controlled invariance for discrete time nonlinear systems with an application to the disturbance decoupling problems invariant distributions are defined for discrete time nonlinear control systems and necessary and sufficient conditions are given for their controlled invariance this extends to discrete time systems the basic tool which has been so important in solving the various synthesis problems for continuous time systems to indicate their utility in the discrete time setting they are used to locally solve the disturbance decoupling problem

the eigenvalues of second order spectral differentiation matrices the eigenvalues of the pseudospectral second derivative matrix with homogeneous dirichlet boundary conditions are important in many applications of spectral methods this paper investigates some of their properties numerical results show that a certain fraction of the eigenvalues approximate the eigenvalues of the continuous operator very accurately but the errors in the remaining ones are large it is demonstrated that the inaccurate eigenvalues correspond to those eigenfunctions of the continuous operator that cannot be resolved by polynomial interpolation in the spectral grid in particular it is proved that 7r points on average per wavelength are sufficient for successful interpolation of the eigenfunctions of the continuous operator in a chebyshev distribution of nodes and six points per wavelength for a uniform distribution these results are in agreement with the observed fractions of accurate eigenvalues by using the characteristic polynomial a bound on the spectral radius of the differentiation matrix is derived that is accurate to 2 or better the effect of filtering on the eigenvalues is studied numerically

hermite biehler routh hurwitz and total positivity simple proofs of the hermite biehler and routh hurwitz theorems are presented the total nonnegativity of the hurwitz matrix of a stable real polynomial follows as an immediate corollary

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

two dimensional fourier series based model for nonminimum phase linear shift invariant systems and texture image classification in this paper chi s 1997 1999 real one dimensional 1 d parametric nonminimum phase fourier series based model fsbm is extended to two dimensional 2 d fsbm for a 2 d nonminimum phase linear shift invariant system by using finite 2 d fourier series approximations to its amplitude response and phase response respectively the proposed 2 d fsbm is guaranteed stable and its complex cepstrum can be obtained from its amplitude and phase parameters through a closed form formula without involving complicated 2 d phase unwrapping and polynomial rooting a consistent estimator is proposed for the amplitude estimation of the 2 d fsbm using a 2 d half plane causal minimum phase linear prediction error filter modeled by a 2 d minimum phase fsbm and then two consistent estimators are proposed for the phase estimation of the 2 d fsbm using the chien et al 1997 2 d phase equalizer modeled by a 2 d all pass fsbm the estimated 2 d fsbm can be applied to modeling of 2 d non gaussian random signals and 2 d signal classification using complex cepstra some simulation results are presented to support the efficacy of the three proposed estimators furthermore classification of texture images 2 d non gaussian signals using the estimated fsbm second and higher order statistics is presented together with some experimental results finally we draw some conclusions

object and texture classification using higher order statistics the problem of the detection and classification of deterministic objects and random textures in a noisy scene is discussed an energy detector is developed in the cumulant domain by exploiting the noise insensitivity of higher order statistics an efficient implementation of this detector is described using matched filtering its performance is analyzed using asymptotic distributions in a binary hypothesis testing framework the object and texture discriminant functions are minimum distance classifiers in the cumulant domain and can be efficiently implemented using a bank of matched filters they are immune to additive gaussian noise and insensitive to object shifts important extensions which can handle object rotation and scaling are also discussed an alternative texture classifier is derived from a ml viewpoint and is statistically efficient at the expense of complexity the application of these algorithms to the texture modeling problem is indicated and consistent parameter estimates are obtained

the spectrum of the chebyshev collocation operator for the heat equation it is shown that the eigenvalues of the pseudospectral chebyshev second derivative operator with separated boundary conditions are real negative and distinct an application to the full potential equation is also presented

zeros at infinity for affine nonlinear control systems a definition of zeros at infinity for affine nonlinear control systems is proposed the definition is local which means that we exclude certain singularities we argue the reasonableness of our definition by showing its relevance to the problem of nonlinear decoupling in particular we give a necessary and sufficient condition for the solvability of the general regular decoupling problem for affine systems in terms of the zeros at infinity

the stability of pseudospectral chebyshev methods abstract the stability of pseudospectral chebyshev methods is demonstrated for parabolic and hyperbolic problems with variable coefficients the choice of collocation points is discussed numerical examples are given for the case of variable coefficient hyperbolic equations author

spectral integration of linear boundary value problems spectral integration was deployed by orszag and co workers 1977 1980 1981 to obtain stable and efficient solvers for the incompressible navier stokes equation in rectangular geometries since then several variations of spectral integration have appeared in the literature in this article we derive yet more versions of spectral integration these new versions of spectral integration rely exclusively on banded matrices as opposed to banded matrices bordered with dense rows in addition we derive a factored form of spectral integration which relies only on bi and tri diagonal matrices key properties such as the accuracy of spectral integration even when green s functions are not resolved by the underlying grid and the accuracy of spectral integration in spite of ill conditioning of underlying linear systems are investigated timed comparisons show that reducing spectral integration to bi and tri diagonal systems leads to significant speed ups

reduced complexity modeling and reproduction of colored textures an unsupervised color texture synthesis by analysis method is described the texture is reproduced to appear perceptually similar to a given prototype by copying its statistical properties up to the second order the synthesized texture is obtained at the output of a single input three output nonlinear system driven by a realization of a white gaussian random field significant complexity reduction is gained by exploiting the rank deficiency of the cross power spectral density matrix of the color texture samples

texture synthesis by analysis with hard limited gaussian processes a twin stage texture synthesis by analysis method is presented it aims to approximate first and second order distributions of the texture accordingly to the julesz conjecture in the first stage the binary textural behavior of a given prototype is represented by means of a hard limited gaussian process in the second stage the texture is synthesized by passing the binary hard limited gaussian process through a linear filter followed by a zero memory histogram equalizer

noninteracting control with stability for hamiltonian systems the problem of noninteraction with stability via dynamic state feedback is addressed and solved for a class of nonlinear hamiltonian systems a simple way to check necessary and sufficient conditions is proposed it is well known that to decide if the problem is solvable and which class of state feedback has to be used the stability properties of some special dynamics are to be investigated for this reason on the way to the main result it is shown that such dynamics are not necessarily hamiltonian several examples clarifying the role of different classes of state feedback control laws either static or dynamic in the solution of the problem are proposed

a geometric approach to the theory of 2 d systems the authors develop a geometric approach to the theory of 2 d two dimensional systems defining in a suitable way the notion of a sub 1 2 b sub 1 2 invariant subspaces and of controlled invariant subspaces such subspaces are shown to have good computational and feedback properties which make them useful in application in particular sufficient conditions and constructive procedures are obtained for the solutions of disturbance decoupling and model matching problems moreover it is shown that certain structural properties of a 2 d system can be described by means of a set of indexes defined in geometric terms and that such structural indexes can be used to reformulate the sufficient condition for model matching

parameterization of decoupling control laws for affine nonlinear systems the problem of parameterizing all the decoupling feedbacks is investigated and applied to the design of a stable noninteracting control for affine nonlinear systems an algebraic study of controlled invariance is presented it covers a new criterion for controlled invariance parameterization and novel properties of the friend set and computational aspects of the maximal controlled invariant distribution this analysis is used to derive falb wolovich like conditions for general decoupling including disturbance decoupling and noninteracting control problems it is shown that to determine all the decoupling feedbacks one usually needs infinitely many sets of controlled invariant or controllability distributions that can arise as solutions to the problems it is also shown that under certain conditions stable noninteracting design based on first parameterizing the decoupling feedbacks is still a feasible approach in the sense that a feedback can be chosen from the friend set of the maximal solution for the exponentially stable and noninteracting design problem

a nonregular solution of the nonlinear dynamic disturbance decoupling problem with an application to a complete solution of the nonlinear model matching problem the nonregular dynamic disturbance decoupling problem for nonlinear control systems is introduced a local solution is given by means of a constructive algorithm that is based on singh s algorithm and the clamped dynamics algorithm further studied is the nonlinear model matching problem that is defined as follows given a nonlinear control system to be referred to as the plant and another nonlinear control system to be referred to as the model can a compensator for the plant be found in such a way that the input output behavior of the compensated plant matches that of the model by proving that the solvability of the nonlinear model matching problem is equivalent to the solvability of an associated nonregular dynamic disturbance decoupling problem a complete local solution of this problem can be established

an instability phenomenon in spectral methods the eigenvalues of chebyshev and legendre spectral differentiation matrices which determine the allowable time step in an explicit time integration are extraordinarily sensitive to rounding errors and other perturbations on a grid of n points per space dimension machine rounding leads to errors in the eigenvalues of size o n 2 this phenomenon may lead to inconsistency between predicted and observed time step restrictions one consequence of it is that spectral differentiation by interpolation in legendre points which has a favorable o n 1 time step restriction for the model problem u t u x in theory is subject to an o n 2 restriction in practice the same effect occurs with chebyshev points for the model problem u t xu x another consequence is that a spectral calculation with a fixed time step may be stable in double precision but unstable in single precision we know of no other examples in numerical computation of this kind of precision dependent stability

spectral integration and two point boundary value problems a numerical method for two point boundary value problems with constant coefficients is developed which is based on integral equations and the spectral integration matrix for chebyshev nodes the method is stable achieves superalgebraic convergence and requires o n log n operations where n is the number of nodes in the discretization although stable spectral methods have been constructed in the past they have generally been based on reformulating the recurrence relations obtained through spectral differentiation in an attempt to avoid the ill conditioning introduced by that process

non linear non interacting control with stability in discrete time a geometric framework the aim of the paper is to set the non linear non interacting control problem with stability in discrete time in a correct geometric framework so providing a solution which recalls the continuous approach and to point out the peculiarities of discrete time dynamics geometric necessary and sufficient conditions for the solvability of the problem are given and a constructive method figures out the regular static state feedback solution it is shown that if the given dynamics is feedback equivalent to a decoupled system characterized by an invertible drift the computation of the distributions involved can be carried out in a simple and elegant way the main results are thus proved exhaustively in this case and then generalized to submersive systems

observability of autonomous discrete time non linear systems a geometric approach in this paper the observability of autonomous discrete time systems is studied from a purely differential geometric point of view as with continuous time systems this approach leads to a local canonical form for an observable system a proposal for the generalization of an invariant subspace is made

a parameterization approach to disturbance decoupling problem with stability of nonlinear systems a parameterization approach is used to deal with the disturbance decoupling problem with stability of nonlinear systems it is shown that one may cast within this approach two different methods proposed earlier a complete solution is also provided to the disturbance decoupling problem with stability for a restricted class of nonlinear systems

on decomposition of nonlinear control systems in this paper the problem is studied when the system x i k 1 u t g t x x 0 x 0 defined on an n dimensional analytic manifold can be decomposed into either independent subsystems or a cascade of subsystems necessary and sufficient conditions for the existence of such local decompositions are given in terms of lie algebras generated by the system

a perceptually lossless model based texture compression technique in natural scenes still images as well as sequences backgrounds and objects surfaces usually have a textural structure therefore in order to efficiently code images it is crucial to investigate the texture compression problem in this paper a perceptually lossless synthesis by analysis texture coding method is presented the proposed approach is model based the parameters of the model consist of a binary excitation signal and the parsimonious representation of the reconstruction filter the estimated parameters which allow to one synthesize at the decoder site a texture that is perceptually indistinguishable from the original one are then compressed using a lossless strategy which is based on a fast binary wavelet transformation specifically tailored to binary images the proposed method leads to very good perceptual results superior to those of existing techniques

dynamic decoupling for right invertible nonlinear systems abstract it is shown that every system with more inputs than outputs that is right invertible in the sense of 5 can be decoupled via a dynamic state feedback that can be computed using a given algorithm this result generalizes the one of 2 and completes the results of 3

decoupling with dynamic compensation for strong invertible affine non linear systems abstract in this paper we tackle for affine non linear systems the morgan problem i e the scalar input scalar output decoupling problem for square systems with dynamic compensation the result provided here theorem 3 1 generalizes that one previously given by wang 1970 for linear systems

a complete characterization of decoupling control laws for a general class of nonlinear systems in the past decade conditions for feedback decoupling of nonlinear systems have been studied extensively the class of control laws which decouple has received relatively little attention in this paper a characterization of the whole class of nonlinear decoupling control laws for real analytic nonlinear systems is obtained this result is important from both mathematical and engineering viewpoints for instance we present an example where former results do not allow stable decoupling while our result does the main result is proved and several examples which illustrate its generality are presented

noninteracting control with stability for a class of nonlinear systems abstract in this paper we address the problem of noninteracting control with stability for the class of nonlinear square systems for which noninteraction can be achieved without stability by means of invertible static state feedback the use of both static state feedback and dynamic state feedback is investigated we prove that in both cases the asymptotic stabilizability of certain subsystems is necessary to achieve noninteraction and stability we use this and some recent results to state a complete set of necessary and sufficient conditions in order to solve the problem

approximate noninteracting control with stability for nonlinear systems a notion of approximate noninteracting control with stability for nonlinear systems is introduced and the design of both static and dynamic state feedback control laws that achieve this property for a given plant is considered this approach to the problem is based on the notion of extended linearization and begins with an extension of the linearization approach pointwise to all constant operating points in an open neighborhood of the nominal under natural assumptions it is shown that obstructions to extract noninteracting control with internal stability or input state output stability can be circumvented in the context of approximate noninteraction

text ad _ f g text ad _ f g and locally text ad _ f g invariant and controllability distributions in the study of nonlinear control systems the concepts of an invariant foliation and an invariant distribution play important roles in this paper we explore various forms of these concepts and show how they occur in the study of controllability observability and decoupling of nonlinear systems

characterization and estimation of two dimensional arma models a class of finite order two dimensional autoregressive moving average arma is introduced that can represent any process with rational spectral density in this model the driving noise is correlated and need not be gaussian currently known classes of arma models or ar models are shown to be subsets of the above class the three definitions of markov property are discussed and the class of arma models are precisely stated which have the noncausal and semicausal markov property without imposing any specific boundary conditions next two approaches are considered to estimate the parameters of a model to fit a given image the first method uses only the empirical correlations and involves the solution of linear equations the second method is the likelihood approach since the exact likelihood function is difficult to compute we resort to approximations suggested by the toroidal models numerical experiments compare the quality of the two estimation schemes finally the problem of synthesizing a texture obeying an arma model is considered

input output decoupling of hamiltonian systems the linear case in this note we give necessary and sufficient conditions for a linear hamiltonian system to be input output decouplable by hamiltonian feedback i e feedback that preserves the hamiltonian structure in a second paper we treat the same problem for nonlinear hamiltonian systems

controlled invariance for nonlinear systems necessary and sufficient conditions are derived for a b invariance called here controlled invariance for nonlinear systems dot x f x u the obtained results generalize and elucidate already known results about systems dot x a x sum min i 1 max m u i b i x a new and direct differential geometric interpretation of the concept of controlled invariance and the derived conditions is given

on the coefficients of differentiated expansions and derivatives of jacobi polynomials a formula expressing explicitly the derivatives of jacobi polynomials of any degree and for any order in terms of the jacobi polynomials themselves is proved another explicit formula which expresses the jacobi expansion coefficients of a general order derivative of an infinitely differentiable function in terms of its original jacobi coefficients is also given the results for the special case of ultraspherical polynomials are considered the results for chebyshev polynomials of the first and second kinds and for legendre polynomials are also noted an application of how to use jacobi polynomials for solving ordinary and partial differential equations is described

a multiresolution approach for texture synthesis using the circular harmonic functions in this paper an unsupervised model based texture reproduction technique is described in accordance with the julesz s 1962 conjecture the statistical properties of the prototype up to the second order are copied in order to generate a synthetic texture perceptually indistinguishable from the given sample however this task is accomplished using a hybrid approach which operates partially in the spatial domain and partially in a multiresolution domain the latter employed is the circular harmonic function chf domain since it has been proven to be well suited for mimicking the behavior of the human visual system hvs this approach allows for a wide range of textures typologies obtaining synthetic textures that better match the prototype with respect to the ones obtained using techniques based on the julesz s conjecture operating only in the spatial domain and to dramatically reduce the computational complexity of similar methods operating only in the multiresolution domain

controlled invariance by static output feedback for nonlinear systems the paper deals with the notion of static output feedback for nonlinear systems necessary and sufficient conditions are derived for c a b invariance here called measured controlled invariance for nonlinear control systems

two dimensional spectrum estimation using noncausal autoregressive models two dimensional 2 d spectrum estimation from raw data is of interest in signal and image processing a parametric technique for spectrum estimation using 2 d noncausal autoregressive ncar models is given the ncar models characterize the statistical dependency of the observation at location s on its neighbors in all directions this modeling assumption reduces the spectrum estimation problem to two subproblems the choice of appropriate structure of the ncar model and the estimation of parameters in ncar models by assuming that the true structure of the ncar model is known we first analyze the existence and uniqueness of gaussian maximum likelihood gml estimates of ncar model parameters due to the noncausal nature of the models the computation of gml estimates is burdensome by assuming specific boundary conditions computationally tractable expressions are obtained for the likelihood function expressions for the asymptotic covariance matrix of the gml estimates as well as the simultaneous confidence bands for the estimated spectrum using gml estimates are derived finally the usefulness of the method is illustrated by computer simulation results

characterization of allowable perturbations for robust decoupling of affine non linear systems for affine non linear systems we study the effects of uncertainties in systems vector fields on decoupled linear input output behaviour a characterization of an allowable class of perturbations which preserve the decoupling properties of the nominal system is given an immediate consequence of this characterization indicates that decoupling position control of rigid robotic manipulators is not robust under any perturbations in robot dynamics the result is applied to simple hamiltonian control systems to characterize the allowable perturbation of total energy function

generalized output regulation problem for a class of nonlinear systems with nonautonomous exosystem the problem of the generalized output regulation is considered here in contrast to the classical output regulation problem where the references to be tracked and disturbances to be rejected are generated by an autonomous exogeneous system for the generalized output regulation an exogenous system is driven by an unknown external reference signal in such a way the class of reference or disturbance signals is expanded presented result solves the full measurement feedback case and is based on the well known notion of the regulator equation combined with the classical concept of the invariant distribution illustrative example including matlab simulink simulations is presented to demonstrate the suggested approach

on solvability of several affine system problems we examine seven problems and properties of single input single output affine control systems and classify the properties topologically as being structural generic or residual these properties are accessibility observability invertibility preservation of a given distribution and partial linearizability the mathematics involved relies upon the thorn transversality theorem

local nonlinear model matching from linearity to nonlinearity the model matching problem consists of designing a compensator for a given system called the plant in such a way that the resulting input output behaviour matches that of a prespecified model in this paper a local solution of the nonlinear model matching problem is given for the case that the model is decouplable by static state feedback the main theorem states that under generic conditions on the plant the problem is solvable around an equilibrium point if and only if it is solvable for the linearization of plant and model the generic conditions are identified they naturally appear in the solution of the dynamic input output decoupling problem for the plant the theory is illustrated by means of two examples

estimation of linear parametric models of nongaussian discrete random fields with application to texture synthesis a general possibly asymmetric noncausal and or nonminimum phase 2d autoregressive moving average random field model driven by an independent and identically distributed 2d nongaussian sequence is considered the model is restricted to be invertible i e system zeros are not allowed to lie on the unit bicircle three performance criteria are investigated for parameter estimation of the system parameters given only the output measurements image pixels the proposed criteria are functions of the higher order cumulant statistics of an inverse filter output one of these criteria is novel and the others have been considered in past only for moving average inverses and without any analysis of their consistency in the paper strong consistency of the proposed methods under the assumption that the system order is known is proved the convergence of the proposed parameter estimators under overparametrization is also analyzed experimental results involving synthesized as well as real life textures are presented to illustrate the performance of two of the considered approaches experimental results of synthesis of 128 spl times 128 textures visually resembling several real life textures in the brodatz album and other sources are presented

texture synthesis using 2 d noncausal autoregressive models the purpose of this paper is to illustrate the usefulness of two dimensional noncausal autoregressive ncar models for the synthesis of textures these models characterize the gray level at a pixel as a linear combination of gray levels at nearby locations in all directions and an additive white noise variable we first show that the class of ncar models is capable of generating a wide variety of image patterns posessing the local replication attribute an essential ingredient of many natural textures it is also shown that the theoretical variograms of many ncar models possess an oscillatory behavior a characteristic of the variograms of many natural textures next we give experimental results of synthesis of 64 64 textures resembling several real textures in the brodatz album the synthetic textures generated by 16 parameter ncar models retain most the visual characteristics of the original textures the variograms of the original and synthetic textures are also similar

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

a sufficient condition for nonlinear noninteracting control with stability via dynamic state feedback a sufficient condition is given to solve the problem of achieving local noninteracting control with asymptotic stability via dynamic state feedback for a nonlinear affine system the condition which is automatically satisfied in the case of linear systems although only sufficient is helpful in overcoming some of the geometric obstructions pointed out in the literature an example in which the author assumptions are satisfied is given clearly showing how to construct a decoupling and stabilizing dynamic state feedback and how the condition can weaken the requirement that the p dynamics be locally asymptotically stable

higher order spectrum factorization in one and two dimensions with applications in signal modeling and nonminimum phase system identification the problem of modeling a given higher order spectrum as that of the output of a linear time invariant lti system driven by a higher order white random signal is discussed this can be posed as a higher order spectrum factorization problem a theorem is provided to discuss the existence of such a factorization a fast algorithm for efficient implementation of the higher order spectrum factorization if it exists is then proposed the results are extended to two dimensions straightforwardly the relationship of the higher order spectrum factorization problem to the well known power spectrum factorization is also discussed as applications the problems of identification of nonminimum phase lti systems given the higher order statistics of both input and output processes and phase reconstruction are presented experimental results are provided for the one dimensional case

geometric tools for solving the fdi problem for linear periodic discrete time systems this paper studies the problem of detecting and isolating faults in linear periodic discrete time systems the aim is to design an observer based residual generator where each residual is sensitive to one fault whilst remaining insensitive to the other faults that can affect the system making use of the geometric tools and in particular of the outer observable subspace notion the fault detection and isolation fdi problem is formulated and necessary and solvability conditions are given an algorithmic procedure is described to determine the solution of the fdi problem

fitting ma models to linear non gaussian random fields using higher order cumulants a general possibly nonminimum phase and or asymmetric noncausal two dimensional 2 d moving average ma model driven by a zero mean i i d 2 d sequence is considered the input sequence is not observed the signal observations may be noisy we consider the problems of model order determination and model parameter estimation using the higher order third or fourth order for example cumulants of the 2 d signal second order statistics of the data can consistently identify only a smaller class of ma models the proposed approaches are illustrated via computer simulations

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

maximum standardized cumulant deconvolution of non gaussian linear processes a linear process is represented as a driving white noise convolved with a system response sequence the concept of natural peakedness of a system response sequence is defined and its properties are investigated utilizing natural peakedness the convergence theory of maximum standardized cumulant deconvolution is established and the uniqueness theorem of non gaussian linear process representations is proved in addition autoregressive models on a countable abelian group are defined and the relation between cumulant deconvolution and autoregressive models is given

the standard decomposed system and noninteracting feedback control of nonlinear systems conditions for achieving noninteraction in nonlinear multivariable systems via the decomposition of state space are well established the main contribution of this paper is to fully characterize the class of decomposing control laws the characterization corresponds to a family of simple control laws which are applied to a standard decomposed system sds the sds is similar to the decomposed system of isidori krener gori giorgi and monaco but has a finer structure the finer structure parallels the one used by gilbert for linear systems a weaker form of noninteraction based on input output behavior is decoupling some connections between decomposition and decoupling are also established an example illustrating the importance of the results is given

spectrum of the jacobi tau approximation for the second derivative operator it is proved that the eigenvalues of the jacobi tau method for the second derivative operator with dirichlet boundary conditions are real negative and distinct for a range of the jacobi parameters special emphasis is placed on the symmetric case of the gegenbauer tau method where the range of parameters included in the theorems can be merged and characteristic polynomials given by successive order approximations interlace this includes the common chebyshev and legendre tau and galerkin methods

the local disturbance decoupling problem with stabilty for nonlinear systems in this paper the disturbance decoupling problem with stability ddps for nonlinear systems is considered the ddps is the problem of finding a feedback such that after applying this feedback the disturbances do not influence the output anymore and x 0 is an exponentially stable equilibrium point of the feedback system for systems that can be decoupled by static state feedback it is possible to define under fairly mild assumptions a distribution s which is the nonlinear analogue of the linear v s the largest stabilizable controlled invariant subspace in the kernel of the output mapping and to prove that the ddps is locally solvable if and only if the disturbance vector fields are contained in s

identification and deconvolution of multichannel linear non gaussian processes using higher order statistics and inverse filter criteria this paper is concerned with the problem of estimation and deconvolution of the matrix impulse response function of a multiple input multiple output mimo system given only the measurements of the vector output of the system the system is assumed to be driven by a temporally i i d and spatially independent non gaussian vector sequence which is not observed an iterative inverse filter criteria based approach is developed using the third order or the fourth order normalized cumulants of the inverse filtered data at zero lag stationary points of the proposed cost functions are investigated the approach is input iterative i e the input sequences are extracted and removed one by one the matrix impulse response is then obtained by cross correlating the extracted inputs with the observed outputs identifiability conditions are analyzed the strong consistency of the proposed approach is also briefly discussed computer simulation examples are presented to illustrate the proposed approaches

a mathcal b invariant distributions and disturbance decoupling of nonlinear systems the concept of a b invariant subspaces has resulted in a unified approach to many of the basic structural properties of time invariant linear systems w m wonham lecture notes in economics and mathematical systems vol 101 springer verlag new york 1974 the purpose of this paper is to introduce the more general notion of a mathcal b invariant distributions on differentiable manifolds and to use this idea to study the disturbance decoupling problem for a class of nonlinear systems which evolve on real analytic manifolds

bisimilar control affine systems the notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation these equivalences are in turn used to simplify verification and synthesis for these models as well as to enable compositional reasoning in systems theory a similar notion is also of interest in order to develop modular verification and design tools for purely continuous or hybrid control systems in this paper we introduce two notions of bisimulation for nonlinear systems we present differential geometric characterizations of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions furthermore we also show that all bisimilar systems of different dimension are of this form

the spectrum of the gegenbauer collocation approximation for the second derivative operator abstract it is proved that the eigenvalues of the gegenbauer collocation method for the second derivative operator with dirichlet boundary conditions are real negative and distinct for a range of the gegenbauer parameter this range includes the chebyshev collocation approximation the result is also extended to neumann and robin boundary conditions

a canonical dynamic extension for noninteraction with stability for affine nonlinear square systems we study the problem of noninteracting control with stability via dynamic feedback for continuous affine nonlinear square systems given a system which may not be decouplable via static state feedback but is decouplable via dynamic feedback a canonical dynamic extension is constructed we show that every dynamic extension contains this canonical one hence the mix dynamics as defined by wagner of the canonical extension is contained in every other dynamic extension following wagner s result the stability of this mix dynamics is necessary for noninteraction with internal stability the results in this paper show that under some regularity assumptions in the investigation of noninteraction with stability one can assume without loss of generality that the system is decouplable via static state feedback

implementation of 2 d digital filters by iterative methods a two dimensional 2 d rational filter can be implemented by an iterative computation involving only finite extent impulse response fir filtering operations provided a certain convergence criterion is met in this paper we generalize this procedure so that the convergence criterion is satisfied for any stable 2 d rational transfer function one formulation which guarantees convergence invokes a relaxed form of the iterative computation along with prefiltering the numerator and denominator polynomials of the rational transfer function this implementation may be applied with a frequency varying relaxation parameter for increasing the rate of convergence an alternative generalization uses several previously computed iterates unlike our first modification which utilizes only the most recently computed iterate this formulation can potentially guarantee convergence and also increase the convergence rate without the requirement of prefiltering another extension of the iterative computation incorporates constraints e g positivity or finite extent on the output of each iteration proof of convergence of such constrained iterations relies on the concept of a nonexpansive operator in particular the error introduced within the converging solution resulting from a finite extent constraint is shown to satisfy a homogeneous partial difference equation finally this error computation leads to an important link between our iterative implementation with constraints and an iterative solution to partial difference equations e g laplace s equation with known boundary conditions

fixed modes and nonlinear noninteracting control with stability the existence of a fixed internal dynamics inherent to the noninteraction requirement is identified when unstable this represents an obstruction to the achievement of noninteracting control with stability by means of static state feedback remarkably whenever one leaves the class of linear systems this obstruction cannot in general be removed by dynamic state feedback

new results on f g invariance abstract the existing result for a nonsingular and involutive distribution to be f g invariant has a priori assumption that g is nonsingular this paper treats the problem of f g invariance for the case where g is singular necessary and sufficient conditions for a nonsingular and involutive distribution to be f g invariant are presented the constructive proof provides an algorithm for the construction of the feedback law

the regular local noninteracting control problem for nonlinear control systems we study the noninteracting control problem for affine nonlinear control systems under the assumption that the number of scalar inputs equals the number of vector outputs our purpose is to find a static state feedback law for the system which achieves noninteraction using the recently developed differential geometric approach to nonlinear systems theory and working under a set of regularity assumptions we give necessary and sufficient conditions for the local solvability of the problem this work extends earlier results in the geometric approach for linear systems

new criteria for blind deconvolution of nonminimum phase systems channels a necessary and sufficient condition for blind deconvolution without observing the input of nonminimum phase linear time invariant systems channels is derived based on this condition several optimization criteria are proposed and their solution is shown to correspond to the desired response these criteria involve the computation only of second and fourth order moments implying a simple tap update procedure the proposed methods are universal in the sense that they do not impose any restrictions on the probability distribution of the unobserved input sequence it is shown that in several important cases e g when the additive noise is gaussian the proposed criteria are essentially unaffected

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

the eps method a new method for constructing pseudospectral derivative operators we develop a new type of derivative matrix for pseudospectral methods the norm of these matrices grows at the optimal rate o n 2 for n by n matrices in contrast to standard pseudospectral constructions that result in o n 4 growth of the norm the smaller norm has a big advantage when using the derivative matrix for solving time dependent problems such as wave propagation the construction is based on representing the derivative operator as an integral kernel and does not rely on the interpolating polynomials in particular we construct second derivative matrices that incorporate dirichlet or neumann boundary conditions on an interval and on the disk but the method can be used to construct a wide variety of commonly used operators for solving pdes and integral equations the construction can be used with any quadrature including traditional gauss legendre quadratures but we have found that by using quadratures based on prolate spheroidal wave functions we can achieve a near optimal sampling rate close to two points per wavelength even for non periodic problems we provide numerical results for the new construction and demonstrate that the construction achieves similar or better accuracy than traditional pseudospectral derivative matrices while resulting in a norm that is orders of magnitude smaller than the standard construction to demonstrate the advantage of the new construction we apply the method for solving the wave equation in constant and discontinuous media and for solving pdes on the unit disk we also present two compression algorithms for applying the derivative matrices in o nlogn operations

a sufficient condition for non linear non interacting control with stability via dynamic state feedback block partitioned outputs a geometric sufficient condition is given for the first time to solve the problem of non linear block non interacting control with stability by means of dynamic state feedback this result extends a previous sufficient condition given by the same author battilotti 1991

image modeling using inverse filtering criteria with application to textures statistical approaches to image modeling have largely relied upon random models that characterize the 2 d process in terms of its first and second order statistics and therefore cannot completely capture phase properties of random fields that are non gaussian this constrains the parameters of noncausal image models to be symmetric and therefore the underlying random field to be spatially reversible research indicates that this assumption may not be always valid for texture images in this paper higher than second order statistics are used to derive and implement two classes of inverse filtering criteria for parameter estimation of asymmetric noncausal autoregressive moving average arma image models with known orders contrary to existing approaches fir inverse filters are employed and image models with zeros on the unit bicircle can be handled one of the criteria defines the smallest set of cumulant lags necessary for identifiability of these models to date consistency of these estimators is established and their performance is evaluated with monte carlo simulations as well as texture classification and synthesis experiments

nonlinear morgan s problem case of p 1 inputs and p outputs noninvertible static state feedback solutions of the row by row decoupling problem are investigated for the class of nonlinear systems having one more input component than output components the analysis involves a combination of geometric and algebraic tools but notably avoids the use of regular or degenerate controllability distribution subspaces the main tools used to date for the class of linear systems the main idea is finding within the system a chain of integrators that may be attached to one of the inputs in order to appropriately modify the system s structure at infinity

internally exponentially stable non linear discrete time non interacting control via static feedback the problem of discrete time block non interacting control with internal exponential stability is treated by identifying the linearized fixed modes common to every non interactive closed loop a necessary condition for achieving an exponentially stable solution to the problem is provided also through a special decomposition of the given system a sufficient condition is obtained owing to peculiarities intrinsic to discrete time non linear systems the development of the solution is not completely parallel to that of the solution for the class of continuous time systems

gegenbauer tau methods with and without spurious eigenvalues it is proven that a class of gegenbauer tau approximations to a fourth order differential eigenvalue problem of a hydrodynamic type provides real negative and distinct eigenvalues as is the case for the exact solutions this class of gegenbauer tau methods includes chebyshev and legendre galerkin and inviscid galerkin but does not include chebyshev and legendre tau rigorous and numerical results show that the results are sharp positive or complex eigenvalues arise outside of this class the widely used modified tau approach is proved to be equivalent to the galerkin method

two dimensional frequency domain blind system identification using higher order statistics with application to texture synthesis in this paper shalvi and weinstein s 1993 super exponential se algorithm using higher order statistics for blind deconvolution of one dimensional 1 d linear time invariant systems is extended to a two dimensional 2 d se algorithm then a 2 d frequency domain blind system identification bsi algorithm for 2 d linear shift invariant lsi systems using the computationally efficient 2 d se algorithm and the 2 d linear prediction error filter is proposed in addition to the lsi system estimate the proposed bsi algorithm also provides a minimum mean square error mmse equalizer estimate and an mmse signal enhancement filter estimate then a texture synthesis method tsm using the proposed bsi algorithm is presented some simulation results to support the efficacy of the proposed bsi algorithm and some experimental results to support the efficacy of the proposed tsm are presented finally some conclusions are drawn