identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

brief paper distributed h consensus filtering in sensor networks with multiple missing measurements the finite horizon case this paper is concerned with a new distributed h consensus filtering problem over a finite horizon for sensor networks with multiple missing measurements the so called h consensus performance requirement is defined to quantify bounded consensus regarding the filtering errors agreements over a finite horizon a set of random variables are utilized to model the probabilistic information missing phenomena occurring in the channels from the system to the sensors a sufficient condition is first established in terms of a set of difference linear matrix inequalities dlmis under which the expected h consensus performance constraint is guaranteed given the measurements and estimates of the system state and its neighbors the filter parameters are then explicitly parameterized by means of the solutions to a certain set of dlmis that can be computed recursively subsequently two kinds of robust distributed h consensus filters are designed for the system with norm bounded uncertainties and polytopic uncertainties finally two numerical simulation examples are used to demonstrate the effectiveness of the proposed distributed filters design scheme

distributed average tracking of networked euler lagrange systems under an extended proportional integral pi control scheme a new class of distributed average tracking dat algorithms has been developed for three different kinds of references references with steady states references with bounded derivatives and references with a common derivative the class of dat algorithms are further applied to solve the dat problem for euler lagrange el systems

a prediction error and stepwise regression estimation algorithm for non linear systems the identification of non linear systems based on a narmax non linear autoregressive moving average model with exogenous inputs model representation is considered and a combined stepwise regression prediction error estimation algorithm is derived the stepwise regression routine determines the model structure by detecting significant terms in the model while the prediction error algorithm provides optimal estimates of the final model parameters implementation of the algorithms is discussed in detail and several simulated examples and industrial applications are included to illustrate that parsimonious models of non linear systems can be identified using the algorithm

representations of error terms in jensen s and some related inequalities with applications abstract we give integral representations of error terms in the classical jensen s inequality as well as in four related inequalities starting from these results it is possible to derive various lower and upper asymptotic expansions for solutions of the functional equation f x 1 f x g x in particular we present several results concerning the gamma function

stability analysis for continuous time positive systems with time varying delays this note addresses the stability problem of continuous time positive systems with time varying delays it is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a hurwitz matrix the result is a time varying version of the widely known asymptotic stability criterion for constant delay positive systems a numerical example illustrates the correctness of our result

brief paper leader following consensus of second order agents with multiple time varying delays in this paper a leader following consensus problem of second order multi agent systems with fixed and switching topologies as well as non uniform time varying delays is considered for the case of fixed topology a necessary and sufficient condition is obtained for the case of switching topology a sufficient condition is obtained under the assumption that the total period over which the leader is globally reachable is sufficiently large we not only prove that a consensus is reachable asymptotically but also give an estimation of the convergence rate an example with simulation is presented to illustrate the theoretical results

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

distributed average consensus via gossip algorithm with real valued and quantized data for 0 q 1 this paper studies the problem of the gossip consensus algorithm with real valued and quantized data we study the effect of the mixing parameter on the convergence rate of the proposed gossip consensus algorithm and show when the proposed bounds are optimized with respect to the mixing parameter for a gossip consensus algorithm with quantized data we prove that it can achieve the consensus almost surely and the expected value of the final states is equal to the average of the initial states moreover we provide a result characterizing the convergence performance of the distance from consensus and make a comparison with the non quantized gossip consensus algorithm finally simulation results are provided to evaluate the effectiveness of the proposed algorithm

model structure selection by cross validation two criteria for choosing between different model structures are proposed their derivation is within a natural cross validatory assessment context and is fairly assumption free in particular the two criteria can be used for discriminating between non nested model structures and more importantly the true system is not required to belong to the considered set of models should the true system belong to the model set the two proposed criteria will asymptotically reduce to some well known structure selection criteria this is believed to be a desirable feature of our proposals on the other hand it provides a nice cross validation interpretation of some well known model structure selection rules also the cross validation interpretation helps one to choose which criteria to use in a given application the paper also has a second purpose somewhat decoupled from that mentioned above it contains an extensive survey of the literature that is useful in its own right

consensus of heterogeneous multi agent systems without velocity measurements this article considers the consensus problem of heterogeneous multi agent system composed of first order and second order agents in which the second order integrator agents cannot obtain the velocity second state measurements for feedback two different consensus protocols are proposed first we propose a consensus protocol and discuss the consensus problem of heterogeneous multi agent system by applying the graph theory and the lyapunov direct method some sufficient conditions for consensus are established when the communication topologies are undirected connected graphs and leader following networks second due to actuator saturation we propose another consensus protocol with input constraint and obtain the consensus criterions for heterogeneous multi agent system finally some examples are presented to illustrate the effectiveness of the obtained criterions

asynchronous rendezvous analysis via set valued consensus theory this paper presents the design and analysis result for asynchronous rendezvous control of multiagent systems with continuous time dynamics and intermittent interactions the protocol designing strategies only impose weak restrictions on anticipated way point sets from which the way points are selected and path planning of each agent and can be applied to the networks of arbitrary dimensional subsystems explicitly the anticipated way point sets are in a polytope like form and the path between any two consecutive way points is required to be included within the minimum convex region covering the two associated anticipated way point sets under the assumption of directed and switching interaction topology and the assumption of intermittent and asynchronous interactions with time varying delays we perform the set valued consensus analysis on the evolution of anticipated way point sets with respect to update times and provide mild sufficient conditions for the solvability of the asynchronous rendezvous problem the proof techniques rely much on graph theory and nonnegative matrix theory the obtained result extends greatly the existing work in the literature and several examples demonstrate its broad potential applications particularly additional distributed control rules different from the circumcenter algorithm are devised for network connectivity maintenance

containment control for second order multi agent systems with time varying delays abstract this paper considers the containment control problem for second order multi agent systems with time varying delays both the containment control problem with multiple stationary leaders and the problem with multiple dynamic leaders are investigated sufficient conditions on the communication digraph the feedback gains and the allowed upper bound of the delays to ensure containment control are given in the case that the leaders are stationary the lyapunov razumikhin function method is used in the case that the leaders are dynamic the lyapunov krasovskii functional method and the linear matrix inequality lmi method are jointly used a novel discretized lyapunov functional method is introduced to utilize the upper bound of the derivative of the delays no matter how large it is which leads to a better result on the allowed upper bound of the delays to ensure containment control finally numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

consensusability of multi agent systems with time varying communication delay abstract this paper studies the consensusability problem of continuous time multi agent systems with time varying communication delay in undirected network we design a consensus protocol based on the low gain solution of a parametric algebraic riccati equation are and not use the precise information of the amount of time varying delay by studying the joint effect of agent dynamic and network topology sufficient conditions are given for consensus when all poles of the system matrix are on the closed left half plane in case of non zero poles on the imaginary axis maximal admissible upper bound of the time varying delay is given in terms of both the agent dynamic and network topology otherwise consensus can be achieved for the time varying delay with arbitrarily large upper bound finally simulation results are presented to demonstrate the effectiveness of the theoretical results

logarithmic convexity and inequalities for the gamma function abstract we propose a method based on logarithmic convexity for producing sharp bounds for the ratio x x as an application we present an inequality that sharpens and generalizes inequalities due to gautschi chu boyd lazarevic lupas and kershaw

simple sufficient conditions for reachability of discrete time polynomial systems we consider reachability of discrete time polynomial systems the reachability of such systems can be interpreted as the surjectivity of the polynomial mappings defined by the systems for a polynomial mapping between suitable spaces of the same dimensions it has been shown that the injectivity of the mapping also implies the surjectivity by utilizing this fact we derive sufficient conditions for the reachability of the polynomial systems which essentially check the injectivity of the polynomial mappings

on determining the structure of a non linear system abstract a method is presented for constructing a model of a non linear system from the input output data the structure of the system is assembled from a library of nonlinear terms that are possible suspects for inclusion in the model while each possible model structure is represented by a node in a tree it is shown that searching the tree for the optimal n term model structure can be done in n stages using an algorithm based on conjugate direction ideas the essential feature of the technique is that it generates a sequence of projection matrices such that the original vector valued functions become conjugate directions this leaves the original non linear terms intact and allows the structure for the optimal n term model to be assembled in n selections from the library examples are presented from regression analysis and non linear dynamic systems

decentralized stabilizability of multi agent systems under fixed and switching topologies abstract the paper studies decentralized stabilizability for multi agent systems with general linear dynamics the stabilizability problem is formulated in a way that the protocol performance can be evaluated by means of the stabilizability region and the feedback gain for fixed topology it is proved that the system is stabilizable if and only if external control inputs are exerted on some indicated agents the result is further shown to be a prerequisite for subsequent design of the corresponding decentralized external self feedback control which is also necessary and sufficient based on this two methods are presented to find the agents under which stabilizability can be reached and the region of stabilizability is given to evaluate the protocol performance for switching interaction topology it is shown that the system is stabilizable even if each of its subsystems is not finally the results are employed to cope with the decentralized set point formation control problem for which some necessary and or sufficient conditions are developed numerical simulations are presented to demonstrate the effectiveness of the proposed results

gurland s ratio for the gamma function we consider the ratio t x y x y 2 x y 2 and its properties related to convexity logarithmic convexity schur convexity and complete monotonicity several new bounds and asymptotic expansions for t are derived sharp bounds for the function x x 1 e x are presented as well as bounds for the trigamma function the results are applied to a problem related to the volume of the unit ball in r n and also to the problem of finding the inverse of the function x t 1 x 3 x which is of importance in applied statistics

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

consensus problem of second order multi agent systems with communication delay and input delay in this paper asynchronously coupled algorithm is used to solve the consensus problem of second order multi agent systems with both communication delay and input delay by constructing lyapunov krasovskii functional sufficient consensus conditions are obtained for second order systems under invariant input delays accompanied with time invariant and time varying communication delays respectively the conditions are all in the forms of linear matrix inequality lmi simulation illustrates the correctness of the results

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

commutative algebraic methods for controllability of discrete time polynomial systems abstractin this paper we consider controllability of discrete time polynomial systems first we present a forward accessibility local reachability condition that can be verified in finite time in contrast to conventional conditions second we give a backward accessibility local controllability condition for an invertible system and a condition to verify invertibility finally we derive sufficient conditions to test whether the forward accessible system is reachable and to test the backward accessible system is controllable

avoiding congestion in cluster consensus of the second order nonlinear multiagent systems in order to avoid congestion in the second order nonlinear leader following multiagent systems over capacity limited paths an approach called cluster lag consensus is proposed which means that the agents in different clusters will pass through the same positions with the same velocities but lag behind the leader at different times lyapunov functionals and matrix theory are applied to analyze such cluster lag consensus it is shown that when the graphic roots of clusters are influenced by the leader and the intracoupling of cluster agents is larger than a threshold the cluster lag consensus can be achieved furthermore the cluster lag consensus with a time varying communication topology is investigated finally an illustrative example is presented to demonstrate the effectiveness of the theoretical results in particular when the physical sizes of the agents are taken into consideration it is shown that with a rearrangement and a position transformation the multiagent system will reach cluster lag consensus in the new coordinate system this means that all agents in the same cluster will reach consensus on the velocity but their positions may be different and yet their relative positions converge to a constant asymptotically

uniqueness of consensus functions for time delayed swarm systems with time varying topologies abstract this paper shows that consensus functions for high order linear swarm systems with time varying interaction topologies and time delays are uniquely determined by initial states if interaction topologies are balanced in addition an explicit expression of the consensus function is presented and the different influences of initial states of agents and protocols on the consensus function are determined respectively

model selection and validation methods for non linear systems the theory of hypothesis testing is used to select a model with the correct structure and the relation of such a method to the aic and fpe criteria is investigated parametric validation and correlation validation methods are developed for non non linear difference equation models several shortcomings of traditional methods especially when applied to non linear systems are described

krull s theory for the double gamma function abstract the barnes g function g x 1 2 satisfies the functional equation log g x 1 log g x log x we complement w krull s work in bemerkungen zur differenzengleichung g x 1 g x x math nachrichten 1 1948 365 376 with additional results that yield a different characterization of the function g new expansions and sharp bounds for g on x 0 in terms of gamma and digamma functions a new expansion for the gamma function and summation formulae with polygamma functions

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

controllability of discrete time multi agent systems with directed topology and input delay this paper investigates the controllability of first order and second order discrete time multi agent systems with directed topology and input delay the problem is studied in the leader follower framework where a number of agents are selected to be leaders and serve as control inputs to all other agents sufficient and necessary conditions are derived for the controllability of first order discrete time multi agent systems with sampling period and feedback gain satisfying certain conditions it is proved under three different protocols that the controllability of second order discrete time multi agent systems is equivalent to that of a pair of submatrices of laplacian matrix in addition the controllability of both first order and second order discrete time multi agent systems with input delay is shown through some transformations to be equivalent to that of the transformed non delayed systems finally some simulation examples are given to illustrate the theoretical results

on the solvability of polynomial systems arising in control we consider a compactification of a general system of polynomial equations in weighted projective space and give some sufficient conditions about the solvability of a polynomial system over c and r we also prove that for generic linear subspaces the inverse eigenvalue problem with perturbations in the linear subspace always has n solutions

distributed consensus of heterogeneous multi agent systems with fixed and switching topologies in this article we study distributed consensus of heterogeneous multi agent systems with fixed and switching topologies the analysis is based on graph theory and nonnegative matrix theory we propose two kinds of consensus protocols based on the consensus protocol of first order and second order multi agent systems some necessary and sufficient conditions that the heterogeneous multi agent system solves the consensus problems under different consensus protocols are presented with fixed topology we also give some sufficient conditions for consensus of the heterogeneous multi agent system with switching topology simulation examples are provided to demonstrate the effectiveness of the theoretical results

l 1 group consensus of multi agent systems with stochastic inputs under directed interaction topology we address l 1 group consensus problems of networked multi agent systems with fixed directed information exchange in this article a discrete time protocol is designed to solve the l 1 group consensus problems via general stochastic inputs under some mild assumptions we derive sufficient conditions to guarantee the l 1 group consensus based on algebraic graph theory and ergodicity theory for finite markov chains moreover the boundedness of the expected infinite sum of the inputs ensures the boundedness of the expected trajectory numerical simulations instantiating the inputs as varied independent and identically distributed random processes as well as autoregressive processes are presented to demonstrate the effectiveness of our theoretical results

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

delay dependent admissible consensualization for singular time delayed swarm systems abstract admissible consensus analysis and design problems for high order linear time invariant singular swarm systems with time delays are investigated firstly by state decomposition the admissible consensus problem is transformed into admissible problems of multiple singular subsystems with lower dimensions then linear matrix inequality lmi criteria for admissible consensualization are presented which only involve eight lmi constraints independent of the number of agents moreover an explicit expression of the consensus function which is independent of time delays is presented and the impacts of protocol states and interaction topologies on the consensus function are revealed finally a numerical example is given to illustrate the effectiveness of theoretical results

flocks herds and schools a quantitative theory of flocking we present a quantitative continuum theory of flocking the collective coherent motion of large numbers of self propelled organisms in agreement with everyday experience our model predicts the existence of an ordered phase of flocks in which all members of even an arbitrarily large flock move together with the same mean velocity stackrel ensuremath rightarrow v ensuremath ne 0 this coherent motion of the flock is an example of spontaneously broken symmetry no preferred direction for the motion is picked out a priori in the model rather each flock is allowed to and does spontaneously pick out some completely arbitrary direction to move in by analyzing our model we can make detailed quantitative predictions for the long distance long time behavior of this broken symmetry state the goldstone modes associated with this spontaneously broken rotational symmetry are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole these goldstone modes mix with modes associated with conservation of bird number to produce propagating sound modes these sound modes lead to enormous fluctuations of the density of the flock far larger at long wavelengths than those in e g an equilibrium gas our model is similar in many ways to the navier stokes equations for a simple compressible fluid in other ways it resembles a relaxational time dependent ginsburg landau theory for an n d component isotropic ferromagnet in spatial dimensions dg4 the long distance behavior is correctly described by a linearized theory and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems for dl4 nonlinear fluctuation effects radically alter the long distance behavior making it different from that of any known equilibrium model in particular we find that in d 2 where we can calculate the scaling exponents exactly flocks exhibit a true long range ordered spontaneously broken symmetry state in contrast to equilibrium systems which cannot spontaneously break a continuous symmetry in d 2 the mermin wagner theorem we make detailed predictions for various correlation functions that could be measured either in simulations or by quantitative imaging of real flocks we also consider an anisotropic model in which the birds move preferentially in an easy e g horizontal plane and make analogous but quantitatively different predictions for that model as well for this anisotropic model we obtain exact scaling exponents for all spatial dimensions including the physically relevant case d 3

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

on the finiteness of accessibility test for nonlinear discrete time systems it is shown that for two large subclasses of discrete time nonlinear systems analytic systems defined on a compact state space and rational systems the minimum length r for input sequences ca

brief paper multi agent consensus with diverse time delays and jointly connected topologies this paper investigates consensus problems in networks of continuous time agents with diverse time delays and jointly connected topologies for convergence analysis of the networks a class of lyapunov krasovskii functions is constructed which contains two parts one describes the current disagreement dynamics and the other describes the integral impact of the dynamics of the whole network over the past by a contradiction approach sufficient conditions are derived under which all agents reach consensus even though the communication structures between agents dynamically change over time and the corresponding graphs may not be connected the obtained conditions are composed of a sum of decoupled parts corresponding to each possible connected component of the communication topology finally numerical examples are included to illustrate the obtained results

dead beat controllability of polynomial systems symbolic computation approaches state and output dead beat controllability tests for a very large class of polynomial systems with rational coefficients may be based on the quantifier elimination by partial cylindrical algebraic decomposition qepcad symbolic computation program the method is unified for a very large class of systems and can handle one or two sided control constraints families of minimum time state output dead beat controllers are obtained the computational complexity of the test is prohibitive for general polynomial systems but by constraining the structure of the system we may beat the curse of complexity a computationally less expensive algebraic test for output dead beat controllability for a class of odd polynomial systems is presented necessary and sufficient conditions are given they are still very difficult to check therefore a number of easier to check sufficient conditions are also provided the latter are based on the grobner basis method and qepcad it is shown on a subclass of odd polynomial systems how it is possible to further reduce the computational complexity by exploiting the structure of the system

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

consensus seeking of high order dynamic multi agent systems with fixed and switching topologies this article studies a consensus problem for a group of high order dynamic agents with fixed and switching topologies two linear consensus protocols which only depend on the agent s own information and its neighbours partial information are proposed respectively for the group with and without communication time delays for the case of fixed topology and zero communication time delay a necessary and sufficient condition for the consensus is established the parameter design of the protocol is also discussed under switching topology the consensus is investigated for two cases the case of zero communication time delay and the case of nonuniform communication time delays for each case a sufficient condition for the consensus is provided moreover for a group of double triple integrator agents with fixed topology and uniform constant time delay some necessary and sufficient conditions for the consensus are given finally numerical simulations are worked out to illustrate the effectiveness of the

synchronization of complex dynamical networks with switching topology a switched system point of view in this paper we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view the synchronization problem is transformed into the stability problem for time varying switched systems we address two basic problems synchronization under arbitrary switching topology and synchronization via design of switching within a pre given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection for the both problems we first establish synchronization criteria for general connection topology then under the condition of simultaneous triangularization of the connection matrices a common lyapunov function for the first problem and a single lyapunov and multiple lyapunov functions for the second problem are systematically constructed respectively by those of several lower dimensional dynamic systems in order to achieve synchronization using multiple lyapunov functions a stability condition and switching law design method for time varying switched systems are also presented which avoid the usual non increasing condition

technical communique on an improved model reduction technique for nonlinear systems an algorithm is presented for reducing the number of terms in a nonlinear static system which can be modeled by a linear combination of nonlinear functions the method is an improvement over a previously presented algorithm desrochers and saridis 1980a the improvements now make it possible to perform all calculations from a single set of input and output data while in the original algorithm n sets of data were required where n is the number of terms retained in addition it is shown how the model error can be calculated at each iteration which relieves the arbitrariness of stopping the algorithm at a preselected value of n as was done originally then the insight gained from this improved technique is used to develop an optimal solution to the model reduction problem a major improvement over the original technique it is then conjectured that some structural concepts for such systems may exist in a matrix formed from the input and output data

transcale average consensus of directed multi vehicle networks with fixed and switching topologies abstractthis paper contributes to solving a class of so called transcale average consensus problems for directed networks of vehicles with single integrator dynamics it generalises the idea of average consensus by taking into account the measurement scale of every vehicle s information state using the nearest neighbour interaction rules distributed algorithms are presented which are shown with the ability to achieve the transcale average consensus for directed networks associated with balanced graphs such consensus results are applicable to networks in the presence of both fixed topology and switching topologies which are also illustrated via simulation tests moreover improved algorithms and results of consensus are given for directed networks associated with unbalanced graphs

structure identification of nonlinear dynamic systems a survey on input output approaches abstract in the past several methods have been elaborated for the identification of nonlinear dynamic systems most of the methods assume that the structure of the system is given a priori therefore they are in reality parameter estimation algorithms and structure identification is thus usually performed by repeated parameter estimation however in nonlinear system theory several methods are known to determine the structure of a system in this paper structure identification of block oriented especially cascade models of semi linear dynamic models with signal dependent parameters and of nonlinear dynamic models being linear in the parameters will be considered different structure selection methods are summarized based on step and impulse tests frequency response measurements correlation analysis repeated reproducible tests and normal operating data

second order consensus for multi agent systems with switching topology and communication delay in this paper two kinds of consensus problems for second order agents under directed and arbitrarily switching topologies are investigated that is the cases without and with communication delay for the former by constructing a new kind of digraph and employing a new graphic method we can specify the least convergence rate for all the agents to reach consensus for the latter in virtue of a matrix inequality method a sufficient condition in the form of feasible matrix inequalities is presented for all the agents to reach consensus this on the other hand shows that consensus can be reached if the delay is small enough finally two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results

consensus in noisy environments with switching topology and time varying delays abstract in this paper the leader following consensus problem of noise perturbed multi agent systems with time varying delays is investigated we analyze two different cases of coupling topologies fixed topology and switching topology based on the lyapunov functional and combining with the linear matrix inequality lmi approach it is analytically proved that the consensus could be achieved almost surely with the perturbation of noise and communication time delays furthermore numerical examples are provided to illustrate the effectiveness of the theoretical results the simulation results show that the speed of convergence in environments with relatively strong noise intensity is lower than that in environments with relatively weak noise intensity

controllability of structured polynomial systems two algorithms based on the grobner basis method which facilitate the controllability analysis for a class of polynomial systems are presented the authors combine these algorithms with some results on output dead beat controllability in order to obtain sufficient as well as necessary conditions for complete and state dead beat controllability for a surprisingly large class of polynomial systems our results are generically applicable to the class of polynomial systems in strict feedback form

orthogonal parameter estimation algorithm for non linear stochastic systems an orthogonal parameter estimation algorithm is derived which allows each parameter in a linear in the parameters non linear difference equation model to be estimated sequentially and quite independently of the other parameters in the model the algorithm can be applied for any persistently exciting input and provides both unbiased estimates in the presence of correlated noise and an indication of which terms to include in the model several simulated examples are included to demonstrate the effectiveness of the algorithm

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

admissible l2 consensus for singular time delayed swarm systems with external disturbances abstract admissible consensus analysis and design problems for high order linear time invariant singular swarm systems with time delays and external disturbances are investigated firstly by the state space decomposition a necessary and sufficient condition for admissible consensus is given and an approach is presented to determine consensus functions on the basis of different impacts of initial states of agents and external disturbances which describe the absolute motions of singular swarm systems as a whole then an l 2 evaluation approach which requires fewer limitations on the structures of consensus functions is proposed to determine the influences of external disturbances on relative motions among agents and linear matrix inequality criteria for admissible l 2 consensus and consensualization are shown finally numerical simulations are presented to demonstrate theoretical results

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