finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information this paper studies the problem of finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information the partly usable model information is considered following a certain bernoulli distributed white noise sequence the objective of the study is to design a state feedback controller such that the augmented closed loop system is mean square stochastically finite time bounded and a tracking performance level is achieved over a finite time interval by using the mode dependent diagonally dominant lyapunov function approach some sufficient conditions are established for the existence of an admissible state feedback controller based on these a state feedback controller can be constructed by using a simple matrix decoupling approach two numerical examples and a modified general economic model are presented to demonstrate the effectiveness of our proposed approach

necessary and sufficient graphical conditions for formation control of unicycles the feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control the directed graph defined by the information flow plays a key role it is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node a similar result is given for formation stabilization to a line and to more general geometric arrangements

corner singularities and boundary layers in a simple convection diffusion problem abstract a singularly perturbed convection diffusion problem posed on the unit square is considered its solution may have exponential and parabolic boundary layers and corner singularities may also be present pointwise bounds on the solution and its derivatives are derived the dependence of these bounds on the small diffusion coefficient on the regularity of the data and on the compatibility of the data at the corners of the domain are all made explicit the bounds are derived by decomposing the solution into a sum of solutions of elliptic boundary value problems posed on half planes then analyzing these simpler problems

robust consensus tracking control for multiagent systems with initial state shifts disturbances and switching topologies this paper deals with the consensus tracking control issues of multiagent systems and aims to solve them as accurately as possible over a finite time interval through an iterative learning approach based on the iterative rule distributed algorithms are proposed for every agent using its nearest neighbor knowledge for which the robustness problem is addressed against initial state shifts disturbances and switching topologies these uncertainties are dynamically changing not only along the time axis but also the iteration axis it is shown that the matrix norm conditions can be developed to achieve the convergence of the considered consensus tracking objectives for which necessary and sufficient conditions are presented in terms of linear matrix inequalities to guarantee their feasibility in the sense of the spectral norm furthermore simulation examples are given to illustrate the effectiveness and robustness of the obtained consensus tracking results

asynchronous control for 2 d switched systems with mode dependent average dwell time abstract this work is concerned with asynchronous control for a class of two dimensional switched systems with mode dependent average dwell time the systems are formulated by the famous fornasini marchesini local state space model and the switching signal of the switched controller involves time delays which lead to the asynchronism between controllers and subsystems by extending mode dependent average dwell time with the switched quadratic lyapunov functional approach the stabilization condition is established for 2 d asynchronously switched systems based on the stabilization result mode dependent state feedback controllers are designed to guarantee h performance and asymptotic stability of the corresponding closed loop system finally two examples are provided to illustrate the effectiveness of the proposed design scheme

stability analysis of two dimensional systems by means of finitely constructed bilateral quadratic forms asymptotic stability of two dimensional 2 d systems in the state space representation is studied the concept of finitely constructed bilateral quadratic forms is introduced for the set of bilateral sequences of vectors and the positivity of a bilateral quadratic form is characterized in terms of the solvability of an algebraic riccati matrix inequality a lyapunov like stability analysis of 2 d systems is conducted by resorting to positivity tests for a sequence of bilateral quadratic forms generated by a recurrence formula the effectiveness is proved in an illustrative example

iterative learning control synthesis based on 2 d system theory an algorithm is presented for iterative learning of the control input for a linear discrete time multivariable system necessary and sufficient conditions are stated for convergence of the proposed algorithm the algorithm synthesis and analysis are based on two dimensional 2 d system theory a numerical example is given

a survey on iterative learning control for nonlinear systems in this article we review the recent advances in iterative learning control ilc for nonlinear dynamic systems in the research field of ilc two categories of system nonlinearities are considered namely the global lipschitz continuous glc functions and local lipschitz continuous llc functions ilc for glc systems is widely studied and analysed using contraction mapping approach and the focus of recent exploration moves to application problems though a number of theoretical issues remain open ilc for llc systems is currently a hot area and the recent research focuses on ilc design and analysis by means of lyapunov approach the objectives of this article are to introduce recent development and advances in nonlinear ilc schemes highlight their effectiveness and limitations as well as discuss the directions for further exploration of nonlinear ilc

geometric bvps hardy spaces and the cauchy integral and transform on regions with corners abstract in this paper we give a new perspective on the cauchy integral and transform and hardy spaces for dirac type operators on manifolds with corners of codimension two instead of considering banach or hilbert spaces we use polyhomogeneous functions on a geometrically blown up version of the manifold called the total boundary blow up introduced by mazzeo and melrose r r mazzeo r b melrose analytic surgery and the eta invariant geom funct anal 5 1 1995 14 75 these polyhomogeneous functions are smooth everywhere on the original manifold except at the corners where they have a taylor series with possible log terms in polar coordinates the main application of our analysis is a complete fredholm theory for boundary value problems of dirac operators on manifolds with corners of codimension two

stability analysis and stabilization of 2 d switched systems under arbitrary and restricted switchings in this paper the problems of stability analysis and stabilization are investigated for discrete time two dimensional 2 d switched systems which are formulated by the well known fornasini marchesini local state space model firstly by using the switched quadratic lyapunov function approach a sufficient stability condition is established for such systems under arbitrary switching signal then the extended average dwell time technique combining with the piecewise lyapunov function approach is developed and it is utilized for the stability analysis of the 2 d switched systems for the restricted switching case based on the stability analysis results sufficient conditions are presented to stabilize the 2 d switched systems finally two examples are provided to illustrate the effectiveness of the proposed new design techniques

robust mixed generalized h sub 2 h sub spl infin filtering of 2 d nonlinear fractional transformation systems this study considers robust filtering problems for uncertain two dimensional 2 d discrete systems in nonlinear fractional transformation nft representations like one dimensional 1 d systems the nft in this paper serves to complement the linear fractional transformation lft linear matrix inequality lmi formulations are given to analyze as well as synthesize robust filters numerical examples show the advantage of the nft over the lft in terms of not only computational savings but also substantial performance gains and verify the efficiency of the proposed techniques

on iterative learning algorithms for the formation control of nonlinear multi agent systems this paper deals with formation control problems for multi agent systems with nonlinear dynamics and switching network topologies using the nearest neighbor knowledge a distributed algorithm is constructed by employing the iterative learning control approach sufficient conditions are given to obtain the desired relative formations of agents which benefits from the strict positiveness of products of stochastic matrices it is shown that the derived results can effectively work although the network topologies dynamically change along both time and iteration axes and the corresponding directed graphs may not have spanning trees such result is also illustrated via numerical simulations

asynchronous h filtering for 2d discrete markovian jump systems with sensor failure this paper investigates the problem of the asynchronous h filtering for a class of two dimensional 2d markovian jump systems with sensor failure the asynchronous phenomenon is considered to be random mismatch between system modes and candidate filters the mismatch behavior is assumed to be stochastic with a certain probability and a new markov chain is proposed to model the jumping process of the filtering error system besides a switching method is proposed to dealing with the sensor failure sufficient conditions for the existence of a desired filter such that the filtering error system is stochastically stable with a guaranteed h performance index are obtained in the form of linear matrix inequalities lmis two examples are provided to illustrate the effectiveness and advantage of the proposed method

brief paper fault tolerant control for a class of nonlinear sampled data systems via a euler approximate observer in this paper a fault tolerant control ftc scheme is developed for a class of nonlinear sampled data systems first a euler approximate discrete model is used to describe the plant under the sampling under this model an observer based fault estimation method is proposed to guarantee the accuracy of both the state and fault estimation values the conditions to make the approximate model consistent with the exact model are presented then an active fault tolerant controller which has a constraint condition for the sampling time is designed to make the faulty system stable finally an inverted pendulum is used to show the efficiency of the proposed method

variance constrained h control for a class of nonlinear stochastic discrete time varying systems in this paper a general event triggered framework is set up to deal with the variance constrained h control problem for a class of discrete time varying systems with randomly occurring saturations stochastic nonlinearities and state multiplicative noises based on the relative error with respect to the measurement signal an event indicator variable is introduced and the corresponding event triggered scheme is proposed in order to determine whether the measurement output is transmitted to the controller or not the stochastic nonlinearities under consideration are characterized by statistical means which can cover several classes of well studied nonlinearities a set of unrelated random variables is exploited to govern the phenomena of randomly occurring saturations stochastic nonlinearities and state dependent noises the purpose of the addressed multiobjective control problem is to design a set of time varying output feedback controller such that over a finite horizon the closed loop system achieves both the prescribed h noise attenuation level and the state covariance constraints a recursive matrix inequality approach is developed to derive the sufficient conditions for the existence of the desired finite horizon controllers and the analytical characterization of such controllers is also given simulation studies are conducted to demonstrate the effectiveness of the developed controller design scheme

two novel iterative learning control schemes for systems with randomly varying trial lengths abstract this paper proposes two novel improved iterative learning control ilc schemes for systems with randomly varying trial lengths different from the existing works on ilc with variable trial lengths that advocate to replace the missing control information by zero the proposed learning algorithms are equipped with a searching mechanism to collect useful but avoid redundant past tracking information which could expedite the learning speed the searching mechanism is realized by the newly defined stochastic variables and an iteratively moving average operator the convergence of the proposed learning schemes is strictly proved based on the contraction mapping methodology two illustrative examples are provided to show the superiorities of the proposed approaches

distributed fusion estimation with square root array implementation for markovian jump linear systems with random parameter matrices and cross correlated noises the distributed fusion estimation is presented for markovian jump linear systems with random parameter matrices and cross correlated noises in sensor networks the lmmse estimator is derived based on gram schmidt orthogonal innovation sequence under a centralized framework the square root array implementation is further presented by recursively triangularizing the square roots of related positive semidefinite matrices in the lmmse estimator via the information filter form the distributed fusion estimation with square root array implementation is proposed incorporated with consensus strategy the convergent condition and the convergence point are also discussed with respect to consensus strategy this study presents the distributed fusion estimation of discrete time markovian jump linear systems with random parameter matrices and cross correlated noises in sensor networks the recursive linear minimum mean square error estimator is proposed based on the gram schmidt orthogonalization procedure under a centralized framework in order to avoid the loss of positive semidefiniteness and reduce dynamical range its square root array implementation is presented by recursively triangularizing the square roots of relevant positive semidefinite matrices furthermore via the information filter form the distributed fusion estimation with square root array implementation is derived from the centralized fusion structure incorporated with consensus strategy a maneuvering target tracking simulation in a sensor network validates the proposed method

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

h h fault detection observer design for two dimensional roesser systems abstract this paper addresses the problem of h h fault detection for two dimensional 2 d systems with disturbances in roesser model a fault detection observer is designed to satisfy a finite frequency h index and an h index simultaneously the finite frequency h index is used to increase the fault sensitivity in low frequency domain while the h index is used to attenuate the effects of disturbances in full frequency domain by the generalized kalman yakubovich popov lemma and some useful lemmas sufficient design conditions are obtained an example is given to illustrate the effectiveness of the proposed method

singularities of electromagnetic fields in polyhedral domains in this paper we investigate the singular solutions of time harmonic maxwell equations in a domain which has edges and polyhedral corners it is now well known that in the presence of non convex edges the solution fields have no square integrable gradients in general and that the main singularities are the gradients of singular functions of the laplace operator 4 5 we show how this type of result can be derived from the classical mellin analysis and how this analysis leads to sharper results concerning the singular parts which belong to h 1 for the singular functions we exhibit simple and explicit formulas based on generalized dirichlet and neumann singularities for the laplace operator these formulas are more explicit than the results announced in our note 10

robust stability and stabilization of uncertain discrete time markovian jump linear systems this note deals with robust stability and control of uncertain discrete time linear systems with markovian jumping parameters systems with polytopic type parameter uncertainty in either the state space model matrices or in the transition probability matrix of the markov process are considered this note develops methods of robust stability analysis and robust stabilization in the mean square sense which are dependent on the system uncertainty the design of both mode dependent and mode independent control laws is addressed the proposed methods are given in terms of linear matrix inequalities numerical examples are provided to demonstrate the effectiveness of the derived results

convergence in uncertain linear systems abstract state convergence is essential in many scientific areas e g multi agent consensus disagreement distributed optimization computational game theory multi agent learning over networks in this paper we study for the first time the state convergence problem in uncertain linear systems preliminarily we characterize state convergence in linear systems via equivalent linear matrix inequalities in the presence of uncertainty we complement the canonical definition of weak convergence with a stronger notion of convergence which requires the existence of a common kernel among the generator matrices of the difference differential inclusion strong convergence we investigate under which conditions the two definitions are equivalent then we characterize strong and weak convergence via lyapunov arguments linear matrix inequalities and separability of the eigenvalues of the generator matrices finally we show that unlike asymptotic stability state convergence lacks of duality

further results on h control for discrete time markovian jump time delay systems abstractthis paper studies the problem of h control for a class of discrete time markovian jump systems with time delay the purpose is to improve the existing results on h controller design for markovian jump systems a novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality which is proved to be less conservative than most results in the literature then the state feedback controller is designed which guarantees the stochastic stability of the closed loop system with a given disturbance attenuation numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques

weighted sobolev spaces and regularity for polyhedral domains we prove a regularity result for the poisson problem u f u p g on a polyhedral domain p r3 using the babuska kondratiev spaces kam p these are weighted sobolev spaces in which the weight is given by the distance to the set of edges 4 33 in particular we show that there is no loss of kam regularity for solutions of strongly elliptic systems with smooth coefficients we also establish a trace theorem for the restriction to the boundary of the functions in kam p

dirichlet problems in polyhedral domains ii approximation by fem and bem the convergence of the classical finite element method fem and boundary element method bem is poor due to the edge and vertex singularities of the solution of the involved dirichlet problem relative to an elliptic operator in a polyhedron using the global regularity results of lubuma and nicaise 1994 we analyse refined fem and bem with optimal rates of convergence

mathcal h_ infty control for 2 d markov jump systems in roesser model this paper considers the problem of asynchronous mathcal h infty control for two dimensional 2 d markov jump systems the underlying system is described based upon the roesser model especially the hidden markov model is employed when dealing with the asynchronization between a controlled system and a controller and the relation between them is constructed through a conditional probability matrix based on the lyapunov function technique the asymptotic mean square stability and mathcal h infty noise attenuation performance are investigated for the closed loop 2 d system moreover the controller gain can be obtained by solving a convex optimization problem an example is presented to show the effectiveness and potential of the proposed new design technique

stochastic stabilization of singular systems with markovian switchings this paper studies the stochastic stabilization problem for a class of singular markovian jump system the aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular markovian jump system smjs a new kind of stochastic controller only in the diffusion part is proposed such that the closed loop system has a unique solution and is almost surely exponentially admissible new sufficient condition for the existence of such a controller is given as linear matrix inequalities lmis based on this more extensions to transition probability matrix tpm with elements partially unknown and system states partially observable are developed a numerical example is used to demonstrate the effectiveness of the proposed methods

krein space based robust h fault estimation for two dimensional uncertain linear discrete time varying systems abstract in this study the robust h fault estimation problem for two dimensional linear time varying systems with norm bounded unknown input measurement noise and time varying process uncertainty is investigated by introducing an equivalent auxiliary system and a new certain indefinite quadratic form performance function the system uncertainty can be appropriately considered into the new performance function and the fault estimator design is converted to the minimization problem of a quadratic form based on the partially equivalence property between the deterministic quadratic form problem and the krein space estimation theory the two dimensional h fault estimation problem can be solved via signal deconvolution in krein space through employing projection operation and riccati like difference equation in two dimensions both the recursive form fault estimator and the explicit condition for existence of the estimator are derived one darboux equation example is provided to illustrate the effectiveness of the proposed fault estimator

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

special finite element methods for a class of second order elliptic problems with rough coefficients in this paper the approximate solution of a class of second order elliptic equations with rough coefficients is considered problems of the type considered arise in the analysis of unidirectional composites where the coefficients represent the properties of the material several methods for this class of problems are presented and it is shown that they have the same accuracy as usual methods have for problems with smooth coefficients the methods are referred to as special finite element methods because they are of finite element type but employ special shape functions chosen to accurately model the unknown solution

brief paper robust fault detection for networked systems with communication delay and data missing in this paper the robust fault detection problem is investigated for a class of discrete time networked systems with unknown input and multiple state delays a novel measurement model is utilized to represent both the random measurement delays and the stochastic data missing phenomenon which typically result from the limited capacity of the communication networks the network status is assumed to vary in a markovian fashion and its transition probability matrix is uncertain but resides in a known convex set of a polytopic type the main purpose of this paper is to design a robust fault detection filter such that for all unknown inputs possible parameter uncertainties and incomplete measurements the error between the residual signal and the fault signal is made as small as possible by casting the addressed robust fault detection problem into an auxiliary robust h filtering problem of a certain markovian jumping system a sufficient condition for the existence of the desired robust fault detection filter is established in terms of linear matrix inequalities a numerical example is provided to illustrate the effectiveness and applicability of the proposed technique

iterative learning control for discrete time systems with event triggered transmission strategy and quantization this paper investigates the iterative learning problem for discrete time systems with event triggered scheme and quantization the event triggered scheme is firstly considered in the iterative learning controllers to reduce the number of iteration steps to be updated here the event triggered scheme is designed depending on time t and iterative learning step k quantization is then introduced in the event triggered controllers and some relaxed conditions are presented to guarantee the tracking problem by using some interval matrix properties finally simulation results are given to illustrate the usefulness of the developed criteria

robust h_ infty filtering for two dimensional uncertain linear discrete time varying systems a krein space based method a robust h infty filtering algorithm is proposed for two dimensional 2 d linear uncertain time varying systems in this study the considered 2 d systems are subject to unknown inputs measurement noises and time varying modeling uncertainties to appropriately deal with the system uncertainties a new problem formulation of robust h infty filter design for 2 d uncertain systems is first presented by introducing an alternative indefinite quadratic performance function in lieu of the standard h infty performance index then the robust 2 d h infty filter design is converted to an optimization problem of finding the positive minimum of the new indefinite quadratic performance function under certain conditions by relating this quadratic form to a specific 2 d state space model in krein space the krein space estimation theory is used to solve the reformulated optimization problem a recursive robust 2 d time varying h infty filter and its explicit condition for the existence are obtained through projection techniques in 2 d krein space one thermal process plant is used to illustrate the effectiveness of the proposed filter

convergence of iterative learning control for siso nonrepetitive systems subject to iteration dependent uncertainties abstract this paper studies the robust convergence properties of iterative learning control ilc for single input single output siso nonrepetitive systems subject to iteration dependent uncertainties that arise in not only initial states and external disturbances but also plant models given an extended relative degree condition it is possible to propose necessary and sufficient nas conditions for robust ilc convergence the tracking error bound is shown to depend continuously on the bounds of the iteration dependent uncertainties when the iteration dependent uncertainties are bounded nas conditions exist to guarantee bounded system trajectories and output tracking error if the iteration dependent uncertainties converge then nas conditions ensure bounded system trajectories and zero output tracking error the results are also extended to a class of affine nonlinear systems satisfying a lipschitz condition simulation tests on a representative batch process demonstrate the validity of the obtained robust ilc convergence results

robust cooperative learning control for directed networks with nonlinear dynamics this paper studies a class of robust cooperative learning control problems for directed networks of agents a with nonidentical nonlinear dynamics that do not satisfy a global lipschitz condition and b in the presence of switching topologies initial state shifts and external disturbances all uncertainties are not only time varying but also iteration varying it is shown that the relative formation of nonlinear agents achieved via cooperative learning can be guaranteed to converge to the desired formation exponentially fast as the number of iterations increases a necessary and sufficient condition for exponential convergence of the cooperative learning process is that at each time step the network topology graph of nonlinear agents can be rendered quasi strongly connected through switching along the iteration axis simulation tests illustrate the effectiveness of our proposed cooperative learning results in refining arbitrary high precision relative formation of nonlinear agents

robust h_ infty fuzzy output feedback control with multiple probabilistic delays and multiple missing measurements in this paper the robust h control problem is investigated for a class of uncertain discrete time fuzzy systems with both multiple probabilistic delays and multiple missing measurements a sequence of random variables all of which are mutually independent but obey the bernoulli distribution is introduced to account for the probabilistic communication delays the measurement missing phenomenon occurs in a random way the missing probability for each sensor satisfies a certain probabilistic distribution in the interval here the attention is focused on the analysis and design of h fuzzy output feedback controllers such that the closed loop takagi sugeno t s fuzzy control system is exponentially stable in the mean square the disturbance rejection attenuation is constrained to a given level by means of the h performance index intensive analysis is carried out to obtain sufficient conditions for the existence of admissible output feedback controllers which ensures the exponential stability as well as the prescribed h performance the cone complementarity linearization procedure is employed to cast the controller design problem into a sequential minimization one that is solved by the semi definite program method simulation results are utilized to demonstrate the effectiveness of the proposed design technique in this paper

brief h control and robust stabilization of two dimensional systems in roesser models feedback control of two dimensional 2 d systems is a problem of considerable importance in both theory and practical applications in this paper we present a state space solution to the problem of h control of 2 d systems for a linear discrete time 2 d system described by a 2 d state space roesser model a 2 d dynamic output feedback controller is designed to achieve the closed loop system asymptotic stability and a specified h performance using a linear matrix inequality lmi approach we further give a solution for robust stabilization of 2 d systems subject to a class of norm bounded uncertainties the results are demonstrated by an application example of stabilization of processes expressed in a darboux equation

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

finite horizon estimation of randomly occurring faults for a class of nonlinear time varying systems this paper is concerned with the finite horizon estimation problem of randomly occurring faults for a class of nonlinear systems whose parameters are all time varying the faults are assumed to occur in a random way governed by two sets of bernoulli distributed white sequences the stochastic nonlinearities entering the system are described by statistical means that can cover several classes of well studied nonlinearities the aim of the problem is to estimate the random faults over a finite horizon such that the influence from the exogenous disturbances onto the estimation errors is attenuated at the given level quantified by an h norm in the mean square sense by using the completing squares method and stochastic analysis techniques necessary and sufficient conditions are established for the existence of the desired finite horizon h fault estimator whose parameters are then obtained by solving coupled backward recursive riccati difference equations rdes a simulation example is utilized to illustrate the effectiveness of the proposed fault estimation method

robust discrete time iterative learning control for nonlinear systems with varying initial state shifts this note is concerned with the robust discrete time iterative learning control ilc design for nonlinear systems with varying initial state shifts a two gain ilc law is considered using a 2d analysis approach sufficient conditions are derived to guarantee both convergence of the learning process for fixed initial condition and boundedness of the tracking error for variable initial condition it is shown that the error data with anticipation in time can well handle the varying initial state shifts in discrete time ilc

learning to cooperate motivated by the prototypical problem of a marching band this paper studies a class of multi agent formation problems characterized by two features i the agents attempt to complete a finite duration coordinated formation task with high precision by repeating the task and ii the feedback mechanism by which the agents control their motions is based on relative differences between nearest neighbors but the underlying graph topology can vary both during a repetition and from one repetition to the next adopting the framework of iterative learning control leads to the notion of multi agent networks with switching topologies along two directions a finite time axis and an infinite iteration axis for such systems we present distributed algorithms using nearest neighbor information whose exponential convergence can be demonstrated it is shown that as the number of repetition increases the relative formation between agents approaches the desired formation exponentially fast if and only if at each time step the union of the interaction graphs has a spanning tree frequently enough along the iteration axis that is the agents can learn to cooperate the remarkable point of this result is that it is not necessary to have a spanning tree at any specific time step or iteration in order for the system to converge two examples are given to illustrate the ideas including a general example where through iteration the agents can form a desired formation and a special case of it where an additional agent specifies a reference to regulate the formation shape simultaneously

fault detection for discrete time linear systems based on descriptor observer approach this paper investigates the problem of actuator fault detection filter design for discrete time linear systems with output disturbance by using the descriptor observer method an h fault detection filter is designed to guarantee the residual system is admissible and satisfies the h performance by utilizing lyapunov function approach a sufficient condition for the admissible of the residual system is obtained in the form of linear matrix inequality lmi the desired fault detection filter can be designed by solving a set of lmis finally a numerical example is proposed to illustrate the effectiveness of the developed method

robust and non fragile finite time h control for uncertain markovian jump nonlinear systems this paper investigates the non fragile and robust finite time h control problem for a class of uncertain markovian jump nonlinear systems with bounded parametric uncertainties and norm bounded disturbance by employing stochastic analysis and linear matrix inequality techniques sufficient criteria of stochastic finite time boundedness and stochastic h finite time boundedness are first provided for the class of stochastic jump systems then a controller is designed such that the class of stochastic nonlinear dynamics are stochastically finite time bounded and have an h attention performance level by utilizing matrix decomposition approach furthermore the analysis and design of non fragile and robust finite time controller are provided to guarantee that the class of uncertain stochastic systems are stochastically finite time boundeded with a prescribed attention index by using non fragile control technique in addition we also deal with the analysis and design of stochastic finite time stability and stochastic finite time stabilization all criterions can be characterized in terms of linear matrix inequalities finally two examples are also given to illustrate the effectiveness of obtained results

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

regularity of the solutions for elliptic problems on nonsmooth domains in ℝ3 part i countably normed spaces on polyhedral domains this is the first of a series of three papers devoted to the regularity of solutions of elliptic problems on nonsmooth domains in 3 the present paper introduces various weighted spaces and countably weighted spaces in the neighbourhood of edges and vertices of polyhedral domains and it concentrates on exploring the structure of these spaces such as the embeddings of weighted sobolev spaces the relation between weighted sobolev spaces and weighted continuous function spaces and the relations between the weighted sobolev spaces and countably weighted sobolev spaces in cartesian coordinates and in the spherical and cylindrical coordinates these well defined spaces are the foundation for the comprehensive study of the regularity theory of elliptic problems with piecewise analytic data in 3 which are essential for the design of effective computation and the analysis of the h p version of the finite element method for solving elliptic problems in three dimensional nonsmooth domains arising from mechanics and engineering

a discrete time learning control algorithm for a class of linear time invariant systems a discretized version of the d type learning control algorithm is presented for a mimo linear discrete time system a necessary and sufficient condition for uniform convergence of the proposed learning algorithm is presented then we prove that the same condition is sufficient for the global robustness of the proposed learning algorithm to state disturbances measurement noise at the output and reinitialization error are present at each iteration a numerical example is given to illustrate the results

exponential stability for discrete time infinite markov jump systems this technical note addresses a class of discrete time stochastic systems with infinite markov jump parameter first of all spectral criterion and lyapunov type criteria are presented for the exponential stability of considered systems further under the condition of strong detectability a barbashin krasovskii stability theorem is shown in terms of a generalized lyapunov equation with a positive semi definite term as an application of the proposed lyapunov stability criterion a sufficient condition of ell 2 input state stability is derived for the infinite markov jump systems disturbed by finite energy random disturbance

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

filtering of two dimensional periodic roesser systems subject to dissipativity abstract in this note the problem of dissipativity based filtering of two dimensional 2d periodic roesser systems is investigated a discrete time periodic roesser model extensively used in practical systems is introduced to describe 2d periodic systems moreover it is assumed that the periods of the augmented system in horizontal and vertical directions are the same which can greatly simplify stability analyses by resorting to the periodic lyapunov functional approach that depends on periodical property of the augmented system less conservative results for the existence of 2d periodic filter are presented to ensure the asymptotic stability and 2d q 1 q 2 q 3 dissipativity particularly the parameters of 2d periodic filter are derived with convex optimization method simulation results are provided to verify the effectiveness and merits of the theoretical findings in addition the correlation between optimal dissipative performance indices and different lyapunov functions is revealed

optimal iterative learning control design for multi agent systems consensus tracking abstract under a repeatable operation environment this paper proposes an iterative learning control scheme that can be applied to multi agent systems to perform consensus tracking under the fixed communication topology the agent dynamics are modeled by time varying nonlinear equations which satisfy the global lipschitz continuous condition in addition the desired consensus trajectory is only accessible to a subset of the followers by using the concept of the graph dependent matrix norm the convergence conditions can be specified at the agent level which depend on a set of eigenvalues that are associated with the communication topology the results are first derived for homogeneous agent systems and then extended to heterogeneous systems next optimal controller gain design methods are proposed in the sense that the norm of tracking error converges at the fastest rate which imposes a tightest bounding function for the actual tracking error in the norm analysis framework in the end an illustrative example of a group of heterogeneous agents is provided to demonstrate the effectiveness of the proposed design methods

robust mixed spl hscr sub 2 spl hscr sub spl infin filtering of 2 d systems this paper deals with several challenging problems of robust filtering for two dimensional 2 d systems first of all new linear matrix inequality lmi characterizations for the spl hscr sub spl infin and spl hscr 2 norms of 2 d systems are introduced and thoroughly established based on these preparatory results convex lmi characterizations for robust spl hscr sub spl infin spl hscr sub 2 and robust mixed spl hscr sub 2 spl hscr sub spl infin filtering are derived the efficiency and viability of the proposed techniques and tools are demonstrated through a set of numerical examples

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

on the full calculus of pseudo differential operators on boundary groupoids with polynomial growth abstract in this paper we enlarge the space of uniformly supported pseudo differential operators on some groupoids by considering kernels satisfying certain asymptotic estimates we show that such enlarged space contains the compact parametrix and the generalized inverse of uniformly supported operators with fredholm vector representation

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

well posedness of the fundamental boundary value problems for constrained anisotropic elastic materials we consider the equations of linear homogeneous anisotropic elasticity admitting the possibility that the material is internally constrained and formulate a simple necessary and sufficient condition for the fundamental boundary value problems to be well posed for materials fulfilling the condition we establish continuous dependence of the displacement and stress on the elastic moduli and ellipticity of the elasticity system as an application we determine the orthotropic materials for which the fundamental problems are well posed in terms of their young s moduli shear moduli and poisson ratios finally we derive a reformulation of the elasticity system that is valid for both constrained and unconstrained materials and involves only one scalar unknown in addition to the displacements for a two dimensional constrained material a further reduction to a single scalar equation is outlined

h sliding mode control for uncertain neutral type stochastic systems with markovian jumping parameters this paper is devoted to the investigation of h sliding mode control smc for uncertain neutral stochastic systems with markovian jumping parameters and time varying delays a sliding surface functional is firstly constructed then the sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite time interval the sufficient conditions for asymptotically stochastic stability of sliding mode dynamics with a given disturbance attenuation level are presented in terms of linear matrix inequalities lmis finally an example is provided to illustrate the efficiency of the proposed method

well posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks we prove a regularity result for the anisotropic linear elasticity equation p u rm div left boldmath mathsf c cdot nabla u right f with mixed displacement and traction boundary conditions on a curved polyhedral domain omega subset mathbb r 3 in weighted sobolev spaces mathcal k m 1 a 1 omega for which the weight is given by the distance to the set of edges in particular we show that there is no loss of mathcal k m a regularity our curved polyhedral domains are allowed to have cracks we establish a well posedness result when there are no neighboring traction boundary conditions and a 0 that depends on p on the boundary conditions and on the domain our results extend to other strongly elliptic systems and higher dimensions

stability analysis of two dimensional markovian jump state delayed systems in the roesser model with uncertain transition probabilities this paper is concerned with the problem of stochastic stability analysis of discrete time two dimensional 2 d markovian jump systems mjss described by the roesser model with interval time varying delays the transition probabilities of the jumping process markov chain are assumed to be uncertain that is they are not exactly known but can be estimated a lyapunov like scheme is first extended to 2 d mjss with delays based on some novel 2 d summation inequalities proposed in this paper delay dependent stochastic stability conditions are derived in terms of linear matrix inequalities lmis which can be computationally solved by various convex optimization algorithms finally two numerical examples are given to illustrate the effectiveness of the obtained results

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

an iterative learning approach to formation control of multi agent systems abstract in this paper an efficient framework is proposed to the formation control problem of multiple agents with unknown nonlinear dynamics by means of the iterative learning approach in particular a distributed d type iterative learning scheme is developed for the multi agent system with switching topology whose switching time and sequence are allowed to be varied at different iterations according to the actual trajectories of agents and a sufficient condition is derived to ensure that the desired formation can be always preserved from the initial starting location to the final one after some iterations simulation results are provided to verify the effectiveness of the proposed approach

boundary layer methods for lipschitz domains in riemannian manifolds abstract we extend to the variable coefficient case boundary layer techniques that have been successful in the treatment of the laplace equation and certain other constant coefficient elliptic partial differential equations on lipschitz domains in euclidean space we treat the laplace operator on lipschitz domains in a manifold with c 1 metric tensor and study the dirichlet neumann and oblique derivative boundary problems

robust filtering for 2 d state delayed systems with nft uncertainties this paper is concerned with the robust filtering problem for two dimensional 2 d state delayed systems with uncertainties represented by nonlinear fraction transformation the authors first establish the stability h sub spl infin performance and generalized h sub 2 performance criteria for the system based on the results the authors propose efficient methods to solve the robust h sub spl infin filtering generalized h sub 2 filtering and mixed generalized h sub 2 h sub spl infin filtering problems by using a parameter dependent lyapunov function approach the methods involve solving linear matrix inequalities two examples are given to show the effectiveness of the proposed approach

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

on the sharpness of certain local estimates for projections into finite element spaces influence of a re entrant corner in a plane polygonal domain with a reentrant corner consider a homogeneous dirichlet problem for poisson s equation au f with f smooth and the corresponding galerkin finite element solutions in a family of piecewise polynomial spaces based on quasi uniform uniformly regular triangulations with the diameter of each element compara