metriques de carnot cartheodory et quasiisometries des espaces symetriques de rang un we exhibit a rigidity property of the simple groups sp n 1 and f7 20 which implies mostow rigidity this property does not extend to o n 1 and u n 1 the proof relies on quasiconformal theory applied in the cr setting extensions are given to a class of solvable lie groups as a byproduct a result on quasiisometries of infinite nilpotent groups is obtained dans cet article on etablit une propriete de rigidite des groupes simples de rang un sp n 1 n 2 2 et fqui entraine la rigidite de mostow 1 theoreme toute quasiisornwtrie de 1 espace hyperbolique quaternionien hhn n 2 resp du plan hyperbolique de cayley cah2 est d distance bornee d une isometrie i e differe d une isomnetrie par une application qui diplace les points d une distance bornee une application f entre espaces metriques est une quasiisometrie s il existe des constantes l et c telles que l image de f soit c dense et que pour tous x y c d x y d fx fy ld x y c l une quasiisometrie entre des g et g est une sorte d isomorphisme virtuel dans la categorie topologique en effet cela correspond a une action de g sur un fibre principal c de groupe g sur une base compacte cf ra un isomorphisme entre sous groupes cocompacts covolume fini suffit pour les groupes simples de rang un de groupes de lie s etend en une quasiisometrie des espaces symetriques ou des groupes de lie si celle ci est proche d une isometrie des espaces symetriques resp un isomorphisme des groupes de lie les sous groupes sont conjugues c est la rigidite de mostow m2 la propriete ci dessus ne s etend pas aux groupes o n 1 et u n 1 en effet paragraphe 11 7 ceux ci ont beaucoup de quasiisometries au moins this content downloaded from 207 46 13 92 on sun 20 nov 2016 04 26 46 utc all use subject to http about jstor org terms

properties of recoverable region and semi global stabilization in recoverable region for linear systems subject to constraints this paper investigates linear systems subject to input and state constraints it is shown that the recoverable region which is the largest domain of attraction that is theoretically achievable can be semiglobally stabilized by continuous nonlinear feedbacks while satisfying the constraints moreover when trying to compute the recoverable region a reduction technique shows that we only need to compute the recoverable region for a system of lower dimension which generally leads to a considerable simplification in the computational effort

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

network amplification of local fluctuations causes high spike rate variability fractal firing patterns and oscillatory local field potentials we investigate a model for neural activity in a two dimensional sheet of leaky integrate and fire neurons with feedback connectivity consisting of local excitation and surround inhibition each neuron receives stochastic input from an external source independent in space and time as recently suggested by softky and koch 1992 1993 independent stochastic input alone cannot explain the high interspike interval variability exhibited by cortical neurons in behaving monkeys we show that high variability can be obtained due to the amplification of correlated fluctuations in a recurrent network furthermore the cross correlation functions have a dual structure with a sharp peak on top of a much broader hill this is due to the inhibitory and excitatory feedback connections which cause hotspots of neural activity to form within the network these localized patterns of excitation appear as clusters or stripes that coalesce disintegrate or fluctuate in size while simultaneously moving in a random walk constrained by the interaction with other clusters the synaptic current impinging upon a single neuron shows large fluctuations at many time scales leading to a large coefficient of variation cv for the interspike interval statistics the power spectrum associated with single units shows a 1 f decay for small frequencies and is flat at higher frequencies while the power spectrum of the spiking activity averaged over many cells equivalent to the local field potential shows no 1 f decay but a prominent peak around 40 hz in agreement with data recorded from cat and monkey cortex gray et al 1990 eckhorn et al 1993 firing rates exhibit self similarity between 20 and 800 msec resulting in 1 f like noise consistent with the fractal nature of neural spike trains teich 1992

semi global stabilization of linear systems subject to output saturation abstract it is established that a siso linear stabilizable and detectable system subject to output saturation can be semi globally stabilized by linear output feedback if all its invariant zeros are in the closed left half plane no matter where the open loop poles are this result complements a recent result that such systems can always be globally stabilized by discontinuous nonlinear feedback laws and can be viewed as dual to a well known result a linear stabilizable and detectable system subject to input saturation can be semi globally stabilized by linear output feedback if all its poles are in the open left half plane no matter where the invariant zeros are

global stabilization with almost disturbance decoupling of a class of uncertain non linear systems in this paper we study the global stabilization of a class of non linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy the class of non linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order although the plants considered are non linear the compensator developed here is linear our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so called matching conditions and or by treating a family of plants for which a single controller simultaneously globally exponentially stabilizes all the plants in while achieving almost disturbance decoupling of the output

estimation of states and parameters for linear systems with nonlinearly parameterized perturbations we consider systems that can be described by a linear part with a nonlinear perturbation where the perturbation is parameterized by a vector of unknown constant parameters under a set of technical assumptions about the perturbation and its relationship to the outputs we present a modular design technique for estimating the system states and the unknown parameters the design consists of a high gain observer that estimates the states of the system together with the full perturbation and a parameter estimator constructed by the designer to invert a nonlinear equation we illustrate the technique on a simulated dc motor with friction

a class of initials dependent dynamical systems the dynamics of initial dependent system is investigated the potential mechanism for initial dependent property is discussed general scheme is proposed to design initial dependent dynamical system this scheme can be used for chaos control by initial setting with memristor nonlinear term is critical for emergence of chaos in autonomous dynamical systems the sampled time series in chaotic system are dependent on the initial selection of variables while the attractors are invariant for fixed parameters in this paper the dynamical behavior of a class of dynamical system is investigated at fixed parameter region it is found that the state selection is dependent on the initials and the potential mechanism is discussed it is confirmed that the system can be switched between stable state periodical state and even chaotic state by selecting appropriate initials even the parameters are fixed we think that nonlinear cross terms with higher order could account for the emergence of this behavior it indicates that initial selection and resetting can be also effective to control some chaotic systems and these chaotic systems could enhance security for possible secure communication because the chaotic attractor depends on the parameter and initials selection as well in the case of secure communication the reconstruction of phase space becomes more difficult because the attractors are changed arbitrarily thus the safety for secure keys is enhanced for chaos control when the initials are reset the controller can be removed and the system can develop to step into the desired target by itself

on the numerical computation of a structural decomposition in systems and control in this paper we develop a new numerical method for a special coordinate basis of a linear time invariant system such a special coordinate basis is essentially a structural decomposition which explicitly displays the finite and infinite zero structures as well as the invertibility structures of the given system the technique is playing important roles in numerous topics in system and control theory such as robust control h sub spl infin and h sub 2 optimal control almost disturbance decoupling and zero placement of linear systems just to name a few our method consists of three steps reduction by orthogonal transformations reduction by generalized sylvester equations and extraction of infinite zero structure the performance of our method is illustrated by some numerical examples

simultaneous finite and infinite zero assignments of linear systems abstract a simultaneous finite and infinite zero assignment problem via sensor selection for linear multivariable systems is proposed by sensor selection we mean an appropriate choice of the output matrix c here by utilizing the well known burnovsky canonical form for a linear system characterized by the matrix pair a b we obtain an explicit construction algorithm that generates a non empty set c of output matrices such that for any member c of this set the corresponding system characterized by the triple a b c has the prescribed finite and infinite zero structures two examples are also given to illustrate our results

construction and parameterization of all static and dynamic h 2 optimal state feedback solutions for discrete time systems abstract this paper considers an h 2 optimization problem via state feedback for discrete time systems the class of problems dealt with here has a left invertible transfer matrix function from the control input to the controlled output the paper constructs and parameterizes all the static and dynamic h 2 optimal state feedback solutions moreover all the eigenvalues of an optimal closed loop system are characterized all optimal closed loop systems share a set of eigenvalues which are termed the optimal fixed modes every h 2 optimal controller must assign among the closed loop eigenvalues the set of optimal fixed modes this set of optimal fixed modes includes a set of optimal fixed decoupling zeros which shows the minimum absolutely necessary number and locations of pole zero cancellations present in any h 2 optimal design most of the results presented here are analogous to but not quite the same as those for continuous time systems in fact there are some fundamental differences between the continuous and discrete time systems reflecting mainly the inherent nature and characteristics of these systems

disturbance decoupling for linear time invariant systems a matrix pencil approach we give a new systematic analysis of disturbance decoupling problems for standard linear time invariant systems based on the theory of matrix pencils this approach is based on the computation of condensed forms under orthogonal equivalence transformations from these forms which can be computed in a numerically stable way we obtain new necessary and sufficient conditions that are numerically verifiable and furthermore we immediately obtain numerically stable algorithms to compute the desired compensators we present a numerical example that demonstrates the properties of the new approach

population rate codes carried by mean fluctuation and synchrony of neuronal firings abstract a population of firing neurons is expected to carry information not only by the mean firing rate but also by fluctuation and synchrony among neurons in order to examine this possibility we have studied responses of neuronal ensembles to three kinds of inputs mean fluctuation and synchrony driven inputs the generalized rate code model including additive and multiplicative noise h hasegawa phys rev e 75 2007 051904 has been studied by direct simulations dss and the augmented moment method amm in which equations of motion for mean firing rate fluctuation and synchrony are derived results calculated by the amm are in good agreement with those by dss the independent component analysis ica of our results has shown that mean firing rate fluctuation or variability and synchrony may carry independent information in the population rate code model the input output relation of mean firing rates is shown to have higher sensitivity for larger multiplicative noise as recently observed in prefrontal cortex a comparison is made between results obtained by the integrate and fire if model and our rate code model

a note on the calculation and placing of finite zeros the finite zeros of a transfer function matrix are defined as the finite points on the complex plane to which the multivariable root loci converge as the loop gain increases infinitely in this paper an example is given where the finite zeros arc not obtained by the algorithm of kouvaritakis and macfarlane 1976 then a modification is suggested for the theorem which states a necessary and sufficient condition that the finite zeros are placed at stipulated n m points

a non iterative method for computing the infimum in h optimization this paper presents a simple and non iterative procedure for the computation of the exact value of the infimum in the singular h optimization problem and is an extension of our earlier work the problem formulation is general and does not place any restriction on the direct feedthrough terms between the control input and the controlled output variables and between the disturbance input and the measurement output variables our method is applicable to a class of singular h optimization problems for which the transfer functions from the control input to the controlled output and from the disturbance input to the measurement output have no invariant zeros on the jw axis and also satisfy certain geometric conditions the computation of the infimum in our method involves solving two well defined riccati and two lyapunov equations

assignment of complete structural properties of linear systems via sensor selection for x ax bu the problem of structural assignment via sensor selection is to find an output equation y cx du such that the resulting system a b c d has the pre specified structural properties such as the finite and infinite zero structures as well as the invertibility properties in this paper we establish a set of necessary and sufficient conditions under which a complete set of system structural properties can be assigned and an explicit algorithm for constructing the required matrix pair c d

squaring down lti systems a geometric approach in this paper the problem of reducing a given lti system into a left or right invertible one is addressed and solved with the standard tools of the geometric control theory first it will be shown how an lti system can be turned into a left invertible system thus preserving key system properties like stabilizability phase minimality right invertibility relative degree and infinite zero structure moreover the additional invariant zeros introduced in the left invertible system thus obtained can be arbitrarily assigned in the complex plane by duality the scheme of a right inverter will be derived straightforwardly moreover the squaring down problem will be addressed in fact when the left and right reduction procedures are applied together a system with an unequal number of inputs and outputs is turned into a square and invertible system furthermore as an example it will be shown how these techniques may be employed to weaken the standard assumption of left invertibility of the plant in many optimization problems

semi global stabilization of partially linear composite systems via feedback of the state of the linear part abstract we consider the problem of semi global stabilization of a class of partially linear composite systems we show by explicit construction of the control laws that a cascade of linear stabilizable and nonlinear asymptotically stable subsystems is semi globally stabilizable by a dynamic feedback of the state of the linear subsystem if a the linear subsystem is right invertible and has all its invariant zeros in the closed left half s plane and b the only linear variables entering the nonlinear subsystem are the output of the linear subsystem our work generalizes previous results by c i byrnes and a isidori 1991 h j sussmann and p v kokotovic 1991 and a r teel 1992

a singular perturbation canonical form of invertible systems determination of multivariate root loci a new canonical form of multivariable invertible systems is given this form is suitable for the singular perturbation analysis of such singular problems as multi variable asymptotic root loci under high gain feedback cheap control state variable estimation with weak measurement noise etc appropriate selection and decomposition of state variables into slow and fast changing groups is a key feature that loads to well defined singular perturbation models the selection of state variables is accomplished without explicitly calculating any eigenvalues of the given system but by knowing the direct relationship of the output and its differential coefficients with the input the use of the canonical form to characterize the multivariable root loci under high gain feedback is demonstrated

spike output jitter mean firing time and coefficient of variation to understand how a single neurone processes information it is critical to examine the relationship between input and output marsalek koch and maunsell s study focused on output jitter standard deviation of output interpike interval found that for the integrate and fire if whereas an input distribution with a more slowly decreasing tail induces divergence of output jitter exact formulae for mean firing time are also obtained which enable us to estimate the coefficient of variation the i f model with leakage is also briefly considered

special coordinate basis for multivariable linear systems finite and infinite zero structure squaring down and decoupling abstract a special coordinate basis for multivariable linear systems is introduced here several fundamental properties of linear systems regarding controllability stabiliza bility observability detectability invariant zeros decoupling zeros infinite zero structure effect of feedback on zero structure squaring down diagonal and triangular decoupling etc can be directly displayed in terms of the special coordinate basis moreover connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established

bistability and resonance in the periodically stimulated hodgkin huxley model with noise we describe general characteristics of the hodgkin huxley neuron s response to a periodic train of short current pulses with gaussian noise the deterministic neuron is bistable for antiresonant frequencies when the stimuli arrive at the resonant frequency the firing rate is a continuous function of the current amplitude i 0 and scales as i 0 i th 1 2 characteristic of a saddle node bifurcation at the threshold i th intervals of continuous irregular response alternate with integer mode locked regions with bistable excitation edge there is an even all multimodal transition between the 2 1 and 3 1 states in the vicinity of the main resonance which is analogous to the odd all transition discovered earlier in the high frequency regime for i 0 i th and small noise the firing rate has a maximum at the resonant frequency for larger noise and subthreshold stimulation the maximum firing rate initially shifts toward lower frequencies then returns to higher frequencies in the limit of large noise the stochastic coherence antiresonance defined as a simultaneous occurrence of i the maximum of the coefficient of variation and ii the minimum of the firing rate vs the noise intensity occurs over a wide range of parameter values including monostable regions results of this work can be verified experimentally

a pre post feedforward compensator design for zero placement we demonstrate the design of a pre post feedforward compensator that places the transmission zeros of a stabilisable and detectable multi input multi output linear time invariant plant at arbitrary locations

responses of a hodgkin huxley neuron to various types of spike train inputs numerical investigations have been made of responses of a hodgkin huxley hh neuron to spike train inputs whose interspike interval isi is modulated by deterministic semi deterministic chaotic and stochastic signals as deterministic one we adopt inputs with the time independent isi and with time dependent isi modulated by sinusoidal signal the rossler and lorentz models are adopted for chaotic modulations of isi stochastic isi inputs with the gamma distribution are employed it is shown that distribution of output isi data depends not only on the mean of isis of spike train inputs but also on their fluctuations the distinction of responses to the three kinds of inputs can be made by return maps of input and output isis but not by their histograms the relation between the variations of input and output isis is shown to be different from that of the integrate and fire if model because of the refractory period in the hh neuron

time scale structure assignment in linear multivariable systems using high gain feedback abstract a systematic design method for assigning a required time scale structure to a given multivariable system is developed the time scale structure assignment is carried out using high gain feedback of either the state or the output the method developed decomposes a given multivariable system into several single input single output subsystems each of which is designed separately a standard method of design for single input single output systems is developed and this forms a building block for the multivariable system design the state feedback design depends only on the stage sequence of the given system while the output feedback design depends only on the set of integers that specifies the order of infinite zeros in this way our design is made robust with respect to certain parameter uncertainties high gain parameter s can be adjusted on line and this provides a tool for the fine tuning of the desired performance characteristics of a control system

dynamical mean field theory of noisy spiking neuron ensembles application to the hodgkin huxley model a dynamical mean field approximation dma previously proposed by the present author h hasegawa phys rev e 67 041903 2003 has been extended to ensembles described by a general noisy spiking neuron model ensembles of n unit neurons each of which is expressed by coupled k dimensional differential equations des are assumed to be subject to spatially correlated white noises the original mathrm kn dimensional stochastic des have been replaced by k k 2 dimensional deterministic des expressed in terms of means and the second order moments of local and global variables the fourth order contributions are taken into account by the gaussian decoupling approximation our dma has been applied to an ensemble of hodgkin huxley hh neurons k 4 for which effects of the noise the coupling strength and the ensemble size on the response to a single spike input have been investigated numerical results calculated by the dma theory are in good agreement with those obtained by direct simulations although the former computation is about a thousand times faster than the latter for a typical hh neuron ensemble with n 100

diffusion entropy approach to complexity for a hodgkin huxley neuron abstract by means of the diffusion entropy method de we analyze the responses of a hodgkin huxley hh neuron to two types of spike train inputs the stimuli can create a living state matter lsm an intermediate condition between dynamics and thermodynamics an anomalous scaling can also be found which is corresponding to the thermodynamic condition the living state matter lsm regresses slowly to the anomalous scaling with almost an exact period the anomalous scaling exponent and the period may be two measures of the dynamical process of a hh neuron under the considered stimuli

estimates on the markov convexity of carnot groups and quantitative nonembeddability abstract we show that every graded nilpotent lie group g of step r equipped with a left invariant metric homogeneous with respect to the dilations induced by the grading this includes all carnot groups with carnot caratheodory metric is markov p convex for all p 2 r we also show that this is sharp whenever g is a carnot group with r 3 a free carnot group or a jet space group such groups are not markov p convex for any p 0 2 r this continues a line of research started by li who proved this sharp result when g is the heisenberg group as corollaries we obtain new estimates on the non bilipschitz embeddability of some finitely generated nilpotent groups into nilpotent lie groups of lower step sharp estimates of this type are known when the domain is the heisenberg group and the target is a uniformly convex banach space or l 1 but not when the target is a nonabelian nilpotent group

direct singular perturbation analysis of high gain and cheap control problems a new and direct approach to the analysis and design of high gain feedback and cheap control problems is developed transformation of such singular problems to singular perturbation models of conventional type early at the onset of analysis or design allows a direct application of the readily available singular perturbation literature the approach permits a simple characterization of a multivariable root loci under a high gain feedback and b asymptotic behavior of optimal closed loop poles state and control trajectories performance index and optimal transfer function as the control cost coefficient in the performance index goes to zero

homogeneous networks of non introspective agents under external disturbances h almost synchronization this paper addresses the problem of h almost synchronization for homogeneous networks of general linear agents subject to external disturbances and under directional communication links agents are presumed to be non introspective i e agents are not aware of their own states or outputs and the only available information for each agent is a network measurement that is a linear combination of relative outputs under a certain set of conditions a family of dynamic protocols is developed such that the impact of disturbances on the synchronization error dynamics expressed in terms of the h norm of the corresponding closed loop transfer function is reduced to any arbitrarily small value

response of autaptic hodgkin huxley neuron with noise to subthreshold sinusoidal signals abstract in this work we investigated the response of a stochastic hodgkin huxley hh neuron with an autapse to subthreshold sinusoidal signals it is found that the autapse not only adjusts the stochastic responses but also improves the detection of subthreshold signals in the case of weak noise the autapse facilitates the response of neuron to the subthreshold sinusoidal signals with a small parameter region in t d e l a y space the increased noise intensity enlarges this parameter region and increases the corresponding response frequency in such range as the autaptic intensity increases however this parameter region shrunks we also observed that there is an optimal range of the delay time of autapse within which the stochastic hh neuron fires action potentials with high frequency the corresponding response spike train for the optimal delay time is nearly a regular sequence with the interspike intervals approximated to the delay time the current results reveal a novel resonance phenomenon facilitated by autapse named autaptic delay induced coherence resonance

on the structure at infinity of linear square decoupled systems the purpose of this note is to demonstrate that a square invertible linear system c a b is decouplable by static state feedback if and only if its infinite zero orders are respectively equal to the infinite zero orders of the subsystems c i a b where c i denotes the i th row of c until now only the necessity of this condition has been established 1

condensed forms of linear control system under output feedback abstract we present two complementary condensed forms of linear control system with output x a x b u x r n u r m y c x y r r under transformation of the state coordinates from them we derive two complementary condensed forms under output feedback as an application of the condensed forms we show that the output feedback control of the linear control systems generically reduces to a matrix completion problem and we provide a partial solution of that problem based on existing methods

strictly observable linear systems a theory of strictly observable linear systems is developed in a module theoretic framework which is consistent with the classical algebraic theory of linear time invariant realization the theory incorporates in a unified framework the reduction of linear systems through precompensation through state feedback and through dynamic output feedback

dynamical response of the hodgkin huxley model in the high input regime the response of the hodgkin huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post synaptic potentials is analyzed in detail the model is examined in its three fundamental dynamical regimes silence bistability and repetitive firing its response is characterized in terms of statistical indicators interspike interval distributions and their first moments as well as of dynamical indicators autocorrelation functions and conditional entropies in the silent regime the coexistence of two different coherence resonances is revealed one occurs at quite low noise and is related to the stimulation of subthreshold oscillations around the rest state the second one at intermediate noise variance is associated with the regularization of the sequence of spikes emitted by the neuron bistability in the low noise limit can be interpreted in terms of jumping processes across barriers activated by stochastic fluctuations in the repetitive firing regime a maximization of incoherence is observed at finite noise variance finally the mechanisms responsible for the different features appearing in the interspike interval distributions like multimodality and exponential tails are clearly identified in the various regimes

convolution profiles for right inversion of multivariable non minimum phase discrete time systems the problem of the non causal inversion of linear multivariable discrete time systems is analyzed in the geometric approach framework and is solved through the computation of convolution profiles which guarantee perfect tracking under the assumption of infinite length preaction and postaction time intervals it is shown how the shape of the convolution profiles is related to both the relative degree and the invariant zeros of the plant a computational setting for the convolution profiles is derived by means of the standard geometric approach tools feasibility constraints are also taken into account a possible implementation scheme based on a finite impulse response system acting on a stabilized control loop is provided

the discrete algebraic riccati equation and linear matrix inequality we study the discrete time algebraic riccati equation in particular we show that even in the most general cases there exists a one one correspondence between solutions of the algebraic riccati equation and deflating subspaces of a matrix pencil we also study the relationship between algebraic riccati equation and the discrete time linear matrix inequality we show that in general only a subset of the set of rank minimizing solutions of the linear matrix inequality correspond to the solutions of the associated algebraic riccati equation and study under what conditions these sets are equal in this process we also derive very weak assumptions under which a riccati equation has a solution

mappings of the finite and the infinite zero structures and invertibility structures of general linear multivariable systems under the bilinear transformation this paper presents a comprehensive picture of the mapping of structural properties associated with general linear multivariable systems under bilinear transformation while the mapping of poles of linear multivariable systems under such a transformation is well known the question of how the structural invariant properties of a given system are mapped remains unanswered this paper addresses this question more specifically we investigate how the finite and infinite zero structures as well as invertibility structures of a general continuous time discrete time linear time invariant multivariable system are mapped to those of its discrete time continuous time counterpart under the bilinear inverse bilinear transformation we demonstrate that the structural invariant indices lists i2 and i3 of morse remain invariant under the bilinear transformation while the structural invariant indices lists i1 and i4 of morse are in general changed

squaring down by static and dynamic compensators given a system which is not necessarily invertible and which has an unequal number of inputs a method of squaring down that is a method of designing pre compensators and postcompensators such that the resulting system has an equal number of inputs and outputs and is invertible is presented the compensators are in general dynamic and have the property that the additional finite zeros induced by them are assignable to the open left half complex plan furthermore the compensators are asymptotically stable and hence do not deteriorate the robustness and performance of an eventual feedback design also the compensator design preserves the stabilizability detectability and minimum phase properties and the infinite zero structure of the original system thus a method of designing nonsquare systems by converting them to square invertible systems is introduced two applications of such a design philosophy 1 diagonal decoupling with state feedback and 2 almost disturbance decoupling with output feedback are pointed out

discrimination with spike times and isi distributions we study the discrimination capability of spike time sequences using the chernoff distance as a metric we assume that spike sequences are generated by renewal processes and study how the chernoff distance depends on the shape of interspike interval isi distribution first we consider a lower bound to the chernoff distance because it has a simple closed form then we consider specific models of isi distributions such as the gamma inverse gaussian ig exponential with refractory period er and that of the leaky integrate and fire lif neuron we found that the discrimination capability of spike times strongly depends on high order moments of isi and that it is higher when the spike time sequence has a larger skewness and a smaller kurtosis high variability in terms of coefficient of variation cv does not necessarily mean that the spike times have less discrimination capability spike sequences generated by the gamma distribution have the minimum discrimination capability for a given mean and variance of isi we used series expansions to calculate the mean and variance of isis for lif neurons as a function of the mean input level and the input noise variance spike sequences from an lif neuron are more capable of discrimination than those of ig and gamma distributions when the stationary voltage level is close to the neuron s threshold value of the neuron

semiglobal l sub 2 performance bounds for disturbance attenuation in nonlinear systems this paper addresses the problem of disturbance attenuation in the sense of l sub 2 gain with internal stability and no cost on the control input for nonlinear systems when the problem of almost disturbance decoupling is not solvable i e when the least achievable attenuation level between disturbance and regulated output is nonzero two different approaches are provided which facilitate the estimation of an upper bound for such a value

a remark on the stabilization of partially linear composite systems we study global stabilization by means of smooth state feedback of partially linear composite systems we show how to compute the stabilizing feedback thanks to a weak lyapunov function for a nonlinear subsystem instead of a strict one

propagation of firing rate by synchronization and coherence of firing pattern in a feed forward multilayer neural network when neurons in layer 1 fire irregularly under stochastic noise it is found synchronous firings can develop gradually in latter layers within a feed forward multilayer neural network which is consistent with experimental findings the underlying mechanism of propagation of firing rate is explored then rate encoding realized by synchronization is clarified furthermore the effects of connection probability between nearest layers stochastic noise and ratio of inhibitory connections to total connection on i propagation of firing rate by synchronization and ii coherence of firing pattern are investigated respectively it is observed that i there is a threshold for connection probability beyond which firing rate of each layer can propagate successfully through the whole network by synchronization the dependence of firing rate on layer index is very different for different connection probability in addition larger the connection probability is more rapidly the synchrony is built up ii increasing intensity of stochastic noise enhances firing rate in output layer stochastic noise plays a constructive role in improving synchrony by causing the synchronization more quickly iii the inhibitory connection offsets excitatory input therefore reduces firing rate and synchrony as layer index increases coherence measure goes through a peak i e the coherence of firing pattern is the worst at certain a layer with increasing the ratio of inhibitory connections the variability of firing train is enhanced exhibiting destructive role of inhibitory connections on coherence of firing pattern

physiological gain leads to high isi variability in a simple model of a cortical regular spiking cell to understand the interspike interval isi variability displayed by visual cortical neurons softky koch 1993 it is critical to examine the dynamics of their neuronal integration as well as

response of a hodgkin huxley neuron to a high frequency input we study the response of a hodgkin huxley neuron stimulated by a periodic sequence of conductance pulses arriving through the synapse in the high frequency regime in addition to the usual excitation threshold there is a smooth crossover from the firing to the silent regime for increasing pulse amplitude g syn the amplitude of the voltage spikes decreases approximately linearly with g syn in some regions of parameter space the response is irregular probably chaotic in the chaotic regime between the mode locked regions 3 1 and 2 1 near the lower excitation threshold the output interspike interval histogram isih undergoes a sharp transition if the driving period is below the critical value t i l t ensuremath ast the output histogram contains only odd multiples of t i for t i g t ensuremath ast even multiples of t i also appear in the histogram starting from the largest values near t ensuremath ast the isih scales logarithmically on both sides of the transition the coefficient of variation of isih has a cusp singularity at t ensuremath ast the average response period has a maximum slightly above t ensuremath ast near the excitation threshold in the chaotic regime the average firing rate rises sublinearly from frequencies of order 1 hz

brief solutions to disturbance decoupling problem with constant measurement feedback for linear systems we study in this paper the problem of disturbance decoupling with constant i e static measurement feedback ddpcm for linear systems for a class of systems which have a left invertible transfer function from the control input to the controlled output or a right invertible transfer function from the disturbance input to the measurement output we obtain a complete characterization of all solutions to the ddpcm for a system that does not satisfy the above invertibility condition we use the special co ordinate basis to obtain a reduced order system then a complete characterization of all possible solutions to the ddpcm for the given system can be explicitly obtained if the obtained reduced order system itself satisfies the invertibility condition the main advantage of these solutions is that the solutions are given in a set of linear equations this resolves the well known difficulty in solving non linear equations associated with the ddpcm

interspike interval attractors from chaotically driven neuron models abstract sequences of intervals between firing times interspike intervals isis from single neuron models with chaotic forcing are investigated we analyze how the dynamical properties of the chaotic input determine those of the output isi sequence and assess how various biophysical parameters affect this input output relationship the attractors constructed from delay embeddings of isis and of the chaotic input are compared from the points of view of geometry and nonlinear forecastability for the three integrate and fire if models investigated the similarity between these attractors is high only when the mean firing rate is high and when firings occur over a large range of the input signal when these conditions are satisfied isis are related to input values at which firings occur by a simple map and their distribution can be derived from that of input signal values attractor reconstruction is found to be more sensitive to mean firing rate than to isi distribution at low firing rates for which the input is under sampled and isis become larger than the short term prediction horizon or when the dynamics do not allow a smooth invertible mapping between signal and isis information is lost our results relevant to all dynamical systems generating events show that information about continuous time dynamics is difficult to retrieve at low event rates and that information about inputs can be isolated only under restricted conditions

smith mcmillan factorizations at infinity of rational matrix functions and their control interpretation in this paper the smith mcmillan factorizations at infinity of a transfer function are studied the non uniqueness of these factorizations is characterized via a multiplicative group of bicausal isomorphisms control interpretations are given in terms of system equivalence under some groups of transformations a characterization of the stabilizer of morse group at a b c is given for irreducible systems

exact computation of infimum for a class of continuous time h optimal control problem with a nonzero direct feedthrough term from the disturbance input to the controlled output a noniterative method for the computation of infimum for a class of continuous time h optimal control problem is considered in this paper the problem formulation is fairly general and does not place any restrictions on any direct feedthrough terms of the given systems the method is applicable to systems where i the transfer function from the disturbance input to the measurement output is free of imaginary axis invariant zeros and left invertible and ii the transfer function from the control input to the controlled output of the given system is free of imaginary axis invariant zeros and right invertible the result presented in this paper is a continuation of the previous work of the author and his co workers chen et al 1992 in which the direct feedthrough term from the disturbance input to the measurement output of the given system are required to be zero

on normal forms of nonlinear systems affine in control the nonlinear equivalences of both finite and infinite zero structures of linear systems have been well understood for single input single output systems and have found many applications in nonlinear control theory the extensions of these notions to multiple input multiple output systems have proven to be highly sophisticated in this paper we propose constructive algorithms for decomposing a nonlinear system that is affine in control these algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs they lead to various normal form representations and reveal the structure at infinity the zero dynamics and the invertibility properties all of which represent nonlinear equivalences of relevant linear system structural properties

the almost disturbance decoupling problem with internal stability for linear systems subject to input saturation state feedback case abstract we consider the almost disturbance decoupling problem addp and or almost d bounded disturbance decoupling problem addp d with internal stability for linear systems subject to input saturation and input additive disturbance via linear static state feedback we show that the almost d bounded disturbance decoupling problem with local asymptotic stability addp las d is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable no matter where the poles of the open loop system are and the locations of these poles play a role only in the solution of addp gas d addp sgas d or addp gas where semi global or global asymptotic stability is required

time structure of the activity in neural network models several neural network models in continuous time are reconsidered in the framework of a general mean field theory which is exact in the limit of a large and fully connected network the theory assumes pointlike spikes which are generated by a renewal process the effect of spikes on a receiving neuron is described by a linear response kernel which is the dominant term in a weak coupling expansion it is shown that the resulting spike response model is the most general renewal model with linear inputs the standard integrate and fire model forms a special case in a network structure with several pools of identical spiking neurons the global states and the dynamic evolution are determined by a nonlinear integral equation which describes the effective interaction within and between different pools we derive explicit stability criteria for stationary incoherent and oscillatory coherent solutions it is shown that the stationary state of noiseless systems is almost always unstable noise suppresses fast oscillations and stabilizes the system furthermore collective oscillations are stable only if the firing occurs while the synaptic potential is increasing in particular collective oscillations in a network with delayless excitatory interaction are at most semistable inhibitory interactions with short delays or excitatory interactions with long delays lead to stable oscillations our general results allow a straightforward application to different network models with spiking neurons furthermore the theory allows an estimation of the errors introduced in firing rate or graded response models

global stabilization of partially linear composite systems a linear stabilizable nonlinear asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if a the linear subsystem is right invertible and weakly minimum phase and b the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output both of these conditions are coordinate free and there is freedom of choice for the linear output variable this result generalizes several earlier sufficient conditions for stabilizability moreover the weak minimum phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem

squaring down of non strictly proper systems in an earlier work a procedure for squaring down proper systems by static and dynamic compensators has been developed the compensators designed there have the following properties a they are asymptotically stable b the additional finite zeros induced by them are assignable to the open left half complex plane and c they preserve the fundamental properties such as stabilizability detectability infinite zero structure and minimum phase nature of the original system the earlier design procedure is extended to non strictly proper systems while retaining all the above mentioned properties

on the structure of strongly controllable systems an important problem in the structure theory of linear systems is the construction of a canonical form for strongly controllable systems i e surjective systems without finite zeros the problem has been solved in principle morse 1973 kronecker 1890 but without a clear identification of the system theoretic meaning of the construction steps this paper proposes the concept of a train basis in order to give this interpretation the second main idea of the paper is the system associated with a sub space through which concept it is possible to translate problems concerning a b invariance etc of subspaces in terms of input output systems in this way we make contact with results of willems 1980 on almost invariance

rational matrix gcds and the design of squaring down compensators a state space theory a state space construction for rational matrix greatest common divisors gcds of rational transfer matrices is given it is shown how the gcd results can be used to solve the problem of designing stable minimum phase squaring down compensators for multi variable plants one application is a direct state space construction for such compensators and a state space solution to fat plant h infinity control problems the results make use of the concepts of strongly observable systems and maximally observable systems and build upon the concepts introduced in the state space gcd extraction results for polynomial matrices of l m silverman and p van dooren 1979

squaring down of general mimo systems to invertible uniform rank systems via pre and or post compensators abstract pre and or post compensators are designed to square down a general mimo system to a uniform rank system the structure of which is almost similar to a siso system the method of squaring down either does not change the finite zero structure of the given mimo system or simply adds additional finite zeros in the left half s plane the significance of such a squaring down lies in the simplicity of the structure of a uniform rank system lending itself for easy analysis and control design

stochastic resonance of ensemble neurons for transient spike trains wavelet analysis by using the wavelet transformation wt i have analyzed the response of an ensemble of n 1 10 100 and 500 hodgkin huxley neurons to transient m pulse spike trains m i to 3 with independent gaussian noises thecross correlation between the input and output signals is expressed in terms of the wt expansion coefficients the signal to noise ratio snr is evaluated by using the denoising method within the wt by which the noise contribution is extracted from the output signals although the response of a single n 1 neuron to subthreshold transient signals with noises is quite unreliable the transmission fidelity assessed by the cross correlation and snr is shown to be much improved by increasing the value of n a population of neurons plays an indispensable role in the stochastic resonance sr for transient spike inputs it is also shown that in a large scale ensemble the transmission fidelity for suprathreshold transient spikes is not significantly degraded by a weak noise which is responsible to sr for subthreshold inputs

system zeros analysis via the moore penrose pseudoinverse and svd of the first nonzero markov parameter a new characterization of system zeros of an arbitrary linear system described by a state space model s a b c d is presented the transmission zeros are characterized as invariant zeros of an appropriate strictly proper system with a smaller number of inputs and outputs than the original system the approach is based on singular value decomposition svd of the first nonzero markov parameter this result together with characterization of invariant and decoupling zeros based on the moore penrose inverse of the first nonzero markov parameter and the kalman canonical decomposition theorem provided in the first part of the paper yield a complete characterization of system zeros of an arbitrary multi input multi output system

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

on structural decomposition and stabilization of large scale control systems graph theoretic concepts are used to decompose a large control system into a block triangular interconnection of input reachable subsystems stabilization of the system is thereby reduced to stabilization of a number of smaller subsystems the special structural properties of the obtained subsystems can be exploited to further simplify the stabilization problem

the state feedback h problem at optimality abstract we discuss the infinite horizon h control problem by state feedback for a linear time invariant plant which is not restricted with respect to its finite or infinite zero structure we provide an algebraic characterization for the optimal value to be attained in terms of the solvability of a nonstrict riccati inequality and propose possibilities for verifying these criteria if the optimum is not achieved we give a complete test for the need of high gain feedback in order to approach the optimal value

a variant of gromov s problem on holder equivalence of carnot groups abstract it is unknown if there exists a locally holder homeomorphism f r 3 h 1 for any 1 2 2 3 although the identity map r 3 h 1 is locally 1 2 holder more generally gromov asked given k and a carnot group g for which does there exist a locally holder homeomorphism f r k g here we equip a carnot group g with the carnot caratheodory metric in 2014 balogh hajlasz and wildrick considered a variant of this problem these authors proved that if k n there does not exist an injective 1 2 holder mapping f r k h n that is also locally lipschitz as a mapping into r 2 n 1 for their proof they use the fact that h n is purely k unrectifiable for k n in this paper we will extend their result from the heisenberg group to model filiform groups and carnot groups of step at most three we will now require that the carnot group is purely k unrectifiable the main key to our proof will be showing that 1 2 holder maps f r k g that are locally lipschitz into euclidean space are weakly contact proving weak contactness in these two settings requires understanding the relationship between the algebraic and metric structures of the carnot group we will use coordinates of the first and second kind for carnot groups

dynamics of membrane excitability determine interspike interval variability a link between spike generation mechanisms and cortical spike train statistics we propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains the key lies in the nonlinear dynamics of cortical spike generation which are consistent with type i membranes where saddle node dynamics underlie excitability rinzel ermentrout 1989 we present a canonical model for type i membranes the neuron the neuron is a phase model whose dynamics reflect salient features of type i membranes this model generates spike trains with coefficient of variation cv above 0 6 when brought to firing by noisy inputs this happens because the timing of spikes for a type i excitable cell is exquisitely sensitive to the amplitude of the suprathreshold stimulus pulses a noisy input current giving random amplitude kicks to the cell evokes highly irregular firing across a wide range of firing rates an intrinsically oscillating cell gives regular spike trains we corroborate the results with simulations of the morris lecar m l neural model with random synaptic inputs type i m l yields high cvs when this model is modified to have type ii dynamics periodicity arises via a hopf bifurcation however it gives regular spike trains cv below 0 3 our results suggest that the high cv values such as those observed in cortical spike trains are an intrinsic characteristic of type i membranes driven to firing by random inputs in contrast neural oscillators or neurons exhibiting type ii excitability should produce regular spike trains

full and reduced order observer based controller design for h_2 optimization in this paper the most general h2 control problem is considered we derive necessary and sufficient conditions when the infimum is attained by state feedback we do the same for the measurement feedback case where we derive necessary and sufficient conditions when the infimum is attained by proper dynamic compensators we also investigate reduced order compensators if some states are observable without noise we discuss for all of these cases the freedom that the non uniqueness of optimal compensators gives us in assigning the closed loop eigenvalues the second half of this paper investigates the case when the infimum cannot be attained we give a constructive algorithm to find a minimizing sequence of stabilizing controllers and discuss the freedom in the asymptotic locations of the closed loop eigenvalues again we do the above for three different cases static state feedback full order measurement feedback and reduced order measurement feedback

generalized rate code model for neuron ensembles with finite populations we have proposed a generalized langevin type rate code model subjected to multiplicative noise in order to study stationary and dynamical properties of an ensemble containing a finite number n of neurons calculations using the fokker planck equation have shown that owing to the multiplicative noise our rate model yields various kinds of stationary non gaussian distributions such as ensuremath gamma inverse gaussian like and log normal like distributions which have been experimentally observed the dynamical properties of the rate model have been studied with the use of the augmented moment method amm which was previously proposed by the author from a macroscopic point of view for finite unit stochastic systems in the amm the original n dimensional stochastic differential equations des are transformed into three dimensional deterministic des for the means and fluctuations of local and global variables the dynamical responses of the neuron ensemble to pulse and sinusoidal inputs calculated by the amm are in good agreement with those obtained by direct simulation the synchronization in the neuronal ensemble is discussed the variabilities of the firing rate and of the interspike interval are shown to increase with increasing magnitude of multiplicative noise which may be a conceivable origin of the observed large variability in cortical neurons

canonical forms of decouplable and controllable linear systems in this paper we present the canonical forms of decouplable and controllable linear systems some of the non zero elements in gilbert s canonically decoupled structure which remain undetermined are explicitly determined by a complete set of invariances our result constitutes the key step to characterization of the whole class of nonlinear systems that are feedback equivalent to decouplable and controllable linear systems

path following for nonlinear systems with unstable zero dynamics in the path following problem formulated in this note it is required that the error between the system output and the desired geometric path eventually be less than any prespecified constant if in a nonlinear multiple input multiple output mimo system the output derivatives do not enter into its zero dynamics a condition relating path geometry and stabilizability of the zero dynamics is given under which a solution to this problem exists the solution is obtained by combining input to state stability and hybrid system methodologies

solvability conditions for disturbance decoupling problems with static measurement feedback two well known disturbance decoupling problems are considered a checkable necessary and sufficient condition is derived under which the disturbance decoupling problem with static measurement feedback ddpkm is solvable for a class of multi input and multi output linear time invariant systems which have a left invertible transfer matrix function from the control input to the controlled output the set of all solutions that solve the ddpkm is constructed and parametrized explicitly this set is then used to solve the disturbance decoupling problem with static measurement feedback and with internal stability ddpkms