noncoherent capacity of underspread fading channels we derive bounds on the noncoherent capacity of wide sense stationary uncorrelated scattering wssus channels that are selective both in time and frequency and are underspread i e the product of the channel s delay spread and doppler spread is small the underspread assumption is satisfied by virtually all wireless communication channels for input signals that are peak constrained in time and frequency we obtain upper and lower bounds on capacity that are explicit in the channel s scattering function are accurate for a large range of bandwidth and allow to coarsely identify the capacity optimal bandwidth as a function of the peak power and the channel s scattering function we also obtain a closed form expression for the first order taylor series expansion of capacity in the infinite bandwidth limit and show that our bounds are tight in the wideband regime for input signals that are peak constrained in time only and hence allowed to be peaky in frequency we provide upper and lower bounds on the infinite bandwidth capacity our lower bound is closely related to a result by viterbi 1967 we find cases where the bounds coincide and hence the infinite bandwidth capacity is characterized exactly the analysis in this paper is based on a discrete time discrete frequency approximation of wssus time and frequency selective channels this discretization takes the underspread property of the channel explicitly into account

identification of sparse linear operators we consider the problem of identifying a linear deterministic operator from its response to a given probing signal for a large class of linear operators we show that stable identifiability is possible if the total support area of the operator s spreading function satisfies 1 2 this result holds for an arbitrary possibly fragmented support region of the spreading function does not impose limitations on the total extent of the support region and most importantly does not require the support region to be known prior to identification furthermore we prove that stable identifiability of almost all operators is possible if 1 this result is surprising as it says that there is no penalty for not knowing the support region of the spreading function prior to identification algorithms that provably recover all operators with 1 2 and almost all operators with 1 are presented

observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

hybrid dead beat observers for a class of nonlinear systems this paper studies both the full order and the reduced order dead beat observer problem for a class of nonlinear systems linear in the unmeasured states a novel hybrid observer design strategy is proposed with the help of the notion of strong observability in finite time the proposed methodology is applied for the estimation of the frequency of a sinusoidal signal the results show that accurate estimation can be provided even if the signal is corrupted by high frequency noise a brief discussion of the robustness properties of the proposed observer with respect to measurement errors is also provided

time frequency localization operators a geometric phase space approach the author defines a set of operators which localize in both time and frequency these operators are similar to but different from the low pass time limiting operator the singular functions of which are the prolate spheroidal wave functions the author s construction differs from the usual approach in that she treats the time frequency plane as one geometric whole phase space rather than as two separate spaces for disk shaped or ellipse shaped domains in time frequency plane the associated localization operators are remarkably simple their eigenfunctions are hermite functions and the corresponding eigenvalues are given by simple explicit formulas involving the incomplete gamma functions

the principal series for a reductive symmetric space ii eisenstein integrals in this paper we develop a theory of eisenstein integrals related to the principal series for a reductive symmetric space g h here g is a real reductive group of harish chandra s class an involution of g and h an open subgroup of the group g of xed points for the group g itself is a symmetric space for the left right action of g g we refer to this setting as the group case up to a normalization our eisenstein integrals generalize those of harish chandra 18 associated with a minimal parabolic subgroup in the group case

on the existence of a kazantzis kravaris luenberger observer we state sufficient conditions for the existence on a given open set of the extension to nonlinear systems of the luenberger observer as it has been proposed by kazantzis and kravaris we prove it is sufficient to choose the dimension of the system giving the observer less than or equal to 2 twice the dimension of the state to be observed we show that it is sufficient to know only an approximation of the solution of a pde needed for the implementation we establish a link with high gain observers finally we extend our results to systems satisfying an unboundedness observability property

non coercive lyapunov functions for infinite dimensional systems abstract we show that the existence of a non coercive lyapunov function is sufficient for uniform global asymptotic stability ugas of infinite dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied for evolution equations in banach spaces with lipschitz continuous nonlinearities these additional assumptions become especially simple the results encompass some recent results on linear switched systems on banach spaces finally we derive new non coercive converse lyapunov theorems and give some examples showing the necessity of our assumptions

identification of parametric underspread linear systems and super resolution radar identification of time varying linear systems which introduce both time shifts delays and frequency shifts doppler shifts is a central task in many engineering applications this paper studies the problem of identification of underspread linear systems ulss whose responses lie within a unit area region in the delay doppler space by probing them with a known input signal it is shown that sufficiently underspread parametric linear systems described by a finite set of delays and doppler shifts are identifiable from a single observation as long as the time bandwidth product of the input signal is proportional to the square of the total number of delay doppler pairs in the system in addition an algorithm is developed that enables identification of parametric ulss from an input train of pulses in polynomial time by exploiting recent results on sub nyquist sampling for time delay estimation and classical results on recovery of frequencies from a sum of complex exponentials finally application of these results to super resolution target detection using radar is discussed specifically it is shown that the proposed procedure allows to distinguish between multiple targets with very close proximity in the delay doppler space resulting in a resolution that substantially exceeds that of standard matched filtering based techniques without introducing leakage effects inherent in recently proposed compressed sensing based radar methods

time frequency analysis of localization operators abstract we study a class of pseudodifferential operators known as time frequency localization operators anti wick operators gabor toeplitz operators or wave packets given a symbol a and two windows 1 2 we investigate the multilinear mapping from a 1 2 s r 2d s r d s r d to the localization operator aa 1 2 and we give sufficient and necessary conditions for aa 1 2 to be bounded or to belong to a schatten class our results are formulated in terms of time frequency analysis in particular we use modulation spaces as appropriate classes for symbols and windows

global exponential observers for two classes of nonlinear systems abstract this paper develops sufficient conditions for the existence of global exponential observers for two classes of nonlinear systems i the class of systems with a globally asymptotically stable compact set and ii the class of systems that evolve on an open set in the first class the derived continuous time observer also leads to the construction of a robust global sampled data exponential observer under additional conditions two illustrative examples of applications of the general results are presented one is a system with monotone nonlinearities and the other is a chemostat system

continuous discrete observer for state affine systems with sampled and delayed measurements the observation of a class of multi input multi output mimo state affine systems with both sampled and delayed output measurements is addressed these two constraints disturb simultaneously the convergence of the observer assuming some persistent excitation conditions to hold and by using lyapunov tools adapted to impulsive systems two classes of global exponential observers are proposed some explicit relations between maximum allowable delay and maximum allowable sampling period are given an extension to some classes of nonlinear systems is also given

identification of channels with single and multiple inputs and outputs under linear constraints abstract the channel identification problem for multiple input multiple output mimo channels under linear constraints can be formulated as solving a linear system which involves finite dimensional gabor matrices and a pre determined unstructured matrix that represents the linear constraints while matrices of the latter type are fixed a priori by the constraints gabor matrices depend on the choice of their generating windows which is often chosen by the user this is important since even if the matrix associated with the linear constraints is ill conditioned the full system may be solvable if the windows are designed appropriately we prove that linear constraints consisting of a single equation always remove a single degree of freedom in the channel identification problem in the sense that preknowledge of such constraints allows identification of mimo channels with support size one greater than the fundamental limit however we give an explicit example showing that this statement does not generalize to the case of multiple constraints in the single input single output siso case we provide some sufficient conditions on the linear side constraints under which the corresponding siso channels are identifiable

a relaxed condition for stability of nonlinear observer based controllers we study certainty equivalence design of observer based controllers and present a new stability condition that exploits state dependent convergence properties of observers this result eliminates the conservatism of treating the observer error as an exogeneous disturbance as an application we show that the reduced order variant of the class of observers in automatica 37 2001 9231 preserves global asymptotic stability in a certainty equivalence implementation in another application we study a nonminimum phase system which cannot be stabilized with the existing output feedback designs

fourier transforms on a semisimple symmetric space let g h be a semisimple symmetric space that is g is a connected semisimple real lie group with an involution and h is an open subgroup of the group of xed points for in g the main purpose of this paper is to study an explicit fourier transform on g h in terms of general representation theory the abstract fourier transform of a compactly supported smooth function f 2 c 1 c g h is given by see 5 1 f f zg h f x x dx for h a unitary irreducible representation of g and 2 h an h invariant distribution vector for here dx is the invariant measure on g h thus f isa smooth vector for h depending linearly on our goal is to obtain an explicit version of the restriction of this fourier transform to representations h in the minimal unitary principal series h for g h under the assumption that the center of g is nite in a sequel 9 to this paper it will be proved that a function f 2 c 1 c g h is uniquely determined by the restriction of f to this series a priori it is known that f is determined by f

observers for linearly unobservable nonlinear systems we provide a method for constructing local observers for some nonlinear systems around a critical point where the linearization is not observable or not detectable two examples are provided to illustrate the results of the paper

singular values of compact pseudodifferential operators abstract this paper investigates the asymptotic decay of the singular values of compact operators arising from the weyl correspondence the motivating problem is to find sufficient conditions on a symbol which ensure that the corresponding operator has singular values with a prescribed rate of decay the problem is approached by using a gabor frame expansion of the symbol to construct an approximating finite rank operator this establishes a variety of sufficient conditions for the associated operator to be in a particular schatten class in particular an improvement of a sufficient condition of daubechies for an operator to be trace class is obtained in addition a new development and improvement of the calderon vaillancourt theorem in the context of the weyl correspondence is given additional results of this type are then obtained by interpolation

global existence of solutions of differential inclusions abstract in this paper we consider sufficient conditions for global existence of solutions to a differential inclusion dx dt f t x assuming existence of local solutions to it by means of lyapunov s second method our theorem includes as special cases s w seah s theorems 1982 j math anal appl 89 648 663

on uniform boundedness of parameterized discrete time systems with decaying inputs applications to cascades a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been established recently within this framework naturally arises the need to investigate stability properties of parameterized discrete time systems further results that guarantee appropriate stability of the parameterized family of discrete time systems that is used within this framework have been also established for systems with cascaded structure a fundamental condition that is required in this framework is uniform boundedness of solutions of the cascade however this is difficult to check in general in this paper we provide a range of sufficient conditions for uniform boundedness that are easier to check these results further contribute to the toolbox for controller design of sampled data nonlinear systems via their approximate discrete time models

on observer based fault detection for nonlinear systems abstract this paper addresses analysis and integrated design of observer based fault detection fd for nonlinear systems to gain a deeper insight into the observer based fd framework definitions and existence conditions for nonlinear observer based fd systems are studied first then a scheme for an integrated design of observer based fd systems for affine nonlinear systems is proposed our work is considerably inspired by the study on input output stability and stabilization of nonlinear systems examples are given at the end of the paper to illustrate the theoretical results

fourier inversion on a reductive symmetric space let x be a semisimple symmetric space in previous papers 8 and 9 we have dened an explicit fourier transform for x and shown that this transform is injective on the space c 1 c x ofcompactly supported smooth functions on x in the present paper which is a continuation of these papers we establish an inversion formula for this transform

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

nonlinear observer design in the siegel domain we extend the method of kazantzis and kravaris systems control lett 34 1998 pp 241 247 for the design of an observer to a larger class of nonlinear systems the extended method is applicable to any real analytic observable nonlinear system it is based on the solution of a first order singular nonlinear pde this solution yields a change of state coordinates which linearizes the error dynamics under very general conditions the existence and uniqueness of the solution is proved lyapunov s auxiliary theorem and siegel s theorem are obtained as corollaries the technique is constructive and yields a method for constructing approximate solutions

global exponential sampled data observers for nonlinear systems with delayed measurements abstract this paper presents new results concerning the observer design for certain classes of nonlinear systems with both sampled and delayed measurements by using a small gain approach we provide sufficient conditions which involve both the delay and the sampling period ensuring exponential convergence of the observer system error the proposed observer is robust with respect to measurement errors and perturbations of the sampling schedule moreover new results on the robust global exponential state predictor design problem are provided for wide classes of nonlinear systems

weighted zak transforms and the dual tiling condition abstract for t 0 and a periodic complex valued sequence c we introduce the weighted zak transform z c t and study its properties as our main result we give characterizations for mapping properties and unitarity of z c t l 2 r l 2 s where functions in the image are understood as restrictions to a set s r 2 in particular we show that for almost every choice of l periodic sequences c the mapping properties of z c t l 2 r l 2 s simplify to statements on the geometry of s they involve a dual tiling condition on s with respect to the lattices t z z and l t z l z where 1 l t

sampling and reconstruction of operators we study the recovery of operators with a bandlimited kohn nirenberg symbol from the action of such operators on a weighted impulse train a procedure we refer to as sampling of operators kailath bello and later kozek and the authors have shown that the sampling of operators is possible if the symbol of the operator is bandlimited to a set with area less than one in this paper we develop the theory of the sampling of operators in analogy with the classical theory of sampling of bandlimited functions we define the notions of sampling set and sampling rate for operators and give necessary and sufficient conditions on the sampling rate that depend on the size and geometry of the bandlimiting set we develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions we give necessary and sufficient conditions on the bandlimiting set under which sampling of operators is possible by their action on a given periodically weighted delta train we show that under mild geometric conditions on the bandlimiting set classes of operators are bandlimited to an unknown set of area less than one half permit sampling and reconstruction we generalize two results of the heckel and bolcskei concerning sampling of operators with area not greater than one half and less than one respectively by finding a larger class of operators to which they apply operators with bandlimited symbols have been used to model doubly dispersive communication channels with slowly time varying impulse response the results in this paper are rooted in work by bello and kailath in the 1960s

estimation of ambiguity functions with limited spread in this correspondence we propose a class of estimators of the ambiguity function of a discrete time process using thresholding to this purpose the distributional and moment properties of the empirical ambiguity function for a realization of an analytic random process are derived and the moments for the special cases of stationary uniformly modulated and deterministic signals immersed in noise processes are determined suitable thresholds are chosen based on the distributional properties of the empirical ambiguity function and the procedure is tested on simulated data

density theorems for sampling and interpolation in the bargmann fock space we give a complete description of sampling and interpolation in the bargmann fock space based on a density concept of beurling roughly speaking a discrete set is a set of sampling if and only if its density in every part of the plane is strictly larger than that of the von neumann lattice and similarly a discrete set is a set of interpolation if and only if its density in every part of the plane is strictly smaller than that of the von neumann lattice

the plancherel decomposition for a reductive symmetric space i spherical functions we prove the plancherel formula for spherical schwartz functions on a reductive symmetric space our starting point is an inversion formula for spherical smooth compactly supported functions the latter formula was earlier obtained from the most continuous part of the plancherel formula by means of a residue calculus in the course of the present paper we also obtain new proofs of the uniform tempered estimates for normalized eisenstein integrals and of the maass selberg relations satisfied by the associated c functions

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example

observer design for systems with multivariable monotone nonlinearities globally convergent observers are designed for a class of systems with multivariable nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a state dependent multivariable nonlinearity we first extend an earlier design automatica 37 12 2001 1923 to multivariable nonlinearities satisfying an analog of the scalar nondecreasing property next we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system this relaxed design renders the feasibility conditions less restrictive and widens the applicability of the observer as illustrated with examples finally output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters

on accumulated spectrograms we study the eigenvalues and eigenfunctions of the time frequency localization operator h on a domain of the time frequency plane the eigenfunctions are the appropriate prolate spheroidal functions for an arbitrary domain r indeed in analogy to the classical theory of landau slepianpollak the number of eigenvalues of h in 1 1 is equal to the measure of up to an error term depending on the perimeter of the boundary of our main results show that the spectrograms of the eigenfunctions corresponding to the large eigenvalues which we call the accumulated spectrogram form an approximate partition of unity of the given domain we derive asymptotic non asymptotic and weak l error estimates for the accumulated spectrogram as a consequence the domain can be approximated solely from the spectrograms of eigenfunctions without information about their phase

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

on the invertibility of rectangular bi infinite matrices and applications in time frequency analysis abstract finite dimensional matrices with more columns than rows have no left inverses while those with more rows than columns have no right inverses we give generalizations of these simple facts to bi infinite matrices our results are then used to obtain density results for p frames of time frequency molecules in modulation spaces and identifiability results for operators with bandlimited kohn nirenberg symbols

measurement of time variant linear channels the goal of channel measurement or operator identification is to obtain complete knowledge of a channel operator by observing the image of a finite number of input signals in this paper it is shown that the spreading support of the operator that is the support of the symplectic fourier transform of the kohn nirenberg symbol of the operator has area less than one then the operator is identifiable if the spreading support is larger than one then the operator is not identifiable the shape of the support region is essentially arbitrary thereby proving a conjecture of bello the input signal considered is a weighted delta train where the weights are the window function of a finite gabor system whose elements satisfy a certain robust completeness property

an efficient parametric technique for doppler delay estimation receiving an output signal that is a weighted sum of doppler and delay shifted versions of an input signal arises in various engineering systems including radar sonar and communications it is often desired to estimate the doppler and delay parameters from noisy measurements of the output signal an estimation algorithm is developed herein for the doppler frequencies delays and amplitudes for a specific choice of the input the algorithm is based on a computationally efficient search free frequency estimation technique for the sum of complex exponentials asymptotic performance bounds are developed for the estimated parameters simulation results show that the variance of the estimation error is close to the bound above a threshold signal to noise ratio indicating that the estimation algorithm is statistically efficient

fourier and poisson transformation associated to a semisimple symmetric space soit g un groupe de lie semisimple connexe contenu dans un groupe de lie semisimple simplement connexe dont l algebre de lie est la complexification de celle de g soit une involution non triviale de g et une involution de cartan commutant avec soit h un groupe point fixe de on etudie les representations h spheriques de dimension finie de g contenant un vecteur k fixe ou k est un sous groupe compact maximal stable de g sous representations de dimension finie de le noyau de poisson la distribution u i la transformation de fourier et poisson formules integrales

estimation of overspread scattering functions in many radar scenarios the radar target or the medium is assumed to possess randomly varying parts the properties of the target are described by a random process known as the spreading function its second order statistics under the wssus assumption are given by the scattering function recent developments in operator sampling theory suggest novel channel sounding procedures that allow for the determination of the spreading function given complete statistical knowledge of the operator echo from a single sounding by a weighted pulse train we construct and analyze a novel estimator for the scattering function based on these findings our results apply whenever the scattering function is supported on a compact subset of the time frequency plane we do not make any restrictions either on the geometry of this support set or on its area our estimator can be seen as a generalization of the averaged periodogram estimator for the case of a non rectangular geometry of the support set of the scattering function

design of continuous discrete observers for time varying nonlinear systems we present a new design for continuous discrete observers for a large class of continuous time nonlinear time varying systems with discrete time measurements using the notion of cooperative systems we show that the solutions of the observers converge to the solutions of the original system under conditions on the nonlinear terms and on the largest sampling interval our conditions are given by explicit expressions

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

non uniform in time robust global asymptotic output stability abstract the notions of non uniform in time robust global asymptotic output stability and robust forward completeness for time varying systems are introduced necessary and sufficient conditions and lyapunov like characterizations are given for these notions

generalised observer design for dissipative lipschitz nonlinear systems in the presence of measurement noise this paper presents two novel observer concepts first it develops a globally exponentially stable nonlinear observer for noise free dissipative nonlinear systems second for a dissipative nonlinear system with measurement noise the paper develops an observer to guarantee a desired performance namely an upper limit on the ratio of the square of the weighted l2 norm of the error to the square of the weighted l2 norm of the measurement noise the necessary and sufficient conditions for both observers are reformulated as algebraic riccati equations ares so that standard solvers can be utilised in addition the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the are and hence the observer design problem has a solution the use of the methodology developed in this paper is demonstrated through illustrative examples in literature there is no previous observer for dissipative system that provides both necessary and sufficient condition

sampling of stochastic operators we develop sampling methodology aimed at identifying stochastic operators that satisfy a support size restriction on the autocorrelation of the operators stochastic spreading function the data that we use to reconstruct the operator or in some cases only the autocorrelation of the spreading function is based on the response of the unknown operator to a known deterministic test signal

from continuous time design to sampled data design of observers in this work a sampled data nonlinear observer is designed using a continuous time design coupled with an inter sample output predictor the proposed sampled data observer is a hybrid system it is shown that under certain conditions the robustness properties of the continuous time design are inherited by the sampled data design as long as the sampling period is not too large the approach is applied to linear systems and to triangular globally lipschitz systems

forward completeness unboundedness observability and their lyapunov characterizations a finite dimensional continuous time system is forward complete if solutions exist globally for positive time this paper shows that forward completeness can be characterized in a necessary and sufficient manner by means of smooth scalar growth inequalities moreover a version of this fact is also proved for systems with inputs and a generalization is also provided for systems with outputs and a notion unboundedness observability of relative completeness we apply these results to obtain a bound on reachable states in terms of energy like estimates of inputs

non fragile observer based robust control for a class of fractional order nonlinear systems abstract the paper is concerned with the problem of the observer based robust control for a class of fractional order nonlinear systems first by introducing a continuous frequency distributed equivalent model and using indirect lyapunov approach the sufficient condition for robust asymptotic stability of the closed loop system via state observer based control is presented which is less conservative than some existing ones in recent literature next using matrix s singular value decomposition svd and linear matrix inequality lmi techniques the existence condition and method of designing a robust non fragile observer based controller are derived finally the validity of the proposed methods are demonstrated by two numerical examples

radon transformation on reductive symmetric spaces support theorems abstract we introduce a class of radon transforms for reductive symmetric spaces including the horospherical transforms and derive support theorems for these transforms a reductive symmetric space is a homogeneous space g h for a reductive lie group g of the harish chandra class where h is an open subgroup of the fixed point subgroup for an involution on g let p be a parabolic subgroup such that p is opposite to p and let n p be the unipotent radical of p for a compactly supported smooth function on g h we define r p g to be the integral of n p n g n h over n p the radon transform r p thus obtained can be extended to a large class of distributions containing the rapidly decreasing smooth functions and the compactly supported distributions for these transforms we derive support theorems in which the support of is partially characterized in terms of the support of r p the proof is based on the relation between the radon transform and the fourier transform on g h and a paley wiener shift type argument our results generalize the support theorem of helgason for the radon transform on a riemannian symmetric space