synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

a halanay type inequality approach to the stability analysis of discrete time neural networks with delays in this paper we consider the stability of discrete time neural networks with time varying delays a new discrete time halanay type inequality is presented based on which we derive sufficient conditions for the globally asymptotic and exponential stability of discrete time delayed neural networks two kinds of neural networks without and with impulsive effects are investigated numerical examples and simulations are given to illustrate the effectiveness of the obtained results

feedback control for linear time invariant systems with state and control bounds in the presence of disturbances the problem of the stabilizing linear control synthesis in the presence of state and input bounds for systems with additive unknown disturbances is considered the only information required about the disturbances is a finite convex polyhedral bound discrete and continuous time systems are considered the property of positive d invariance of a region is introduced and it is proved that a solution of the problem is achieved by the selection of a polyhedral set s and the computation of a feedback matrix k such that s is positively d invariant for the closed loop system it is shown that if polyhedral sets are considered the solution involves simple linear programming algorithms however the procedure suggested requires a great amount of computational work offline if the state space dimension is large because the feedback matrix k is obtained as a solution of a large set of linear inequalities all of the vertices of s are required

birational rigidity of complete intersections we prove that every smooth complete intersection x x d 1 ldots d s subset mathbb p sum i 1 s d i defined by s hypersurfaces of degree d 1 ldots d s is birationally superrigid if 5s 1 le frac 2 sum i 1 s d i 1 sqrt prod i 1 s d i in particular x is non rational and mathrm bir x mathrm aut x we also prove birational superrigidity of singular complete intersections with similar numerical condition these extend the results proved by tommaso de fernex

rational spl lscr sup 1 suboptimal compensators for continuous time systems the persistent disturbance rejection problem spl lscr sup 1 optimal control for continuous time systems leads to nonrational compensators even for single input single output systems as noted in dahleh and pearson 1987 the difficulty of physically implementing these controllers suggests that the most significant application of the continuous time spl lscr sup 1 theory is to furnish achievable performance bounds for rational controllers in this paper the authors use the theory of positively invariant sets to provide a design procedure based upon the use of the discrete euler approximating system for suboptimal rational spl lscr sup 1 controllers with a guaranteed cost the main results of the paper show that i the spl lscr sup 1 norm of a continuous time system is bounded above by the l sup 1 norm of an auxiliary discrete time system obtained by using the transformation z 1 rs and ii the proposed rational compensators yield spl lscr sup 1 cost arbitrarily close to the optimum even in cases where the design procedure proposed in the above mentioned paper fails due to the existence of plant zeros on the stability boundary

log canonical thresholds of certain fano hypersurfaces we study log canonical thresholds on quartic threefolds quintic fourfolds and double spaces as an important application we show that they have kahler einstein metrics if they are general

synchronization of continuous dynamical networks with discrete time communications in this paper synchronization of continuous dynamical networks with discrete time communications is studied though the dynamical behavior of each node is continuous time the communications between every two different nodes are discrete time i e they are active only at some discrete time instants moreover the communication intervals between every two communication instants can be uncertain and variable by choosing a piecewise lyapunov krasovskii functional to govern the characteristics of the discrete communication instants and by utilizing a convex combination technique a synchronization criterion is derived in terms of linear matrix inequalities with an upper bound for the communication intervals obtained the results extend and improve upon earlier work simulation results show the effectiveness of the proposed communication scheme some relationships between the allowable upper bound of communication intervals and the coupling strength of the network are illustrated through simulations on a fully connected network a star like network and a nearest neighbor network

minimization of a regulated response to a fixed input the problem of minimizing a regulated output due to a specific bounded input is solved in the siso single input single output discrete time case it is shown that in most situations the optimal solution will not exist but given any epsilon 0 it is possible to find a suboptimal solution with performance within epsilon of the optimal performance the proposed approach is extended to the problem of shaping the error transient response it is shown how time domain templates can be used in this problem in the same way that frequency weighting functions are used in the h sup infinity and h sup 2 problems

fuzzy impulsive control for uncertain nonlinear systems with guaranteed cost in this paper a guaranteed cost fuzzy impulsive control gcfic problem is addressed for uncertain continuous time nonlinear systems which can be represented by the takagi sugeno t s fuzzy model with parametric uncertainties based on the t s fuzzy model a novel time varying lyapunov function is initially constructed to derive the existence condition of guaranteed cost fuzzy impulsive controllers which cannot only exponentially stabilize the uncertain fuzzy system but also provide an upper bound on the quadratic cost function then two procedures for designing suboptimal guaranteed cost fuzzy impulsive controllers are given in the sense of minimizing an upper bound of the cost function one casts the controller design into a parameter dependent linear matrix inequality lmi optimization problem and the other casts the controller design into a sequential minimization problem subject to lmi constraints by using the cone complementary linearization ccl algorithm finally an example is presented to illustrate the effectiveness of the proposed method

exponential synchronization of coupled stochastic memristor based neural networks with time varying probabilistic delay coupling and impulsive delay this paper deals with the exponential synchronization of coupled stochastic memristor based neural networks with probabilistic time varying delay coupling and time varying impulsive delay there is one probabilistic transmittal delay in the delayed coupling that is translated by a bernoulli stochastic variable satisfying a conditional probability distribution the disturbance is described by a wiener process based on lyapunov functions halanay inequality and linear matrix inequalities sufficient conditions that depend on the probability distribution of the delay coupling and the impulsive delay were obtained numerical simulations are used to show the effectiveness of the theoretical results

impulsive stabilization and impulsive synchronization of discrete time delayed neural networks this paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete time delayed neural networks ddnns two types of ddnns with stabilizing impulses are studied by introducing the time varying lyapunov functional to capture the dynamical characteristics of discrete time impulsive delayed neural networks didnns and by using a convex combination technique new exponential stability criteria are derived in terms of linear matrix inequalities the stability criteria for didnns are independent of the size of time delay but rely on the lengths of impulsive intervals with the newly obtained stability results sufficient conditions on the existence of linear state feedback impulsive controllers are derived moreover a novel impulsive synchronization scheme for two identical ddnns is proposed the novel impulsive synchronization scheme allows synchronizing two identical ddnns with unknown delays simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of ddnns finally an application of the obtained impulsive synchronization result for two identical chaotic ddnns to a secure communication scheme is presented

minimization of the maximum peak to peak gain the general multiblock problem a comprehensive study of the general l sub 1 optimal multiblock problem and a new linear programming algorithm for computing suboptimal controllers are presented by formulating the interpolation conditions in a concise and natural way the general theory is developed in simpler terms and with a minimum number of assumptions in addition further insight is gained into the structure of the optimal solution and different classes of multiblock problems are distinguished this leads to a conceptually attractive iterative method for finding approximate solutions

distributed consensus for sampled data control multi agent systems with missing control inputs abstract this paper is concerned about the distributed consensus problem for general sampled data control multi agent systems without or with a leader under control inputs missing over some sampling intervals for these two cases a distributed adaptive dynamical consensus algorithm is proposed based only on the relative information of network structure under the assumption that the dynamical network contains a directed spanning tree some sufficient consensus conditions are induced under a switched model these obtained consensus criteria are independent of dynamical network topology namely they are valid for both undirected and directed topology besides they do not rely on the spectra and the eigenvalue of laplacian matrix furthermore some quantitative relations included in dynamical systems such as sampling period admissible control inputs missing rate and exponential reaching rate of the consensus performance are established finally simulation examples are given to show the effectiveness of the proposed results

new approach to synchronization analysis of linearly coupled ordinary differential systems in this paper a general framework is presented for analyzing the synchronization stability of linearly coupled ordinary differential equations lcodes the uncoupled dynamical behavior at each node is general and can be chaotic or otherwise the coupling configuration is also general with the coupling matrix not assumed to be symmetric or irreducible on the basis of geometrical analysis of the synchronization manifold a new approach is proposed for investigating the stability of the synchronization manifold of coupled oscillators in this way criteria are obtained for both local and global synchronization these criteria indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold furthermore the roles of the uncoupled dynamical behavior on each node and the coupling configuration in the synchronization process are also studied

stabilization of delay systems delay dependent impulsive control the stabilization problem of delay systems is studied under the delay dependent impulsive control the main contributions of this technical note are that for one thing it shows that time delays in impulse term may contribute to the stabilization of delay systems that is a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks for another it shows the robustness of impulsive control that is the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization in this technical note from impulsive control point of view we firstly propose an impulsive delay inequality then we apply it to the delay systems which may be originally unstable and derive some delay dependent impulsive control criteria to ensure the stabilization of the addressed systems the effectiveness of the proposed strategy is evidenced by two illustrative examples

synchronization control for nonlinear stochastic dynamical networks pinning impulsive strategy in this paper a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling pinning state feedback controllers have been proved to be effective for synchronization control of state coupled dynamical networks we will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks some generic mean square stability criteria are derived in terms of algebraic conditions which guarantee that the whole state coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes an effective method is given to select the nodes which should be controlled at each impulsive constants the proportion of the controlled nodes guaranteeing the stability is explicitly obtained and the synchronization region is also derived and clearly plotted numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper

h_ infty state estimation for discrete time complex networks with randomly occurring sensor saturations and randomly varying sensor delays in this paper the state estimation problem is investigated for a class of discrete time delay nonlinear complex networks with randomly occurring phenomena from sensor measurements the randomly occurring phenomena include randomly occurring sensor saturations rosss and randomly varying sensor delays rvsds that result typically from networked environments a novel sensor model is proposed to describe the rosss and the rvsds within a unified framework via two sets of bernoulli distributed white sequences with known conditional probabilities rather than employing the commonly used lipschitz type function a more general sector like nonlinear function is used to describe the nonlinearities existing in the network the purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that for all probabilistic sensor saturations and sensor delays the dynamics of the estimation error is guaranteed to be exponentially mean square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an h norm in terms of a novel lyapunov krasovskii functional and the kronecker product sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method a simulation example is provided to show the usefulness of the proposed state estimation conditions

correspondence a comment on l optimal control of siso continuous time systems the paper l optimal control of siso continuous time systems by wang and sznaier wang sznaier 1997 automatica 33 1 85 90 studies the problem of designing a controller that optimally minimizes the peak absolute value of system output due to a fixed input signal with a newly defined function space a it was claimed that the set of all l bounded outputs could be parameterized and that the problem could be transformed to a minimal distance problem on l space we believe however their formulation has essential flaws

birational automorphisms of fano hypersurfaces v v y v 0 between smooth three dimensional quartics v v4 v 0 v 0 4 in p is a projective isomorphism this is the original wording of their theorem in fact the arguments of im give a much stronger result namely they actually prove that smooth quartics are birationally superrigid the concept of birational rigidity is not visual being rather technical it makes little impression it is immediate implications of the property of being birationally super rigid that are really impressive for a projective variety x smooth in codimension 1 and a linear system jdj free from xed components we de ne the threshold of canonical adjunction or brie y just threshold of the pair x d setting

minimum overshoot design for siso discrete time systems the problem of designing a controller to minimize the maximum negative error due to a specific bounded input is studied it is found that the solution can be obtained by solving an infinite linear programming problem in the special case of a step input a simple analytical formula for minimum overshoot is derived for a plant with one unstable pole and one nonminimum phase zero the solution technique has potential application to other control problems which seek to minimize quantities not directly representable as a norm

l sub 1 suboptimal pole placement design we incorporate an arbitrary number of candidate positive distinct poles into the scalar l sub 1 optimization framework in order to obtain low order rational suboptimal solutions to constrained l sub 1 optimization problems our approach uses a single linear program to minimize an upper bound on the l sub 1 norm and gives a solution which uses only the best out of the prespecified poles rational suboptimal solutions to a scalar two block problem are obtained similarly

stably irrational hypersurfaces of small slopes we show that over any uncountable field of characteristic different from two a very general hypersurface of dimension n 2 and degree at least log 2 n 2 is not stably rational this significantly improves earlier results of kollar and totaro as a byproduct of our proof we obtain new counterexamples to the integral hodge conjecture answering a question of voisin and colliot thelene voisin

a minimum time control for boolean control networks with impulsive disturbances this paper investigates a mayer type optimal control and minimum time control of a boolean control network bcn with impulsive disturbances using the semi tensor product the bcn with impulsive disturbances is converted into algebraic discrete time impulsive dynamic systems and several necessary conditions for optimality are derived then we consider the problem of steering a bcn with impulsive disturbances from a given initial state to a desired state in minimal time and a necessary condition stated in the form of maximum principle is obtained for a control to be time optimal it shows that the impulsive disturbances play an important role in the optimal control problem for bcns at last a biological example is given to illustrate the effectiveness and advantage of the obtained results

rational suboptimal continuous time controller design we obtain rational suboptimal continuous time solutions to some optimal control problems specified via time domain performance criteria these include spl lscr sub 1 and spl lscr sub spl infin norms and peak overshoot the approach uses linear semi infinite programming to compute weights for a given finite set of rational basis functions and makes the best possible use of the basis the closed loop transfer functions obtained satisfy appropriate interpolation constraints for internal stability and the formulation allows additional linear constraints to be incorporated

birational superrigidity and slope stability of fano manifolds we prove a relation between birational superrigidity of fano manifold and its slope stability in the sense of ross and thomas j alg geom 16 201 205 2007

state estimation for stochastic complex networks with switching topology this technical note studies the state estimation problem for stochastic complex networks with switching topology a set of bernoulli random variables are used to describe the switching behavior of the network by using the structure of the extended kalman filter ekf a recursive estimator is developed for each node to guarantee an optimized upper bound on the state estimation error covariance despite the switching coupling and linearization errors compared with the existing results on state estimation for stochastic complex networks a distinct feature for the proposed estimator is that the estimation errors for all nodes are not formulated in an augmented vector so that the gain matrix can be determined separately for each node by solving two riccati like difference equations based on the stochastic analysis theory it is shown that the estimation error is bounded in mean square under certain conditions simulation results are provided to verify the effectiveness of the proposed estimator

robust exponential stability of uncertain delayed neural networks with stochastic perturbation and impulse effects this paper focuses on the hybrid effects of parameter uncertainty stochastic perturbation and impulses on global stability of delayed neural networks by using the ito formula lyapunov function and halanay inequality we established several mean square stability criteria from which we can estimate the feasible bounds of impulses provided that parameter uncertainty and stochastic perturbations are well constrained moreover the present method can also be applied to general differential systems with stochastic perturbation and impulses

efficient algorithm for solving semi infinite programming problems and their applications to nonuniform filter bank designs an efficient algorithm for solving semi infinite programming problems is proposed in this paper the index set is constructed by adding only one of the most violated points in a refined set of grid points by applying this algorithm for solving the optimum nonuniform symmetric antisymmetric linear phase finite impulse response fir filter bank design problems the time required to obtain a globally optimal solution is much reduced compared with that of the previous proposed algorithm

robust exponential stability of uncertain stochastic neural networks with distributed delays and reaction diffusions this paper considers the problem of stability analysis for uncertain stochastic neural networks with distributed delays and reaction diffusions two sufficient conditions for the robust exponential stability in the mean square of the given network are developed by using a lyapunov krasovskii functional an integral inequality and some analysis techniques the conditions which are expressed by linear matrix inequalities can be easily checked two simulation examples are given to demonstrate the reduced conservatism of the proposed conditions

global synchronization criteria of linearly coupled neural network systems with time varying coupling in this paper global synchronization of linearly coupled neural network nn systems with time varying coupling is investigated the dynamical behavior of the uncoupled system at each node is general which can be chaotic or others the coupling configuration is time varying i e the coupling matrix is not a constant matrix based on lyapunov function method and the specific property of householder transform some criteria for the global synchronization are obtained by these criteria one can verify whether the coupled system with time varying coupling is globally synchronized which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration finally two simulations are given to demonstrate the effectiveness of the theoretical results

pinning stabilization of linearly coupled stochastic neural networks via minimum number of controllers pinning stabilization problem of linearly coupled stochastic neural networks lcsnns is studied in this paper a minimum number of controllers are used to force the lcsnns to the desired equilibrium point by fully utilizing the structure of the network in order to pinning control the lcsnns to a certain desired state only one controller is required for strongly connected network topology and m controllers which will be shown to be the minimum number are needed for lcsnns with m reducible coupling matrix the isolate node of the lcsnns can be stable periodic or even chaotic the coupling laplacian matrix of the lcsnns can be symmetric irreducible asymmetric irreducible or m reducible which means that the network topology can be strongly connected weakly connected or even unconnected there is no constraint on the network topology some criteria are derived to judge whether the lcsnns can be controlled in mean square by using designed controllers the given criteria are expressed in terms of strict linear matrix inequalities which can be easily checked by resorting to recently developed algorithm moreover numerical examples including small world and scale free networks are also given to demonstrate that our theoretical results are valid and efficient for large systems

exponential synchronization of linearly coupled neural networks with impulsive disturbances this brief investigates globally exponential synchronization for linearly coupled neural networks nns with time varying delay and impulsive disturbances since the impulsive effects discussed in this brief are regarded as disturbances the impulses should not happen too frequently the concept of average impulsive interval is used to formalize this phenomenon by referring to an impulsive delay differential inequality we investigate the globally exponential synchronization of linearly coupled nns with impulsive disturbances the derived sufficient condition is closely related with the time delay impulse strengths average impulsive interval and coupling structure of the systems the obtained criterion is given in terms of an algebraic inequality which is easy to be verified and hence our result is valid for large scale systems the results extend and improve upon earlier work as a numerical example a small world network composing of impulsive coupled chaotic delayed nn nodes is given to illustrate our theoretical result

global synchronization for discrete time stochastic complex networks with randomly occurred nonlinearities and mixed time delays in this paper the problem of stochastic synchronization analysis is investigated for a new array of coupled discrete time stochastic complex networks with randomly occurred nonlinearities rons and time delays the discrete time complex networks under consideration are subject to 1 stochastic nonlinearities that occur according to the bernoulli distributed white noise sequences 2 stochastic disturbances that enter the coupling term the delayed coupling term as well as the overall network and 3 time delays that include both the discrete and distributed ones note that the newly introduced rons and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment e g internet based control systems by constructing a novel lyapunov like matrix functional the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem by employing a combination of the linear matrix inequality lmi techniques the free weighting matrix method and stochastic analysis theories several delay dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete time stochastic complex networks with time delays the criteria derived are characterized in terms of lmis whose solution can be solved by utilizing the standard numerical software a simulation example is presented to show the effectiveness and applicability of the proposed results

extended dissipative state estimation for markov jump neural networks with unreliable links this paper is concerned with the problem of extended dissipativity based state estimation for discrete time markov jump neural networks nns where the variation of the piecewise time varying transition probabilities of markov chain is subject to a set of switching signals satisfying an average dwell time property the communication links between the nns and the estimator are assumed to be imperfect where the phenomena of signal quantization and data packet dropouts occur simultaneously the aim of this paper is to contribute with a markov switching estimator design method which ensures that the resulting error system is extended stochastically dissipative in the simultaneous presences of packet dropouts and signal quantization stemmed from unreliable communication links sufficient conditions for the solvability of such a problem are established based on the derived conditions an explicit expression of the desired markov switching estimator is presented finally two illustrated examples are given to show the effectiveness of the proposed design method

synchronization of markovian coupled neural networks with nonidentical node delays and random coupling strengths in this paper a general model of coupled neural networks with markovian jumping and random coupling strengths is introduced in the process of evolution the proposed model switches from one mode to another according to a markovian chain and all the modes have different constant time delays the coupling strengths are characterized by mutually independent random variables when compared with most of existing dynamical network models which share common time delay for all modes and have constant coupling strengths our model is more practical because different chaotic neural network models can have different time delays and coupling strength of complex networks may randomly vary around a constant due to environmental and artificial factors by designing a novel lyapunov functional and using some inequalities and the properties of random variables we derive several new sufficient synchronization criteria formulated by linear matrix inequalities the obtained criteria depend on mode delays and mathematical expectations and variances of the random coupling strengths as well numerical examples are given to demonstrate the effectiveness of the theoretical results meanwhile right continuous markovian chain is also presented

fundamental limitations on the time domain shaping of response to a fixed input in this paper we examine time domain limitation of performance problems in feedback control system design the main result is a theorem which gives a dual formulation to the problem of determining absolute limits on the time domain shaping of the response to a fixed input the duals that arise are particularly illuminating they have a simple interpretation as optimizing the impulse response of a transfer function whose poles are readily constructed from the data much insight is obtainable from the dual for example in helping to classify classes of plants with the same quantitative behavior new results on classical performance measures such as overshoot and undershoot are presented we also examine minimization of the difference between the maximum and minimum values of the error response a quantity we term fluctuation

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

coordination of multiagents interacting under independent position and velocity topologies we consider the coordination control for multiagent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs different algorithms are proposed and analyzed for different settings including the case without leaders and the case with a virtual leader under fixed position and velocity interaction topologies as well as the case with a group velocity reference signal under switching velocity interaction it is finally shown that the proposed algorithms are feasible in achieving the desired coordination behavior provided the interaction topologies satisfy the weakest possible connectivity conditions such conditions relate only to the structure of the interactions among agents while irrelevant to their magnitudes and thus are easy to verify rigorous convergence analysis is preformed based on a combined use of tools from algebraic graph theory matrix analysis as well as the lyapunov stability theory

further results on rational approximations of spl lscr sup 1 optimal controllers the continuous time persistent disturbance rejection problem spl lscr sup 1 optimal control leads to nonrational compensators even for siso systems the difficulty of physically implementing these controllers suggests that the most significant applications of the continuous time spl lscr sup 1 theory is to furnish bounds for the achievable performance of the plant previously two different rational approximations of the optimal spl lscr sup 1 controller were developed by ohta et al 1992 and by blanchini and sznaier 1994 in this paper the authors explore the connections between these two approximations the main result of the paper shows that both approximations belong to the same subset spl omega sub t of the set of rational approximations and that the method proposed by blanchini and sznaier gives the best approximation in the sense of providing the tightest upper bound of the approximation error among the elements of this subset additionally the authors exploit the structure of the dual to the spl lscr sup 1 optimal control problem to obtain rational approximations with approximation error smaller than a prespecified bound

birationally rigid hypersurfaces we prove that for n 4 all smooth hypersurfaces of degree n in n are birationally superrigid first discovered in the case n 4 by iskovskikh and manin in a work that started this whole direction of research this property was later conjectured to hold in general by pukhlikov the proof relies on the method of maximal singularities in combination with a formula on restrictions of multiplier ideals

exponential synchronization of complex networks of linear systems and nonlinear oscillators a unified analysis a unified approach to the analysis of synchronization for complex dynamical networks i e networks of partial state coupled linear systems and networks of full state coupled nonlinear oscillators is introduced it is shown that the developed analysis can be used to describe the difference between the state of each node and the weighted sum of the states of those nodes playing the role of leaders in the networks thus making it feasible to consider the error dynamics for the whole network system different from the other various methods given in the existing literature the analysis employed in this paper is demonstrated successfully in not only providing the consistent convergence analysis with much simpler form but also explicitly specifying the convergence rate

brief paper a unified synchronization criterion for impulsive dynamical networks this paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks two types of impulses are considered synchronizing impulses and desynchronizing impulses in previous literature all of the results are devoted to investigating these two kinds of impulses separately thus a natural question arises is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses in this paper a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named average impulsive interval the derived criterion is theoretically and numerically proved to be less conservative than existing results numerical examples including scale free and small world structures are given to show that our results are applicable to large scale networks

exponential h synchronization and state estimation for chaotic systems via a unified model in this paper h synchronization and state estimation problems are considered for different types of chaotic systems a unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems such as hopfield neural networks cellular neural networks chua s circuits unified chaotic systems qi systems chaotic recurrent multilayer perceptrons etc based on the h performance analysis of this unified model using the linear matrix inequality approach novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the state estimation problem is then studied for the same unified model where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level the parameters of these controllers and filters are obtained by solving the eigenvalue problem most chaotic systems can be transformed into this unified model and h synchronization controllers and state estimators for these systems are designed in a unified way three numerical examples are provided to show the usefulness of the proposed h synchronization and state estimation conditions

rational l sub spl infin suboptimal controllers for siso continuous time systems we study the problem of minimizing the weighted amplitude of the time response due to a given fixed input signal for single input single output siso continuous time systems and focus on obtaining rational suboptimal solutions an eas euler approximating system based method is proposed for designing a rational l sub spl infin suboptimal controller for siso systems it is shown that this rational approximation is the best one among a set of rational approximations in the sense of providing the tightest upper bound and that it can approximate the optimal cost arbitrarily close

rational approximation of l sub 1 optimal controllers for siso systems the l sub 1 optimal control problem with rational controllers for continuous time systems is considered in which it is shown that the optimal l sub 1 performance index with rational controllers is equal to that of irrational controllers a sequence of rational controllers that approximates the optimal index is constructed convergence properties of such a sequence are studied that the corresponding sequence of objective transfer functions is shown to converge in weak topology in bv r sub in the time domain and uniformly in a wider sense in the frequency domain

l optimal control of siso continuous time systems abstract in this paper we study the problem of designing a controller that minimizes the weighted amplitude of the time response due to a given fixed input signal for siso continuous time systems the main result of the paper shows that this problem admits a minimizing solution in l and that the optimal closed loop system has a special structure a sum of delayed step functions all having the same amplitude thus the optimal controller has a non rational transfer function although in the general case finding this controller entails solving an infinite dimensional linear programming problem we show that in some special cases the optimal solutions have closed form expressions and can be found by solving a set of algebraic equations finally we address the issue of selecting time and frequency domain weighting functions this paper together with our paper rational l suboptimal controller for siso continuous time systems ieee trans autom control ac 41 1358 1363 1996 which deals with the design of rational l suboptimal controllers for general systems give a complete solution of the l control problem

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

consensus analysis of multiagent networks via aggregated and pinning approaches in this paper the consensus problem of multiagent nonlinear directed networks mndns is discussed in the case that a mndn does not have a spanning tree to reach the consensus of all nodes by using the lie algebra theory a linear node and node pinning method is proposed to achieve a consensus of a mndn for all nonlinear functions satisfying a given set of conditions based on some optimal algorithms large size networks are aggregated to small size ones then by applying the principle minor theory to the small size networks a sufficient condition is given to reduce the number of controlled nodes finally simulation results are given to illustrate the effectiveness of the developed criteria

l sub 1 analysis and design of sampled data systems the focus of this work is l sub 1 optimal control of sampled data systems a converging approximation procedure is derived to compute the l sub infinity induced norm of closed loop finite dimensional linear time invariant lti sampled data systems an approximation method is developed to synthesize l sub 1 optimal sampled data regulators finally an example is provided that illustrates the l sub 1 analysis and design techniques presented

l 1 optimal feedback controllers for mimo discrete time systems the problem considered in this paper is the design of a closed loop system consisting of a mimo discrete time plant and compensator in such a way that the system is internally stable and optimally tracks all persistent bounded inputs the solution consists of two parts first the calculation of the minimum value of the performance index a weighted transfer function which is done by solving a linear programming problem and second construction of the optimal transfer function by solving a set of linear equations it is shown that in general the discrete time problem will have a rational solution and thus appears to be of considerable practical significance

mode dependent stochastic synchronization for markovian coupled neural networks with time varying mode delays this paper investigates the stochastic synchronization problem for markovian hybrid coupled neural networks with interval time varying mode delays and random coupling strengths the coupling strengths are mutually independent random variables and the coupling configuration matrices are nonsymmetric a mode dependent augmented lyapunov krasovskii functional lkf is proposed where some terms involving triple or quadruple integrals are considered which makes the lkf matrices mode dependent as much as possible this gives significant improvement in the synchronization criteria i e less conservative results can be obtained in addition by applying an extended jensen s integral inequality and the properties of random variables new delay dependent synchronization criteria are derived the obtained criteria depend not only on upper and lower bounds of mode delays but also on mathematical expectations and variances of the random coupling strengths finally two numerical examples are provided to demonstrate the feasibility of the proposed results

robust synchronization of an array of coupled stochastic discrete time delayed neural networks this paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete time neural networks with time varying delay the individual neural network is subject to parameter uncertainty stochastic disturbance and time varying delay where the norm bounded parameter uncertainties exist in both the state and weight matrices the stochastic disturbance is in the form of a scalar wiener process and the time delay enters into the activation function for the array of coupled neural networks the constant coupling and delayed coupling are simultaneously considered we aim to establish easy to verify conditions under which the addressed neural networks are synchronized by using the kronecker product as an effective tool a linear matrix inequality lmi approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally robustly exponentially synchronized in the mean square the lmi based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time varying delay and can be solved efficiently via the matlab lmi toolbox two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme

birational geometry of fano hypersurfaces of index two we prove that every non trivial structure of a rationally connected fibre space on a generic in the sense of zariski topology hypersurface v of degree m in the m 1 dimensional projective space for m ge 16 is given by a pencil of hyperplane sections in particular the variety v is non rational and its group of birational self maps coincides with the group of biregular automorphisms and for that reason is trivial the proof is based on the techniques of the method of maximal singularities and inversion of adjunction

pinning synchronization in t s fuzzy complex networks with partial and discrete time couplings communication constraints which may lead to the degradation of performance are common and unavoidable in a real world network in this paper two kinds of communication constraints are considered during the process of information transmission in takagi sugeno ts fuzzy complex network 1 partial couplings where only some part of nodes state information can be transmitted and the channel matrices are introduced to reflect such a phenomenon and 2 discrete time couplings where the nodes information are sampled at certain time instants this is the first time when both communication constraints are simultaneously considered in fuzzy complex networks compared with the perfect communication much less information is available for synchronization to overcome this difficulty a regrouping method is employed to reconstruct the fuzzy network the concise conditions are then proposed to ensure pinning synchronization of fuzzy complex networks with partial and discrete time couplings simulation examples are also provided to demonstrate the effectiveness of the theoretical results

optimal rejection of persistent disturbances robust stability and mixed sensitivity minimization the problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case the minimum value of the objective function can be obtained by solving a semi infinite linear programming problem and an iterative procedure for obtaining approximate solutions is introduced application of the l sup 1 optimal problem to robustness is discussed a mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations

scaling and percolation in the small world network model in this paper we study the small world network model of watts and strogatz which mimics some aspects of the structure of networks of social interactions we argue that there is one nontrivial length scale in the model analogous to the correlation length in other systems which is well defined in the limit of infinite system size and which diverges continuously as the randomness in the network tends to zero giving a normal critical point in this limit this length scale governs the crossover from large to small world behavior in the model as well as the number of vertices in a neighborhood of given radius on the network we derive the value of the single critical exponent controlling behavior in the critical region and the finite size scaling form for the average vertex vertex distance on the network and using series expansion and pad e approximants find an approximate analytic form for the scaling function we calculate the effective dimension of small world graphs and show that this dimension varies as a function of the length scale on which it is measured in a manner reminiscent of multifractals we also study the problem of site percolation on small world networks as a simple model of disease propagation and derive an approximate expression for the percolation probability at which a giant component of connected vertices first forms in epidemiological terms the point at which an epidemic occurs the typical cluster radius satisfies the expected finite size scaling form with a cluster size exponent close to that for a random graph all our analytic results are confirmed by extensive numerical simulations of the model

l 1 optimal compensators for continuous time systems previous work has been concerned with minimizing the l 1 norm of an error pulse response for discrete time siso 1 and mimo 2 systems in this paper we study the problem of minimizing the l1 norm of the error impulse response for siso continuous time systems this problem is quite different from the discrete time problem in that irrational solutions are obtained even when the problem data are rational two methods are suggested for the solution of the continuous time problem an exact method which leads to a finite dimensional nonlinear programming problem and an approximate method which leads to a linear programming problem

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

local exponential synchronization in complex dynamical networks with time varying delay and hybrid coupling in this paper the local exponential synchronization of complex dynamical networks with time varying delay and hybrid coupling is investigated we assume that the coupling configuration matrices are asymmetric and the inner coupling matrices are not restricted to be diagonal or positive definite through constructing the appropriate lyapunov krasovskii functional and applying the linear matrix inequality lmi technique several novel delay depend sufficient conditions and the decay rate are deduced for the local exponential synchronization moreover the derivative of the time varying delay is extended to any value finally the numerical simulations are given to show the effectiveness of the theoretical results

exponential synchronization of delayed markovian jump complex networks with generally uncertain transition rates this paper investigates the exponential synchronization problem for a class of markovian jump complex networks mjcns with generally uncertain transition rates gutrs in this gutr neural network model each transition rate can be completely unknown or only its estimate value is known this new uncertain model could be applied to many practical cases based on the lyapunov functional method and kronecker product technique a sufficient condition on the exponentially synchronization in mean square is derived in terms of linear matrix inequalities lmis which can be easily solved by using the matlab lmi toolbox finally one numerical example is well studied to illustrate the effectiveness of the developed method

h sub 2 control with time domain constraints theory and an application in this paper we study the problem of minimizing the h sub 2 norm of a given transfer function subject to time domain constraints on the time response of a different transfer function to a given test signal the main result of this paper shows that this problem admits a minimizing solution in r h sub 2 moreover rational solutions with performance arbitrarily close to optimal can be found by constructing families of approximating problems each one of these problems entails solving a finite dimensional quadratic programming problem whose dimension can be determined before hand these results are illustrated and experimentally validated by designing a controller for an active vision application

impulsive synchronization of reaction diffusion neural networks with mixed delays and its application to image encryption this paper presents a new impulsive synchronization criterion of two identical reaction diffusion neural networks with discrete and unbounded distributed delays the new criterion is established by applying an impulse time dependent lyapunov functional combined with the use of a new type of integral inequality for treating the reaction diffusion terms the impulse time dependent feature of the proposed lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction diffusion neural networks than the conventional impulse time independent lyapunov functions functionals while the new integral inequality which is derived from wirtinger s inequality overcomes the conservatism introduced by the integral inequality used in the previous results numerical examples demonstrate the effectiveness of the proposed method later the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image the experimental results verify that the proposed image encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks