on the l r hodge theory in complete non compact riemannian manifolds we study solutions for the hodge laplace equation delta u omega on p forms with displaystyle l r estimates for displaystyle r 1 our main hypothesis is that delta has a spectral gap in displaystyle l 2 we use this to get sl non classical displaystyle l r hodge decomposition theorems an interesting feature is that to prove these decompositions we never use the boundedness of the riesz transforms in displaystyle l s par these results are based on a generalisation of the raising steps method to complete non compact riemannian manifolds

comments on constrained infinite horizon model predictive control for fuzzy discrete time systems this letter points out the errors in a previous paper by the authors ieee trans fuzzy syst vol 18 no 2 pp 429 436 apr 2010 an improved result is given

theory of differential forms on manifolds in this paper we establish a hodge type decomposition for the lp space of differential forms on closed i e compact oriented smooth rieman nian manifolds critical to the proof of this result is establishing an lp es timate which contains as a special case the l2 result referred to by morrey as gaffney s inequality this inequality helps us show the equivalence of the usual definition of sobolev space with a more geometric formulation which we provide in the case of differential forms on manifolds we also prove the lp boundedness of green s operator which we use in developing the lp theory of the hodge decomposition for the calculus of variations we rigorously verify that the spaces of exact and coexact forms are closed in the lp norm for nonlinear analysis we demonstrate the existence and uniqueness of a solution to the a harmonic equation

modeling and identification of nonlinear systems in the short time fourier transform domain in this paper we introduce a novel approach for improved nonlinear system identification in the short time fourier transform stft domain we first derive explicit representations of discrete time volterra filters in the stft domain based on these representations approximate nonlinear stft models which consist of parallel combinations of linear and nonlinear components are developed the linear components are represented by cross band filters between subbands while the nonlinear components are modeled by multiplicative cross terms we consider the identification of quadratically nonlinear systems and show that a significant reduction in computational cost as well as substantial improvement in estimation accuracy can be achieved over a time domain volterra model particularly when long memory systems are considered experimental results validate the theoretical derivations and demonstrate the effectiveness of the proposed approach

wigner ville spectral analysis of nonstationary processes the wigner ville spectrum has been recently introduced as the unique generalized spectrum for time varying spectral analysis its properties are revised with emphasis on its central role in the analysis of second order properties of nonstationary random signals we propose here a general class of spectral estimators of the wigner ville spectrum this class is based on arbitrarily weighted covariance estimators and its formal description corresponds to the general class of conjoint time frequency representations of deterministic signals with finite energy classical estimators like short time periodograms and the recently introduced pseudo wigner estimators are shown to be special cases of the general class the generalized framework allows the calculation of the moments of general spectral estimators and comparing the results emphasizes the versatility of the new pseudo wigner estimators the effective numerical implementation by an n point fft of pseudo wigner estimators of 2n points is indicated and various examples are given

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

brief paper quadratic boundedness via dynamic output feedback for constrained nonlinear systems in takagi sugeno s form this paper studies output feedback stabilization of takagi sugeno fuzzy systems with input or state constraint and bounded noise a dynamic output feedback controller is adopted rather than a controller based on the state observer the notion of quadratic boundedness specified by a common lyapunov matrix which is novel in fuzzy control is invoked to handle the noise under the proposed controller the state of the closed loop system is stabilizing to an ellipsoid specified by this common lyapunov matrix two numerical examples are given to show the effectiveness of the controller

an efficient approach for reducing the conservatism of lmi based stability conditions for continuous time t s fuzzy systems this paper deals with reducing the conservatism of stability conditions for continuous time t s fuzzy systems previous stability conditions are relaxed by further exploring the properties of the time derivatives of normalized fuzzy weighting functions and by introducing more slack matrix variables by relying on analysis of the positive and negative characteristics of the time derivatives of normalized fuzzy weighting functions some redundant terms are removed from the problem formulation furthermore more slack matrix variables are introduced to enlarge the design space consequently less conservative stability conditions are obtained finally a well known numerical example is provided to illustrate the effectiveness of the proposed result

riesz transforms and spectral multipliers of the hodge laguerre operator abstract on r d endowed with the laguerre probability measure we define a hodge laguerre operator l acting on differential forms here is the laguerre exterior differentiation operator defined as the classical exterior differential except that the partial derivatives x i are replaced by the laguerre derivatives x i x i and is the adjoint of with respect to inner product on forms defined by the euclidean structure and the laguerre measure we prove dimension free bounds on l p 1 p for the riesz transforms l 1 2 and l 1 2 as applications we prove the strong hodge de rahm kodaira decomposition for forms in l p and deduce existence and regularity results for the solutions of the hodge and de rham equations in l p we also prove that for suitable functions m the operator m l is bounded on l p 1 p

output feedback robust mpc with one free control move for the linear polytopic uncertain system with bounded disturbance in this paper a previous approach for the robust model predictive control mpc for a linear polytopic uncertain system is extended to the case with bounded disturbance and unmeasurable state the controller on line optimizes a free control move followed by an output feedback control law based on the pre specified state estimator a key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem the quadratic boundedness qb of the augmented state is guaranteed by the proposed approach a numerical example is given to illustrate the effectiveness of the proposed controller

on estimation error bounds for receding horizon filters using quadratic boundedness quadratic boundedness is used to deal with stability and design of receding horizon estimators upper bounds on the norm of the estimation error have been found by means of invariant sets that can be constructed by using quadratic boundedness moreover these bounds are expressed in terms of linear matrix inequalities and are well suited to being minimized for the purpose of design

time frequency analysis of the impulse response the impulse response is a key function for the analysis and design of systems therefore understanding its properties is a fundamental problem to investigate the nonstationary structure of the impulse response we derive its time frequency representation both in the wigner and smoothed wigner distribution domains first we consider the class of single input single output siso systems which models a wide variety of physical phenomena the obtained wigner distribution for the class of siso systems is made by frequency translated versions of the wigner distribution of the impulse response for a first order system a t shaped function of time and frequency plus the interference terms which are effectively filtered out in the smoothed wigner domain then we consider the case of multiple input multiple output mimo systems whose impulse response is the collection of the individual responses obtained by applying an impulse to every input separately also in this case the wigner distribution of the impulse response depends on the t function we apply our results to a two dimensional mimo harmonic oscillator and to a siso system with three resonances finally we propose the key idea of a system identification method that operates directly in the time frequency domain by fitting the smoothed t function we show that the method works for a nonlinear oscillator with a large cubic term as well as for a time varying harmonic oscillator and that it can tolerate the presence of both stationary and nonstationary noise

erratum to on the weak l p hodge decomposition and beurling ahlfors transforms on complete riemannian manifolds based on a new martingale representation formula we prove some quantitative upper bound estimates of the l p norm of some singular integral operators on complete riemannian manifolds this leads us to establish the weak l p hodge decomposition theorem and to prove the l p boundedness of the beurling ahlfors transforms on complete non compact riemannian manifolds with non negative weitzenbock curvature operator

optimal kernels for nonstationary spectral estimation current theories of a time varying spectrum of a nonstationary process all involve either by definition or by difficulties in estimation an assumption that the signal statistics vary slowly over time this restrictive quasistationarity assumption limits the use of existing estimation techniques to a small class of nonstationary processes we overcome this limitation by deriving a statistically optimal kernel within cohen s 1989 class of time frequency representations tfr s for estimating the wigner ville spectrum of a nonstationary process we also solve the related problem of minimum mean squared error estimation of an arbitrary bilinear tfr of a realization of a process from a correlated observation both optimal time frequency invariant and time frequency varying kernels are derived it is shown that in the presence of any additive independent noise optimal performance requires a nontrivial kernel and that optimal estimation may require smoothing filters that are very different from those based on a quasistationarity assumption examples confirm that the optimal estimators often yield tremendous improvements in performance over existing methods in particular the ability of the optimal kernel to suppress interference is quite remarkable thus making the proposed framework potentially useful for interference suppression via time frequency filtering

further studies on control synthesis of discrete time t s fuzzy systems via useful matrix equalities this paper is concerned with further studies on the control synthesis of discrete time nonlinear systems in the takagi sugeno t s fuzzy form to do this a novel slack variable technique is presented by developing some useful matrix equalities which are homogenous polynomially parameter dependent on both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions under the framework of homogenous matrix polynomials the algebraic properties of both the current time normalized fuzzy weighting functions and the past time normalized fuzzy weighting functions are collected for the first time into sets of united collection matrices consequently the relaxation quality of control synthesis of discrete time t s fuzzy systems is improved i e the convergence of asymptotically necessary and sufficient stabilization conditions is further sped up finally a numerical example is provided to illustrate the effectiveness of the proposed result

dynamic output feedback predictive control for nonlinear systems represented by a takagi sugeno model this paper addresses the output feedback predictive control for a takagi sugeno t s fuzzy system with bounded noise the controller optimizes an infinite horizon objective function respecting the input and state constraints the control law is parameterized as a dynamic output feedback that is dependent on the membership functions and the closed loop stability is specified by the notion of quadratic boundedness online algorithms that guarantee the recursive feasibility of the convex optimization problem and the convergence of the augmented state to a neighborhood of the equilibrium point are proposed in this paper a numerical example is given to illustrate the effectiveness of the proposed output feedback controllers

the uncertainty principle global local or both we address the issue of the relation between local quantities and the uncertainty principle we approach the problem by defining local quantities as conditional standard deviations and we relate these to the uncertainty product appearing in the standard uncertainty principle we show that the uncertainty product for the average local standard deviations is always less than or equal to the standard uncertainty product and that it can be arbitrarily small we apply these results to the short time fourier transform spectrogram to explore the commonly held notion that the uncertainty principle somehow limits local quantities we show that indeed for the spectrogram there is a lower bound on the local uncertainty product of the spectrogram due to the windowing operation of this method this limitation is an inherent property of the spectrogram and is not a property of the signal or a fundamental limit we also examine the local uncertainty product for a large class of time frequency distributions that satisfy the usual uncertainty principle including the wigner distribution the choi williams distribution and many other commonly used distributions we obtain an expression for the local uncertainty product in terms of the signal and show that for these distributions the local uncertainty product is less than that of the spectrogram and can be arbitrarily small extension of our approach to an entropy formulation of the uncertainty principle is also considered

fractional fourier analysis of random signals and the notion of spl alpha stationarity of the wigner ville distribution in this paper a generalized notion of wide sense stationarity for random signals is presented the notion of stationarity is fundamental in the fourier analysis of random signals for this purpose a definition of the fractional correlation between two random variables is introduced it is shown that for wide sense stationary random signals the fractional correlation and the fractional power spectral density functions form a fractional fourier transform pair thus the concept of stationarity plays an important role in the analysis of random signals through the fractional fourier transform for signals nonstationary in the standard formulation but stationary furthermore we define the wigner ville distribution in terms of the fractional correlation function in which the standard fourier analysis is the particular case for 2 and it leads to the wiener khinchin theorem

blind source separation based on time frequency signal representations blind source separation consists of recovering a set of signals of which only instantaneous linear mixtures are observed thus far this problem has been solved using statistical information available on the source signals this paper introduces a new blind source separation approach exploiting the difference in the time frequency t f signatures of the sources to be separated the approach is based on the diagonalization of a combined set of spatial t f distributions in contrast to existing techniques the proposed approach allows the separation of gaussian sources with identical spectral shape but with different t f localization properties the effects of spreading the noise power while localizing the source energy in the t f domain amounts to increasing the robustness of the proposed approach with respect to noise and hence improved performance asymptotic performance analysis and numerical simulations are provided

delay dependent guaranteed cost control for t s fuzzy systems with time delays this study introduces a guaranteed cost control method for nonlinear systems with time delays which can be represented by takagi sugeno t s fuzzy models with time delays the state feedback and generalized dynamic output feedback approaches are considered the generalized dynamic output feedback controller is presented by a new fuzzy controller architecture which is of dual indexed rule base it considers both the dynamic part and the output part of t s fuzzy model which guarantees that the controller without any delay information can stabilize time delay t s fuzzy systems based on delay dependent lyapunov functional approach some sufficient conditions for the existence of state feedback controller are provided via parallel distributed compensation pdc first second the corresponding conditions are extended into the generalized dynamic output feedback closed loop system via so called generalized pdc technique the upper bound of time delay can be obtained using convex optimization such that the system can be stabilized for all time delays whose sizes are not larger than the bound the minimizing method is also proposed to search the suboptimal upper bound of guaranteed cost function the effectiveness of the proposed method can be shown by the simulation examples

dynamic output feedback predictive control of a takagi sugeno model with bounded disturbance this paper considers predictive control of a takagi sugeno fuzzy model with bounded disturbance strictly satisfying the input and state constraints the membership function dependent dynamic output feedback law as in a previous work is utilized the novelty lies in the following technical improvements for the notion of quadratic boundedness which specifies closed loop stability and invariance properties the full lyapunov matrix is utilized the real time ellipsoidal bound of true state is recursively optimized by invoking the s procedure some relaxation scalars being optimized by the norm bounding technique are introduced for better handling the input and state constraints the multistep approach where a sequence of dynamic output feedback laws are optimized at each sampling instant is given to improve the single step approach numerical examples are given to illustrate the effectiveness of the proposed controllers

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

testing stationarity with surrogates a time frequency approach an operational framework is developed for testing stationarity relatively to an observation scale in both stochastic and deterministic contexts the proposed method is based on a comparison between global and local time frequency features the originality is to make use of a family of stationary surrogates for defining the null hypothesis of stationarity and to base on them two different statistical tests the first one makes use of suitably chosen distances between local and global spectra whereas the second one is implemented as a one class classifier the time frequency features extracted from the surrogates being interpreted as a learning set for stationarity the principle of the method and of its two variations is presented and some results are shown on typical models of signals that can be thought of as stationary or nonstationary depending on the observation scale used

new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi the problems of relaxed quadratic stability conditions fuzzy observer designs and h controller designs for t s fuzzy systems have been studied first new stability conditions are obtained by relaxing the stability conditions derived in previous papers secondly new fuzzy observers based on the relaxed stability conditions for the t s fuzzy systems have been proposed thirdly two sufficient lmi conditions which guarantee the existence of the h controllers based on fuzzy observers for the t s fuzzy systems have been proposed the conditions are not only simple but also consider the interactions among the fuzzy subsystems finally by some examples using the lmi technique we show that the regulators the fuzzy observers and the h controller designs based on new observers for the t s fuzzy systems are very practical and efficient

the transient spectrum of a random system the frequency spectrum is a fundamental quantity for the analysis and design of a system when a system is turned on or off the frequency spectrum of its output changes with time we define the transient spectrum as the time frequency spectrum of the system output during the transient phase we obtain the exact transient spectrum for a wide class of random systems and we formulate it with respect to the classical power spectrum which is reached for large times we apply the developed method to the case of a harmonic oscillator and of a system with two resonances

technical communique design of state estimators for uncertain linear systems using quadratic boundedness the notion of quadratic boundedness which allows one to address the stability of a dynamic system in the presence of bounded disturbances is applied to the design of state estimators for discrete time linear systems with polytopic uncertainties necessary and sufficient stability conditions are stated and upper bounding sequences on the estimation error are derived for the purpose of design such conditions can be expressed in terms of linear matrix inequalities lmis thus guaranteeing the numerical tractability simulation results are reported to show the effectiveness of the approach

on the generalized local stability and local stabilization conditions for discrete time takagi sugeno fuzzy systems in this paper local stability and local stabilization problems are considered for discrete time nonlinear systems represented by takagi sugeno t s fuzzy systems improved methods to assess the local stability design locally stabilizing control laws and estimate the domain of attraction are developed in terms of single parameter minimization problems subject to linear matrix inequality lmi constraints the improvement is achieved by applying a convergent lmi relaxation technique to prove positivity of homogeneous polynomial parameter dependent matrices of arbitrary degree with variables in the simplex we also take advantage of the recently developed parameter variation modeling technique to deal with the case that the variation rate of the membership functions of the t s fuzzy systems is bounded and less than one finally several illustrative examples demonstrate the validity and efficiency of the proposed method

riesz transform and l p cohomology for manifolds with euclidean ends let m be a smooth riemannian manifold which is the union of a compact part and a finite number of euclidean ends rr n setminus b 0 r for some r 0 each of which carries the standard metric our main result is that the riesz transform on m is bounded from l p m to l p m t m for 1 n the result is new for 2 2 for a more general class of manifolds assume that m is a n dimensional complete manifold satisfying the nash inequality and with an o r n upper bound on the volume growth of geodesic balls we show that boundedness of the riesz transform on l p for some p 2 implies a hodge de rham interpretation of the l p cohomology in degree 1 and that the map from l 2 to l p cohomology in this degree is injective

fuzzy constrained min max model predictive control based on piecewise lyapunov functions this paper proposes two novel stable fuzzy model predictive controllers based on piecewise lyapunov functions and the min max optimization of a quasi worst case infinite horizon objective function the main idea is to design state feedback control laws that minimize the worst case objective function based on fuzzy model prediction and thus to obtain the optimal transient control performance which is of great importance in industrial process control moreover in both of these predictive controllers piecewise lyapunov functions have been used in order to reduce the conservatism of those existent predictive controllers based on common lyapunov functions it is shown that the asymptotic stability of the resulting closed loop discrete time fuzzy predictive control systems can be established by solving a set of linear matrix inequalities moreover the controller designs of the closed loop control systems with desired decay rate and input constraints are also considered simulations on a numerical example and a highly nonlinear benchmark system are presented to demonstrate the performance of the proposed fuzzy predictive controllers

receding horizon control strategies for constrained lpv systems based on a class of nonlinearly parameterized lyapunov functions in this technical note we present a receding horizon control rhc design method for linear parameter varying lpv systems subject to input and or state constraints based on a class of nonlinearly parameterized lyapunov functions recently introduced by guerra and vermeiren as it will be made clear their use gives rise to less conservative stabilizability conditions w r t those arising from quadratic lyapunov functions a workable convex optimization procedure is first presented for control design purposes which allows the synthesis of stabilizing scheduling state feedback control laws complying with the prescribed constraints this control design method is then arranged into a receding horizon framework and its feasibility and stability properties are carefully analyzed numerical comparisons with existing rhc methods for lpv systems are reported in the final example

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

constrained robust feedback model predictive control for uncertain systems with polytopic description for the constrained uncertain systems with polytopic description a new design method of robust feedback model predictive control is proposed by using a sequence of feedback control laws and designing the parameter dependent lyapunov function for each model the design method provides more degrees of freedom and then can improve the control performance and enlarge the feasible region based on the characteristic property of the design method an offline design algorithm is developed to reduce the mpc controller s online computation burden the numerical examples verify the effectiveness of the results presented in this article

robust model predictive control for discrete time takagi sugeno fuzzy systems with structured uncertainties and persistent disturbances in this paper robust model predictive control for uncertain discrete time takagi sugeno t s fuzzy systems with input constraints and persistent disturbances is considered the robust positively invariant set for t s fuzzy systems is investigated based on this result computation of the terminal constraint set is proposed which is of crucial importance in the robust predictive controller design a zero step predictive controller is discussed first which has a time varying terminal constraint set the recursive feasibility and input to state stability can be ensured then a novel controller with n step prediction is further proposed which can be used to deal with the case of fixed terminal constraint set the implementation of the n step controller involves both online and offline computations it is shown that a sequence of approximating robust one step sets can be computed offline then bisection searches are carried out online as well as a constrained convex optimization problem the n step controller guarantees that the system state can be steered to the terminal constraint set in less than n steps if the initial state lies in a specific region simulation results are finally presented to show the effectiveness of the proposed controllers

asymptotically necessary and sufficient conditions for stability and performance in fuzzy control applications of polya s theorem stability and performance requirements in fuzzy control of takagi sugeno systems are usually stated as fuzzy summations i e sums of terms related to lyapunov functions which are weighted by membership functions or products of them this paper presents an application to fuzzy control of polya s theorems on positive forms on the standard simplex the result provides a set of progressively less conservative sufficient conditions for proving positivity of fuzzy summations such conditions are less and less conservative as a complexity parameter n increases particular cases of such conditions are those in c h fang y s liu s w kau l hong c h lee a new lmi based approach to relaxed quadratic stabilization of t s fuzzy control systems ieee trans fuzzy systems 14 2006 286 397 x liu q zhang new approaches to h controller designs based on fuzzy observers for t s fuzzy systems via lmi automatica 39 9 2003 1571 1582 with n 2 and 3 respectively the proposed conditions are asymptotically exact i e necessary and sufficient when n tends to infinity or equivalently when a tolerance parameter tends to zero

a novel observer based output feedback controller design for discrete time fuzzy systems this paper addresses the problem of observer based output feedback controller designs for discrete time t s fuzzy systems based on a relaxed approach in which the fuzzy lyapunov functions are used different from the existing two step method a single step linear matrix inequality method is provided for the observer based controller design it is shown that the controller and observer parameters can be obtained by solving a set of strict linear matrix inequalities that are numerically feasible with commercially available software the new design method not only overcomes the drawback induced by the two step approach but also provides less conservative results over some existing results finally the effectiveness of the proposed approach is demonstrated by an example

time frequency representation of mimo dynamical systems many deterministic and random physical signals can be modeled as the output of a multi input multi output mimo dynamical system since physical signals are typically nonstationary their frequency content changes with time to understand this time variation we transform the mimo system to the time frequency domain the result is a time frequency mimo dynamical system whose input and output are the time frequency spectra of the original input and output signals in the time domain the time frequency system reveals the spectral mechanisms involved in the generation of nonstationary signals we apply our method to the case of a mimo system with two vibrational modes and a nonstationary noise at the input we obtain the time frequency spectrum of the output which shows how the spectrum of the modes changes with time this result cannot be achieved with classical spectral techniques because they require the input random process to be wide sense stationary

bilinear time frequency representations new insights and properties an analysis of the interference terms of cohen class bilinear time frequency representations tfr of multicomponent signals is presented constraints for achieving new interference properties are derived imposing these interference time and interference frequency concentration constraints on a tfr guarantees that the tfr will be zero everywhere the signal s t is zero and the tfr will contain only those frequencies that occur in the signal thus these new constraints guarantee strong finite support in a tfr when these interference concentration properties are combined with interference attenuation tradeoffs between finite support the marginals and the interference properties are shown to be unavoidable the useful class of product kernels are considered and generalized further to allow tfr with potentially superior interference properties the interference frequency concentration and attenuation properties allow tfr with spectrogram like interference suppression but without the spectrogram s inherent time frequency resolution tradeoff other useful combinations of properties are discussed and analyzed and properties and tradeoffs are illustrated by examples

martingale transforms and lp norm estimates of riesz transforms on complete riemannian manifolds under the condition that the bakry emery ricci curvature is bounded from below we prove a probabilistic representation formula of the riesz transforms associated with a symmetric diffusion operator on a complete riemannian manifold using the burkholder sharp l p inequality for martingale transforms we obtain an explicit and dimension free upper bound of the l p norm of the riesz transforms on such complete riemannian manifolds for all 1 p in the euclidean and the gaussian cases our upper bound is asymptotically sharp when p 1 and when p

lp estimates and existence theorems for the operator on complete kahler manifolds abstract in this paper we establish some l p estimates and existence theorems for the operator on a holomorphic hermitian vector bundle over a complete kahler manifold as applications we prove some vanishing theorems of the l p dolbeault cohomology on complete kahler manifolds with suitable geometric conditions

fractional fourier transform wigner distribution and filter design for stationary and nonstationary random processes in this paper we derive the relationship among the fractional fourier transform frft the linear canonical transform lct and the stationary and nonstationary random processes we find many interesting properties for example if we perform the frft for a stationary process although the result is no longer stationary the amplitude of the autocorrelation function is still independent of time we also find that the lct of a white noise is still a white one for the frft of a stationary process the ambiguity function af is a tilted line and the wigner distribution function wdf is invariant along a certain direction we also define the fractional stationary random process and find that a nonstationary random process can be expressed by a summation of fractional stationary random processes in addition after performing the filter designed in the frft domain for a white noise we can use the segment length of the axis on the wdf plane to estimate the power of the noise and use the area circled by cutoff lines to estimate its energy thus in communication to reduce the effect of the white noise the area of the wdf of the transmitted signal should be as small as possible

lmi based relaxed nonquadratic stabilization conditions for nonlinear systems in the takagi sugeno s form this paper presents the stabilization analysis for a class of nonlinear systems that are represented by a takagi and sugeno ts discrete fuzzy model takagi and sugeno ieee trans systems man cybern 15 1 1985 116 the main result given here concerns their stabilization using new control laws and new nonquadratic lyapunov functions new relaxed conditions and linear matrix inequality based design are proposed that allow outperforming previous results found in the literature two examples are also provided to demonstrate the efficiency of the approaches

on the strong l p hodge decomposition over complete riemannian manifolds we establish the strong lp hodge decomposition theorem and the lp poincare inequalities on differential forms over complete non compact riemannian manifolds as applications we prove some lp estimates and existence theorems for the de rham operator as well as some vanishing theorems for the lp cohomology and the lp torsion over complete non compact riemannian manifolds with suitable geometric conditions

heat equation derivative formulas for vector bundles we use martingale methods to give bismut type derivative formulas for differentials and co differentials of heat semigroups on forms and more generally for sections of vector bundles the formulas are mainly in terms of weitzenbock curvature terms in most cases derivatives of the curvature are not involved in particular our results improve b k driver s formula in 1997 j math pures appl 9 76 703 737 for logarithmic derivatives of the heat kernel measure on a riemannian manifold our formulas also include the formulas of k d elworthy and x m li 1998 c r acad sci paris ser i math 327 87 92

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