best possible global bounds for jensen s inequality in this article we found the form of best possible global upper bound for jensen s inequality thereby previous results on this topic are essentially improved we also give some applications in analysis and information theory

novel summation inequalities and their applications to stability analysis for systems with time varying delay the inequality technique plays an important role in stability analysis for time delay systems this technical note presents a new sequence of novel summation inequalities by introducing some free matrices which includes the newly developed wirtinger based and free matrix based summation inequalities as special cases moreover the idea can be easily extended to the multiple summation inequality case based on the proposed inequalities relaxed stability conditions are obtained for systems with time varying delay numerical examples are given to demonstrate the effectiveness of the proposed approach

ll filters a new class of order statistic filters the ll filters are introduced to generate the order statistic filters l filters and the nonrecursive linear or finite duration impulse response fir filters such estimators are particularly effective filtering signals that do not necessarily follow gaussian distributions they can be designed to restore one dimensional or multidimensional signals corrupted by noise of impulsive type such filters are appealing since they are suitable for being made robust against the presence of spurious outliers in the data

second order volterra filtering and its application to nonlinear system identification some recent results on the design and implementation of second order volterra filters are presented the second order volterra filter is a nonlinear filter with the filter structure of second order volterra series a simple minimum mean square error solution for the volterra filter is derived based on the assumption that the filter input is gaussian also we propose an iterative factorization technique to design a subclass of the volterra filters which can alleviate the complexity of the filtering operations considerably furthermore an adaptive algorithm for the volterra filter is investigated along with its mean convergence and asymptotic excess mean square error finally the utility of the volterra filter is demonstrated by utilizing it in studies of nonlinear drift oscillations of moored vessels subject to random sea waves

schwarz and gruss type inequalities for c seminorms and positive linear functionals on banach modules abstract let a be a unital banach algebra a c seminorm or a positive linear functional on a and x be a semi inner product a module we define a real function on x by x x x 1 2 and show that the schwarz inequality holds therefore x is a semi hilbert a module we also obtain some gruss type inequalities for c seminorms and positive linear functionals on a

exponential stability of impulsive systems with application to uncertain sampled data systems we establish exponential stability of nonlinear time varying impulsive systems by employing lyapunov functions with discontinuity at the impulse times our stability conditions have the property that when specialized to linear impulsive systems the stability tests can be formulated as linear matrix inequalities lmis then we consider lti uncertain sampled data systems in which there are two sources of uncertainty the values of the process parameters can be unknown while satisfying a polytopic condition and the sampling intervals can be uncertain and variable we model such systems as linear impulsive systems and we apply our theorem to the analysis and state feedback stabilization we find a positive constant which determines an upper bound on the sampling intervals for which the stability of the closed loop is guaranteed the control design lmis also provide controller gains that can be used to stabilize the process we also consider sampled data systems with constant sampling intervals and provide results that are less conservative than the ones obtained for variable sampling intervals

an iqc approach to robust stability of aperiodic sampled data systems conditions for robust stability of sampled data systems with non uniform sampling patterns and structural uncertainties are derived the problem is tackled under the integral quadratic constraint iqc framework where the aperiodic sampling operation is modelled by an delay integration operator characterization based on integral quadratic constrains iqc is identified for this operator and the iqc theory is applied to derive convex stability criteria compared to the dominating lyapunov approach where the candidate lyapunov krasovskii functionals or looped functionals need to be tailored for the systems under consideration and therefore the stability conditions need to be re derived whenever additional uncertainties are considered the proposed approach has the advantage of avoiding such endeavor numerical examples are given to illustrate this main point and effectiveness of the proposed approach

adaptive weighted myriad filter algorithms for robust signal processing in spl alpha stable noise environments stochastic gradient based adaptive algorithms are developed for the optimization of weighted myriad filters wmyfs wmyfs form a class of nonlinear filters motivated by the properties of spl alpha stable distributions that have been proposed for robust non gaussian signal processing in impulsive noise environments the weighted myriad for an n long data window is described by a set of nonnegative weights w sub i sub i l sup n and the so called linearity parameter k 0 in the limit as k spl rarr spl infin the filter reduces to the familiar weighted mean filter which is a constrained linear fir filter necessary conditions are obtained for optimality of the filter weights under the mean absolute error criterion an implicit formulation of the filter output is used to find an expression for the gradient of the cost function using instantaneous gradient estimates an adaptive steepest descent algorithm is then derived to optimize the weights this algorithm involves a very simple update term that is computationally comparable to the update in the classical lms algorithm the robust performance of this adaptive algorithm is demonstrated through a computer simulation example involving lowpass filtering of a one dimensional chirp type signal in impulsive noise

a note on relationship between two classes of integral inequalities this technical note firstly introduces two classes of integral inequalities with and without free matrices respectively and points out that they although in different forms are actually equivalent in the sense of conservatism i e the two corresponding ones produce the same tight upper bounds secondly the relationship between the method of integral inequalities with free matrices and the free weighting matrix technique is intensively investigated it is shown that these two different methods are actually equivalent in assessing the stability of time delay systems

some remarks on the chebyshev functional identities are provided for the chebyshev functional defined on a real linear space equipped with a bilinear form in addition some inequalities for the functional are discussed

on the inequality f x d 2u ge f u g u du q we consider fully nonlinear degenerate elliptic equations with zero and first order terms we provide a priori upper bounds and characterize the existence of entire subsolutions under growth conditions on the lower order coefficients which extend the classical keller osserman condition for semilinear equations

harnack inequality for nonlinear elliptic equations with strong absorption abstract we develop harnack inequalities for two different types of equations first we consider a fully nonlinear uniformly elliptic equation related to the pucci s maximal and the minimal operators next we consider a quasilinear equation related to the p laplacian in both cases we consider lower order terms of keller osserman type although the equations considered are quite different we employ a unified method to approach both problems and the results we find are similar

commutators and accretive operators abstract in this paper singular values of commutators of hilbert space operators are estimated to this aim the accretivity of a transform of the operators is applied some recent results of kittaneh f kittaneh singular value inequalities for commutators of hilbert space operators linear algebra appl 430 2009 2362 2367 are extended

gruss and ostrowski type inequalities abstract in this paper we use a method originated in s s dragomir some gruss type inequalities in inner product spaces j inequal pure appl math 4 2 2003 article 42 to establish some gruss and ostrowski type inequalities

a note on the liouville method applied to elliptic eventually degenerate fully nonlinear equations governed by the pucci operators and the keller osserman condition this paper is devoted to the study of the viscosity solutions of begin array l mathbb f rm d 2 u u x f 0 end array in the whole space mathbb r rm n under suitable structural assumptions on mathbb f involving the pucci extremal operators for the leading part and the keller osserman condition on the zeroth order term by means a kind of liouville method we prove that uniqueness of solutions holds therefore a unique growth at infinity is compatible with the structure of the equations furthermore the knowledge of these growth at infinity of solutions is not required a priori due to the presence of a strong absorption term the liouville theorem proved is independent on the dimension

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

design and performance of combination filters for signal restoration a class of nonlinear moving window filters is investigated for restoration and detection of signals embedded in additive white gaussian and non gaussian noise the filters of this class called combination filters c filters use both rank order and temporal order information from the input observation sequence within finite processing windows to produce the outputs a c filter combines the characteristics of linear fir finite impulse response filters and nonlinear filters of the order statistics type the output of a c filter in each processing window is defined to be the rank order dependent weighting of temporal order data both analytical and training procedures for designing the c filters are considered to get further improvement in overall performance the authors extend the concept of c filters and introduce a class of generalized c filters gc filters which are shown to have desirable properties performance characteristics of c and gc filters in signal restoration are considered through computer simulation

convergence and equivalence results for the jensen s inequality application to time delay and sampled data systems the jensen s inequality plays a crucial role in the analysis of time delay and sampled data systems its conservatism is studied through the use of the gruss inequality it has been reported in the literature that fragmentation or partitioning schemes allow to empirically improve the results we prove here that the jensen s gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases finally a family of bounds is characterized and a comparison with other bounds of the literature is provided it is shown that the other bounds are equivalent to jensen s and that they exhibit interesting well posedness and linearity properties which can be exploited to obtain better numerical results

gruss type inequalities in normed spaces abstract generalizations of the classic gruss inequality in normed spaces are given the results are illustrated with some specific examples

an extended reciprocally convex matrix inequality for stability analysis of systems with time varying delay abstract the reciprocally convex combination lemma rccl is an important technique to develop stability criteria for the systems with a time varying delay this note develops an extended reciprocally convex matrix inequality which reduces the estimation gap of the rccl based matrix inequality and reduces the number of decision variables of the recently proposed delay dependent rccl a stability criterion of a linear time delay system is established through the proposed matrix inequality finally a numerical example is given to demonstrate the advantage of the proposed method

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

a generalization of gruss s inequality in inner product spaces and applications a generalization of the classical gruss s integral inequality in inner product spaces is given some applications for positive linear functionals and integrals are also pointed out

brief paper robust h filtering for a class of uncertain linear systems with time varying delay this paper deals with the problem of delay dependent robust h filtering for uncertain linear systems with time varying delay two cases of time varying delays are fully considered one is the time varying delay being continuous uniformly bounded while the other is the time varying delay being differentiable uniformly bounded with delay derivative bounded by a constant a stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of h noise attenuation based on a new integral inequality delay dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities lmis through deriving these conditions neither model transformation nor bounding technique for cross terms is employed moreover the relationship between the sufficient conditions for the two cases of time varying delay is disclosed finally two examples are also given to illustrate the effectiveness of the proposed methodology

weighted iterative truncated mean filter the iterative truncated arithmetic mean itm filter was proposed recently it offers a way to estimate the sample median by simple arithmetic computing instead of the time consuming data sorting in this paper a rich class of filters named weighted itm witm filters are proposed by iteratively truncating the extreme samples the output of the witm filter converges to the weighted median proper stopping criterion makes the witm filters own merits of both the weighted mean and median filters and hence outperforms the both in some applications three structures are designed to enable the witm filters being low band and high pass filters properties of these filters are presented and analyzed experimental evaluations are carried out on both synthesis and real data to verify some properties of the witm filters

generalized jensen inequalities with application to stability analysis of systems with distributed delays over infinite time horizons the jensen inequality has been recognized as a powerful tool to deal with the stability of time delay systems recently a new inequality that encompasses the jensen inequality was proposed for the stability analysis of systems with finite delays in this paper we first present a generalized integral inequality and its double integral extension it is shown how these inequalities can be applied to improve the stability result for linear continuous time systems with gamma distributed delays then for the discrete time counterpart we provide an extended jensen summation inequality with infinite sequences which leads to less conservative stability conditions for linear discrete time systems with poisson distributed delays the improvements obtained by the introduced generalized inequalities are demonstrated through examples

technical communique absolute stability of time delay systems with sector bounded nonlinearity this paper deals with the problem of absolute stability of time delay systems with sector bounded nonlinearity some new delay dependent stability criteria are obtained and formulated in the form of linear matrix inequalities lmis neither model transformation nor bounding technique for cross terms is involved through derivation of the stability criteria numerical examples show that the results obtained in this paper improve the estimate of the stability limit over some existing result

quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation topological separation is investigated in the case of an uncertain time invariant matrix interconnected with an implicit linear transformation a quadratic separator independent of the uncertainty is shown to prove losslessly the closed loop well posedness several applications for lti descriptor system analysis are then given first some known results for stability and pole location of descriptor systems are demonstrated in a new way second contributions to robust stability analysis and time delay systems stability analysis are exposed these prove to be new even when compared to results for usual lti systems not in descriptor form all results are formulated as linear matrix inequalities lmis

cal h _ infty delay scheduled control of linear systems with time varying delays this paper deals with h infin delay scheduled control of linear systems with time varying delays first a new model transformation is given which allows to provide a unified approach to stability analysis and state feedback control synthesis for time delay systems represented in linear fractional transformation lft form a new type of controller is then synthesized where the state feedback is scheduled by the value of the delay delay scheduled controllers the results are provided in terms of linear matrix inequalities lmis which are known to be efficiently solvable

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

new bounds for moments of continuous random variables in this paper some gruss and ostrowski gruss type inequalities are applied to estimate the moments of continuous random variables whose probability density function is in l p space some results of kumar are generalized p kumar inequalities involving moments of a continuous random variable defined over a finite interval comput math appl 48 2004 257 273 p kumar the ostrowski type moment integral inequalities and moment bounds for continuous random variables comput math appl 49 2005 1929 1940

sampled data fuzzy stabilization of nonlinear systems under nonuniform sampling this paper investigates the sampled data fuzzy stabilization problem for a class of nonlinear systems that is exactly modeled in takagi sugeno fuzzy form at least locally a new method for designing parallel distribution compensation fuzzy controller is proposed which just requires that the nonlinear function is locally lipschitz by considering the sample and hold behavior of the system and using jensen s integral inequality an inequality constrain condition is derived from the locally lipschitz property further by defining a time dependent lyapunov krasovskii functional term a new technique instead of the use of s procedure is developed and stabilization conditions for state feedback and observer based output feedback under nonuniform sampling are obtained compared with the existing ones the new design method not only avoids the difficulty of finding exact upper bounds of asynchronous errors of mismatch membership functions but contains less conservatism and less numerical complexity as well finally some illustrative examples are given to show the effectiveness of the proposed design method and the significant improvement over the existing results

a survey on some inequalities for expectation and variance inequalities for continuous random variables having the probability density function defined on a finite interval obtained recently by the authors are surveyed

state feedback synchronization control of impulsive neural networks with mixed delays and linear fractional uncertainties abstract this study examines the synchronization problem of impulsive neural networks with mixed time varying delays and linear fractional uncertainties the mixed time varying delays include distributed leakage discrete and distributed time varying delays moreover the restrictions on derivatives of time varying delays with upper bounds to smaller than one is relaxed by introducing free weight matrices based on suitable lyapunov krasovskii functionals and integral inequalities linear matrix inequality approach is used to derive the sufficient conditions that guarantee the synchronization criteria of impulsive neural networks via delay dependent state feedback control finally three numerical examples are given to show the effectiveness of the theoretical results

stability and stabilization of discrete time tźs fuzzy systems with time varying delay via cauchyźschwartz based summation inequality this paper proposes new stability and stabilization conditions for discrete time fuzzy systems with time varying delays by constructing a suitable lyapunov krasovskii functional and introducing a new summation inequality based on the inequality of cauchy schwartz form which enhances the feasible region of the stability criterion for discrete time systems with time varying delay a stability criterion for such systems is established in order to show the effectiveness of the proposed inequality which provides more tight lower bound of a summation term of quadratic form a delay dependent stability criterion for such systems is derived within the framework of linear matrix inequalities which can be easily solved by various effective optimization algorithms going one step forward the proposed inequality is applied to a stabilization problem in discrete time fuzzy systems with time varying delays the advantages of the proposed stability and stabilization criteria are illustrated via two numerical examples

a general class of nonlinear normalized adaptive filtering algorithms the normalized least mean square nlms algorithm is an important variant of the classical lms algorithm for adaptive linear filtering it possesses many advantages over the lms algorithm including having a faster convergence and providing for an automatic time varying choice of the lms stepsize parameter that affects the stability steady state mean square error mse and convergence speed of the algorithm an auxiliary fixed step size that is often introduced in the nlms algorithm has the advantage that its stability region step size range for algorithm stability is independent of the signal statistics in this paper we generalize the nlms algorithm by deriving a class of nonlinear normalized lms type nlms type algorithms that are applicable to a wide variety of nonlinear filter structures we obtain a general nonlinear nlms type algorithm by choosing an optimal time varying step size that minimizes the next step mse at each iteration of the general nonlinear lms type algorithm as in the linear case we introduce a dimensionless auxiliary step size whose stability range is independent of the signal statistics the stability region could therefore be determined empirically for any given nonlinear filter type we present computer simulations of these algorithms for two specific nonlinear filter structures volterra filters and the previously proposed class of myriad filters these simulations indicate that the nlms type algorithms in general converge faster than their lms type counterparts

some qualitative properties for geometric flows and its euler implicit discretization abstract we study the geometric flow parabolic equation and its implicit discretization which yield a family of nonlinear elliptic problems we show that there are important differences in the study of those equations which concerns the propagation of level sets of data our study is based on the previous study of radially symmetric solutions of the corresponding equation curiously in radial coordinates both equations reduce to suitable singular hamilton jacobi first order equations after considering the case of monotone data we point out a new peculiar behavior for non monotone data with a profile of batman type g min g 1 g 2 g 1 r increasing g 2 r decreasing and g 1 r d g 2 r d for some r d 0 in the parabolic regime and when the velocity of the convexity part of the level sets is greater than the velocity of the concavity part we show that the level set u g r d develops a non empty interior set for any t 0 nothing similar occurs in the stationary regime we also present some numerical experiences

nonlinear elliptic equations in rn without growth restrictions on the data abstract we show existence and regularity of solutions in rn to nonlinear elliptic equations of the form div a x du g x u when is just a locally integrable function under appropriate growth conditions on a and g but not on roughly speaking in the model case p u u s 1u with p 2 1 n existence of a nonnegative solution in rn is guaranteed for every nonnegative l1loc rn if and only if s p 1

permutation filter lattices a general order statistic filtering framework a general nonlinear filtering framework permutation order statistic filter lattices is introduced which defines a highly modular and robust class of filters which effectively addresses both the nonlinear characteristics of a system as well as the possible noise contamination permutation filters much like polynomial filters are flexible and modular where instead of having polynomial expansions we have permutation lattice expansions at the simplest level in the filter lattice permutation filters reduce to either a simple linear fir or to an order statistic os filter but at higher levels in the lattice the obtained filters can model complicated nonlinear systems more accurately while still preserving their robust properties in order to enhance the robustness of permutation fitters we develop spl alpha trimmed permutation indicators and their associated filter lattices we conclude by presenting simulation examples where permutation filters are used in nonlinear system identification and in the rejection of narrowband interference in a direct sequence multiple access system this paper thus extends the potential of order statistic filters which have been shown to be somewhat limited in general nonlinear estimation problems

a new inequality of ostrowski gruss type and applications to some numerical quadrature rules in this paper we derive some gruss and ostrowski gruss type inequalities for functions in l p spaces as applications we provide some new estimates for the error in some numerical integration rules in particular we deal with the mid point and trapezoid quadrature rules

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

the aα spread of a graph abstract let a g and d g be the adjacency matrix and the degree diagonal matrix of a graph g respectively for any real number 0 1 nikiforov defined the a matrix of a graph g as a g d g 1 a g the a spread of a graph is the difference between the largest eigenvalue and the smallest eigenvalue of the a matrix of the graph in this paper we obtain some new lower bounds on a spread and characterize the extremal graphs for certain cases which extend the results of a spread and q spread moreover some graph operations on a spread are presented

translation invariant maps and applications in this paper we study translation invariant maps on a linear space a method for estimating quantities induced by such maps is presented applications for differences of operators commutators g contractive maps and gruss type inequalities are also given

gruss type inequalities abstract a connection between gruss inequality and the error of best approximation is revealed a gruss type inequality that unifies the continuous and discrete versions of the classical gruss inequalities is established

optimal pivot selection in fast weighted median search weighted median filters are increasingly being used in signal processing applications and thus fast implementations are of importance this paper introduces a fast algorithm to compute the weighted median wm of n samples which has linear time and space complexity as opposed to o n log n which is the time complexity of traditional sorting algorithms a popular selection algorithm often used to find the wm in large data sets is quickselect whose performance is highly dependent on how the pivots are chosen we introduce an optimization based pivot selection strategy which results in significantly improved performance as well as a more consistent runtime compared to traditional approaches the selected pivots are order statistics of subsets in order to find the optimal order statistics as well as the optimal subset sizes a set of cost functions are derived which when minimized lead to optimal design parameters we compare the complexity to floyd and rivest s algorithm select which to date has been the fastest median finding algorithm and we show that the proposed algorithm compared with select requires close to 30 fewer comparisons it is also shown that the proposed selection algorithm is asymptotically optimal for large n

ellipsoidal sets for resilient and robust static output feedback the implementation of a controller if not exact may lead to the so called fragility problem i e the loss of expected closed loop properties in the present note this difficult problem is dealt with considering robust static output feedback sof control for uncertain linear time invariant systems by analogy with robust analysis theory based on quadratic separation a new formulation for the sof design is shown to be a valuable way to tackle fragility issues indeed the use of a quadratic separator for design purpose allows to define a whole resilient nonfragile set of sof control laws results are formulated as matrix inequalities one of which is nonlinear a numerical algorithm based on nonconvex optimization is provided ant its running is illustrated on classical examples from literature

new inequalities of the kantorovich type for bounded linear operators in hilbert spaces some new inequalities of the kantorovich type are established they hold for larger classes of operators and subsets of complex numbers than considered before in the literature and provide refinements of the classical results in the case when the involved operator satisfies the usual conditions several new reverse inequalities for the numerical radius of a bounded linear operator are obtained as well

an inequality of ostrowski gruss type and its applications to the estimation of error bounds for some special means and for some numerical quadrature rules abstract in this paper we derive a new inequality of ostrowski gruss type and apply it to the estimation of error bounds for some special means and for some numerical quadrature rules

alexandroff bakelman pucci estimate and harnack inequality for degenerate singular fully non linear elliptic equations in this paper we study fully non linear elliptic equations in non divergence form which can be degenerate when the gradient is small typical examples are either equations involving the m laplace operator or bellman isaacs equations from stochastic control problems we establish an alexandroff bakelman pucci estimate and we prove a harnack inequality for viscosity solutions of such degenerate elliptic equations

adaptive filters based on order statistics an adaptive filter structure which is based on linear combinations of order statistics is proposed an efficient method to update the filter coefficients is presented which is based on the minimal mean square error criterion and which is similar to the widrow algorithm for the linear adaptive filters another method for coefficient update is presented which is similar to the recursive least squares rls algorithm and which has faster convergence properties the proposed filter can adapt well to a variety of noise probability distributions including impulsive noise it also performs well in the case of nonstationary signals and therefore it is suitable for image processing applications

direct delay decomposition approach to synchronization of chaotic fuzzy cellular neural networks with discrete unbounded distributed delays and markovian jumping parameters in this paper the problem of synchronization of chaotic fuzzy cellular neural networks fcnns with discrete unbounded distributed delays and markovian jumping parameters mjps is investigated sufficient delay dependent stability criteria are obtained in terms of linear matrix inequalities lmis to ensure the chaotic delayed fcnns to be stochastic asymptotically synchronous with the help of free weighting matrix and some inequality techniques the information of the delayed plant states can be taken into full consideration here the delay interval is decomposed into two subintervals by using the tuning parameter such that 0 1 by developing a delay decomposition approach and constructing suitable lyapunov krasovskii functional lkf sufficient conditions for synchronization are established for each subinterval numerical example and its simulations are provided to demonstrate the effectiveness and less conservatism of the derived results

the behavior of lms and nlms algorithms in the presence of spherically invariant processes the behavior of least mean square lms and normalized least mean square nlms algorithms with spherically invariant random processes sirps as excitations is shown many random processes fall into this category and sirps closely resemble speech signals the most pertinent properties of these random processes are summarized the lms algorithm is introduced and the first and second order moments of the weight error vector between the wiener solution and the estimated solution are shown the behavior of the nlms algorithm is obtained and the first and second order moments of the weight error vector are calculated the results are verified by comparison with known results when a white noise process and a colored gaussian process are used as input sequences some simulation results for a k sub 0 process are then shown

a gruss type discrete inequality in inner product spaces and applications a gruss type inequality in inner product spaces and applications for the discrete fourier transform mellin transform of sequences polynomials with coefficients in hilbert spaces and lipschitzian vector valued mappings are given

a unified approach to some inequalities of ostrowski gruss type based on the euler maclaurin formula in the spirit of 1 we provide a unified approach to some inequalities of ostrowski gruss type which include some existing results as special cases some illustrative examples are also included

pre specified performance based model reduction for time varying delay systems in fuzzy framework this paper attempts to provide a new solution to the model approximation problem for dynamic systems with time varying delays under the fuzzy framework for a given high order system our focus is on the construction of a reduced order model which approximates the original one in a prescribed error performance level and guarantees the asymptotic stability of the corresponding error system based on the reciprocally convex technique a less conservative stability condition is established for the dynamic error system with a given error performance index furthermore the reduced order model is eventually obtained by applying the projection approach which converts the model approximation into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm finally two numerical examples are provided to illustrate the effectiveness of the proposed method

on generalized gruss type inequalities for k fractional integrals the aim of the present paper is to investigate some new integral inequalities of gruss type for k riemann liouville fractional integrals from our results new weighted or classical gruss type inequalities have been established for some special cases moreover special cases of the integral inequalities in this paper have been obtained by dahmani and tabharit 2010 in 5

partially decoupled volterra filters formulation and lms adaptation the adaptation of volterra filters by one particular method the method of least mean squares lms while easily implemented is complicated by the fact that upper hounds for the values of step sizes employed by a parallel update lms scheme are difficult to obtain in this paper we propose a modification of the volterra filter in which the filter weights of a given order are optimized independently of those weights of higher order using this approach we then solve the minimum mean square error mmse filtering problem as a series of constrained optimization problems which produce a partially decoupled normal equation for the volterra filter from this normal equation we are able to develop an adaptation routine that uses the principles of partial decoupling that is similar in form to the volterra lms algorithm but with important structural differences that allow a straightforward derivation of bounds on the algorithm s step sizes these bounds can be shown to depend on the respective diagonal blocks of the volterra autocorrelation matrix this produces a reliable set of design guidelines that allow more rapid convergence of the lower order weight sets

detection of digital amplitude phase modulated signals in symmetric alpha stable noise in this paper we propose a scheme for the detection of digital amplitude phase modulated signals in flat fading channels with non gaussian noise the additive noise is modeled by a symmetric alpha stable distribution a well known model of man made and natural noise that appears in various environments a major challenge in the design of signal detection schemes is that detectors typically operate without knowledge of the transmitted data channel state and noise statistics the design becomes especially difficult for the considered noise model since conventional signal processing approaches are not applicable for this reason we propose a five stage signal detection scheme that is based on the use of a matched myriad filter an important contribution of this paper is the development of new algorithms for the estimation of noise distribution parameters in the presence of an unknown signal results are presented which show that the proposed detector outperforms a zero memory non linearity based scheme

on the generalization of ostrowski and gruss type discrete inequalities abstract the main purpose of this paper is to establish a generalization of discrete inequalities of the ostrowski and gruss type involving two functions the analysis used in the proofs is fairly elementary

notes on stability of time delay systems bounding inequalities and augmented lyapunov krasovskii functionals the bounding inequalities and the lyapunov krasovskii functionals lkfs are important for the stability analysis of time delay systems much attention has been paid to develop tighter inequalities for improving stability criteria while the contribution of the lkfs has not been considered when discussing the relationship between the tightness of inequalities and the conservatism of criteria this note is concerned with this issue firstly it is proved that when a simple lkf is applied the stability criteria obtained by the wirtinger based inequality and the jensen inequality are equivalent although the wirtinger based inequality is tighter it means that the tighter inequality does not always lead to a less conservative criterion secondly it is found that a suitable augmented lkf with necessary integral vectors in its derivative is required to achieve the advantage of the wirtinger based inequality based on this observation two delay product type terms are introduced into the lkf to establish new stability criteria finally a numerical example is given to verify the equivalence statements and to show the benefit of the proposed criteria

a note on wirtinger type integral inequalities for time delay systems different integral inequalities play important role when problems of stability analysis and controller synthesis for time delay systems are considered the connection of jensen s inequality and extended jensen s inequality is well understood now to reduce the conservativeness introduced by the application of jensen s inequality several versions of the wirtinger integral inequality have been published recently this note presents a comparison between some of these inequalities