near optimal control of nonstandard singularly perturbed systems abstract near optimal control of nonstandard multiparameter multitime scale singularly perturbed systems is studied using the descriptor variable approach in particular the slow models of the considered systems are allowed to exhibit impulses in the case of multiparameter singular perturbations the near optimal control is a cascade connection of separately designed slow and fast subregulators in the case of multitime scale singular perturbations the near optimal control is hierarchically composed of n 1 subregulators a parallel algorithm is provided for designing the subregulators separately the knowledge of the small singular perturbation parameters is not required in the overall design furthermore the frequency responses of the near optimal systems are analyzed and several design examples are given

on initial instantaneous jumps of singular systems this paper is concerned with instantaneous jumps in the state trajectory of a singular system it is shown that such jumps generically exist at the initial time due to inconsistent initial states the formula for the jumps is derived which indicates that the jumps linearly depend on the initial state moreover the set of all initial states which do not cause any state jumps for any output feedback is characterized and is revealed to be a linear subspace in the meantime the necessary and sufficient conditions are given for the existence of an output feedback to suppress completely the jumps for a given initial state finally we formulate the problem of designing an output feedback not only to stabilize the plant but also to achieve minimum initial jumps as a minimization problem

observability of structured linear systems in descriptor form a graph theoretic approach this paper deals with the right hand side observability of structured linear systems in descriptor form the method we propose is based on a graph theoretic approach it is applicable to a large class of descriptor systems including regular and nonregular systems even if they are square underdetermined or overdetermined after defining digraphs which represent such systems we express in graphic terms necessary and sufficient conditions to achieve the observability of the whole or of a given part of the state these conditions are easy to check because they are based on comparison of integers and on finding edges and subgraphs in a digraph therefore our approach is suited to study large scale and or uncertain systems

feedback and pole placement in descriptor variable systems the effects and uses of applying linear feedback to continuous time descriptor systems are studied structural changes resulting from feeding back the slow and fast parts of the trajectory separately are characterized it is shown that under certain conditions related to controllability the poles of the slow subsystem may be shifted arbitrarily and the impulsive behaviour of the fast subsystem may be eliminated

a frequency domain approach to control of singular systems in this paper singular control systems are studied from the frequency domain point of view the proper stable factorization of a singular system is derived the stability of the closed loop system consisting of a singular system and controller is addressed most significantly all proper stabilizing controllers are parameterized for a given singular system

controllability observability and duality in singular systems the concepts of controllability and observability for systems of the form e dot x ax bu y cx e singular are considered a theory is presented which unifies the three main approaches to this topic already existing in the literature the development includes a generalization of the duality theorem from state space theory

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

state feedback impulse elimination of linear time varying singular systems abstract linear time varying singular systems e t x a t x b t u are treated a necessary and sufficient condition for the existence of linear state feedback to eliminate impulsive behavior is derived the condition obtained is a natural extension of existing time invariant theory

synchronization transitions on scale free neuronal networks due to finite information transmission delays we investigate front propagation and synchronization transitions in dependence on the information transmission delay and coupling strength over scale free neuronal networks with different average degrees and scaling exponents as the underlying model of neuronal dynamics we use the efficient rulkov map with additive noise we show that increasing the coupling strength enhances synchronization monotonously whereas delay plays a more subtle role in particular we found that depending on the inherent oscillation frequency of individual neurons regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases these delay induced synchronization transitions manifest as well expressed minima in the measure for spatial synchrony appearing at every multiple of the oscillation frequency larger coupling strengths or average degrees can broaden the region of regular propagating fronts by a given information transmission delay and further improve synchronization these results are robust against variations in system size intensity of additive noise and the scaling exponent of the underlying scale free topology we argue that fine tuned information transmission delays are vital for assuring optimally synchronized excitatory fronts on complex neuronal networks and indeed they should be seen as important as the coupling strength or the overall density of interneuronal connections we finally discuss some biological implications of the presented results

stability of impulsive functional differential equations abstract in this paper the stability of impulsive functional differential equations in which the state variables on the impulses are related to the time delay is studied by using lyapunov functions and razumikhin techniques some criteria of stability asymptotic stability and practical stability for impulsive functional differential equations in which the state variables on the impulses are related to the time delay are provided some examples are also presented to illustrate the efficiency of the results obtained

stationary lqg control of singular systems the stationary linear quadratic gaussian control problem is formulated and solved for single input single output singular systems the control system is required to be internally proper and stable in order to avoid both impulsive and unstable exponential behavior the set of all controllers resulting in such a control system is specified in parametric form all controllers that yield finite cost are identified once again in parametric form within this set necessary and sufficient conditions are then established for an optimal controller to exist all optimal controllers are shown to possess the same transfer function the problem is analyzed in the complex domain the transfer functions are expressed as quotients of proper strict hurwitz rational functions by means of this maneuver the powerful tools of algebra are made available the synthesis of the optimal controller is reduced to the solution of two linear diophantine equations whose coefficients are obtained by spectral factorization

a closed formula for the determination of the impulsive solutions of linear homogeneous matrix differential equations a closed formula is given which allows the determination of the impulsive solutions of linear homogeneous matrix differential equations lhmde directly in terms of finite and infinite spectral data of the associated polynomial matrix specifically the notions of finite and infinite jordan pairs for a general polynomial matrix are defined and it is pointed out the strong relationship among them and the impulsive solutions of lhmde

duration of transient oscillations in ring networks of unidirectionally coupled neurons abstract properties of the duration of long lasting transient oscillations in ring networks of unidirectionally coupled sigmoidal neurons are derived with a kinematical model of traveling waves in the network the duration of the transient oscillations occurring from random initial conditions increases exponentially as the number of neurons the distribution of the duration is approximated by a power law function when the number of neurons is large further transient oscillations which oscillate about one thousand cycles before ceasing are observed in a network of forty neurons in circuit experiments though the duration decreases owing to random biases

robust stabilization of discrete generalized systems the robust stabilization problem for generalized discrete time systems described by polynomial or improper transfer function matrices subject to perturbations acting on the normalized coprime factors is solved the maximum achievable stability margin and the robust stabilizing controller are given in terms of realizations and solutions to appropriate riccati equations

delay induced spatial correlations in one dimensional stochastic networks with nearest neighbor coupling we consider a network of deterministic and stochastic locally coupled oscillators with positive or negative dissipation and local time delayed feedback i for a deterministic system we study propagation of waves through the network we show that time delay leads to a coexistence of several neutral modes with different wave numbers and group velocities which we compute analytically ii for noisy system we study the response of the network to external random forcing correlated in space and uncorrelated in time below the threshold of spatial instability noise induces spatiotemporal fluctuations which can be characterized by the structure function we give an analytical expression for the structure function and demonstrate the effect of the time delay and of the correlation length of noise on the wave number of the most excited mode

periodic patterns in a ring of delay coupled oscillators we describe the appearance and stability of spatiotemporal periodic patterns rotating waves in unidirectional rings of coupled oscillators with delayed couplings we show how delays in the coupling lead to the splitting of each rotating wave into several new ones the appearance of rotating waves is mediated by the hopf bifurcations of the symmetric equilibrium we also conclude that the coupling delays can be effectively replaced by increasing the number of oscillators in the chain the phenomena are shown for the stuart landau oscillators as well as for the coupled fitzhugh nagumo systems modeling an ensemble of spiking neurons interacting via excitatory chemical synapses

phase locked patterns and amplitude death in a ring of delay coupled limit cycle oscillators we study the existence and stability of phase locked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical hopf bifurcation the coupling is limited to nearest neighbors and is linear we analyze a model set of discrete dynamical equations using the method of plane waves the resultant dispersion relation which is valid for any arbitrary number of oscillators displays important differences from similar relations obtained from continuum models we discuss the general characteristics of the equilibrium states including their dependencies on various system parameters we next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay time delay is found to expand the range of possible phase locked patterns and to contribute favorably toward their stability the amplitude death state is studied in the parameter space of time delay and coupling strength it is shown that death island regions can exist for any number of oscillators n in the presence of finite time delay a particularly interesting result is that the size of an island is independent of n when n is even but is a decreasing function of n when n is odd

boundary value descriptor systems well posedness reachability and observability in this paper we introduce the class of two point boundary value descriptor systems tpbvds discrete time systems described by possibly linear dynamics and a set of boundary conditions constraining the values of the system state at the two endpoints of the system s interval of definition by introducing a standard form for regular pencils we obtain a new and simple generalized cayley hamilton theorem that simplifies our investigation of well posedness green s function solutions and reachability and observability for tpbvds there are two distinct notions of reachability and observability that one can define for tpbvds associated with processes that propagate inward from and outward toward the boundaries we investigate each of these in detail obtaining among other things far simpler forms for the reachability and observability results than found previously in the literature in addition we describe several methods for the efficient solution of tpbvds one involving recursions from each end of t

observability of singular systems with commensurate time delays and neutral terms this paper deals with the observability problem of a sort of singular systems with commensurate time delays in the trajectories of the system in the time derivative of the trajectories neutral terms and in the output system by using a recursive algorithm sufficient conditions easy testable are proposed for guaranteeing the backward and the algebraic observability of the system this condition implies that the trajectories of the system can be reconstructed by using the actual and past values of the system output

permutation tests for least absolute deviation regression a permutation test based on proportionate reduction in sums of absolute deviations when passing from reduced to full parameter models is developed for testing hypotheses about least absolute deviation lad estimates of conditional medians in linear regression models sampling simulations demonstrated that the permutation test on full model lad estimates had greater relative power 1 06 1 43 than normal theory tests on least squares estimates for asymmetric chi square error distributions and symmetric double exponential error distributions for models with one n 35 and n 63 and three n 63 independent variables relative power was 77 84 for normal error distributions power simulations demonstrated the low sensitivity of lad estimates and permutation tests to outlier contamination and heteroscedasticity that was a linear function of x and increased sensitivity to heteroscedasticity that was a function of x2 for simple regression models three permutation procedures for testing partial models in multiple regression were compared permuting residuals from the reduced model permuting residuals from the full model and permuting the dependent variable permuting residuals from the reduced model maintained nominal error rates best under the null hypothesis for all error distributions and for correlated and uncorrelated independent variables power under the alternative hypotheses for this partial testing procedure was similar to full lad regression model tests four example applications of lad regression are provided

synchronization of self sustained oscillators by common white noise abstract we study the stability of self sustained oscillations under the influence of external noise for small noise amplitude a phase approximation for the langevin dynamics is valid a stationary distribution of the phase is used for an analytic calculation of the maximal lyapunov exponent we demonstrate that for small noise the exponent is negative which corresponds to synchronization of oscillators

solvability controllability and observability of continuous descriptor systems in this paper we investigate the properties of the continuous descriptor system e dot x t ax t bu t 0 leqt leqb where e a and b are complex and possibly singular matrices and u t is a complex function differentiable sufficiently many times the traditional approach to such systems is to separate the state equations from the algebraic equations however such algorithms usually destroy the natural physically based sparsity and structure of the original system therefore we consider descriptor systems in their original form such systems possess numerous properties not shared by the well known state variable systems first we relate classical theories of matrix pencils to the solvability of descriptor systems then we extend the concepts of reachability controllability and observability of state variable systems to descriptor systems and describe the set of reachable states for descriptor systems

inner outer factorization for strictly proper functions with j w axis zeros abstract this paper discussed the inner outer factorization for square real rational matrices which may have zeros on the j axis including infinity a factorization method is given in terms of the descriptor form representation of the rational matrix this method uses the solution of a generalized riccati equation we also propose an efficient computation algorithm for solving the generalized riccati equation

a framework for the solution of the generalized realization problem in this paper we present a novel way of constructing generalized state space representations e a b c d of interpolants matching tangential interpolation data the loewner and shifted loewner matrices are the key tools in this approach

construction of permutation tests abstract a general method for constructing permutation tests for various experimental designs follows from invariance and sufficiency in this framework randomization or rerandomization tests are just special cases of permutation tests the methodology extends the applicability of permutation tests an example demonstrates a test for an interaction effect in a factorial experiment a problem thought to be unapproachable by permutation or randomization methods tests are constructed as follows the modeling of block and treatment effects closely parallels classical analysis of variance anova the anova assumptions of iid normal random errors are replaced however by the much weaker assumption of exchangeability of subsets of random errors distributional dependences on the unknown nuisance parameters for blocks covariates and untested treatments and on the unknown error distribution are eliminated by invariance and sufficiency respectively initial reduction of the data by invariance appears to ex

analysis of descriptor systems using numerical algorithms in this paper we analyze numerical methods for the solution of the large scale dynamical system e dot y t ay t g t y t 0 y 0 where e and a are matrices possibly singular systems of this type have been referred to as implicit systems and more recently as descriptor systems since they arise from formulating system equations in physical variables special cases of such systems are algebraic differential systems we discuss the numerical advantages of this formulation and identify a class of numerical integration algorithms which have accuracy and stability properties appropriate to descriptor systems and which preserve structure detect nonsolvable systems resolve initial value consistency problems and are applicable to stiff descriptor systems we also present an algorithm for the control of the local truncation error on only the state variables

a further interpretation of inconsistent initial conditions in descriptor variable systems initial conditions for systems of the form e dot x ax bu are discussed a new interpretation of inconsistent initial conditions is proposed and shown to apply to a larger class of problems than that which has been so far described in the literature

robustness of regional pole placement for uncertain continuous time implicit systems in this note under assumptions that the nominal linear implicit system is regular impulse free with all its generalized eigenvalues lying inside some specified regions sufficient conditions are proposed to preserve the assumed properties when structured perturbations are added into the nominal system explicit bounds on perturbations with different structures are given in terms of the spectral radii of some nonnegative matrices

descriptor variable systems and optimal state regulation linear systems of the form e dot x ax bu with e singular are treated it is desired to find a control which drives the system asymptotically to the origin minimizing a quadratic cost functional no restrictions are placed on initial conditions the cost associated with the impulsive behavior of the system is examined as well as existence and uniqueness of the optimal control through a sequence of coordinate transformations it is proven that the optimal control can be found by solving a reduced order riccati equation

state feedback and transfer matrix in singular systems abstract the influence of state feedback on the transfer matrix in singular systems is considered we first discuss the problem for siso systems then by utilizing the time scale transformation the same problem is solved for mimo systems we also consider realizations of the feedback control strategies given here it is pointed out that the singular system is distinguished from the normal one by an important feature we can design a pure input prediction system for it finally the results are applied to the model matching problem

multistability in spiking neuron models of delayed recurrent inhibitory loops we consider the effect of the effective timing of a delayed feedback on the excitatory neuron in a recurrent inhibitory loop when biological realities of firing and absolute refractory period are incorporated into a phenomenological spiking linear or quadratic integrate and fire neuron model we show that such models are capable of generating a large number of asymptotically stable periodic solutions with predictable patterns of oscillations we observe that the number of fixed points of the so called phase resetting map coincides with the number of distinct periods of all stable periodic solutions rather than the number of stable patterns we demonstrate how configurational information corresponding to these distinct periods can be explored to calculate and predict the number of stable patterns

stochastic switching in delay coupled oscillators a delay is known to induce multistability in periodic systems under influence of noise coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns for coupled phase oscillators we reduce the delay system to a nondelayed langevin equation which allows us to analytically compute the distribution of frequencies and their corresponding residence times the number of stable periodic orbits scales with the roundtrip delay time and coupling strength but the noisy system visits only a fraction of the orbits which scales with the square root of the delay time and is independent of the coupling strength in contrast the residence time in the different orbits is mainly determined by the coupling strength and the number of oscillators and only weakly dependent on the coupling delay finally we investigate the effect of a detuning between the oscillators we demonstrate the generality of our results with delay coupled fitzhugh nagumo oscillators

controllability and observability of second order descriptor systems we analyze controllability and observability conditions for second order descriptor systems and show how the classical conditions for first order systems can be generalized to this case we show that performing a classical transformation to first order form may destroy some controllability and observability properties as an example we demonstrate that the loss of impulse controllability in constrained multibody systems is due to the representation as a first order system to avoid this problem we will derive a canonical form and new first order formulations that do not destroy the controllability and observability properties

fundamental properties of the manifold of singular and regular linear systems abstract we construct a real analytic manifold l of systems of the form e x ax bu y cx and show that l is the completion with respect to solutions of the set of regular state space systems i e those systems with nonsingular e other geometric and analytic properties of l are established including genericity of the regular systems

waves and patterns in ring lattices with delays abstract we investigate the existence and the stability of waves and phase locked states in rings of coupled oscillators with delayed interactions using center manifold reduction and the normal form method we reduce the equation governing the dynamics of the whole network to an amplitude phase model i e a set of coupled ordinary differential equations describing the evolution of both the amplitudes and the phases of the oscillators then we prove the existence of traveling waves in phase and anti phase locked oscillations in both one dimensional and two dimensional lattices the influence of the interaction strength and the number of oscillators is investigated and the possible coexistence of waves and phase locked oscillations is shown

on minimal order inverses of discrete time descriptor systems in this paper linear discrete time control systems of the form e k x k 1 a k x k b k u k y k c k x k d k u k are considered where e k and a k are not necessarily square matrices the problem to be solved is this find a system of the form e k v k 1 k v k bcirc k k u k kvk dcirc k k where k is a partitioned column vector whose blocks are linear combinations of some of the output vectors of the original system and which possesses either or both of the following properties i if the outputs of the original system are known then the output equation of the second system uniquely specifies the same inputs that generated the known outputs of the original system ii if the output vectors of the original system are desired outputs then the equation uk kvk dcirc k k yields one or more sequences of inputs for the original system that can generate the desired outputs we shall furthermore seek the system which among all systems having property i or ii or both has the sm

on the solutions of linear differential equations with singular coefficients abstract equations of the form e ax u with e and a square matrices and e singular are considered the controversy that exists in the literature concerning the solutions of such equations is investigated solutions are arrived at through an application of singular perturbation theory

time domain solution to descriptor variable systems the time domain solution to the fast subsystem of the descriptor variable system of the form ex spl dot ax bu with e singular is given by laplace inverse transformation a new and significant feature of the solution is that it contains impulse terms excited by the values of sufficiently smooth input u and its derivatives at the initial time point based on the solution the notions of consistent initial conditions classical solutions and impulse free solutions are discussed perfectly the impulse controllability is discussed also which admits the same interpretation as the controllability at infinity in frequency domain

convergence in the boundary layer for singularly perturbed equations a singularly perturbed linear finite dimensional ordinary differential equation is considered on the half line 0 the reduced system is assumed to have a unique solution in the sense of distributions it is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense and the order of the limiting distribution is computed an application to the optimal linear quadratic regulator with cheap control is described

threshold free cluster enhancement addressing problems of smoothing threshold dependence and localisation in cluster inference many image enhancement and thresholding techniques make use of spatial neighbourhood information to boost belief in extended areas of signal the most common such approach in neuroimaging is cluster based thresholding which is often more sensitive than voxel wise thresholding however a limitation is the need to define the initial cluster forming threshold this threshold is arbitrary and yet its exact choice can have a large impact on the results particularly at the lower e g t z 4 cluster forming thresholds frequently used furthermore the amount of spatial pre smoothing is also arbitrary given that the expected signal extent is very rarely known in advance of the analysis in the light of such problems we propose a new method which attempts to keep the sensitivity benefits of cluster based thresholding and indeed the general concept of clusters of signal while avoiding or at least minimising these problems the method takes a raw statistic image and produces an output image in which the voxel wise values represent the amount of cluster like local spatial support the method is thus referred to as threshold free cluster enhancement tfce we present the tfce approach and discuss in detail roc based optimisation and comparisons with cluster based and voxel based thresholding we find that tfce gives generally better sensitivity than other methods over a wide range of test signal shapes and snr values we also show an example on a real imaging dataset suggesting that tfce does indeed provide not just improved sensitivity but richer and more interpretable output than cluster based thresholding

validating cluster size inference random field and permutation methods cluster size tests used in analyses of brain images can have more sensitivity compared to intensity based tests the random field rf theory has been widely used in implementation of such tests however the behavior of such tests is not well understood especially when the rf assumptions are in doubt in this paper we carried out a simulation study of cluster size tests under varying smoothness thresholds and degrees of freedom comparing rf performance to that of the permutation test which is known to be exact for gaussian images we find that the rf methods are generally conservative especially for low smoothness and low threshold for t images the rf tests are found to be conservative at lower thresholds and do not perform well unless the threshold is high and images are sufficiently smooth the permutation test performs well for any settings though the discreteness in cluster size must be accounted for we make specific recommendations on when permutation tests are to be preferred to rf tests

synchronization of coupled time delay systems analytical estimations the synchronization threshold of coupled time delay chaotic systems is estimated by two different analytical approaches one of them is based on the krasovskii lyapunov theory that represents an extension of the second lyapunov method for delay differential equations another approach uses a perturbation theory of large delay time the analytical expression relating synchronization threshold to the maximal lyapunov exponent of uncoupled driving and response subsystems is derived the analytical results are compared with the numerical simulations for two coupled mackey glass systems

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

generalized synchronization of chaos in directionally coupled chaotic systems synchronization of chaotic systems is frequently taken to mean actual equality of the variables of the coupled systems as they evolve in time we explore a generalization of this condition which equates dynamical variables from one subsystem with a function of the variables of another subsystem this means that synchronization implies a collapse of the overall evolution onto a subspace of the system attractor in full space we explore this idea in systems where a response system bold y ital t is driven with the output of a driving system bold x ital t but there is no feedback to the driver we lose generality but gain tractability with this restriction to investigate the existence of the synchronization condition bold y ital t phi bold x ital t we introduce the idea of mutual false nearest neighbors to determine when closeness in response space implies closeness in driving space the synchronization condition also implies that the response dynamics is determined by the drive alone and we provide tests for this as well examples are drawn from computer simulations on various known cases of synchronization and on data from nonlinear electrical circuits determining the presence of generalized synchronization will be quite important when one has only scalarmore observations from the drive and from the response systems since the use of time delay or other embedding methods will produce imperfect coordinates in which strict equality of the synchronized variables is unlikely to transpire less

the optimal regulation of generalized state space systems with quadratic cost abstract in this paper the optimal feedback control for regulating generalized state space systems with quadratic cost is presented by using an algebraic method and the weighting matrix q in the cost is allowed to be positive semi definite

delay and periodicity systems with time delay play an important role in modeling of many physical and biological processes in this paper we describe generic properties of systems with time delay which are related to the appearance and stability of periodic solutions in particular we show that delay systems generically have families of periodic solutions which are reappearing for infinitely many delay times as delay increases the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions we also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers we show that the spectrum of multipliers can be split into two parts pseudocontinuous and strongly unstable the pseudocontinuous part of the spectrum mediates destabilization of periodic solutions

an algorithm for normalizing variable control systems in this paper an algorithm for obtaining feedbacks to normalize variable linear systems is presented for that conditions to obtain an invariant singular system from a variable system are established the relation between them is used to construct feedbacks in order to remove the impulses that disturb the behaviour of the singular system in addition some examples clarify the obtained results

synchronized states in a ring of mutually coupled self sustained electrical oscillators we investigate in this paper different states of synchronization in a ring of mutually coupled self sustained electrical oscillators the good coupling parameters leading to complete and partial synchronization or disordered states are calculated using the properties of the variational equations of stability a stability map showing domains of synchronization to an external excitation locally injected in the ring is also obtained in both cases the numerical simulation validates and complements the results of the analytical investigation

controllability and observability at infinity of multivariable linear second order models in this note we give in the spirit of 4 numerically attractive tests of controllability and observability of linear multivariable second order systems in which the leading matrix is singular

state feedback impulse elimination for singular systems over a hermite domain we reduce the problem of impulse elimination via state feedback in singular differential equations to algebra our results are developed for systems over an arbitrary hermite domain we show that the established theories for the time invariant and the real analytic time varying settings can be unified in this way besides the constant and real analytic functions several other function rings are considered our algebraic theory is applied to these cases providing solutions to the impulse elimination problem for classes of systems not previously studied in particular our work allows the restriction of the feedback matrix to certain function rings

multiple scale analysis of delayed dynamical systems abstract the model equations of a semiconductor laser with delayed feeback are studied as a prototype of general delayed systems in the case of long delay thermodynamic limit it is shown that its behaviour in the vicinity of the hopf bifurcation can be described by suitable amplitude equations the derivation of the final model follows naturally from the space time representation of the evolution and by the corresponding re formulation of the linear stability problem regions characterized by both direct and inverse hopf bifurcations are found and in particular parameter values are identified for which a chaotic evolution is expected

information storage loop motifs and clustered structure in complex networks we use a standard discrete time linear gaussian model to analyze the information storage capability of individual nodes in complex networks given the network structure and link weights in particular we investigate the role of two and three node motifs in contributing to local information storage we show analytically that directed feedback and feedforward loop motifs are the dominant contributors to information storage capability with their weighted motif counts locally positively correlated to storage capability we also reveal the direct local relationship between clustering coefficient s and information storage these results explain the dynamical importance of clustered structure and offer an explanation for the prevalence of these motifs in biological and artificial networks

the algorithm for computing nonmonic second order multivariable systems abstract an efficient method for computing impulse response matrices of nonmonic multivariable second order systems is proposed a procedure has been developed which uses some properties of regular matrix polynomials p s s 2 a 2 sa 1 a 0 with a 2 identically singular an algorithm suitable for computer use is established and its applications can be effectively controlled via the newly introduced special graphical scheme it produces simultaneously the adjoint and determinant of the matrix polynomial p s and avoids the inversion of any matrix moreover all computations can be performed on constant matrices and coefficients only it is shown that substantial economy may be achieved in computation time and storage when solving large order problems characteristic of many physical plants and engineering structures

h infinity kalman estimation for rectangular descriptor systems with unknown inputs this note considers h filtering and prediction for rectangular descriptor systems with unknown inputs that affect both the system and the output an optimal h descriptor kalman estimator hdke which can simultaneously solve the h filtering and prediction problems for rectangular descriptor systems with unknown inputs is developed based on the maximum likelihood descriptor kalman filtering method the hdke serves as a unified solution to solve h and kalman filtering for descriptor systems and standard systems with or without unknown inputs to reduce the computational complexity problem some efficient alternatives to the developed hdke are further proposed the relationship between the hdke and the existing literature results is also addressed an illustrative example is given to show the usefulness of the proposed results

destabilization patterns in chains of coupled oscillators we describe the mechanism of destabilization in a chain of identical coupled oscillators along with the transition from stationary to oscillatory behavior of the single oscillator the network undergoes a complicated bifurcation scenario including the coexistence of multiple periodic orbits with different frequencies spatial patterns and modulation instabilities this scenario which is similar to the well known eckhaus scenario in spatially extended systems occurs here also in the case of purely convective unidirectional coupling and hence it cannot be explained as a simple discretization of its spatially continuous counterpart although the number of coexisting periodic orbits grows with the number of oscillators we are able to treat this problem independently of the actual size of the network by investigating the limiting equations for the related spectral problems

a geometric approach to eigenstructure assignment for singular systems moore s well known result on the feedback assignment of eigenstructure in linear state space systems 5 was generalized to descriptor systems in 9 in this note we make some useful extensions to fill out the theory to begin with we do not assume controllability of the plant it is shown that the maximum number of finite closed loop eigenvalues is equal to dim el where l is the supremal a e r b invariant subspace in order to relate the possible closed loop structure to the open loop plant structure we define a set of indexes for descriptor systems which are in many respects similar to the controllability indexes of state space systems in terms of these controllability indexes we give a systematic approach to selecting the closed loop eigenvectors a major contribution of this note is the fact that it is geometric in nature and hence avoids any decomposition of the system matrices into a special form e g weierstrass form 1 the geometric setting introduced here should constitute a basis for further research in generalizing the well known results in geometric system theory disturbance decoupling input output decoupling etc to singular systems

observers for singular systems the following three major aspects of the design of observers for linear time invariant singular systems are resolved the necessary and sufficient conditions for the problem to have a solution the order of the minimal observer and the properties of the closed loop system separation principle an algorithm is presented for the construction of the minimal order observer

embedding the dynamics of a single delay system into a feed forward ring we investigate the relation between the dynamics of a single oscillator with delayed self feedback and a feed forward ring of such oscillators where each unit is coupled to its next neighbor in the same way as in the self feedback case we show that periodic solutions of the delayed oscillator give rise to families of rotating waves with different wave numbers in the corresponding ring in particular if for the single oscillator the periodic solution is resonant to the delay it can be embedded into a ring with instantaneous couplings we discover several cases where the stability of a periodic solution for the single unit can be related to the stability of the corresponding rotating wave in the ring as a specific example we demonstrate how the complex bifurcation scenario of simultaneously emerging multijittering solutions can be transferred from a single oscillator with delayed pulse feedback to multijittering rotating waves in a sufficiently large ring of oscillators with instantaneous pulse coupling finally we present an experimental realization of this dynamical phenomenon in a system of coupled electronic circuits of fitzhugh nagumo type

reachability and controllability of discrete time descriptor systems the causal and non causal reachability grammians are used in order to define the reachability subspace of discrete time systems controllability of the discrete time regular descriptor system by means of the forward solution is also examined and new criteria for testing reachability controllability from the origin and controllability to the origin in the forward sense are proved

emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback interaction via pulses is common in many natural systems especially neuronal in this article we study one of the simplest possible systems with pulse interaction a phase oscillator with delayed pulsatile feedback when the oscillator reaches a specific state it emits a pulse which returns after propagating through a delay line the impact of an incoming pulse is described by the oscillator s phase reset curve prc in such a system we discover an unexpected phenomenon for a sufficiently steep slope of the prc a periodic regular spiking solution bifurcates with several multipliers crossing the unit circle at the same parameter value the number of such critical multipliers increases linearly with the delay and thus may be arbitrary large this bifurcation is accompanied by the emergence of numerous jittering regimes with nonequal interspike intervals isis each of these regimes corresponds to a periodic solution of the system with a period roughly proportional to the delay the number of different jittering solutions emerging at the bifurcation point increases exponentially with the delay we describe the combinatorial mechanism that underlies the emergence of such a variety of solutions in particular we show how a periodic solution exhibiting several distinct isis can imply the existence of multiple other solutions obtained by rearranging of these isis we show that the theoretical results for phase oscillators accurately predict the behavior of an experimentally implemented electronic oscillator with pulsatile feedback

observers for discrete singular systems the author considers the design of observers for the discrete singular system ex k 1 ax k bu k y k cx k placing special emphasis on the problems of state reconstruction and minimal time state reconstruction it is shown that for a singular system finite poles can be moved to infinity by state feedback and the state can be reconstructed by causal observers

a geometric approach to proportional plus derivative feedback using quotient and partitioned subspaces abstract in this paper a new characterization of invariant subspaces is presented using the notions of partitioned and quotient subspaces this classification is based on a feedback approach that exhibits the importance of these subspaces for the problem of proportional plus derivative feedback it also provides the ability to decompose the closed loop system into two subsystems that completely characterize the closed loop behavior a feedback free formulation is also considered which opens new horizons for the problem of general semistate feedback by utilizing nonsquare pencils for spectrum assignability the importance of this technique arises from the fact that we deal with reduced order pencils therefore the computational methods are more stable in order to accomplish this we use two generalized lyapunov equations and exploit the generalized hessenberg form

interaction of chaotic rotating waves in coupled rings of chaotic cells abstract the interaction of two chaotic rotating waves of the type recently reported by matias et al europhys lett 37 1997 379 is studied experimentally with arrays of non linear electronic circuits arranged in ring geometries unidirectional coupling is assumed for the cell to cell coupling within the same ring but between rings cells are coupled diffusively depending on the relative sense of driving competition between a rotating chaotic wave and a global synchronized state has been observed the results are rationalized by means of a linear stability analysis around the uniform synchronized behavior where the circulant symmetry of the system allows to express the problem as a superposition of a series of fourier modes

synchronization of oscillators through time shifted common inputs shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems however due to finite signal transmission speeds and differences in the distance to the source time shifts between otherwise common inputs are unavoidable since common inputs can be a source of correlation between the elements of multi unit dynamical systems regardless of whether these elements are directly connected with one another or not it is of importance to understand their impact on synchronization as a canonical model that is representative for a variety of different dynamical systems we study limit cycle oscillators that are driven by stochastic time shifted common inputs we show that if the oscillators are coupled time shifts in stochastic common inputs do not simply shift the distribution of the phase differences but rather the distribution actually changes as a result the best synchronization is therefore achieved at a precise intermediate value of the time shift which is due to a resonance like effect with the most probable phase difference that is determined by the deterministic dynamics

symmetry models and hypotheses for structured data layouts on peut utiliser des proprietes de symetrie pour deriver des tests valides d hypotheses nulles et pour construire des modeles statistiques appropries pour les donnees on developpe des idees generales et on les illustre dans le contexte d une classification a deux criteres