efficient parallel rooting of complex polynomials on the unit circle an efficient method is presented for rooting complex polynomial equations of any order where the root space is restricted to the unit circle the method restates the evaluation of polynomials as a recursive algorithm involving only additions by means of the bilinear transformation the straight line uniformly spaced recursive polynomials evaluation method of a h nuttall 1987 is extended to the unit circle where the root positions are determined by thresholding general coefficient transformations are provided along with a comparison to the horner method

computation of correlation sequences in two dimensional digital filters two approaches to the computation of correlations or variances in 2 d digital filters are presented the first one establishes the correlation equations and shows that the equations are consistent for the special cases of one dimensional 1 d filters and 2 d symmetric filters the second one is a direct application of the theory of 2 d complex integrals whereby the first of the two integrations becomes a euclid problem and the second becomes a 1 d complex integration problem this second method is applicable to general 2 d digital filters

on reliable stabilization via rectangular dilated lmis and dissipativity based certifications in this short note we consider the problem of reliable stabilization for multi channel systems where our main objective is to maintain the robust stability of the perturbed closed loop system when there is a single controller failure in any of the control channels specifically we present a less conservative result than results in the literature in terms of a set of dilated lmis for the reliable state feedback stabilization of the nominal system while a dissipativity based certification is used to extend the stability condition when there is an additive model perturbation in the system finally a numerical example is presented to illustrate the applicability of the proposed technique

on fast multivariable bilinear and hadamard transforms applying the bilinear transformation to an n variance polynomial n or 1 one arrives at a rational function whose numerator is the transformed polynomial based on i j good s 1958 results and the symmetry properties of the single dimensional bilinear transformation matrix a fast implementation for computing the coefficients of such n variable transformed polynomials is proposed letting q denote the matrix relating the coefficients of the original polynomial to those of the transformed polynomials it is shown that sylvester type hadamard matrices coincide with the transformation matrices for the n variable polynomials for which the highest degree of each variable is one this new observation is used to derive w r crowther and c m rader s 1966 formulation of the fast hadamard transform

approaches to t s fuzzy affine model based reliable output feedback control for nonlinear ito stochastic systems this paper deals with the problem of reliable and robust mathscr h infty static output feedback sof controller synthesis for continuous time nonlinear stochastic systems with actuator faults the nonlinear stochastic plant is expressed by an ito type takagi sugeno fuzzy affine model with parametric uncertainties and a markov process is employed to model the occurrence of actuator fault the purpose is to design an admissible piecewise sof controller such that the resulting closed loop system is stochastically stable with a prescribed disturbance attenuation level in an mathscr h infty sense specifically based on a markovian lyapunov function combined with ito differential formula s procedure and some matrix inequality convexification procedures two new approaches to the reliable sof controller analysis and synthesis are proposed for the underlying stochastic fuzzy affine systems it is shown that the existence of desired reliable controllers is fully characterized in terms of strict linear matrix inequalities finally simulation examples are presented to illustrate the effectiveness and advantages of the developed methods

walsh function analysis of 2 d generalized continuous systems the importance of the generalized or singular 2d continuous systems are demonstrated by showing their use in the solution of partial differential equations in two variables a technique is presented for solving these systems in terms of walsh functions the method replaces the solution of a two variable partial differential equation with the solution of a linear algebraic generalized 2d sylvester equation an efficient technique for the recursive solution of the latter equation is offered all the results apply also in the usual roesser 2d state space case

reliable h_ infty control of linear systems with adaptive mechanism this technical note studies the problem of designing reliable h controllers with adaptive mechanism for linear systems a new method for designing indirect adaptive reliable controller via state feedback is presented for actuator fault compensations based on the on line estimation of eventual faults the proposed reliable controller parameters are updated automatically to compensate the fault effects on systems a notion of adaptive h performance index is proposed to describe the disturbance attenuation performances of closed loop systems the design conditions are given in terms of solutions to a set of linear matrix inequalities lmis the resultant designs can guarantee the asymptotic stability and adaptive h performances of closed loop systems even in the cases of actuator failures the effectiveness of the proposed design method is illustrated via a numerical example

parameter identification in noisy extended systems a hydrodynamic case abstract this paper is concerned with the robustness of parameter identification methods with respect to the noise levels typically found in experiments more precisely we focus on the case of an extended nonlinear system a system of coupled local maps akin to a discretized complex ginzburg landau equation modeling a wake experiment after a brief description of this hydrodynamic experiment as well as of the associated cost function and synthetic data generation we introduce two inversion methods a one time step approach and a more sophisticated n time step optimization procedure solved by a backpropagation method the one time step approach reduces to a small linear system for the unknown parameters while the n time step approach involves a backpropagation equation for a set of lagrage multipliers the sensitivity of each method with respect to noise is then discussed while the n time step method is very robust even with large amounts of noise the one time step approach is shown to be affected by small noise levels

efficient evaluation of 1 d and 2 d polynomials at equispaced points an extension to the two dimensional case of a previously published fast algorithm for evaluating exponential functions and polynomials over periodically distributed points is generalized to evaluate two dimensional polynomials efficiently over general periodic parallelograms the problem of getting the initial values required for other fast algorithms is treated in a general manner fast algorithms are presented for computing initial values in both cases of one and two dimensional polynomials it is observed that the two dimensional recursion is not always advantageous compared with taking the one dimensional recursion for each variable separately

the bilinear transformation of two dimensional state space systems many authors have used the two dimensional 2 d bilinear transformation to obtain 2 d digital filters from stable 2 d analog filters in this paper a technique is proposed for performing the bilinear transformation on 2 d state space systems this technique is also applicable to multidimensional mimo systems programming this algorithm is straightforward if there is access to computer subroutines that add multiply and invert matrices

new efficient ls and svd based techniques for high resolution frequency estimation new least squares and singular value decomposition based methods for the estimation of the frequencies of complex sinusoids in white noise are presented the methods are based on a new symmetric prediction problem that has some very useful properties leading to algorithms that have considerably reduced complexity the new symmetric predictor is superior in performance as compared to the well known symmetric smoother and has a performance comparable to other well known methods finally a new ls based method which combines the new prediction technique with the fblp method is proposed this method performs slightly better than the fblp offering at the same time a significant computational saving as a by product in the derivation of the new methods is the establishment of some useful properties concerning the eigenstructure of hermitian and persymmetric matrices

fitting partial differential equations to space time dynamics the partial differential equations pdes governing the dynamics of reaction diffusion systems are reconstructed from data representing the spatially extended systems the fitted equations are validated by a comparison of their numerical solutions and the input data and by computation of the isoclines of the fitted pdes

identification of parameters in amplitude equations describing coupled wakes abstract we study the flow behind an array of equally spaced parallel cylinders a system of stuart landau equations with complex parameters is used to model the oscillating wakes our purpose is to identify a set of six scalar parameters which accurately reproduces the experimental data of chauve and le gal physica d 58 1992 407 413 to do so we perform a computational search for the minimum of a distance j we define j as the sum square difference of the experimental data and reconstructed data obtained from our model the differences are computed over a training window a finite time interval the initial conditions are obtained from observations at te beginning of the interval boundary conditions are zero amplitude oscillations just outside the domain the search algorithm uses a backpropagation technique for the computation of the descent direction using the parameters computed via the backpropagation method the coupled stuart landau equations accurately predicted the experimental data from chauve and le gal over several wake oscillations and reproduced the qualitative features of the dynamics a relatively large degree of uncertainty remains on the parameters controlling the coupling between adjacent cylinders this ambiguity does not prevent short time predictions which indicates that a family of parameter values are nearly equivalent for the description of the system synthetic data were obtained using the model system of equation together with a model of the noisy measurement process these data allow to reproduce the uncertainty in parameter identification the horizon time after which forecasts of the system behavior loose their accuracy has been measured we show that as expected the horizon time increases slightly with the length of the data series but seems to reach a limit interestingly there is also an optimal length for the training window that yields the largest horizon time

estimating varying coefficients for partial differential equation models partial differential equations pdes are used to model complex dynamical systems in multiple dimensions and their parameters often have important scientific interpretations in some applications pde parameters are not constant but can change depending on the values of covariates a feature that we call varying coefficients we propose a parameter cascading method to estimate varying coefficients in pde models from noisy data our estimates of the varying coefficients are shown to be consistent and asymptotically normally distributed the performance of our method is evaluated by a simulation study and by an empirical study estimating three varying coefficients in a pde model arising from lidar data

transformation matrices in the general bilinear transformation of multivariable polynomials the structure of the transformation matrix t for the general bilinear transformation of a single variable polynomial is examined this is applied to produce an efficient algorithm for the transformation of a multivariable polynomial

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

characterization of a two parameter mixed mode electrochemical behavior regime using neural networks abstract we use nonlinear signal processing techniques based on artificial neural networks to construct a continuous time model set of ordinary differential equations odes from experimental observations of mixed mode oscillations during the galvanostatic oxidation of hydrogen on platinum in the presence of bismuth and chloride ions the data was in the form of time series of the potential for different values of the applied current and chloride ion concentration we use the model to reconstruct the experimental dynamics and to explore the associated bifurcation structures in phase space using numerical bifurcation techniques we locate stable and unstable periodic solutions calculate eigenvalues and identify bifurcation points this approach constitutes a promising data post processing procedure for investigating phase space and parameter space of real experimental systems it allows us to infer phase space structures which the experiments can only probe with limited measurement precision and only at a discrete number of operating parameter settings for example the fitted model suggests the existence of a sub critical hopf bifurcation near the range of parameters probed in the experiments this might explain the experimental difficulty in locating small amplitude simple oscillations

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

complex bi orthogonal decomposition of a chain of coupled wakes abstract this work is devoted to the experimental analysis of the flow created by a row of cylinders as each cylinder wake appears by the hopf bifurcation of a global oscillating mode this experiment is similar to a chain of coupled non linear oscillators and this dynamic system can be modelled using a ginzburg landau type equation a video analysis technique is performed on visualization pictures in order to obtain the spatio temporal evolution of the wakes this diagram is then analysed using the bi orthogonal decomposition extended to its complex form it is shown that only a few eigenmodes are excited giving a low dimensional dynamic system that enables the different parameters of the model to be estimated

brief paper reliable stabilization with integral action in decentralized control systems reliable stabilization with integral action is studied in a linear time invariant multi input multi output two channel decentralized control system where the plant is stable the objective is to achieve closed loop stability when both controllers act together and when each controller acts alone necessary and sufficient conditions are obtained for existence of block diagonal decentralized controllers that ensure reliable stabilization and integral action and all such decentralized controllers are parametrized explicit controller design approaches are discussed for the case of square channels

reliable control of nonlinear systems via variable structure scheme this study proposes a class of variable structure stabilizing laws which make the closed loop system be capable of tolerating the abnormal operation of actuators within a pre specified subset of actuators the ranges of acceptable change in control gain magnitude that preserves system s stability are estimated for the whole set of actuators these ranges are shown to be able to be made larger than those obtained by linear quadratic regulator lqr reliable design veillette 1995 and liang 2000 by the choice of control parameters besides this approach does not need the solution of hamilton jacobi hj equation or inequality which is essential for optimal approaches such as lqr and h infin reliable designs as a matter of fact this approach can also relax the computational burden for solving the hj equation or inequality

efficient evaluation of polynomials and exponentials of polynomials for equispaced arguments a kth order polynomial can be evaluated by means of k additions and no multiplications when done in a recursive fashion at equispaced arguments the evaluation of an exponential of a kth order polynomial can be accomplished by k multiplications and no additions or exponentiations combinations of rational functions and exponentials can therefore be realized very efficiently by combining these properties

identification of nonlinear spatiotemporal systems via partitioned filtering the problem of identifying continuous spatiotemporal nonlinear systems from noisy and indirect observations is determined by its computational complexity we propose a solution by means of nonlinear state space filtering along with a state partition technique the method is demonstrated to be computationally feasible for spatiotemporal data with properties that occur typically in experimental recordings it is applied to one component of the simulated chaotic data of a two component reaction diffusion system yielding estimates of both the unobserved state component and the diffusion constant

robust h sub spl infin filtering for uncertain2 d continuous systems this paper considers the problem of robust h sub spl infin filtering for uncertain two dimensional 2 d continuous systems described by the roesser state space model the parameter uncertainties are assumed to be norm bounded in both the state and measurement equations the purpose is the design of a 2 d continuous filter such that for all admissible uncertainties the error system is asymptotically stable and the h sub spl infin norm of the transfer function from the noise signal to the estimation error is below a prespecified level a sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired h sub spl infin filter is given finally a simulation example is provided to demonstrate the effectiveness of the proposed method

algebraic aspects of linear control system stability after formulating the problem of linear control system stability in very general terms the problem is resolved by 1 establishing a necessary and sufficient condition for stability 2 exploring in some detail the nature of this condition and 3 developing a parametric characterization of all controllers which stabilize a given plant the problem formulation is based on a ring theoretic setting for linear systems and is distinguished by the use of a novel control system configuration any interconnection of two distinct systems can be represented in terms of this configuration while preserving the distinction between the two systems furthermore no other configuration has this property several benefits and extensions are accrued as a result of using this configuration first a completely general yet physically meaningful problem formulation results consequently state space and operator theoretic approaches to linear control system stability are thoroughly reconciled this reconciliation embraces continuous time as well as discrete time systems lumped as well as distributed systems and 1 d as well as n d systems second the controller parametrization affords four degrees of freedom two more than any existing parametrization the additional degrees of freedom make explicit the design opportunity associated with controller implementation and thus determine several important control system characteristics this result is expected to provide a theoretical basis for the development of comprehensive control system design methodologies wherein design considerations related to controller implementation are addressed

comparison of tests for embeddings it is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test the classical tests which depend on real numbers fractal dimensions lyapunov exponents averaged over an attractor are compared with a topological test that depends on integers the comparison can only be done for mappings into three dimensions we find that the classical tests fail to predict when a mapping is an embedding and when it is not we point out the reasons for this failure which are not restricted to three dimensions

efficient evaluation of multivariate polynomials over multidimensional grids let p x 1 x 2 x n be a multivariate polynomial in n variables x 1 x 2 x n and suppose that p x 1 x 2 x n is of degree m i in x i i 1 2 n it is shown how p x 1 x 2 x n may be evaluated at x i x 0i n i i for n i 0 1 2 and i 1 2 n using not more than m 1 m 2 m n additions per point feasibility of reduction from this upper bound is demonstrated in the n 2 case

general spectral transformations for digital filters constantinides 1 gave a method of transforming a prototype low pass digital filter into a high pass bandpass or bandstop filter by conformally mapping the complex variable z 1 we generalize here his method to transformations from prototype low pass filters to filters containing any number of pass and stopbands the computation procedure involves only the solution of a set of simultaneous linear equations the number of which is related only to the number of band edges and not to the order of the prototype filter

bilinear transformation of multivariable polynomials using the horner method the general bilinear transformation of a single variable polynomial using the horner method of synthetic division has been described by davies 1974 and by policastro 1979 the procedure which is very simple to apply is extended to multivariable polynomials

the emergence of coherent structures in coupled map lattices we show how increasing spatial interaction leads to the merging of coherent structures from chaos in some systems of coupled map lattices this phenomenon reflects the arising of new ground states in the corresponding model of statistical mechanics if we further increase the coupling then new ground states appear showing the coexistence of a large scale coherent structure with a small scale chaotic motion this allows us to propose a generalization of the notion of spatial intermittency

spatiotemporal analysis of complex signals theory and applications we present a space time description of regular and complex phenomena which consists of a decomposition of a spatiotemporal signal into orthogonal temporal modes that we call chronos and orthogonal spatial modes that we call topos this permits the introduction of several characteristics of the signal three characteristic energies and entropies one temporal one spatial and one global and a characteristic dimension although the technique is general we concentrate on its applications to hydrodynamic problems specifically the transition to turbulence we consider two cases of application a coupled map lattice as a dynamical system model for spatiotemporal complexity and the open flow instability on a rotating disk in the latter we show a direct relation between the global entropy and the different instabilities that the flow undergoes as reynolds number increases

a storage efficient method for solving banded toeplitz systems a method is presented for solving the banded toeplitz system tx y by decomposing t into its asymptotic upper and lower triangular factors which are banded and toeplitz and a rank p correction matrix where p is the bandwidth of t this way of representing t requires only o p sup 2 words of storage and allows computation of x in o 2np operations a similar method is presented for the case in which t is bi infinite and y is zero outside a finite region

a new transformation matrix for bilinear transformation a new transformation matrix technique is proposed for the bilinear transformation of polynomials the number of multiplications and additions involved in the new method is less than the number involved in the q matrix method of transformation

s plane to z plane mapping using a simultaneous equation algorithm based on the bilinear transformation this note presents an algorithm for transforming a continuous transfer function to an approximate discrete equivalent by means of the bilinear transformation

secondary structures in a one dimensional complex ginzburg landau equation with homogeneous boundary conditions experiments in extended systems such as the counter rotating couette taylor flow or the taylor dean flow system have shown that patterns with vanishing amplitude may exhibit periodic spatio temporal defects for some range of control parameters these observations could not be interpreted by the complex ginzburg landau equation cgle with periodic boundary conditions we have investigated the one dimensional cgle with homogeneous boundary conditions we found that in the benjamin feir stable region the basic wave train bifurcates to state with periodic spatio temporal defects the numerical results match the observations quite well we have built a new state diagram in the parameter plane spanned by the criticality or equivalently the linear group velocity and the nonlinear frequency detuning

stability analysis of plane wave solutions of the discrete ginzburg landau equation the discrete ginzburg landau model for a family of oscillators linearly coupled with their first neighbors is studied the full linear stability analysis of the nonlinear plane wave solutions is performed by considering both the wave number k of the basic states and the wave number q of the perturbations as free parameters in particular it is shown that nonlinear plane waves can be destabilized not only by long q 0 or short q5p wave perturbations but also by intermediate wave numbers 0 q p finite size effects are also considered and discussed in connection with experiments on coupled oscillating wakes the interest in the dynamics of discrete systems comes from the diversity of their numerous applications in physical and biological sciences the structure of such systems implies that their dynamics is the result of an interaction between individual dynamical entities molecular chains and arrays of wave guides in optics 1 josephson junctions 2 are examples referred to as coupled oscillators 3 also models for life sciences can be investigated by considering the behavior of coupled cells cardiac muscle defibrillation 4 legged locomotion 5 fireflies synchrony 6 neural networks 7 we focus in this paper on the complex ginzburg landau equation cgle in one space dimension very often used in fluid mechanics as a phenomenological equation the cgle and its different forms were analytically derived in various applications see ref 8 for instance where it appears as an amplitude equation for a rapidly oscillating wave propagating in a nonlinear medium the discretized form of the cgle has been used for describing vortex line dynamics 9 and in the study of coupled wakes 10 in these two examples the oscillation of each isolated cell each vortex or each wake obeys a landau equation which is the normal form of the hopf bifurcation that gives birth to each oscillator the global behavior of the vortex or wake arrays can consequently be described by the dynamics of coupled hopf oscillators various mathematical shapes of coupling can be considered such as linear or nonlinear local or global 11 motivated by the observation of a short range interaction between wakes 12 we restrict our analysis to a first neighbors linear coupling as it was also the case in the studies of willaime et al 9 and le gal 10 since eckhaus 13 most stability analysis have been carried out for the continuous version of the ginzburg landau equation the instability arises from a resonance mechanism between wave trains and is called the benjamin feir instability 14 or the sideband instability newell s criterion provides a condition for the destabilization of plane waves by long wavelength modulations 15 more recently matkowsky and volpert 16 considered perturbations of arbitrary wave numbers they showed that destabilization can occur due to finite wave number perturbations which implies more complex dynamical behaviors as those usually analyzed direct numerical simulations of the continuous version of the cgle also demonstrated the richness of the coupled oscillator system for which spatiotemporal chaos was in particular observed 17 here it is our purpose to fully describe the stability of the nonlinear plane wave solutions of the discretized complex ginzburg landau equation for a discrete system the possible wave numbers of the nonlinear plane wave are related to the number of oscillators the boundary conditions and the nature of the coupling term between the oscillators these wave numbers range between k50 where the oscillators are in phase and k5p where two consecutive oscillators are in phase opposition as far as we know the stability analysis of a nonlinear plane wave was performed for the modulation wave numbers q 0 and q 5p only 9 in this paper we extend this study to account for any modulation wave number

reliable mixed l2 h fuzzy static output feedback control for nonlinear systems with sensor faults this paper is concerned with the design of reliable mixed l 2 h static output feedback sof fuzzy controllers for nonlinear continuous time systems with complete sensor faults the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system a sufficient condition for the existence of reliable mixed l 2 h sof fuzzy controllers is presented in terms of a set of quadratic matrix inequalities qmis which not only guarantees that the closed loop fuzzy system satisfies a desired h disturbance attenuation constraint for all admissible operating regimes including the normal and sensor fault cases but also provides different upper bounds on the l 2 performance criterion for different operating regimes a suboptimal reliable fuzzy controller is obtained by the proposed iterative linear matrix inequality ilmi algorithm for minimizing the normal l 2 performance bound while maintaining acceptable lower levels of the bounds in the sensor fault cases finally a numerical example is given to illustrate the effectiveness of the proposed design method

recursive algorithms for two dimensional filters spectral transformations in this correspondence a fast algorithm for two dimensional 2 d digital filters spectral transformations is developed the whole algorithm is based on the 1 d and 2 d horner s form all the considered spectral transformations are arbitrary 2 d rational transformations the method is successfully applied in an example concerning 2 d digital filter design

parameter space methods for robust control design a guided tour the results obtained in studies of robust stability and stabilizability of control systems with parametric structured uncertainties are reviewed both the algebraic methods based upon characteristic equations and the methods using lyapunov functions and riccati equations are discussed and compared in the context of algebraic methods most promising are the kharitonov type approach and the optimization procedure of embedding a geometric figure of some kind inside the stability regions of the parameter space maximizing its size using minimax or some other mathematical programming technique in the framework of lyapunov s direct method the dominant approach has been a quadratic function estimation of stability regions in the parameter space in large sale systems the concept of vector lyapunov functions has been used with the possibility of choosing quadratic forms norm like functions and their combinations

an fft algorithm based fast algorithm for arbitrary polynomial transformation a fast algorithm for the arbitrary polynomial transformation is described this algorithm is based on the fast fourier transform fft algorithm and reduces the computational complexity of a recently proposed recursive algorithm by an order of magnitude

recovering coefficients of the complex ginzburg landau equation from experimental spatio temporal data two examples from hydrodynamics there are many examples where the description of the complexity of flows can only be achieved by the use of simple models these models obtained usually from phenomenological arguments need in general the knowledge of some parameters the challenge is then to determine the values of these parameters from experiments we will give two examples where we have been able to evaluate the coefficients of the complex ginzburg landau equation cgle from space time chaotic data applied to first a row of coupled cylinder wakes and then to wave propagation in the ekman layer of a rotating disk in the first case our analysis is based on a proper decomposition of experimental chaotic flow fields followed by a projection of the cgle onto the proper directions we show that our method is able to recover the parameters of the model which permits to reconstruct the spatio temporal chaos observed in the experiment the second physical system under consideration is the flow above a rotating disk and its cross flow instability our aim is to study the properties of the wavefield through a volterra series equation the kernels of the volterra expansion which contain relevant physical information about the system are estimated by fitting two point measurements via a nonlinear parametric model we then consider describing the wavefield with the cgle and derive analytical relations which express the coefficients of the ginzburg landau equation in terms of the kernels of the volterra expansion

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

brief paper algebraic and topological aspects of the regulator problem for lumped linear systems the regulator problem with robustness is solved for systems modelled by rational transfer matrices a topology for possibly unstable plants is presented a necessary and sufficient condition is derived for the existence of a proper controller which provides internal stability and output regulation throughout an open neighbourhood of the plant a characterization of all such controllers is determined

solitary dilation waves in a circular array of liquid columns abstract solitary dilation waves and self sustained oscillations optical mode are observed in a one dimensional pattern of liquid columns produced in the pouring of a liquid film from a solid ceiling a new experiment carried out on a circular fountain allows us to achieve periodic boundary conditions and thus to observe free propagation of the dilation waves in an infinite medium measurements of the drift and group velocities of the dilation waves and of the optical pulsation are presented as functions of the flow rate in addition starting from qualitative observations and order of magnitude estimates we build a discrete model of non linear dynamics in this system in which dissipation is compensated by an external energy supply transient drop formation this model allows us to recover the appearance of the optical mode induced by a wavelength increase and predicts the focusing of this mode into a localized kink traveling at a constant speed along the column array the kink structure is reminiscent of the dilation waves observed experimentally both the model and experiment support a relationship between the wave velocity and the oscillation frequency similar to that observed by michalland and rabaud in the printer s instability

low dimensional dynamics for the complex ginzburg landau equation abstract a method is presented which results in low dimensional dynamical systems for situations in which low dimensional attractors are known to exist the method is based on the use of the karhunen loeve procedure for the determination of an optimal basis and the subsequent use of the galerkin procedure to generate the dynamical system the method is applied to two problems for the ginzburg landau equation for which large databases have been obtained in each instance a dynamical system is generated which has roughly twice the number of degrees of freedom as the hausdorff dimension of the exact case it is also demonstrated that the approximations are robust in that they are accurate over a wide range of parameter space

a homotopy approach for stabilizing single input systems with control structure constraints a linear state feedback gain vector used in the control of a single input dynamical system may be constrained because of the way feedback is realized some examples of feedback realizations which impose constraints on the gain vector are static output feedback constant gain feedback for several operating points of a system and two controller feedback we consider a general class of problems of stabilization of single input dynamical systems with such structural constraints and give a numerical method to solve them each of these problems is cast into a problem of solving a system of equalities and inequalities in this formulation the coefficients of the quadratic and linear factors of the closed loop characteristic polynomial are the variables to solve the system of equalities and inequalities a continuous realization of the gradient projection method and a barrier method are used under the homotopy framework our method is illustrated with an example for each class of control structure constraint

stochastic stability analysis for continuous time fault tolerant control systems active fault tolerant control systems are feedback control systems that reconfigure the control law in real time based on the response from an automatic failure detection and identification fdi scheme the dynamic behaviour of such systems is characterized by stochastic differential equations because of the random nature of the failure events and the fdi decisions the stability analysis of these systems is addressed in this paper using stochastic lyapunov functions and supermartingale theorems both exponential stability in the mean square and almost sure asymptotic stability in probability are addressed in particular for linear systems where the coefficients of the closed loop system dynamics are functions of two random processes with markovian transition characteristics one representing the random failures and the other representing the fdi decision behaviour necessary and sufficient conditions for exponential stability in the mean square are developed

fitting parameters in partial differential equations from partially observed noisy data abstract we describe a new method for parameter estimation in systems with nonlinear spatiotemporal dynamics the technique is able to reliably determine parameter estimates from noisy data and is even applicable in cases with unobserved components in a simulation study we investigate its performance in comparison to standard methods and show its superiority as numerical example we analyze in detail a complex ginzburg landau equation under realistic conditions

exact solutions of discrete complex cubic ginzburg landau equation via extended tanh function approach in this paper we obtained rich solutions for the discrete complex cubic ginzburg landau equation by means of the extended tanh function approach these solutions include chirpless bright soliton chirpless dark soliton triangular function solutions and some solutions with alternating phases and so on meanwhile the range of parameters where some exact solution exists is given

brief paper reliable stabilization using a multi controller configuration given a plant p we consider the problem of designing a pair of controllers c 1 and c 2 such that their sum stabilizes p and in addition each of them also stabilizes p should the other one fail this is referred to as the reliable stabilization problem it is shown that every strongly stabilizable plant can be reliably stabilized moreover one of the two controllers can be specified arbitrarily subject only to the constraint that it should be stable the stabilization technique is extended to reliable regulation

a simple algorithm for arbitrary polynomial transformation a very simple algorithm is developed for the arbitrary rational transformation of a polynomial the fact that many of the multiplications performed involve one zero factor is not explicitly taken into account if desired this could be done with some increase in the complexity of the algorithm itself finally if roundoff error is expected to be a problem double precision arithmetic could be used

on the evaluation of double square integral in the s 1 s 2 complex biplane in this correspondence a method of evaluating the double square integral int min 0 max infin int min 0 max infin h t 1 t 2 2 dt 1 dt 2 frac 1 2 pij 2 int min j infin max j infin int min j infin max j infin h s 1 s 2 ds 1 ds 2 where h t 1 t 2 l 1 h s 1 s 2 is discussed the method of evaluation is based on using the double bilinear transformation dbt s k 1 z k 1 z k k 1 2 to reduce the above complex integral to a double integral in the complex z 1 z 2 bidisk sum min m 0 max infin sum min n 0 max infin a m n 2 frac 1 2 pij 2 oint min z1 1 oint min z2 1 a z 1 z 2 cdot a z 1 1 z 2 1 frac dz 1 z 1 frac dz 1 z 2 there exist several methods for evaluating the above double integral in this correspondence we mention one promising method also a matrix method is proposed for applying the dbt to a quotient of two dimensional 2 d polynomials

fuzzy model based reliable static output feedback mathscr h _ infty control of nonlinear hyperbolic pde systems this paper investigates the problem of output feedback robust mathscr h infty control for a class of nonlinear spatially distributed systems described by first order hyperbolic partial differential equations pdes with markovian jumping actuator faults the nonlinear hyperbolic pde systems are first expressed by takagi sugeno fuzzy models with parameter uncertainties and then the objective is to design a reliable distributed fuzzy static output feedback controller guaranteeing the stochastic exponential stability of the resulting closed loop system with certain mathscr h infty disturbance attenuation performance based on a markovian lyapunov functional combined with some matrix inequality convexification techniques two approaches are developed for reliable fuzzy static output feedback controller design of the underlying fuzzy pde systems it is shown that the controller gains can be obtained by solving a set of finite linear matrix inequalities based on the finite difference method in space finally two examples are presented to demonstrate the effectiveness of the proposed methods

stability margin of two dimensional continuous systems the margin of stability of two dimensional 2 d continuous systems is considered in particular the definition of the stability margins for a 2 d discrete system is extended to a 2 d continuous one two methods to compute the stability margin of 2 d continuous systems are presented illustrative examples are provided

reliable control using redundant controllers this paper presents a methodology for the design of reliable control systems by using multiple identical controllers to a given plant the resulting closed loop control system is reliable in the sense that it provides guaranteed internal stability and h sub spl infin performance in terms of disturbance attenuation not only when all controllers are operational but also when some controller outages sensor and or actuator occur a numerical example is given to illustrate the proposed design procedures

brief paper reliable control of uncertain nonlinear systems this paper is concerned with the reliable controller design problem for a class of uncertain nonlinear systems for the primary contingency problem a procedure of designing reliable nonlinear controllers is presented in terms of solutions of hamilton jacobi inequalities the resulting closed loop nonlinear system is reliable in the sense that the performance i e internal stability and h attenuation of the closed loop system is guaranteed not only when all sensors and actuators are operational but also when some sensor and actuator outages occur

parameter estimation of partial differential equation models partial differential equation pde models are commonly used to model complex dynamic systems in applied sciences such as biology and finance the forms of these pde models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system parameters in pde models often have interesting scientific interpretations but their values are often unknown and need to be estimated from the measurements of the dynamic system in the presence of measurement errors most pdes used in practice have no analytic solutions and can only be solved with numerical methods currently methods for estimating pde parameters require repeatedly solving pdes numerically under thousands of candidate parameter values and thus the computational load is high in this article we propose two methods to estimate parameters in pde models a parameter cascading method and a bayesian approach in both methods the underlying dynamic process modeled with the pde model is represented via basis function

a novel approach to reliable output feedback control of fuzzy affine systems with time delays and sensor faults this paper proposes a novel system augmentation approach to the delay dependent reliable piecewise affine mathscr h infty static output feedback control for nonlinear systems with time varying delay and sensor faults in the piecewise markovian lyapunov functional based framework the nonlinear plant is described by a continuous time takagi sugeno fuzzy affine model with parametric uncertainties and the sensor faults are characterized by a markov process specifically by applying a state input augmentation technique the original closed loop system is first reformulated into a descriptor fuzzy affine system based on a new piecewise markovian lyapunov krasovskii functional combined with a wirtinger based integral inequality improved reciprocally convex inequality and s procedure a novel bounded real lemma is then derived for the underlying closed loop system furthermore by taking advantage of the redundancy of descriptor system formulation together with a linearization procedure the piecewise affine controller synthesis is carried out it is shown that the desired piecewise affine controller gains can be attained by solving a linear matrix inequality based optimization problem finally simulation examples are performed to confirm the effectiveness and less conservatism of the presented approach

a new algorithm for arbitrary transformation of polynomial and rational functions a new algorithm for performing the arbitrary polynomial transformation for single and multiple variables is presented it is based on the polynomial interpolation of the numerator and the denominator polynomials of the rational functions at the roots of unity using the discrete fourier transform dft by proper modification of the algorithm it is possible to compute the q matrix of the transformation generalization of the algorithm to higher dimensions is also presented

reliable control of nonlinear systems in this paper we extend veillette s results 1995 to the study of reliable linear quadratic regulator problem for nonlinear systems this is achieved by employing the hamilton jacobi inequality in the nonlinear case instead of algebraic riccati equation in the linear one the proposed state feedback controllers are shown to be able to tolerate the outage of actuators within a prespecified subset of actuators both the gain margins of guaranteeing system stability and retaining a performance bound are estimated

computational aspects of the bilinear transformation based algorithm for s plane to z plane mapping the author analyzes the computational complexity of an algorithm by f d groutage et al ibid vol ac 32 no 7 p 635 7 july 1987 for performing the transformation of a continuous transfer function to a discrete equivalent by a bilinear transformation groutage et al defend their method by noting that their technique is not limited to the bilinear transformation rather it can be extended to any higher order integration rule simpson runge kutta etc or to any higher order expansion of the ln function in general using the method s can be any appropriate mapping function s f z

infinite gain margin problem in multivariable feedback systems this paper deals with the problem of designing feedback compensators that achieve infinite gain margin for stability in the face of the uncertainty in the gain factor of the plant a necessary and sufficient condition is given for the existence of compensators in terms of the closed right half plane zeros of the plant

pulse bifurcations and instabilities in an excitable medium computations in finite ring domains we investigate the instabilities and bifurcations of traveling pulses in a model excitable medium in particular we discuss three different scenarios involving either the loss of stability or disappearance of stable pulses in numerical simulations beyond the instabilities we observe replication of pulses backfiring resulting in complex periodic or spatiotemporally chaotic dynamics as well as modulated traveling pulses we approximate the linear stability of traveling pulses through computations in a finite albeit large domain with periodic boundary conditions the critical eigenmodes at the onset of the instabilities are related to the resulting spatiotemporal dynamics and act upon the back of the pulses the first scenario has been analyzed earlier m g zimmermann et al physica d 110 92 1997 for high excitability low excitation threshold it involves the collision of a stable pulse branch with an unstable pulse branch in a so called t point in the framework of traveling wave ordinary differential equations pulses correspond to homoclinic orbits and the t point to a double heteroclinic loop we investigate this transition for a pulse in a domain with finite length and periodic boundary conditions numerical evidence of the proximity of the infinite domain t point in this setup appears in the form of two saddle node bifurcations alternatively for intermediate excitation threshold an entire cascade of saddle nodes causing a spiraling of the pulse branch appears near the parameter values corresponding to the infinite domain t point backfiring appears at the first saddle node bifurcation which limits the existence region of stable pulses the third case found in the model for large excitation threshold is an oscillatory instability giving rise to breathing traveling pulses that periodically vary in width and speed

reliable h sub spl infin control for affine nonlinear systems this paper addresses the reliable h sub spl infin control problems for affine nonlinear systems based on the hamilton jacobi inequality approach developed in the h spl infin control problems for affine nonlinear systems a method for the design of reliable nonlinear control systems is presented the resulting nonlinear control systems are reliable in that they provide guaranteed local asymptotic stability and h sub spl infin performance not only when all control components are operational but also in the case of some component outages within a prespecified subset of control components a numerical example is also given

a multiple controller structure and design strategy with stability analysis this paper proposes a multi controller structure for a plant and develops associated stability results the main theoretical result of the paper is a quite simple necessary and sufficient condition for the closed loop stability of the scheme the result also specializes as a multi controller generalization of the single controller youla kucera theory for the class of all stabilizing controllers for a plant and to known results concerning simultaneous stabilization the plants considered are recursively expressed in terms of a set of approximations of frequency shaped plant model errors the controllers in successive loops can be designed based on increasing refinement in model approximation perhaps via on line identification an advantage of the proposed multi controller strategy is that a number of various controller design techniques can be employed to achieve performance objectives which are not conveniently achievable by any one technique a design example is included with first an lqg design applied for stabilization of a crude nominal model and then an h optimal design and finally an h2 optimal design the latter two designs are aimed at enhancing h h2 performances there could even be a further adaptive loop for on line performance enhancement

characterization of dispersive chaos and related states of binary fluid convection abstract we describe an extensive series of experiments on traveling wave convection in an ethanol water mixture with separation ratio 0 020 in a long narrow annular container as the stress parameter is quasi statically increased through the range 0 2 above onset this system evolves through a series of complex spatiotemporal states before settling into an extended pattern of steady spatially uniform convective rolls much of the dynamical behavior is influenced by strong nonlinear dispersion which causes the repeated and often irregular appearance and sudden collapse of spatially localized bursts of traveling waves small amplitude states seen very close to onset are analyzed quantitatively using a complex ginzburg landau equation complex dynamical states encountered further above onset are analyzed using a number of classical statistical techniques focusing mainly on correlation functions and fourier spectra in addition we use the technique of biorthogonal decomposition in an effort to extract the basic structures of the patterns and to characterize the complexty of their dynamics

stability and overflow oscillations in 2 d state space digital filters an important theorem relating to the lyapunov stability of two dimensional discrete systems is proven using this theorem it is shown that for any 2 d digital filter satisfying shanks criterion there exists a realization that cannot support overflow oscillations in the process of proving the theorem some interesting results on the multi dimensional bilinear transformation are developed one of these results yields a simple test that can be used to check the stability of a 2 d discrete transfer function that has been obtained from the bilinear transform of a 2 d continuous transfer function with a 2 d hurwitzian denominator polynomial a technique is given for determining whether a normal realization exists for a given 2 d discrete system also a theorem is presented that allows the determination of the norm of the minimum norm realization of a given transfer function a noniterative technique for obtaining a low norm realization and an iterative technique for obtaining a minimum norm realization are developed

front motion metastability and subcritical bifurcations in hydrodynamics metastability occurs whenever under given external conditions as defined by the reynolds number in hydrodynamics more than one linearly stable solution may exist in variational problems the preferred state is usually claimed to be the one with the lowest energy but in hydrodynamics and except for very special conditions no energy functional exists from an analogy between amplitude and reaction diffusion equations it is argued that the border separating in space two possible solutions of the flow equations as turbulent and laminar in pipe flows or boundary layers moves with a constant mean velocity depending on the control parameter the sign of this velocity allows to decide which state is stable and which is metastable possible physical implications of these ideas for various problems of hydrodynamics are discussed

reliable rm h_infty fuzzy control for continuous time nonlinear systems with actuator failures this paper is concerned with the design of reliable hinfin fuzzy controllers for continuous time nonlinear systems with actuator failures the takagi and sugeno fuzzy model is employed to represent a nonlinear system the objective is to find a stabilizing state feedback fuzzy controller such that the nominal hinfin performance is optimized while satisfying a prescribed hinfin performance constraint in the actuator failure cases based on the linear matrix inequality lmi techniques two efficient methods for the design of a suboptimal reliable hinfin fuzzy controller are proposed different lyapunov functions are used during the design for the nominal and actuator failure cases which lead to a less conservative controller design in the first method a single lyapunov function is used for the actuator failure cases the second method adopts a parameter dependent lyapunov function for the actuator failure cases which further reduces the conservatism of the design finally numerical simulations on the chaotic rossler system are given to illustrate the effectiveness of the proposed design methods

a necessary and sufficient condition for the stabilisation of a matrix and its principal submatrices abstract we present a necessary and sufficient condition for the existence of a real diagonal matrix such that its product with a given real square matrix is hurwitz together with all its principal submatrices we also give an explicit formula for a matrix which in particular supplies all the involved matrices with negative distinct eigenvalues

reliable regulation in decentralised control systems this article addresses the design of decentralised regulators which supply the control systems with signal tracking and disturbance rejection this property has to be attained to the maximum possible extent even when instrumentation faults occur thus causing the opening of some feedback loops the problem is tackled for lti asymptotically stable plants subject to perturbations under the assumption that the laplace transforms of the exogenous signals have multiple poles on the imaginary axis the proposed regulator is composed of an lti nominal controller supervised by a reconfiguration block once the actions of the reconfiguration block have been settled the synthesis of the nominal controller is reformulated as a suitable regulation problem a constructive sufficient condition for its solvability is established this condition turns out to be also necessary if the exogenous signals are polynomial in time

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

choice of dynamical variables for global reconstruction of model equations from time series the success of modeling from an experimental time series is determined to a significant extent by the choice of dynamical variables we propose a method for preliminary investigation of a time series whose purpose is to find out whether a global dynamical model with smooth functions can be constructed for the chosen variables the method consists in the estimation of single valuedness and continuity of relations between dynamical variables and variables to enter left hand sides of model equations the method is explained with numerical examples its efficiency is demonstrated by modeling a real nonlinear electric circuit

a note on efficient evaluation of polynomials and exponentials of polynomials for equispaced arguments by a h nuttall a h nuttall s see ibid vol assp 35 no 10 p 1486 7 1987 algorithm for the evaluation of a polynomial at a large number of arguments is addressed the authors supplement nuttall s treatment of the problem by 1 giving a relationship between the coefficients of the original polynomial and those of the equivalent one in terms of the integer variable n and 2 by deriving a formula for the computation of the initial values required for nuttall s recursive procedure to commence as a result of these supplements the recursive algorithm is completely programmable and can be efficiently implemented for any order n of the polynomial some general observations are made on the computational complexity in recursive evaluation in contrast to direct evaluation of a polynomial