 2d formalism derived in liang and kleeman x s liang r kleeman information transfer between dynamical system components phys rev lett 95 24 2005 244101 using different methods it also possesses a property of unidirectionalism which has been emphasized by schreiber t schreiber measuring information transfer phys rev lett 85 2 2000 461 464 we apply our formalism to a two mode four dimensional truncated burgers hopf system no significant information exchange is identified between the four components save for a transfer from the cosine direction of mode 2 to the sine direction of mode 1 this transfer occurs continuously and at a nearly constant rate the present work should serve as a starting point for the development of a rigorous dynamics free formalism for the information transfer of multivariate time series c 2007 elsevier b v all rights reserved

problems on time varying port controlled hamiltonian systems geometric structure and dissipative realization to apply time varying port controlled hamiltonian pch systems to practical control designs two basic problems should be dealt with one is how to provide such time varying systems a geometric structure to guarantee the completeness of representations in mathematics and the other is how to express the practical system under consideration as a time varying pch system which is called the dissipative hamiltonian realization problem the paper investigates the two basic problems a suitable geometric structure for time varying pch systems is proposed first then the dissipative realization problem of time varying nonlinear systems is investigated and serval new methods and sufficient conditions are presented for the realization

distributed consensus for multi agent systems with delays and noises in transmission channels this paper studies the distributed consensus problem for linear discrete time multi agent systems with delays and noises in transmission channels due to the presence of noises and delays existing techniques such as the lifting technique and the stochastic lyapunov theory are no longer applicable to the analysis of consensus in this paper a novel technique is introduced to overcome the difficulties induced by the delays and noises a consensus protocol with decaying gains satisfying persistence condition is adopted necessary and sufficient conditions for strong consensus and mean square consensus are respectively given for non leader follower and leader follower cases under a fixed topology under dynamically switching topologies and randomly switching topologies sufficient conditions for strong consensus and mean square consensus are also obtained numerical examples are given to demonstrate the effectiveness of the proposed protocols

information transfer between dynamical system components we present a rigorous formalism of information transfer for systems with dynamics fully known this follows from an accurate classification of the mechanisms for the entropy change of one component into a self evolution plus a transfer from the other component the formalism applies to both continuous flows and discrete maps the resulting transfer measure possesses a property of asymmetry and is qualitatively consistent with the classical measures it is further validated with the baker transformation and the henon map

technical communique semi global stabilization of linear time delay systems with control energy constraint this note is concerned with the problem of semi globally stabilizing a linear system with an input delay and a constraint on the energy of its input under the condition of null controllability with vanishing energy the parametric lyapunov equation based l 2 low gain feedback is adopted to solve the problem the proposed approach is applied to the linearized model of the relative motion in the orbit plane of a spacecraft with respect to another spacecraft in a circular orbit around the earth to validate its effectiveness

interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

improved h control of discrete time fuzzy systems a cone complementarity linearization approach in this paper new results are presented for h analysis and synthesis problems of discrete time takagi sugeno ts fuzzy systems by defining a multiple lyapunov function a new sufficient condition guaranteeing the h performance of the ts fuzzy systems is first derived which is expressed by a set of linear matrix inequalities lmis both theoretical analysis and numerical examples show that such a new condition is less conservative than previous results obtained within the quadratic framework based on this new condition for h performance the corresponding h controller design problem is then investigated different from the traditional quadratic framework the synthesis problem is solved by exploiting the cone complementarity linearization ccl method together with a sequential minimization problem subject to lmi constraints obtained for the existence of admissible controllers which can be readily solved by using standard numerical software

consensus of high order multi agent systems with large input and communication delays we study in this paper the consensus problem for multi agent systems with agents characterized by high order linear systems with time delays in both the communication network and inputs provided that the open loop dynamics of the agents is not exponentially unstable but may be polynomially unstable and the communication topology contains a directed spanning tree a truncated predictor feedback approach is established to solve the consensus problem it is shown that if the delays are constant and exactly known the consensus problems can be solved by both full state feedback and observer based output feedback protocols for arbitrarily large yet bounded delays if it is further assumed that the open loop dynamics of the agents only contains zero eigenvalues the delays are allowed to be time varying and unknown numerical examples are worked out to illustrate the effectiveness of the proposed approaches

saturated delayed controls for feedforward nonlinear systems the saturated delayed feedback is presented to globally stabilize a class of feedforward nonlinear systems whose nominal dynamics is the cascade of multiple oscillators and multiple integrators key strategies are stated as follows 1 to compensate the arbitrarily large input delay and to carry out the recursive analysis we transform the concerned system into a normal form 2 in the convergence analysis for multiple oscillators that are relatively difficult to treat we combine the saturated delayed terms define the composite lyapunov functions and use the cauchy formula 3 for ease of the analysis on nonlinear terms we employ saturation levels to restrict them as applications the usual feedforward nonlinear systems with multiple integrators as the nominal dynamics and the null controllable linear systems are dealt with in some new manners and a saturated delayed controller is presented for the well known tora system

a robust method for detecting interdependences application to intracranially recorded eeg we present a measure for characterizing statistical relationships between two time sequences in contrast to commonly used measures like cross correlations coherence and mutual information the proposed measure is non symmetric and provides information about the direction of interdependence it is closely related to recent attempts to detect generalized synchronization however we do not assume a strict functional relationship between the two time sequences and try to define the measure so as to be robust against noise and to detect also weak interdependences we apply our measure to intracranially recorded electroencephalograms of patients suffering from severe epilepsies

linear systems subject to input saturation and time delay global asymptotic stabilization this note deals with the problem of global asymptotic stabilization of linear systems by bounded static feedbacks subject to time delay under standard necessary conditions we provide two constructions of controllers of nested saturation type which extends to the general case partial results of previous papers for arbitrary small bound on the control and large constant delay to validate the approach a third order integrator and oscillator with multiplicity two example is presented

consensus seeking over markovian switching networks with time varying delays and uncertain topologies stochastic consensus problems for linear time invariant multi agent systems over markovian switching networks with time varying delays and topology uncertainties are dealt with by using the linear matrix inequality method and the stability theory of markovian jump linear system we show that consensus can be achieved for appropriate time delays and topology uncertainties which are not caused by the markov process provided the union of topologies associated with the positive recurrent states of the markov process admits a spanning tree and the agent dynamics is stabilizable feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying delays numerical examples are given to show the feasibility of theoretical results

l_p stabilization of integrator chains subject to input saturation using lyapunov based homogeneous design consider the n th integrator dot x j nx sigma u e n where x in mathbb r n u in mathbb r j n is the n th jordan block and e n 0 cdots 0 1 t in mathbb r n we provide easily implementable state feedback laws u k x which not only render the closed loop system globally asymptotically stable but also are finite gain l p stabilizing with arbitrarily small gain as in a saberi p hou and a stoorvogel ieee trans automat control 45 2000 pp 1042 1052 these l p stabilizing state feedbacks are built from homogeneous feedbacks appearing in finite time stabilization of linear systems we also provide additional l infty stabilization results for the case of both internal and external disturbances of the n th integrator namely for the perturbed system dot x j nx e n sigma k x d d where d in mathbb r and d in mathbb r n

delay robustness in consensus problems we investigate the robustness of consensus schemes for linear multi agent systems mas to feedback delays to achieve this we develop a unified framework that considers linear mas models with different feedback delays e g affecting only the neighbor s output or affecting both the agent s own and its neighbors output this framework has the advantage of providing scalable simple and accurate set valued conditions for consensus using these set valued conditions previous results on consensus in mas with delays can be recovered and generalized moreover we use them to derive conditions for the convergence rate of single integrator mas with feedback delays finally building on this framework we propose a scalable delay dependent design algorithm for consensus controllers for a large class of linear mas

technical communique average consensus in networks with nonlinearly delayed couplings and switching topology the paper addresses consensus under nonlinear couplings and bounded delays for multi agent systems where the agents have the single integrator dynamics the network topology is undirected and may alter as time progresses the couplings are uncertain and satisfy a conventional sector condition with known sector slopes the delays are uncertain time varying and obey known upper bounds the network satisfies a symmetry condition that resembles the newton s third law explicit analytical conditions for the robust consensus are offered that employ only the known upper bounds for the delays and the sector slopes

local predictability and information flow in complex dynamical systems abstract predictability is by observation a local notion in complex dynamical systems its spatiotemporal structure implies a flow or transfer in discrete cases of information that redistributes the local predictability within the state space of concern information flow is a fundamental concept in general physics which has applications in a wide variety of disciplines such as neuroscience material science atmosphere ocean science and turbulence research to name but a few in this study it is rigorously formulated with respect to relative entropy within the framework of a system with many components each signifying a location or a structure given a component the mechanism governing the evolution of its predictability can be classified into two groups one due to the component itself another due to a transfer of information from its peers a measure of the transfer is rigorously derived and an explicit expression obtained this measure possesses a form reminiscent of that we have obtained before with respect to absolute entropy in x s liang and r kleeman a rigorous formalism of information transfer between dynamical system components physica d 227 2007 173 182 in particular when the system is of dimensionality 2 there is no difference between the formalisms with respect to absolute entropy and relative entropy except for a minus sign properties have been explored and discussed particularly discussed is the property of asymmetry or causality which states that information transfer from one component to another carries no hint about the transfer in the other direction in contrast to the transfer of other quantities such as energy this formalism has been applied to the study of the scale scale interaction and information transfer between the first two modes of the truncated burgers equation it is found that all 12 transfers are essentially zero or negligible save for a strong transfer between the sine components from the low frequency mode to the high frequency mode that is to say the predictability of the high frequency mode is controlled by the knowledge of the low frequency mode this result though from a highly idealized system has interesting implications about the dynamical closure problem in turbulence research and atmosphere ocean science i e the subgrid processes may to some extent be parameterized by the large scale dynamics this study can be adopted to investigate the propagation of uncertainties in fluid flows which has important applications in problems such as atmospheric observing platform design and may be utilized to identify the route of information flowing within a complex network

distributed robust adaptive equilibrium computation for generalized convex games this paper considers a class of generalized convex games where each player is associated with a convex objective function a convex inequality constraint and a convex constraint set the players aim to compute a nash equilibrium through communicating with neighboring players the particular challenge we consider is that the component functions are unknown a priori to associated players we study two distributed computation algorithms and analyze their convergence properties in the presence of data transmission delays and dynamic changes of network topologies the algorithm performance is verified through demand response on the ieee 30 bus test system our technical tools integrate convex analysis variational inequalities and simultaneous perturbation stochastic approximation

output feedback regulation of a chain of integrators with unknown time varying delays in states and input we consider a problem of global asymptotic regulation of a chain of integrators that has unknown time varying delays in both states and input by output feedback the time varying delays are only known to be bounded and their bounds and time varying rates are unknown to solve the considered problem we introduce a newly designed adaptive output feedback controller for system analysis we give a new transformation and techniques in order to deal with new phenomena associated with unknown time varying delays in states

robust synchronization of uncertain linear multi agent systems this paper deals with robust synchronization of uncertain multi agent networks given a network with for each of the agents identical nominal linear dynamics we allow uncertainty in the form of additive perturbations of the transfer matrices of the nominal dynamics the perturbations are assumed to be stable and bounded in h norm by some a priori given desired tolerance we derive state space formulas for observer based dynamic protocols that achieve synchronization for all perturbations bounded by this desired tolerance it is shown that a protocol achieves robust synchronization if and only if each controller from a related finite set of feedback controllers robustly stabilizes a given single linear system our protocols are expressed in terms of real symmetric solutions of certain algebraic riccati equations and inequalities and also involve weighting factors that depend on the eigenvalues of the graph laplacian for undirected network graphs we show that within the class of such dynamic protocols a guaranteed achievable tolerance can be obtained that is proportional to the quotient of the second smallest and the largest eigenvalue of the laplacian we also extend our results to additive nonlinear perturbations with l2 gain bounded by a given tolerance

a unifying framework for robust synchronization of heterogeneous networks via integral quadratic constraints a general framework for analysing robust synchronization in large scale heterogenous networks is proposed based on the theory of integral quadratic constraints iqcs dynamic agents are represented as linear time invariant single input single output systems the agents exchange information according to a sparse dynamical interconnection operator in order to achieve synchronization where their outputs are steered to the same possibly time varying signal the main technical hindrance to applying iqcs in this context lies with the presence of the marginally stable dynamics which define the trajectory to which the agents outputs synchronize it is shown that by working with conditions defined on modified signal spaces of interest and exploiting the graph structure underlying the connections between the dynamic systems iqc methods can be applied directly to synchronization analysis without recourse to loop transformations which may obscure the inherent structural properties of the multi agent networked systems decentralized and scalable conditions for synchronization are proposed within this setting the iqc framework is demonstrated to unify and generalize some of the existing results in the literature including certain nyquist type consensus certificates for time delay systems moreover it allows the role of feedback in robustness against uncertainty to be better manifested within the context of synchronization

consensus reaching in multi agent packet switched networks with non linear coupling an important task for multi agent systems mas is to reach a consensus e g to align their velocity vectors recent results propose appropriate consensus protocols to achieve such tasks but most of them do not consider the effect of communication constraints such as the presence of time delays in the exchange of information between the agents in this article we provide conditions for a non linear locally passive mas of arbitrary size to reach a consensus when the agents communicate over a packet switched network that is characterised by a given topology both the cases of constant and switching topologies are considered the nature of the communication channel imposes constraints that are modelled using stochastic delays of arbitrary distribution we first embed this model in another distributed but deterministic delay model and provide conditions for the error introduced by this simplification in our main result we provide conditions for the locally passive mas with distributed delays to reach

a general result on the stabilization of linear systems using bounded controls we present two constructions of controllers that globally stabilize linear systems subject to control saturation we allow essentially arbitrary saturation functions the only conditions imposed on the system are the obvious necessary ones namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold one of the constructions is in terms of a neural network type one hidden layer architecture while the other one is in terms of cascades of linear maps and saturations

mas consensus and delay limits under delayed output feedback in this technical note we study the consensus problem for discrete time multi agent systems over an undirected fixed network communication graph focusing on the robustness of consensus with respect to communication delay we assume that the agents input is subject to a constant albeit possibly unknown time delay and is generated by a distributed dynamic output feedback control protocol drawing upon concepts and techniques from robust control notably those concerning gain margin optimization and analytic interpolation we derive explicit closed form conditions for general linear agents to achieve consensus our results display an explicit dependence of the consensus condition on the delay value as well as on the agent s unstable poles and non minimum phase zeros showing that delayed communication between agents will generally hinder consensus and impose restrictions on the network topology we also show that a lower bound on the maximal delay allowable for consensus can be computed by a simple line search method

input delay margin for consensusability of multi agent systems in this paper we are concerned with the consensus of multi agent systems with input delay among all standard static protocols that achieve the consensus for the multi agent system under no input delay we aim to find the maximum input delay such that the system remains consensusable under the same protocols in the case of continuous time systems in view of the continuity of stability with respect to the time delay the maximum delay margin for consensusability is given for scalar systems and vector systems with a single unstable open loop pole for scalar discrete time systems we show that the maximum delay margin for consensusability is strictly greater than zero if and only if the open loop pole of the system is located in a specified interval

a rigorous formalism of information transfer between dynamical system components i discrete mapping we put the concept of information transfer on a rigorous footing and establish for it a formalism within the framework of discrete maps the resulting transfer measure possesses a property of directionality or transfer asymmetry as emphasized by schreiber t schreiber measuring information transfer phys rev lett 85 2 2000 461 it also verifies the transfer measure for two dimensional systems which was obtained by liang and kleeman x s liang r kleeman information transfer between dynamical system components phys rev lett 95 24 2005 244101 through a different avenue connections to classical formalisms are explored and applications presented we find that in the context of the baker transformation there is always information flowing from the stretching direction to the folding direction while no transfer occurs in the opposite direction we also find that within the henon map system the transfer from the quadratic component to the linear component is of a simple form as expected on physical grounds this latter result is unique to our formalism

guaranteed cost synchronization of chaotic cellular neural networks with time varying delay synchronization of cellular neural networks with time varying delay is discussed in this letter based on razumikhin theorem a guaranteed cost synchronous controller is given unlike lyapunov krasovskii analysis process there is no constraint on the change rate of time delay the saturated terms emerging in the razumikhin analysis are amplified by zoned discussion and maximax synthesis rather than by lipschitz condition and vector inequality which will bring more conservatism then the controller criterion is transformed from quadratic matrix inequality form into linear matrix inequality form with the help of a sufficient and necessary transformation condition the minimization of the guaranteed cost is studied and a further criterion for getting the controller is presented finally the guaranteed cost synchronous control and its corresponding minimization problem are illustrated with examples of chaotic time varying delay cellular neural networks

deviation bounds in multi agent systems described by undirected graphs the theory of port hamiltonian systems is used to derive upper bounds for the state deviations in multi agent systems described by undirected graphs pinned to a reference signal the upper bounds for the deviations in networks of first or second order agents respectively depend on the minimal eigenvalue of the extended laplacian of the system in networks of first order agents the deviations decay exponentially with a rate depending on the same minimal eigenvalue in case networks of second order systems meet specific design properties it can be shown that the deviations also decay exponentially with half the rate compared to first order systems

robust stability and stabilization methods for a class of nonlinear discrete time delay systems this paper establishes new robust delay dependent stability and stabilization methods for a class of nonlinear discrete time systems with time varying delays the parameter uncertainties are convex bounded and the unknown nonlinearities are time varying perturbations satisfying lipschitz conditions in the state and delayed state an appropriate lyapunov functional is constructed to exhibit the delay dependent dynamics and compensate for the enlarged time span the developed methods for stability and stabilization eliminate the need for over bounding and utilize smaller number of lmi decision variables new and less conservative solutions to the stability and stabilization problems of nonlinear discrete time system are provided in terms of feasibility testing of new parametrized linear matrix inequalities lmis robust feedback stabilization methods are provided based on state measurements and by using observer based output feedback so as to guarantee that the corresponding closed loop system enjoys the delay dependent robust stability with an l 2 gain smaller that a prescribed constant level all the developed results are expressed in terms of convex optimization over lmis and tested on representative examples

synchronization of networks of heterogeneous agents with common nominal behavior this paper deals with the problem of synchronization in networks of heterogeneous agents with common nominal behavior the agents are modeled as possibly nonlinear perturbed versions of a common siso nominal lti operator and they are interconnected via a sparse memoryless interconnection operator coherent with the communication graph underlying the network the network is said to synchronize if the outputs of the agents tend to align along given directions the most important case being consensus or agreement the paper provides a general result based on iqcs that ensures synchronization of the network with robustness w r t uncertainties in the interconnection and in each agent s dynamics scalability issues are discussed in the scenario where the interconnection operator is a constant normal matrix yielding the generalization of the very popular linear consensus algorithm the wide range of applicability of the proposed criterion is shown by providing synchronization conditions in some important examples whenever possible graphical criteria are proposed for checking the required conditions

simultaneous stabilization of a set of nonlinear port controlled hamiltonian systems this paper investigates simultaneous stabilization of a set of nonlinear port controlled hamiltonian pch systems and proposes a number of results on the design of simultaneous stabilization controllers for the pch systems firstly the case of two pch systems is studied using the dissipative hamiltonian structural properties the two systems are combined to generate an augmented pch system with which some results on the control design are then obtained for the case that there exist parametric uncertainties in the two systems hamiltonian structures an adaptive simultaneous stabilization controller is proposed when there are external disturbances and parametric uncertainties in the two systems two simultaneous stabilization controllers are designed for the systems one is a robust controller and the other is a robust adaptive one secondly the case of more than two pch systems is investigated and a new result is proposed for the simultaneous stabilization of the systems finally two illustrative examples are studied by using the results proposed in this paper simulations show that the simultaneous stabilization controllers obtained in this paper work very well

global output regulation for a class of single input port controlled hamiltonian disturbed systems abstract the problem of global output regulation for a class of single input port controlled hamiltonian disturbed systems is studied a composite control method is developed by combining the damping injection and the nonlinear disturbance observer techniques together a series of coordinate transformation is presented to transform the system with mismatched disturbance into matched disturbance system by means of lyapunov stability theorems global stability analysis for the closed loop hamiltonian system is presented it is shown that the system output is regulated to zero asymptotically in the presence of mismatched disturbance without larger overshoots and longer settling time caused by integral action study on two examples with simulation results demonstrates the effectiveness of the proposed control method

delay dependent robust stabilization of uncertain systems with multiple state delays this paper deals with the problem of robust stabilization for uncertain systems with multiple state delays the parameter uncertainties are time varying and unknown but are norm bounded and the delays are time varying a new method for achieving robust stabilization is presented for a class of uncertain time delay systems via linear memoryless state feedback control the results depend on the size of the delays and are given in terms of several linear matrix inequalities

global stabilization of the multiple integrators system by delayed and bounded controls this note is concerned with global stabilization of multiple integrators by delayed and bounded controllers three types of new nonlinear control laws are proposed based on some special canonical forms and explicit conditions are proposed to guarantee the global stability of the closed loop systems differently from the existing canonical forms the new special canonical forms used in this note contain not only time delay in the input but also time delays in its state which are essential in the recursive design since they lead to natural cancellation moreover some free parameters are introduced into these controllers these advantages can help to improve the transient performance of the closed loop system significantly numerical simulations for the fourth order integrators illustrate that the proposed new controllers can indeed outperform the existing one

energy based lyapunov functions for forced hamiltonian systems with dissipation in this paper we propose a constructive procedure to modify the hamiltonian function of forced hamiltonian systems with dissipation in order to generate lyapunov functions for nonzero equilibria a key step in the procedure which is motivated from energy balance considerations standard in network modeling of physical systems is to embed the system into a larger hamiltonian system for which a series of casimir functions can be easily constructed interestingly enough for linear systems the resulting lyapunov function is the incremental energy thus our derivations provide a physical explanation to it an easily verifiable necessary and sufficient condition for the applicability of the technique in the general nonlinear case is given some examples that illustrate the method are given

consensus of networked mechanical systems with communication delays a unified framework this technical note addresses the consensus problem of networked uncertain mechanical systems which interact on directed graphs containing a spanning tree and are subjected to nonuniform communication delays the challenge lies in the unclear input output property of a linear networked system containing communication delays and the unclear convergent property of this system under an external input we establish a new input output property of this linear networked system and moreover its convergent property under an external input upon which we establish a unified framework to resolve the consensus problem of multiple mechanical systems the proposed consensus framework unifies extends the existing results and in addition yields a fully cascaded closed loop system with lyapunov like analysis and frequency domain input output analysis we show that the proposed unified consensus control scheme ensures consensus without the integral action of the sliding vector and scaled weighted average consensus with the integral action of the sliding vector simulation results are provided to demonstrate the performance of the proposed consensus schemes

brief paper oscillation analysis of linearly coupled piecewise affine systems application to spatio temporal neuron dynamics this paper discusses oscillation analysis of a large number of linearly coupled piecewise affine pwa systems motivated by various kinds of reaction diffusion systems including cell signaling dynamics and neural dynamics we derive a sufficient condition under which the system shows an oscillatory behavior called y oscillation it is known that the analysis of pwa systems is difficult due to their switching nature an important feature of the result obtained is that under the assumption that every subsystem has a specific property in common the criteria can be rewritten in terms of coupling topology in an easily checkable way so it is applicable to large scale systems the results obtained are applied to theoretical investigation of the cardiac action potential generation propagation represented by spatio temporal fitzhugh nagumo equations

distributed adaptive consensus for multiple mechanical systems with switching topologies and time varying delay abstract this paper studies the adaptive consensus problem of networked mechanical systems with time varying delay and jointly connected topologies two different consensus protocols are proposed first we present an adaptive consensus protocol for the connected switching topologies based on graph theory lyapunov stability theory and switching control theory the stability of the proposed algorithm is demonstrated then we investigate the problem under the more general jointly connected topologies and with concurrent time varying communication delay the proposed consensus protocol consists of two parts one is for the connected agents which contains the current states disagreement among them and the other is designed for the isolated agents which contains the states difference between the current and past a distinctive feature of this work is to address the consensus control problem of mechanical systems with unknown parameters time varying delay and switching topologies in a unified theoretical framework numerical simulation is provided to demonstrate the effectiveness of the obtained results

truncated predictor feedback stabilization of polynomially unstable linear systems with multiple time varying input delays this technical note is concerned with stabilization of polynomially unstable linear systems with multiple time varying input delays a truncated predictor feedback tpf which is obtained by truncating the distributed terms in the traditional predictor feedback is proposed the proposed tpf is a linear static partial state feedback with a time varying feedback gain that is constructed from the steady solution to a class of parametric lyapunov differential equations under the assumption that the open loop system is only polynomially unstable and is uniformly controllable it is shown that for sufficiently small value of the design parameter the resulting closed loop system is exponentially stable no matter how large the time varying delays are as long as they are bounded simulation demonstrates these theoretical results

consensus in multi agent systems with coupling delays and switching topology the robustness of consensus in single integrator multi agent systems mas to coupling delays and switching topologies is investigated it is shown that consensus is reached for arbitrarily large constant time varying or distributed delays if consensus is reached without delays this delay robustness holds under the weakest possible connectivity assumptions on the underlying graph i e as long as the graph is uniformly quasi strongly connected and switches with a dwell time the proof is based on a contraction argument and allows to remove technical assumptions that were used in previous publications moreover the result also applies to non scalar single integrators an important extension toward consensus and rendezvous in higher dimensions

on finite gain stabilizability of linear systems subject to input saturation this paper deals with global finite gain input output stabilization of linear systems with saturated controls for neutrally stable systems it is shown that the linear feedback law suggested by the passivity approach indeed provides stability with respect to every l p norm explicit bounds on closed loop gains are obtained and they are related to the norms for the respective systems without saturation these results do not extend to the class of systems for which the state matrix has eigenvalues on the imaginary axis with nonsimple size 1 jordan blocks contradicting what may be expected from the fact that such systems are globally asymptotically stabilizable in the state space sense this is shown in particular for the double integrator

average consensus in multi agent systems with uncertain topologies and multiple time varying delays abstract in this paper we investigate average consensus problem in continuous time multi agent systems with uncertain topologies as well as multiple time varying communication delays the network of dynamic agents is directed and both fixed and switching topologies are considered by using the linear matrix inequality method we prove that all the nodes in the network can achieve average consensus asymptotically for appropriate delays and uncertainties if the network topology is weakly connected and balanced feasible linear matrix inequalities are established to determine the maximal allowable upper bounds of multiple delays numerical examples are presented to illustrate the availability of the theoretical results

information flow through a chaotic channel prediction and postdiction at finite resolution we reconsider the persistence of information under the dynamics of the logistic map in order to discuss communication through a nonlinear channel where the sender can set the initial state of the system with finite resolution and the recipient measures it with the same accuracy we separate out the contributions of global phase space shrinkage and local phase space contraction and expansion to the uncertainty in predicting and postdicting the state of the system we determine how the amplification parameter the time lag and the resolution influence the possibility for communication a novel clockwork representation for real numbers is introduced that allows for a visualization of the flow of information between scales

trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations this paper addresses trajectory tracking control of port controlled hamiltonian systems via generalized canonical transformations and passivity based control the main strategy adopted in this paper is to construct an error system which describes the dynamics of the tracking error by a passive port controlled hamiltonian system after obtaining the error system tracking control of the original system can be achieved by stabilizing the error system via passivity based approach first a fundamental framework is provided for constructing the error system via generalized canonical transformations then a concrete design procedure is derived for a class of electro mechanical systems furthermore the proposed method is applied to a magnetic levitation system and laboratory experiments demonstrate its effectiveness

h consensus of second order multi agent systems with asymmetric delays abstract this paper is concerned with the problem of consensus in the h sense for second order continuous time multi agent systems with multiple asymmetric time varying delays by using a model transformation approach and matrix theory we establish several conditions in terms of linear matrix inequalities such that consensus of multi agent systems can be achieved in the h sense the feasibility of the consensus conditions is also analyzed as an application we consider the case of intermittent measurement between agents numerical examples are presented to illustrate the theoretical results which can be applied to the case of negative information weights

stability analysis for continuous system with additive time varying delays a less conservative result this paper presents a less conservative result for stability analysis of continuous time systems with additive delays by constructing a new lyapunov krasovskii functional and utilizing free matrix variables in approximating certain integral quadratic terms in obtaining the stability condition in terms of linear matrix inequalities numerical example is provided to show the effectiveness of the proposed method compared to some recent results

stabilization of stochastic functional differential systems with delayed impulses abstract this paper is concerned with the stabilization problem for a class of stochastic functional differential system with delayed impulses by applying a generalized comparison principle and the average dwell time method some sufficient criteria for input to state stable iss type and exponential stability properties are derived the coefficients of the upper bound for the diffusion operator of lyapunov functions are allowed to be time varying which improves the existing results greatly two numerical examples are presented to illustrate the effectiveness of the proposed results

global asymptotic stabilization for chains of integrators with a delay in the input the problem of the global uniform asymptotic stabilization by bounded feedback of a chain of integrators with a delay in the input is solved no limitation on the size of the delay is imposed to validate the approach a third order example is presented

stabilization of hamiltonian systems with dissipation stabilization of generalized hamiltonian systems with dissipation is investigated first we generalize the casimir submanifold approach with constant controls to the static state feedback control case secondly a direct hamiltonian function method is proposed and it is shown that this method is equivalent to the casimir sub manifold approach furthermore a dynamic state feedback control is proposed some sufficient conditions and a constructive process for determining controllers are provided it is shown that the dynamic state feedback control is more powerful than the static one finally the problem of a dissipative type realization of the general controlled hamiltonian system is discussed

dynamical consensus seeking of second order multi agent systems based on delayed state compensation abstract by introducing delayed state compensation into the normal asynchronously coupled consensus algorithm a new consensus algorithm is constructed to solve the dynamical consensus problem of second order multi agent systems subjected to communication delay based on frequency domain analysis a sufficient and necessary condition which depends on the communication delay and the control parameters is obtained for two coupled second order dynamic agents converging to the dynamical consensus and it is proved that the proposed algorithm can tolerate higher communication delay than the synchronously coupled consensus algorithm according to linear fractional transformation and the small gain theorem sufficient conditions are gained for second order multi agent systems with communication delay under a general digraph simulation illustrates the correctness of the results

continuous time average consensus under dynamically changing topologies and multiple time varying delays abstract the average consensus in continuous time multi agent systems with dynamically changing topologies and multiple time varying delays is studied in this paper the network topology is captured by weighted digraphs which are weakly connected and balanced some feasible linear matrix inequalities are established to determine the allowable upper bounds of multiple delays that guarantee the average consensus of the system numerical examples are provided to show the usefulness of the theoretical results

information flow within stochastic dynamical systems information flow or information transfer is an important concept in general physics and dynamical systems which has applications in a wide variety of scientific disciplines in this study we show that a rigorous formalism can be established in the context of a generic stochastic dynamical system an explicit formula has been obtained for the resulting transfer measure which possesses a property of transfer asymmetry and if the stochastic perturbation to the receiving component does not rely on the giving component has a form the same as that for the corresponding deterministic system this formula is further illustrated and validated with a two dimensional langevin equation a remarkable observation is that for two highly correlated time series there could be no information transfer from one certain series say x 2 to the other x 1 that is to say the evolution of x 1 may have nothing to do with x 2 even though x 1 and x 2 are highly correlated information flow analysis thus extends the traditional notion of correlation analysis and or mutual information analysis by providing a quantitative measure of causality between dynamical events

predictor based control of linear systems with large and variable measurement delays this paper concerns the problem of the control of linear systems by means of feedback from delayed output where the delay is known and time varying the main advantage of the approach is that it can be applied to systems with any delay bound i e not only small delays the predictor is based on a combination of finite dimensional elementary predictors whose number can be suitably chosen to compensate any delay the single predictor element is an original proposal and the class of delays to which the schema can be applied includes but it is not limited to continuous delay functions

delay robustness in non identical multi agent systems we investigate the robustness of consensus protocols on sensor networks to different types of feedback delays we provide set valued conditions for consensus of linear multi agent systems mas with nonidentical agent dynamics and heterogeneous delays these conditions consider different feedback delay configurations and are robust and scalable to unknown arbitrary large topologies and unknown but bounded self delays and communication delays moreover we provide consensus conditions for relative degree two mas with different feedback delays in order to illustrate the applicability of these set valued conditions

simple saturated designs for ancbc systems and extension to feedforward nonlinear systems this article re examines the robust stabilisation of the asymptotically null controllable with bounded controls ancbc systems and extends the established algorithm to a wide class of feedforward nonlinear systems whose nominal dynamics contains both multiple integrators and multiple oscillators based on the notion of converging input bounded state cibs rather than small input small state siss the computation burden in sussmann et al sussmann h j sontag e d and yang y 1994 a general result on the stabilization of linear systems using bounded controls ieee transactions on automatic control 39 2411 2425 is reduced and a class of simple saturated control laws is presented for the cibs stabilisation of ancbc systems then by combining the technique of dealing with higher order terms the algorithm for ancbc systems is extended to feedforward nonlinear systems

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

spatio temporal structure in coupled map lattices two point correlations versus mutual information a one dimensional lattice of logistic maps is investigated in the case of strong nonlinearity and strong coupling although the dynamics may be classified as fully developed turbulence spatio temporal structure can be detected by computing time delayed mutual information and two point correlations the correlation is found to be superior in detecting weak structure an improved algorithm for mutual information is described

stabilization analysis of time delay hamiltonian systems in the presence of saturation abstract the stabilization of a class of hamiltonian systems with state time delay and input saturation is addressed in this paper sufficient conditions are derived by using lyapunov krasovskii functional theorem to guarantee the systems as well as the resulted closed loop systems by output feedback to be asymptotically stable when input saturation effectively occurs a numerical example is presented to illustrate the effectiveness of the obtained results in this paper

exact stability analysis of second order leaderless and leader follower consensus protocols with rationally independent multiple time delays abstract an investigation of double integrator agents with directed asymmetric consensus protocols and multiple rationally independent time delays is presented in this paper from two novel perspectives first we complement the group consensus literature on crucial stability analysis using a recent technique called the cluster treatment of characteristic roots ctcr for the first time on this class of time delayed systems the ctcr paradigm is pursued after a block diagonalization mode decoupling transformation on the system this treatment produces some unique stability tables for the dynamics in the space of the delays which are non conservative and exhaustive second a novel concept of spectral delay space is presented as an overture to the ctcr for the determination of the complete set of stability crossing switching hypersurfaces in the delay space examples are provided to display the strengths and efficiency of this new stability analysis mechanism

observer based output feedback control of linear systems with input and output delays abstract this paper is concerned with observer based output feedback control of linear systems with both multiple input and output delays our recently developed truncated predictor feedback tpf approach for state feedback stabilization of time delay systems is generalized to the design of observers by imposing some restrictions on the open loop system two classes of observer based output feedback controllers one being finite dimensional and the other infinite dimensional are constructed it is further shown that the infinite dimensional observer based output feedback controllers can be generalized to linear systems with both time varying input and output delays it is also shown that the separation principle holds for the infinite dimensional observer based output feedback controllers but does not hold for the finite dimensional ones numerical examples are worked out to illustrate the effectiveness of the proposed approaches

information transfer in continuous processes we discuss a recently proposed quantity called transfer entropy which uses time series data to measure the amount of information transferred from one process to another in order to understand its foundation merits and limitations we review some aspects of information theoretic functionals while for symbol sequences these measures have an intuitive interpretation their application to continuous state processes and in particular their estimation from finite data sets is problematic for mutual information finite length scale estimates converge from below and can thus be used to reject the assumption that the observed processes are independent however mutual information does not provide any directional information conversely transfer entropy does resolve the directionality of information exchange but no similar monotonic convergence seems to hold thus only in the case of zero transfer entropy in one direction we can reliably infer an asymmetry of the information exchange

robust controller design of uncertain discrete time delay systems with input saturation and disturbances this technical note deals with the problem of robust controller design of uncertain discrete time delay systems subject to control input saturation and bounded external disturbances a sufficient condition is obtained which guarantees the existence of state feedback controllers and an admissible initial condition domain such that the resulting closed loop system is uniformly exponentially convergent to a ball with certain exponential decay rate for every initial condition emanating from the admissible domain an iterative linear matrix inequality relaxation scheme can be used to construct desired state feedback controllers a simulation example is provided to demonstrate the effectiveness of the proposed method

global stabilization of oscillators with bounded delayed input the problem of globally asymptotically stabilizing by bounded feedback of an oscillator with an arbitrary large delay in the input is solved a first solution follows from a general result on the global stabilization of null controllable linear systems with delay in the input by bounded control laws with a distributed term next it is shown through a lyapunov analysis that the stabilization can be achieved as well when neglecting the distributed terms it turns out that this main result is intimately related to the output feedback stabilization problem

linear systems subject to input saturation and time delay finite gain l lowercase p stabilization this paper deals with finite gain stabilization of linear systems by static feedbacks which are bounded and time delayed for neutrally stable continuous time linear systems we provide a saturated linear feedback law ensuring finite gain stability with respect to every l p norm p in 1 infty with an arbitrary small bound on the control and large constant delay moreover we provide upper bounds for the corresponding l p gains which are delay independent

lyapunov analysis and information flow in coupled map lattices abstract lyapunov analysis for the coupled map lattices is presented the co moving lyapunov exponent is calculated which is related with the propagation of the disturbance in space the propagation speed agrees with the zero crossing point of the co moving lyapunov exponent the co moving mutual information flow is introduced which shows the selective transmission of the information at some speed lyapunov spectra and vectors are calculated spatial structures of the vectors are investigated possible analogy with the anderson localization problem is discussed

consensus problems in networks of agents with double integrator dynamics and time varying delays in this article we consider consensus problems in networks of agents with double integrator dynamics and non uniform time varying delays the agent dynamics is adopted as a typical point mass model based on newton s law without assuming that the weighting factors in the information update schemes are non negative we propose two protocols such that both the state and the velocity of agents achieve consensus an equivalent reduced order system is introduced to analyse the convergence of the protocols some necessary and or sufficient conditions for consensus are established in terms of linear matrix inequalities simulation results are provided that demonstrate the effectiveness of our theoretical results

on asymptotic stabilizability of linear systems with delayed input this paper examines the asymptotic stabilizability of linear systems with delayed input by explicit construction of stabilizing feedback laws it is shown that a stabilizable and detectable linear system with an arbitrarily large delay in the input can be asymptotically stabilized by either linear state or output feedback as long as the open loop system is not exponentially unstable i e all the open loop poles are on the closed left half plane a simple example shows that such results would not be true if the open loop system is exponentially unstable it is further shown that such systems when subject to actuator saturation are semiglobally asymptotically stabilizable by linear state or output feedback

properties of the parametric lyapunov equation based low gain design with applications in stabilization of time delay systems this technical note studies some properties of the recently developed parametric lyapunov equation based low gain feedback design method as applications of these new properties alternative and simpler solutions are proposed to the global stabilization problem for a class of linear systems with input delay and the semi global stabilization problem when the systems are in addition subject to actuator saturation besides the simplicity in their construction the new solutions can also be easily scheduled online to achieve global result in the presence of input saturation