solving boundary value problems integral and integro differential equations using gegenbauer integration matrices we introduce a hybrid gegenbauer ultraspherical integration method hgim for solving boundary value problems bvps integral and integro differential equations the proposed approach recasts the original problems into their integral formulations which are then discretized into linear systems of algebraic equations using gegenbauer integration matrices gims the resulting linear systems are well conditioned and can be easily solved using standard linear system solvers a study on the error bounds of the proposed method is presented and the spectral convergence is proven for two point bvps tpbvps comparisons with other competitive methods in the recent literature are included the proposed method results in an efficient algorithm and spectral accuracy is verified using eight test examples addressing the aforementioned classes of problems the proposed method can be applied on a broad range of mathematical problems while producing highly accurate results the developed numerical scheme provides a viable alternative to other solution methods when high order approximations are required using only a relatively small number of solution nodes

a numerical comparison of chebyshev methods for solving fourth order semilinear initial boundary value problems in solving semilinear initial boundary value problems with prescribed non periodic boundary conditions using implicit explicit and implicit time stepping schemes both the function and derivatives of the function may need to be computed accurately at each time step to determine the best chebyshev collocation method to do this the accuracy of the real space chebyshev differentiation spectral space preconditioned chebyshev tau real space chebyshev integration and spectral space chebyshev integration methods are compared in the l 2 and w 2 2 norms when solving linear fourth order boundary value problems and in the l 0 t l 2 and l 0 t w 2 2 norms when solving initial boundary value problems we find that the best chebyshev method to use for high resolution computations of solutions to initial boundary value problems is the spectral space chebyshev integration method which uses sparse matrix operations and has a computational cost comparable to fourier spectral discretization

robust stability of a class of polynomials with coefficients depending multilinearly on perturbations necessary and sufficient conditions are given for robust stability of a family of polynomials each polynomial is obtained by a multilinearity perturbation structure restrictions on the multilinearity are involved but in contrast to existing literature these restrictions are derived from physical considerations stemming from analysis of a closed loop interval feedback system the main result indicates that all polynomials in the family of polynomials have their zeros in the strict left half plane if and only if two requirements are satisfied at each frequency the first requirement is the zero exclusion condition involving four kharitonov rectangles the second requirement is that a specially constructed theta 0 parameterized set of 16 intervals must cover the positive reals for each theta epsilon 0 2 pi

efficient high order method for differential equations in unbounded domains using generalized coordinate transformation abstract many physical phenomena are localized in space where physical quantities of interest extend to large distances effectively to infinity where they vanish smoothly thus its modeling necessitates the imposition of vanishing boundary conditions bcs to the formulated differential equations des numerical solutions for such des can be complicated as they involve operations on physical quantities expanding infinitely in space currently many approaches have been implemented in this context where they mostly use techniques like domain truncation using functions intrinsic to unbounded domains and domain transformation however since the actual solutions have a decaying nature solving such problems with high accuracy and efficiency while taking into consideration a wide range of decaying rates and oscillation frequencies is a major challenge in this work we present an efficient high order method based on galerkin method to solve des in unbounded domains using properly designed domain transformations where the physical unbounded domain is mapped into a computational bounded domain 0 1 the mapped sine series is then used to solve the differential equation in the computational domain 0 1 where the vanishing quantities at infinities are mapped to 0 corresponding to physical and 1 corresponding to physical the designed transformations maintain the orthogonality in both physical and computational spaces moreover using sine series basis allows in most cases analytical integrations for verification the proposed method is applied to solve 1 helmholtz equation in one dimension where the exact solutions for various cases decaying exponential or algebraic function are known and 2 three dimensional schrodinger wave equation with harmonic oscillator for the helmholtz problem the error in the approximate solution was less than 10 40 using 100 basis functions while for the second problem the error is less than 10 25 using the same number of bases all results and the analyses demonstrate how the properly designed mapped basis sets can be used to develop efficient high order methods to solve des with vanishing boundary conditions and with wide range of decaying rates and oscillation frequencies simultaneously

integration preconditioning matrix for ultraspherical pseudospectral operators in this paper we give an integration rectangular preconditioner for ultraspherical pseudospectral operators we present an explicit solution of matrix equations with the structure provided by the pseudospectral discretization of the nth order differential operator subject to various types of boundary conditions this occurs in two steps in the first step we introduce an integration rectangular preconditioner in the second step we use a new strategy to impose the boundary conditions on the condition that the coefficients matrix has a known inverse computational examples are given

a well conditioned collocation method using a pseudospectral integration matrix in this paper a well conditioned collocation method is constructed for solving general p th order linear differential equations with various types of boundary conditions based on a suitable birkhoff interpolation we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features the condition number of the linear system is independent of the number of collocation points and the underlying boundary conditions are imposed exactly moreover the new basis leads to an exact inverse of the pseudospectral differentiation matrix of the highest derivative at interior collocation points which is therefore called the pseudospectral integration matrix psim we show that psim produces the optimal integration preconditioner and stable collocation solutions with even thousands of points

extremal robustness properties of multilinear interval systems this paper deals with robustness properties of a control system subject to parameter uncertainty when the parameters appear affine multilinearly in the coefficients of the characteristic polynomial the robust hurwitz stability of such a multilinear interval polynomial family reduces to that of the stability of a set of manifolds derived from the kharitonov polynomials several extremal properties of these stability manifolds are derived these properties are useful in determining the worst case parametric h and nonlinear sector bounded stability margins for control systems containing interval parametric uncertainty they generalize previous results obtained by the authors for the linear case

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

stability of parallel volterra runge kutta methods abstract in this paper we analyse parallel iteration of volterra runge kutta methods pivrk methods for solving second kind volterra integral equations on parallel computers we focus on the determination of the region of convergence c and on the stability region sm of the iterated method obtained after m iterations results are presented for the convolution test equation it turns out that the stability region sm does not necessarily converge to the stability region s of the corrector however for finite m sm need not to be contained in c or s and may be much larger than c

backward differentiation type formulas for volterra integral equations of the second kind numerical integration formulas are discussed which are obtained by differentiation of the volterra integral equation and by applying backward differentiation formulas to the resulting integro differential equation in particular the stability of the method is investigated for a class of convolution kernels the accuracy and stability behaviour of the method proposed in this paper is compared with that of i a block implicit runge kutta scheme and ii the scheme obtained by applying directly a quadrature rule which is reducible to the backward differentiation formulas the present method is particularly advantageous in the case of stiff volterra integral equations

on characterization of the optimal biorthogonal window functions for gabor transform gabor transforms have been recognized as useful tools in signal analysis it is known that the solutions for the biorthogonal analysis window function spl gamma t given a synthesis window function h t in gabor transforms are not unique in general among these solutions the minimum norm solution has already been given by wexler and raz 1990 in the discrete time case and has been studied by janssen ron and shen and daubechies et al 1995 in the continuous time case the minimum norm solution in the discrete time case was also proved to be equal to the most orthogonal like solution by qian and chen 1993 in this note we consider a general optimal solution problem where the minimum norm and the most orthogonal like solutions are two special cases we prove that these optimal solutions in many cases are equal we also prove that it remains true in the continuous time case

robust strict positive realness new results for interval plant controller families a frequency domain approach is used to derive several robust strict positive realness results for interval plants and interval plant plus controller families of transfer functions based on simple frequency domain properties of transfer functions the approach provides a framework for obtaining new results and constructing easy proofs of several important existing results on robust strict positive realness the main new result states that the minimum of the real part of the transfer functions belonging to an interval plant controller family is achieved on one of the 32 kharitonov segments of the interval plant the argument used in the proof is of wider interest and suggests easy ways of proving that robustness of other different frequency properties of interval plant plus controller families of transfer functions such as robust stability of h sub infinity norm computation can be deduced from a fixed number of segments of transfer functions of the family

brief paper simultaneous schur stability of interval matrices interval matrix structures are ubiquitous in nature and engineering ordinarily in an uncertain system there is associated with a set of coupled interval matrices a basic issue of exploring its asymptotic stability here we introduce the notion of simultaneous schur stability by linking the concepts of the majorant and the joint spectral radius and prove the asymptotic stability of a set of interval matrices governed by simultaneous schur stability the present result may lead to the stability analysis of discrete dynamical interval systems

bilinear signal synthesis the authors discuss the signal synthesis problem in the general framework of bilinear signal representations bsrs thereby obtaining a unified treatment which encompasses e g the wigner distribution and ambiguity function as special cases the inclusion of a signal space constraint serves to impart flexibility to the signal synthesis process and to relax mathematical requirements the characterization of signal spaces either by orthogonal projection operators or by orthonormal bases leads to two different signal synthesis methods both methods assume the bsr to be unitary i e satisfy moyal s formula on the signal space on which signal synthesis is performed as an application of the general signal synthesis methods band limited signal synthesis in the case of the wigner distribution is considered

on the robust popov criterion for interval lur e system the classical popov criterion is generalized to include problems with parametric uncertainty as well as nonlinear sector bounded perturbations the parametric dependence is modeled by an interval plant description a robust popov criterion is obtained for a plant controller configuration stronger external results are obtained for a special class of controllers an example illustrating the numerical implementation of these results is presented

discrete time waveform relaxation volterra runge kutta methods convergence analysis the discrete time relaxation methods based on volterra runge kutta methods for solving large system of second kind volterra integral equations are proposed convergence of the discrete time iteration process with particular attention to parallel methods is investigated

easily testable sufficient conditions for the robust stability of systems with multilinear parameter dependence abstract a number of robust stability problems take the following form a polynomial has real coefficients which are multilinear in real parameters that are confined to a rectangular axis parallel box in parameter space an efficient method is required for checking the stability of this set of polynomials we present two sufficient conditions in this paper which can be applied in many cases they involve checking certain properties at the corners and edges of the parameter space box

robust stability and performance of interval plants abstract in this paper we consider the problem of robust performance for systems with unstructured and parametric perturbations the parametric uncertainty is modeled through a single input single output interval system description and the unstructured uncertainty through a norm bounded perturbation for this type of parametric robust performance we show that in order to synthesize a controller that achieves robust performance for a family of interval systems it is sufficient to synthesize that controller for a much smaller subset of the interval family regardless of the number of uncertain parameters in the original problem this reduced set is composed of thirty two one parameter families of systems a special class of controllers with stronger results is also presented

convergence results for continuous time waveform methods for volterra integral equations in this paper the waveform methods for solving systems of second kind volterra integral equations are introduced the convergence properties of continuous time waveform methods on finite length and infinite length time intervals are investigated with particular regard to parallel waveform relaxation methods

discrete gabor transform a feasible algorithm for implementing the gabor expansion the coefficients of which are computed by the discrete gabor transform dgt is presented for a given synthesis window and sampling pattern computing the auxiliary biorthogonal function of the dgt is nothing more than solving a linear system the dgt presented applies for both finite as well as infinite sequences by exploiting the nonuniqueness of the auxiliary biorthogonal function at oversampling an orthogonal like dgt is obtained as the discrete fourier transform dft is a discrete realization of the continuous time fourier transform similarly the dgt introduced provides a feasible vehicle to implement the useful gabor expansion

kharitonov like theorems for robust performance of interval systems abstract the sensitivity function of a control system is an important concept in performance analysis classical filter design as well as modern robust h control for an interval system we prove that the maximal h norm of its sensitivity function is achieved at twelve out of sixteen kharitonov vertices similar kharitonov like results are established for the complementary sensitivity function and strict positive realness of interval systems these results are useful in robust performance analysis and h control design for dynamic systems under parametric perturbations

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

computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties consideration is given to the problem of robust stability analysis of linear dynamic systems with uncertain physical parameters entering as polynomials in the state equation matrices a method is proposed giving necessary and sufficient conditions for computing the uncertain system stability margin in parameter space which provides a measure of maximal parameter perturbations preserving stability of the perturbed system around a known stable nominal system a globally convergent optimization algorithm that enables solutions to the problem to be obtained is presented using the polynomial structure of the problem the algorithm generates a convergent sequence of interval estimates of the global extremum these intervals provide a measure of the accuracy of the approximating solution achieved at each step of the iterative procedure some numerical examples are reported showing attractive features of the algorithm from the point of view of computational burden and convergence behavior

a quantitative snr analysis for the pseudo wigner ville distribution a quantitative analysis for short time fourier transform has been previously given we analyze the snr for the pseudo wigner ville distribution with rectangular windows for multicomponent signals in additive noise the snr for the pseudo wigner ville distribution in terms of a sampling rate is given for a fixed window length

a generalization of kharitonov s theorem robust stability of interval plants the robust stability problem is considered for interval plants in the case of single input multioutput or single output multi input systems a necessary and sufficient condition for the robust stabilization of such plants is developed using a generalization of v l kharitonov s theorem 1978 the generalization given provides necessary and sufficient conditions for the stability of a family of polynomials delta s q sub 1 s p sub 1 s q sub m s p sub m s where the q sub i are fixed and the p sub i are interval polynomials the coefficients of which are regarded as a point in parameter space which varies within a prescribed box this generalization called the box theorem reduces the question of the stability of the box in parameter space to the equivalent problem of the stability of a prescribed set of line segments it is shown that for special classes of polynomials q sub i s the set of line segments collapses to a set of points and this version of the box theorem in turn reduces to kharitonov s original theorem

computation of the frequency response of multilinear affine systems deals with the problem of computing the frequency response of an uncertain transfer function whose numerator and denominator polynomials are multiples of independent uncertain polynomials of the form p s q l sub o q l sub 1 q s spl middot spl middot spl middot l sub n q s sup n whose coefficients depend linearly on q q sub 1 q sub 2 q sub q sup t and the uncertainty box is q q q sub i spl epsiv q sub i q sub i i 1 2 q using the geometric structure of the value set of p s q a powerful edge elimination procedure is proposed for computing the bode nyquist and nichols envelopes of these uncertain systems a numerical example is included to illustrate the benefit of the method presented

stability analysis of the de hoog and weiss implicit runge kutta methods for the volterra integral and integrodifferential equations abstract the stability of the de hoog and weiss runge kutta methods is analyzed for the volterra integrodifferential equations with respect to the basic test equation and for volterra integral equations with respect to the linear convolution equation stability regions are determined for some choices of the parameters

closed loop hyperstability of interval plants this note examines the conditions for robust bounded input bounded output closed loop stability of interval plants when there is a nonlinear element in the feedback path specifically the authors present the robust generalized circle criterion and popov s criterion

on robust stability of interval control systems the authors develop results on the robust stability of a nonlinear control system containing both parametric as well as unstructured uncertainty the basic system considered is that of the classical lur e problem of nonlinear control theory a robust version of the lur e problem consisting of a family of linear time invariant systems subjected simultaneously to bounded parameter variations and feedback perturbations from a family of sector bounded nonlinear gains is presently treated by using the kharitonov theorem to develop some extremal results on positive realness of interval transfer functions i e a family of rational transfer functions with bounded independent coefficient perturbations the authors determine the size of a sector of nonlinear feedback gains for which absolute stability can be guaranteed these calculations amount to the determination of the stability margin of the system under joint parametric and nonlinear feedback perturbations

system identification using nonstationary signals the conventional method for identifying the transfer function of an unknown linear system consists of a least squares fit of its input to its output it is equivalent to identifying the frequency response of the system by calculating the empirical cross spectrum between the system s input and output divided by the empirical auto spectrum of the input process however if the additive noise at the system s output is correlated with the input process e g in case of environmental noise that affects both system s input and output the method may suffer from a severe bias effect we present a modification of the cross spectral method that exploits nonstationary features in the data in order to circumvent bias effects caused by correlated stationary noise the proposed method is particularly attractive to problems of multichannel signal enhancement and noise cancellation when the desired signal is nonstationary in nature e g speech or image

highly stable parallel volterra runge kutta methods a new family of parallel v stable methods for second kind volterra integral equations are proposed the methods belong to the class of volterra runge kutta methods and can be applied provided that some not very restrictive conditions on the integral equation kernel are satisfied

robust strict positive real stabilization criteria for siso uncertain systems abstract this paper is devoted to the study of robust strict positive real stabilization criteria for siso uncertain systems i e considering the problem of when a single controller not only robustly stabilizes a plant with uncertainty under unity feedback but also enables the closed loop system to be robustly strictly positive real the uncertain system models with both parameter variation and unstructured perturbation are considered and some necessary and sufficient conditions for the problem are derived

optimal biorthogonal analysis window function for discrete gabor transform like the dft spl minus a discrete version of the fourier transform spl minus the recently developed discrete gabor transform dgt provides a feasible vehicle to implement the very useful gabor expansion in general the choice of the biorthogonal window function spl gamma i is not unique the authors discuss the solution of spl gamma i that is optimally close to an arbitrary desired function d i when the synthesis window h i and sampling pattern are given for d i h i the resulting spl gamma sub opt i directly leads to so called orthogonal like dgt combining the dgt they believe that the result presented in this paper is rather significant for digital signal processing

response of dynamical systems to nonstationary inputs we obtain the time frequency response of the output of a dynamical system when the input belongs to a class of common nonstationary signals namely an impulse a linear chirp a causal sinusoid and a short duration sinusoid the obtained results clarify how the system processes the time varying frequencies of the input signal to generate the time frequency spectrum of the output all analytic results are exact the solution is obtained by developing a method which can be used to evaluate the output of a dynamical system for complex combinations of nonstationary inputs we show numerical examples which prove that the response of a system to a nonstationary input is made by a series of events occurring in the joint time frequency domain

parallel algorithm with spectral convergence for nonlinear integro differential equations we discuss a numerical algorithm for solving nonlinear integro differential equations and illustrate our findings for the particular case of volterra type equations the algorithm combines a perturbation approach meant to render a linearized version of the problem and a spectral method where unknown functions are expanded in terms of chebyshev polynomials el gendi s method this approach is shown to be suitable for the calculation of two point green functions required in next to leading order studies of time dependent quantum field theory

robust parametric classical control design this paper extends well known graphical design tools such as the nyquist plot bode plot and nichols charts to the domain of control systems containing parameter uncertainty we have specifically considered linear interval control systems namely those where the uncertain parameters appear linearly in the characteristic polynomial and vary in intervals because in these cases exact construction of frequency envelopes is possible using these developments we calculate various extremal stability margins for such systems and these are used with standard classical control design techniques to deal with robustness with respect to parametric uncertainty in addition we give an effective technique to iteratively select values of the design parameters within given ranges so that the closed loop system produces improved gain or phase margin

time varying filtering and signal estimation using wigner distribution synthesis techniques the short time fourier transform stft the ambiguity function af and the wigner distribution wd are mixed time frequency signal representations that use fourier transform techniques to map a one dimensional function of time into a two dimensional function of time and frequency these mixed time frequency mappings have been used to analyze the local frequency characteristics of a variety of signals and systems although much work has also been done to develop stft and af synthesis algorithms that can be used to implement a variety of time varying signal processing operations no such synthesis techniques have thus far been developed for the wd in this paper a signal synthesis algorithm that works directly with the real valued high resolution wd will be derived examples of how this wd synthesis procedure can be used to perform time varying filtering operations or signal separation will be given

numerical approximations using chebyshev polynomial expansions el gendi s method revisited we present numerical solutions for differential equations by expanding the unknown function in terms of chebyshev polynomials and solving a system of linear equations directly for the values of the function at the extrema or zeros of the chebyshev polynomial of order n el gendi s method the solutions are exact at these points apart from round off computer errors and the convergence of other numerical methods used in solving the linear system of equations applications to initial value problems in time dependent quantum field theory and second order boundary value problems in fluid dynamics are presented

characterization of zak space support of a discrete chirp general conditions are derived for an n kl2 point discrete chirp with chirp rate a and carrier frequency b to have minimal support on the ltimeskl zak transform lattice earlier it has been shown that when the normalized chirp parameters amacr ak amacr ak 2 and 2bmacr 2bk are integers the last two of the same parity then the discrete chirp is supported at kl points here this condition is relaxed by allowing amacr to be a rational number i e amacr n d n disin z n d 1 and requiring only that amacr and bmacrl be integers of arbitrary parity it is shown that the support of the zak space chirp satisfying the new condition then increases to dkl points the results provide foundations for future constructions of sophisticated radar and communications signal processing algorithms examples of direct applications of the zak space conditions in chirp parameter estimation chirp detection and chirp de noising are included

robust stability under structured and unstructured perturbations the problem of robust stability for linear time invariant single output control systems subject to both structured parametric and unstructured h sub infinity perturbations is studied a generalization of the small gain theorem which yields necessary and sufficient conditions for robust stability of a linear time invariant dynamic system under perturbations of mixed type is presented the solution involves calculating the h sub infinity norm of a finite number of extremal plants the problem of calculating the exact structured and unstructured stability margins is then constructively solved a feedback control system containing a linear time invariant plant which is subject to both structured and unstructured perturbations is considered the case where the system to be controlled is interval is treated and a nonconservative easily verifiable necessary and sufficient condition for robust stability is given the solution is based on the extremal of a finite number of line segments in the plant parameter property of a finite number of line segments in the plant parameter space along which the points closest to instability are encountered

necessary and sufficient conditions on negative imaginariness for interval siso transfer functions and their interconnection this article is concerned with the study of the negative imaginariness of interval transfer functions necessary and sufficient conditions for strictly negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on kharitonov s theorem then certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed finally an example is provided to illustrate the main results of the article

a kharitonov like theorem for interval polynomial matrices abstract as an extension of kharitonov s theorem robust stability of interval polynomial matrices is studied here a polynomial matrix is said to be stable if its determinant has all roots with negative real parts the present paper shows that the robust stability of interval polynomial matrices is equivalent to that of the subclasses where each row column has only one element that involves kharitonov edge polynomials and all the other elements take on one of the four kharitonov vertex polynomials

numerical solutions of the generalized kuramoto sivashinsky equation by chebyshev spectral collocation methods chebyshev spectral collocation methods known as el gendi method s e el gendi chebyshev solution of differential integral and integro differential equations comput j 12 1969 282 287 b mihaila i mihaila numerical approximation using chebyshev polynomial expansions el gendi s method revisited j phys a 35 2002 731 746 are extended to deal with the generalized kuramoto sivashinsky equation the problem is reduced to a system of ordinary differential equations that are solved by combinations of backward differential formula and appropriate explicit schemes implicit explicit bdf methods g akrivis y s smyrlis implicit explicit bdf methods for the kuramoto sivashinsky equation appl numer math 51 2004 151 169 good numerical results have been obtained and compared with the exact solutions

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

technical communique robust stability and performance with fixed order controllers this paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order for a linear time invariant plant for a fixed plant as well as for an uncertain family of plants containing parameter uncertainty so that stability robust stability and robust performance are attained the desired closed loop specifications considered here are given in terms of a target performance vector representing a desired closed loop design in general these point targets are unattainable with a fixed order controller by enlarging the target from a fixed point set to an interval set the solvability conditions are relaxed and a solution is enabled results from the parametric robust control literature can be used to design the interval target family so that the poles and zeros of the closed loop system are guaranteed to remain in a prescribed region of the complex plane and closed loop performance measured for instance in the h norm are attained even when plant uncertainty is present it is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed loop specifications the approach developed here gives the entire set of controllers attaining the specifications as a convex set and also can be recast to give the lowest order controller attaining specifications

some results on quadratic stability of switched systems with interval uncertainty in this paper we present some results on the quadratic stability of switched systems with uncertain parameters we show that the quadratic stability of a class of switched uncertain systems may be readily verified using simple algebraic conditions

unbounded power input signals in optimum experiment design for parameter estimation in linear systems abstract the aim of this paper is to propose and investigate an approach to optimum experiment design problems for parameter estimation in linear systems contrary to the frequency domain approach used bo far our approach allows us to consider input signals with unbounded mean power it is based on a certain correlation type characteristic of a signal introduced by wiener however the approach retains all the advantages of the frequency domain approach in particular an application to d optimum experiment design is presented it is also shown that the optimum input signals are combinations of sinusoids modulated by polynomials

convergence of an iterative time variant filtering based on discrete gabor transform an iterative time variant filtering based on the discrete gabor transform dgt has been previously proposed by the authors in this article we present a proof of the convergence of the iterative algorithm under a sufficient condition on the analysis and synthesis window functions of the dgt in the meantime we show that the iterative algorithm refines the least squares solution

efficient and stable generation of higher order pseudospectral integration matrices the main purpose of this work is to provide new higher order pseudospectral integration matrices hpims for the chebyshev type points and present an exact efficient and stable approach for computing the hpims the essential idea is to reduce the computation of hpims to that of higher order chebyshev integration matrices hcims and take a very simple and recursive way to compute the hcims efficiently and stably extensive numerical results show that the new approach for computing the hpims has better stability than that of the recently derived elgindy s approach for large number of chebyshev type points

system identification using chirp signals and time variant filters in the joint time frequency domain we propose a novel method to identify an unknown linear time invariant lti system in low signal to noise ratio snr environment the method is based on transmitting chirp signals for the transmitter and using linear time variant filters in the joint time frequency tf domain for the receiver to reduce noise before identification due to the tf localization property of chirp signals a large amount of additive white noise can be reduced and therefore the snr before identification can be significantly increased this however cannot be achieved in the conventional methods where pseudo random signals are used and therefore noise reduction techniques do not apply our simulation results indicate that the method proposed outperforms the conventional methods significantly in a low snr environment this paper provides a good application of time frequency analysis and synthesis

time frequency signal synthesis with time frequency extrapolation and don t care regions the application of wigner distribution wd based signal synthesis to signal separation problems is often adversely affected by wd interference terms we present a modified signal synthesis method where the use of a masked wd allows the definition of don t care regions in the don t care regions detrimental interference terms whose time frequency location is assumed to be known are ignored the synthesis result is calculated using a modified version of the quasi power algorithm previously proposed for smoothed wd s the new synthesis method is shown to possess a desirable time frequency extrapolation capability as well as a potential tendency to produce spurious signal components in the don t care regions the occurrence of spurious signal components can be avoided by the inclusion of an energy penalty

optimal gegenbauer quadrature over arbitrary integration nodes this paper treats definite integrations numerically using gegenbauer quadratures the novel numerical scheme introduces the idea of exploiting the strengths of the chebyshev legendre and gegenbauer polynomials through a unified approach and using a unique numerical quadrature in particular the developed numerical scheme employs the gegenbauer polynomials to achieve rapid rates of convergence of the quadrature for the small range of the spectral expansion terms for a large scale number of expansion terms the numerical quadrature has the advantage of converging to the optimal chebyshev and legendre quadratures in the l norm and l 2 norm respectively the key idea is to construct the gegenbauer quadrature through discretizations at some optimal sets of points of the gegenbauer gauss gg type in a certain optimality sense we show that the gegenbauer polynomial expansions can produce higher order approximations to the definite integrals 1 x if x dx of a smooth function f x c 1 1 for the small range by minimizing the quadrature error at each integration point x i through a pointwise approach the developed gegenbauer quadrature can be applied for approximating integrals with any arbitrary sets of integration nodes exact integrations are obtained for polynomials of any arbitrary degree n if the number of columns in the developed gegenbauer integration matrix gim is greater than or equal to n the error formula for the gegenbauer quadrature is derived moreover a study on the error bounds and the convergence rate shows that the optimal gegenbauer quadrature exhibits very rapid convergence rates faster than any finite power of the number of gegenbauer expansion terms two efficient computational algorithms are presented for optimally constructing the gegenbauer quadrature we illustrate the high order approximations of the optimal gegenbauer quadrature through extensive numerical experiments including comparisons with conventional chebyshev legendre and gegenbauer polynomial expansion methods the present method is broadly applicable and represents a strong addition to the arsenal of numerical quadrature methods