stability analysis and synthesis of nonlinear time delay systems via linear takagi sugeno fuzzy models abstract this paper concerns with the stability analysis and synthesis of nonlinear retarded systems via linear takagi sugeno ts fuzzy model approach first the ts fuzzy models with time delay are present and the stability conditions are derived using lyapunov razumikhin functional approach then a stabilization approach for nonlinear retarded systems through fuzzy state feedback and fuzzy observer based controller is proposed it shows that the analysis results provide an efficient technique for the design of fuzzy controllers sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain of the time delay systems are derived through the numerical solution of a set of coupled linear matrix inequalities

fuzzy piecewise multilinear and piecewise linear systems as universal approximators in sobolev norms a piecewise multilinear and a piecewise linear model for fuzzy systems are introduced and their approximation capabilities investigated classical results on the approximation of regular functions are improved showing that fuzzy systems may keep their semantic structure while approximating to any degree of accuracy not only sufficiently regular functions but also their derivatives

output feedback direct adaptive fuzzy controller based on frequency domain methods this paper describes a design method that guarantees the stability of an adaptive fuzzy control system the system consists of an unstable plant with an irrational transfer function a takagi sugeno fuzzy adaptive controller a nonlinear reference model and an adaptation mechanism the gradient based adaptation mechanism changes the consequents of the controller rules in such a way that the closed loop system behaves like the reference model the proposed design procedure utilizes frequency domain methods in the forms of the nyquist and circle criteria it is assumed that the function of the fuzzy controller is a nonlinearity described by a sector condition this condition means that the controller function lies between two lines passing through the origin in this method the function of the fuzzy controller is verified during online adaptation therefore it stays in the allowed sector this method is illustrated by an example of a control system containing an unstable plant with a transport delay the main contribution of this paper is to use frequency methods combined with adaptive fuzzy control these methods have previously been used for nonadaptive fuzzy control but in this paper they are used for the first time for adaptive fuzzy control

subspace based algorithm for parameter estimation of polynomial phase signals in this correspondence parameter estimation of a polynomial phase signal pps in additive white gaussian noise is addressed assuming that the order of the pps is at least 3 the basic idea is first to separate its phase parameters into two sets by a novel signal transformation procedure and then the multiple signal classification music method is utilized for joint estimating the phase parameters with second order and above in doing so the parameter search dimension is reduced by a half as compared to the maximum likelihood and nonlinear least squares approaches in particular the problem of cubic phase signal estimation is studied in detail and its simplification for a chirp signal is given the effectiveness of the proposed approach is also demonstrated by comparing with several conventional techniques via computer simulations

improved h control of discrete time fuzzy systems a cone complementarity linearization approach in this paper new results are presented for h analysis and synthesis problems of discrete time takagi sugeno ts fuzzy systems by defining a multiple lyapunov function a new sufficient condition guaranteeing the h performance of the ts fuzzy systems is first derived which is expressed by a set of linear matrix inequalities lmis both theoretical analysis and numerical examples show that such a new condition is less conservative than previous results obtained within the quadratic framework based on this new condition for h performance the corresponding h controller design problem is then investigated different from the traditional quadratic framework the synthesis problem is solved by exploiting the cone complementarity linearization ccl method together with a sequential minimization problem subject to lmi constraints obtained for the existence of admissible controllers which can be readily solved by using standard numerical software

h output feedback control design for uncertain fuzzy singularly perturbed systems an lmi approach this paper examines the problem of designing a robust h output feedback controller for a class of singularly perturbed systems described by a takagi sugeno fuzzy model based on a linear matrix inequality lmi approach lmi based sufficient conditions for the uncertain singularly perturbed nonlinear systems to have an h performance are derived to eliminate the ill conditioning caused by the interaction of slow and fast dynamic modes solutions to the problem are presented in terms of lmis which are independent of the singular perturbation the proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems a numerical example is provided to illustrate the design developed in this paper

collet eckmann and holder we prove that collet eckmann condition for rational functions which requires exponential expansion only along the critical orbits yields the holder regularity of fatou components this implies geometric regularity of julia sets with non hyperbolic and critically recurrent dynamics in particular polynomial collet eckmann julia sets are locally connected if connected and their hausdorff dimension is strictly less than 2 the same is true for rational collet eckmann julia sets with at least one non empty fully invariant fatou component

product high order ambiguity function for multicomponent polynomial phase signal modeling parameter estimation and performance analysis issues are studied for multicomponent polynomial phase signals ppss embedded in white gaussian noise identifiability issues arising with existing approaches are described first when dealing with multicomponent pps having the same highest order phase coefficients this situation is encountered in applications such as synthetic aperture radar imaging or propagation of polynomial phase signals through channels affected by multipath and is thus worthy of a careful analysis a new approach is proposed based on a transformation called product high order ambiguity function phaf the use of the phaf offers a number of advantages with respect to the high order ambiguity function haf more specifically it removes the identifiability problem and improves noise rejection capabilities performance analysis is carried out using the perturbation method and verified by simulation results

robust backstepping control for a class of time delayed systems in this note the problem of robust output feedback control for a class of nonlinear time delayed systems is considered the systems considered are in strict feedback form state observer is first designed then based on the observed states the controller is designed via backstepping method both the designed observer and controller are independent of the time delays based on lyapunov stability theory we prove that the constructed controller can render the closed loop system asymptotically stable simulation results further verify the effectiveness of the proposed approach

stability and stabilization of a class of fuzzy time delay descriptor systems this paper studies a class of fuzzy time delay descriptor systems in the extended takagi sugeno t s fuzzy model sufficient conditions are derived for the stability and stabilization in terms of linear matrix inequalities lmis illustrative examples are given to show the effectiveness and the advantages of the present results

on quasisymmetry of quasiconformal mappings abstract suppose that f d d is a quasiconformal mapping where d and d are domains in r n and that d is a broad domain we show that for every arcwise connected subset a in d the weak quasisymmetry of the restriction f a a f a implies its quasisymmetry as a consequence we see that the answer to one of the open problems raised by heinonen from 1989 is affirmative under the additional condition that a is arcwise connected

multiple emitter location and signal parameter estimation processing the signals received on an array of sensors for the location of the emitter is of great enough interest to have been treated under many special case assumptions the general problem considers sensors with arbitrary locations and arbitrary directional characteristics gain phase polarization in a noise interference environment of arbitrary covariance matrix this report is concerned first with the multiple emitter aspect of this problem and second with the generality of solution a description is given of the multiple signal classification music algorithm which provides asymptotically unbiased estimates of 1 number of incident wavefronts present 2 directions of arrival doa or emitter locations 3 strengths and cross correlations among the incident waveforms 4 noise interference strength examples and comparisons with methods based on maximum likelihood ml and maximum entropy me as well as conventional beamforming are included an example of its use as a multiple frequency estimator operating on time series is included

common limits of fibonacci circle maps we show that limits for the critical exponent tending to exist in both critical circle homeomorphism of golden mean rotation number and fibonacci circle coverings moreover they are the same the limit map is not analytic at the critical point which is flat but has non trivial complex dynamics

fixed points and dynamics of two parameter family of hyperbolic cosine like functions abstract in this paper the two parameter family f b f z b z b z for z c 0 of transcendental entire functions is considered by investigating on the existence and nature of the fixed points of f the dynamics of functions f f b is studied it is shown that the julia set of f is nowhere dense and not locally connected whenever parameters and satisfy 1 4 ln b 2 ln 1 1 4 ln b 2 2 ln b and the julia set is the whole of extended complex plane for 1 4 ln b 2 ln 1 1 4 ln b 2 2 ln b

polynomial wigner ville distributions and their relationship to time varying higher order spectra the wigner ville distribution wvd has optimal energy concentration for linear frequency modulated fm signals this paper presents a generalization of the wvd in order to effectively process nonlinear polynomial fm signals a class of polynomial wvd s pwvd s that give optimal concentration in the time frequency plane for fm signals with a modulation law of arbitrary polynomial form are defined a class of polynomial time frequency distributions ptfd s are also defined based on the class of pwvd s the optimal energy concentration of the pwvd enables it to be used for estimation of the instantaneous frequency if of polynomial fm signals finally a link between pwvd s and time varying higher order spectra tvhos is established just as the expected value of the wvd of a nonstationary random signal is the time varying power spectrum the expected values of the pwvd s have interpretations as reduced tvhos

random walks kleinian groups and bifurcation currents let be a holomorphic family of representations of a finitely generated group g into psl 2 parameterized by a complex manifold we define a notion of bifurcation current in this context that is a positive closed current on describing the bifurcations of this family of representations in a quantitative sense it is the analogue of the bifurcation current introduced by demarco for holomorphic families of rational mappings on 1 our definition relies on the theory of random products of matrices so it depends on the choice of a probability measure on g

new results on h_ infty tracking control based on the t s fuzzy model for sampled data networked control system this study deals with the problem of h infty tracking control for a sampled data networked control system based on a takagi sugeno fuzzy model an error model is established by combining the input delay and parallel distributed compensation techniques so as to transform the sampling period of a sampler a signal transmission delay and data packet dropouts to the refreshing interval of a zero order hold the method introduces a new augmented lyapunov krasovskii functional to derive a sufficient condition to ensure a prescribed h infty tracking performance with less conservativeness than others a fuzzy controller can easily be designed using the condition a numerical example demonstrates the validity of the method

quasiconformal homeomorphisms and dynamics i solution of the fatou julia problem on wandering domains on demontre un resultat dynamique sur l iteration d une application analytique complexe sur la sphere de riemann

robust sliding mode control of nonlinear systems with delay a design via polytopic formulation this paper outlines the possibility to control nonlinear uncertain systems with single possibly time varying state delay these systems are submitted to additive perturbations possibly nonvanishing the control is of sliding mode type and the sliding surface is designed so to maximize the calculable set of delays which do not destabilize the system the way to deal with the nonlinear parts of the model relies on a polytopic formulation the conditions for the existence of the sliding regime are studied by using both a lyapunov krasovskii functionnal and a lyapunov razumikhin function the optmization precedure for the choice of the sliding surface is expressed in terms of lmis an example illustrates the proposed method

a fast algorithm for estimating the parameters of a quadratic fm signal this paper describes a fast algorithm that can be used for estimating the parameters of a quadratic frequency modulated fm signal the proposed algorithm is fast in that it requires only one dimensional 1 d maximizations the optimal maximum likelihood method by contrast requires a three dimensional 3 d maximization which can only be realized with an exhaustive 3 d grid search asymptotic statistical results are derived for all the estimated parameters the amplitude estimate is seen to be optimal whereas the phase parameters are in general suboptimal of the four phase parameter estimates two approach optimality as the signal to noise ratio snr tends to infinity the other two have mean square errors that are within 50 of the theoretical lower bounds for high snr simulations are provided to support the theoretical results extensions to multiple components and higher order fm signals are also discussed

the set of maps f_ ɑ b x x ɑ b 2π sin 2πx with any given rotation interval is contractible consider the two parameter family of real analytic maps f b x x b 2 sin 2 x which are lifts of degree one endomorphisms of the circle the purpose of this paper is to provide a proof that for any closed interval i the set of maps f b whose rotation interval is i form a contractible set

adaptive iterative learning control for nonlinearly parameterised systems with unknown time varying delays and input saturations in this work an adaptive iterative learning control ailc scheme is proposed to address a class of nonlinearly parameterised systems with both unknown time varying delays and input saturations by incorporating a saturation function a novel iterative learning control mechanism is constructed with a feedback term in the time domain and a fully saturated adaptive learning term in the iteration domain which is used to estimate the unknown time varying system uncertainty a new time weighted lyapunov krasovskii like composite energy function lkl cef is designed for the convergence analysis where time weighted inputs states and estimates of system uncertainty are all considered despite the existence of time varying parametric uncertainties time varying delays input saturations and local lipschitz nonlinearities the learning convergence is guaranteed with rigorous mathematical analysis simulation results verify the correctness and effectiveness of the proposed method further

robust adaptive sliding mode control for fuzzy systems with mismatched uncertainties this paper is devoted to design adaptive sliding mode controllers for the takagi sugeno t s fuzzy system with mismatched uncertainties and exogenous disturbances the uncertainties in state matrices are mismatched and norm bounded while the exogenous disturbances are assumed to be bounded with an unknown bound which is estimated by a simple and effective adaptive approach both state and static output feedback sliding mode control problems are considered in terms of linear matrix inequalities lmis both sliding surfaces and sliding mode controllers can be easily obtained via a convex optimization technique finally two simulation examples and a real experiment are utilized to illustrate the applicability and effectiveness of the design procedures proposed in this paper

h sub spl infin controller synthesis of fuzzy dynamic systems based on piecewise lyapunov functions and bilinear matrix inequalities this work presents an h sub spl infin controller design method for fuzzy dynamic systems based on techniques of piecewise smooth lyapunov functions and bilinear matrix inequalities it is shown that a piecewise continuous lyapunov function can be used to establish the global stability with h sub spl infin performance of the resulting closed loop fuzzy control systems and the control laws can be obtained by solving a set of bilinear matrix inequalities bmis two examples are given to illustrate the application of the proposed methods

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

polynomial phase signal analysis based on the polynomial derivatives decompositions an exact decomposition of the derivatives of any order of a polynomial spl phi t is proposed in terms of spl phi t t sub 0 spl phi t t sub n this result allows us to introduce generalized time frequency distributions for studying signals having a polynomial phase and a constant amplitude in order to determine the degree and the coefficients of the corresponding phase the relationships between these distributions and the already known polynomial distributions i e the polynomial phase transform and the polynomial wigner ville distribution are discussed illustrations by example are proposed

a decomposition theorem for herman maps abstract in 1980s thurston established a topological characterization theorem for postcritically finite rational maps in this paper a decomposition theorem for a class of postcritically infinite branched covering termed herman map is developed it s shown that every herman map can be decomposed along a stable multicurve into finitely many siegel maps and thurston maps such that the combinations and rational realizations of these resulting maps essentially dominate the original one this result is motivated by a non expanding version of mcmullen s problem and thurston s theory on characterization of rational maps it enables us to prove a thurston type theorem for rational maps with herman rings

fuzzy systems as universal approximators an additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy an additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input output state space and averaging patches that overlap the fuzzy system computes a conditional expectation e y x if we view the fuzzy sets as random sets each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state space geometry neural or statistical clustering systems can approximate the unknown fuzzy patches from training data these adaptive fuzzy systems approximate a function at two levels at the local level the neural system approximates and tunes the fuzzy rules at the global level the rules or patches approximate the function

design of higher order polynomial wigner ville distributions the polynomial wigner ville distribution pwvd is a time frequency signal analysis tool for representing polynomial frequency modulated fm signals we present an optimization procedure to design pwvds and discuss the need for higher order pwvds

robust stability analysis and fuzzy scheduling control for nonlinear systems subject to actuator saturation takagi sugeno ts fuzzy models can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output submodels in this paper the ts fuzzy modeling approach is utilized to carry out the stability analysis and control design for nonlinear systems with actuator saturation the ts fuzzy representation of a nonlinear system subject to actuator saturation is presented in our ts fuzzy representation the modeling error is also captured by norm bounded uncertainties a set invariance condition for the system in the ts fuzzy representation is first established based on this set invariance condition the problem of estimating the domain of attraction of a ts fuzzy system under a constant state feedback law is formulated and solved as a linear matrix inequality lmi optimization problem by viewing the state feedback gain as an extra free parameter in the lmi optimization problem we arrive at a method for designing state feedback gain that maximizes the domain of attraction a fuzzy scheduling control design method is also introduced to further enlarge the domain of attraction an inverted pendulum is used to show the effectiveness of the proposed fuzzy controller

stable adaptive fuzzy sliding mode control of interconnected systems the problem of stable adaptive fuzzy control for a class of interconnected systems with unknown control gains is studied in this paper by using fuzzy modeling method a design scheme of an adaptive fuzzy controller is proposed the design is capable of incorporating linguistic and numerical information into controllers by theoretical analysis the closed loop adaptive fuzzy control system is proved to be globally stable in the sense that all signals involved are bounded with tracking errors converging to a neighborhood of zero

joint model order selection and parameter estimation of chirps with harmonic components we consider the problem of jointly determining the number of harmonic components of a fundamental linear chirp and estimating its parameters i e its initial frequency and frequency rate given time samples of the observed signal common model order criteria select the number of harmonics based on the maximum likelihood estimator we develop exact and approximated maximum likelihood estimators of these parameters to avoid an exhaustive search in the initial frequency frequency rate space involved by those estimators we propose an alternative low complexity two step estimation method the first step separates the signal to its harmonic components then in the second step the parameters of interest are estimated using least squares method given the phases of the harmonic components the method is compared to the exact and approximated maximum likelihood estimators and to the well known high order ambiguity function based method numerical simulations and real data examples demonstrate that the proposed low complexity method can successfully replace the maximum likelihood estimator in the model order criteria at moderate to high signal to noise ratio since the estimates obtained by the proposed method achieve the cramer rao lower bound at these signal to noise ratios

nonexistence of wandering domains for strongly dissipative infinitely renormalizable henon maps at the boundary of chaos this article generalizes the nonexistence of wandering domains from unimodal maps to infinitely period doubling renormalizable henon like maps in the strongly dissipative area contracting regime this solves an open problem proposed by van strien discrete contin dyn syst 27 2 557 588 2010 and lyubich and martens invent math 186 1 115 189 2011 we partition the phase space of a henon like map into two regions the good region and the bad region the good region is where the method of proof for unimodal maps applies to henon like maps while the bad region is where serious difficulties occur these difficulties are resolved by the two row lemma an inequality that relates the contraction of areas to the contraction of bad regions after analyzing the competition of the two types of contraction we show that the case of bad regions happens at most finitely many times and complete the proof as an application the theorem enriches our understanding of the topological structure of the heteroclinic web the union of the stable manifolds of periodic orbits forms a dense set in the domain

adaptive neural control for a class of nonlinearly parametric time delay systems in this paper an adaptive neural controller for a class of time delay nonlinear systems with unknown nonlinearities is proposed based on a wavelet neural network wnn online approximation model a state feedback adaptive controller is obtained by constructing a novel integral type lyapunov krasovskii functional which also efficiently overcomes the controller singularity problem it is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed loop systems an example is provided to illustrate the application of the approach

a transform based covariance differencing approach for some classes of parameter estimation problems a method of parameter estimation is presented for a class of problems in which the desired signal is embedded in colored noise with unknown covariance the proposed algorithm does not require multiple estimates of the signal covariance matrix instead it uses a priori knowledge of the structure of the noise covariance matrix to transform the array covariance matrix in a way that leaves its noise component unchanged while the signal component is transformed in some appropriate manner the noise component is then eliminated by forming the difference of the original and transformed covariance differencing methods to be applied to a wider class of problems than was previously possible this is illustrated by applying the algorithm to the problems of bearing estimation resolution of overlapping echos and transient response analysis simulation results demonstrate that the technique affords significant improvement in certain situations over conventional methods

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

the discrete polynomial phase transform the discrete polynomial phase transform dpt is a new tool for analyzing constant amplitude polynomial phase signals the main properties of the dpt are its ability to identify the degree of the phase polynomial and to estimate its coefficients the transform is robust to deviations from the ideal signal model such as slowly varying amplitude additive noise and nonpolynomial phase the authors define the dpt derive its basic properties and use it to develop computationally efficient estimation and detection algorithms a statistical accuracy analysis of the estimated parameters is also presented

estimating signal parameters using the nonlinear instantaneous least squares approach a novel method for signal parameter estimation is presented termed the nonlinear instantaneous least squares nils estimator the basic idea is to use the observations in a sliding window to compute an instantaneous short term estimate of the amplitude used in the separated nonlinear least squares nlls criterion the effect is a significant improvement of the numerical properties in the criterion function which becomes well suited for a signal parameter search for small sized sliding windows the global minimum in the nlis criterion function is wide and becomes easy to find for maximum size windows the nils is equivalent to the nlls estimator which implies statistical efficiency for gaussian noise a blind signal parameter search algorithm that does not use any a priori information is proposed the nils estimator can be interpreted as a signal subspace projection based algorithm moreover the nils estimator can be interpreted as an estimator based on the prediction error of a structured linear predictor hereby a link is established between nlls signal subspace fitting and linear prediction based estimation approaches the nils approach is primarily applicable to deterministic signal models specifically polynomial phase signals are studied and the nils approach is evaluated and compared with other approaches simulations show that the signal to noise ratio snr threshold is significantly lower than that of the other methods and it is confirmed that the estimates are statistically efficient just as the nlls approach the nils estimator can be applied to nonuniformly sampled data

stabilization of uncertain fuzzy time delay systems via variable structure control approach in view of a recent new application of variable structure control vsc to the stabilization problem for takagi sugeno t s fuzzy models this paper aims to study the stabilization of uncertain fuzzy time delay systems in t s fuzzy model via vsc approach there are mainly two features in this paper one lies in the incorporation of time delays both smooth and nonsmooth delays in which case lyapunov functionals and razumikhin theorem are required to solve the stabilization problem the other feature is that not only matched uncertainties but also mismatched uncertainties in the state variables are considered as a sequence the contribution of this paper consists of various control schemes proposed for the vsc design and the present results are in terms of linear matrix inequalities lmis an illustrative example is given to show the effectiveness of our various results

rational maps with fatou components of arbitrarily large connectivity abstract we study the family of singular perturbations of blaschke products b a z z 3 z a 1 a z z 2 we analyse how the connectivity of the fatou components varies as we move continuously the parameter we prove that all possible escaping configurations of the critical point c a take place within the parameter space in particular we prove that there are maps b a which have fatou components of arbitrarily large finite connectivity within their dynamical planes

on local connectivity for the julia set of rational maps newton s famous example we show that newton s cubic methods famous rational maps have a locally connected julia set except in some very specific cases in particular when those maps are infinitely renormalizable their julia set is locally connected and contains small copies of nonlocally connected quadratic julia sets this also holds when newton s method is renormalizable and has cremer points unlike the polynomial case after a dynamical description we show the necessity of the brjuno condition within this family

a fast and accurate single frequency estimator a novel frequency estimator for a single complex sinusoid in complex white gaussian noise is proposed the estimator is more computationally efficient that the optimal maximum likelihood estimator yet attains equally good performance at moderately high signal to noise ratios the estimator is shown to be related to the linear prediction estimator this relationship is used to reveal why the linear prediction estimator does not attain the cramer rao bound even at high signal to noise ratios

area distortion of quasiconformal mappings in recent years quasiconformal mappings have been an efficient tool in the study of dynamical systems of the complex plane we show here that in turn methods or ideas from dynamical systems can be used to solve a number of open questions in the theory of planar quasiconformal mappings it has been known since the work of ahlfors a and mori mo that k quasiconformal mappings are locally h51der continuous with exponent 1 k the function

estimating the doa and the polarization of a polynomial phase signal using a single polarized vector sensor this paper introduces a novel algorithm to estimate the direction of arrival doa and the polarization of a completely polarized polynomial phase signal of an arbitrary degree the algorithm utilizes a polarized vector sensor comprising a spatially collocated six component electromagnetic vector sensor a dipole triad or a loop triad this esprit based algorithm is based on a time invariant matrix pencil pair derived from the time delayed data sets collected by a single polarized vector sensor the high order difference function of the signal s phase constructs the invariant factor used in the esprit algorithm the steering vector is estimated from the signal subspace eigenvector of the data correlation matrix following which the closed form doa and polarization can be obtained given the degree of the polynomial phase signal this approach resolves the two dimensional azimuth elevation angle and the polarization of the source and requires neither a priori knowledge of the polynomial phase signal s coefficients nor a priori knowledge of the polynomial phase signal s frequency spectrum the efficacy of the proposed algorithm is verified by monte carlo simulations estimation accuracies of the doa and the polarization parameters are evaluated by the closed form cramer rao bounds which are independent of the polynomial coefficients the degree of the polynomial phase signal and the azimuth angle of the source

analysis and synthesis of nonlinear time delay systems via fuzzy control approach takagi sugeno ts fuzzy models 1985 1992 can provide an effective representation of complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear input output i o submodels in this paper the ts fuzzy model approach is extended to the stability analysis and control design for both continuous and discrete time nonlinear systems with time delay the ts fuzzy models with time delay are presented and the stability conditions are derived using lyapunov krasovskii approach we also present a stabilization approach for nonlinear time delay systems through fuzzy state feedback and fuzzy observer based controller sufficient conditions for the existence of fuzzy state feedback gain and fuzzy observer gain are derived through the numerical solution of a set of coupled linear matrix inequalities an illustrative example based on the cstr model is given to design a fuzzy controller

an extended fatou shishikura inequality and wandering branch continua for polynomials abstract let p be a polynomial of degree d with julia set j p let n be the number of non repelling cycles of p by the famous fatou shishikura inequality n d 1 the goal of the paper is to improve this bound the new count includes wandering collections of non pre critical branch continua i e collections of continua or points q i j p all of whose images are pairwise disjoint contain no critical points and contain the limit sets of eval q i 3 external rays also we relate individual cycles which are either non repelling or repelling with no periodic rays landing to individual critical points that are recurrent in a weak sense a weak version of the inequality reads n n irr i eval q i 2 d 1 where n irr counts repelling cycles with no periodic rays landing at points in the cycle q i form a wandering collection b c of non pre critical branch continua 1 if b c is non empty and 0 otherwise

estimating the frequency of a noisy sinusoid by linear regression corresp the estimation of the parameters of a sinusoid from observations of signal samples corrupted by additive noise is investigated at high signal to noise ratios the additive noise is viewed as an equivalent phase noise suggesting frequency and phase estimation by linear regression on the signal phase the variances of the regression estimates are shown to achieve the cramer rao bounds a formula for the variance of the regression frequency estimator is derived in terms of the noise power spectrum a simple formula for the variance with 1 f 2 phase noise is presented

a structure theorem in one dimensional dynamics on considere la classe 7b a des applications c f 0 1 0 1 telles que f 0 f 1 0 et f a un unique point critique c 0 1 si le point critique de f 7b a est non plat alors f n a pas d intervalle errant

music maximum likelihood and cramer rao bound the performance of the music and ml methods is studied and their statistical efficiency is analyzed the cramer rao bound crb for the estimation problems is derived and some useful properties of the crb covariance matrix are established the relationship between the music and ml estimators is investigated as well a numerical study is reported of the statistical efficiency of the music estimator for the problem of finding the directions of two plane waves using a uniform linear array an exact description of the results is included

robust stabilization of a class of nonlinear time delay systems the problem of robust stabilization for a class of uncertain dynamic systems with multiple delayed state perturbations is considered it is assumed that perturbations of the time delayed sections are not bounded by first order linear functions but bounded by high order functions with unknown gains and the time delay considered is time varying two classes of controllers are proposed when the time derivative of each time varying time delay is less than 1 a class of adaptive state feedback controllers are proposed based on lyapunov krasovskii method which can render the closed loop systems uniformly ultimately bounded stable novel nonlinear feedback controllers are developed by employing razumikhin lemma and the controller also can render the closed loop systems stable in the sense of uniform ultimate boundedness finally several examples are given to show the potential of the proposed techniques

output tracking control of mimo fuzzy nonlinear systems using variable structure control approach the output tracking control problem for nonlinear systems in the presence of both parameter perturbations and external disturbances is studied our approach is based on the takagi sugeno t s fuzzy modeling method and a variable structure control vsc technique therefore the systems considered are not and need not be in the triangular and parametric strict feedback form which are prevalent among adaptive model following control for nonlinear systems or in the normal form which pervades almost all existing results in neuro fuzzy model following control approach we first study the problem of stabilization of t s fuzzy systems by using a vsc technique a method for the design of a switching surface based on linear matrix inequalities is developed and a stabilizing controller based on a reaching law concept in the presence of both parameter perturbations and external disturbances is proposed then the method is extended to design controllers for output tracking of t s fuzzy nonlinear systems in two cases i e systems which possess the so called strong passive subsystems and strong stable zero dynamics respectively finally illustrative examples are presented to demonstrate the whole design procedure from the original nonlinear systems to their fuzzification and finally to the realization of the desired controllers simulation results show that the goal of output tracking can be achieved by the proposed controllers

h tracking based decentralized hybrid adaptive output feedback fuzzy control for a class of large scale nonlinear systems this paper proposes a novel h tracking based decentralized hybrid adaptive fuzzy controller via output feedback for a class of large scale uncertain nonlinear systems to achieve better adaptation properties the proposed controller is a weighted combination of indirect and direct adaptive fuzzy controls iafc and dafc such that both fuzzy descriptions and control rules can be incorporated at the same time after proper filtering of the observation error dynamics the developed observer based feedback and adaptation mechanisms become implementable indeed by using fuzzy inference systems a state observer and h tracking technique the decentralized combined indirect and direct adaptive fuzzy control algorithm is developed based upon a united h tracking controller design for the modification of the previous work of huang et al the resultant closed loop systems are guaranteed to be stable and a good h tracking performance is obtained simulation results of interrelated inverted pendulums substantiate that the proposed cafc system stands out as being better properties than typical iafc and dafc systems in that the tracking performance is much better while the control effort is even smaller

adaptive fault tolerant control for a class of uncertain t s fuzzy systems with guaranteed time varying performance abstract this paper is concerned with the problem of adaptive fault tolerant control with guaranteed time varying performance for a class of t s fuzzy systems subject to parameter uncertainties and actuator faults different from the existing adaptive fault tolerant prescribed performance results the proposed control method which provides more design degrees of freedom can be applied to more general nonlinear systems by introducing two step backstepping like method and the generalized restrict potential function the adaptive controller guaranteeing a priori user defined time varying performance bounds is constructed in the presence of parameter uncertainties and actuator failures it is shown that all the signals of the resulting closed loop systems are bounded and system state can be constrained with a priori user defined time varying performance bounds finally the effectiveness of the proposed method is verified by simulation results

robust adaptive controller design for nonlinear time delay systems via t s fuzzy approach the robust control problem is investigated for a class of uncertain nonlinear time delay systems via the takagi sugeno t s fuzzification we obtain the t s fuzzy systems with each local model in the form of time delay systems with uncertain nonlinear functions the mismatched nonlinear functions satisfy the lipschitz condition while the matched parts are bounded by nonlinear functions with unknown coefficients based on the input matrix the system is decomposed into two cascade subsystems the virtual controller is designed for the first subsystem and then a memoryless adaptive controller is presented by employing a new lyapunov krasovskii functional we show that the resulting closed loop system is exponentially stable and the solutions are uniformly ultimately bounded finally simulation examples are given to show the effectiveness of our main results

components of degree two hyperbolic rational maps we examine the structure of hyperbolic components and some boundary points of these for degree two rational maps rather than using quasi conformal deformation theory we use a technique from a theorem of thurston about the existence of rational maps this involves regarding a rational map as acting on the teichmuller space of punctured sphere

a new class of multilinear functions for polynomial phase signal analysis this paper introduces a new class of multilinear functions which can be used for analyzing a signal with time varying frequency the new class subsumes a number of existing functions including the higher order ambiguity functions hafs the polynomial wigner ville distributions pwvds and the higher order phase hp functions as well as establishing a link between these existing functions the new class provides a formalism which allows for the creation of useful new multilinear functions a number of new functions are derived from the class

factoring the logarithmic spiral distortion of length and angle are widely studied in geometry and dynamics much of the success in the study of one dimensional complex dynamics flow from the ahlfors bers sullivan a b s 1 theory for deforming conformal structures essentially from the existence and uniqueness theory for the beltrami equation d f d f no comparable analytic theory exists for the distortion of length in the plane or of length or angle in higher dimensions in these cases the local distortion is specified by more than d parameters in dimension d so the analogous equations are over determined what exists instead is a coarser more topological discussion initiated by sullivan of structures extension and isotopy of imbeddings s 2 t v in the quasiconformal and bilipschitz quasi isometric categories the coarseness is the use of the alexander isotopy which crushes rather than unwinds homeomorphisms in this paper we find a constraint on the more delicate method of returning a quasi isometry to the identity factorization into maps of small isometric distortion we study the following l quasi isometry of the closed unit disk a xl x2 x 2 x2 1

on polynomial phase signals with time varying amplitudes we address the parameter estimation problem for a class of nonstationary signals modeled as polynomial phase signals with time varying amplitudes exponentially damped polynomial phase signals are treated as a special case and are analyzed in detail high order instantaneous moments provide the basic analytical tool but links are shown to exist with either the usually employed fft based technique or the high resolution kumaresan tufts 1982 music and matrix pencil methods asymptotic properties of the relevant estimators are established cramer rao lower bounds on the amplitude and phase parameter estimates are derived and computer simulations are carried out to evaluate the performance of various schemes we focus on parametric modeling of am fm signals mainly because parametric techniques offer parsimony and allow for theoretically unlimited resolution