rigorous application of the stochastic functional method to plane wave scattering from a random cylindrical surface the stochastic functional method is applied to plane wave scattering from a random cylindrical surface whereupon the dirichlet boundary condition is rigorously imposed analytical results accurate to second and fourth order in surface roughness are obtained for the coefficients of the wiener hermite expansion of the secondary scattered wave field the validity of approximate solutions is numerically investigated by means of the boundary condition criterion and of the energy consistency criterion the former which is introduced herein states that any approximate solution should be in conformity with the boundary condition whereas the latter pertains to the energy conservation law the numerical investigation indicates that the rigorous application of the stochastic functional method yields more accurate results in terms of both criteria than did previous treatments of the problem under consideration moreover it is suggested that applicability limits should be set through the mean boundary condition criterion instead of the energy consistency criterion the latter may lead to underestimating deficiencies of the approximate solution under test

technical communique new conditions for delay derivative dependent stability two recent lyapunov based methods have significantly improved the stability analysis of time delay systems the delay fractioning approach of gouaisbaut and peaucelle 2006 for systems with constant delays and the convex analysis of systems with time varying delays of park and ko 2007 in this paper we develop a convex optimization approach to stability analysis of linear systems with interval time varying delay by using the delay partitioning based lyapunov krasovskii functionals lkfs novel lkfs are introduced with matrices that depend on the time delays these functionals allow the derivation of stability conditions that depend on both the upper and lower bounds on delay derivatives

new results on stability analysis for systems with discrete distributed delay the integral inequality technique is widely used to derive delay dependent conditions and various integral inequalities have been developed to reduce the conservatism of the conditions derived in this study a new integral inequality was devised that is tighter than existing ones it was used to investigate the stability of linear systems with a discrete distributed delay and a new stability condition was established the results can be applied to systems with a delay belonging to an interval which may be unstable when the delay is small or nonexistent three numerical examples demonstrate the effectiveness and the smaller conservatism of the method

further improvement of jensen inequality and application to stability of time delayed systems this paper is concerned with the delay dependent stability for the linear systems with a time varying delay to get a result in the form of lmi from a lyapunov krasovskii functional an integral inequality is necessary and jensen inequality has been a most powerful inequality in the last few years recently based on wirtinger inequality an improved integral inequality encompassing jensen inequality was proposed and its application to the stability showed a quite improvement in this paper without using wirtinger inequality a further improved integral inequality in the form of infinite series is derived and based on this a delay dependent stability condition in the form of lmi is derived finally its contribution on the stability criterion is shown by well known two examples

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

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

h_ infty filtering for discrete time switched systems with known sojourn probabilities this technical note deals with the design of mode dependent h infty filters for a class of discrete time switched systems with nonlinearities in this class of systems when the system mode changes the filter designed for the specific subsystem also switches accordingly the main contribution is on the use of the information of the sojourn probability the probability of the switched system staying in each subsystem to build new kind of switched system model when this additional information is available sojourn probabilities are easier to obtain than the transition probabilities commonly used in markovian jump systems applying the lyapunov functional method the bounded real lemma brl for the resulting filtering error system is obtained in theorem 1 the filter parameters are designed in theorem 2 by solving a set of linear matrix inequalities finally two illustrative examples are given to demonstrate the effectiveness and potential of the proposed approach

scattering of a scalar wave from a slightly random surface scalar wave scattering from a slightly random surface is analyzed by a probabilistic method we make use of the homogeneity of an infinite random surface that is the shift invariance property of the strictly homogeneous random field by the group theoretic consideration of such a shift invariance property the wave solution proves to be a homogeneous random field multiplied by an exponential function then such a homogeneous random field is approximately solved for a slightly random surface to yield a wave solution involving multiple scattering several statistical properties of the scattering are calculated and shown in the figures the accuracy of the approximate solution is examined in terms of the error of the boundary value equation

turnpike properties and strict dissipativity for discrete time linear quadratic optimal control problems we analyze the connection between turnpike behaviors and strict dissipativity properties for discrete time finite dimensional linear quadratic optimal control problems we first use strict dissipativity as a sufficient condition for the turnpike property next we characterize strict dissipativity and the newly introduced property of strict pre dissipativity in terms of the system matrices related to the linear quadratic problem these characterizations then lead to new necessary conditions for the turnpike properties under consideration and thus eventually to necessary and sufficient conditions in terms of spectral criteria and matrix inequalities one of the key novelties which distinguishes the results in the present paper from earlier ones on linear quadratic optimal control problems is the consideration of state and input constraints

approximate solution of a mixed nonlinear stochastic oscillator in this paper nonlinear oscillators under mixed quadratic and cubic nonlinearities with stochastic inputs are considered different methods are used to obtain second order approximations namely the wiener hermite and perturbation whep technique and the homotopy perturbation method hpm some statistical moments are computed for the different methods using mathematica 5 comparisons are illustrated through figures for different case studies

technical communique improved delay dependent stability criteria for systems with a delay varying in a range this paper provides improved delay dependent stability criteria for systems with a delay varying in a range the criteria improve over some previous ones in that they have fewer matrix variables yet less conservatism which is established theoretically an example is given to show the advantages of the proposed results

scattering of waves from a random spherical surface mie scattering the stochastic theory developed by the authors for the scattering from a random planar surface is extended to the case of a random spherical surface which is assumed to be a homogeneous random field on the sphere homogeneous with respect to spherical rotations based on the group theoretical analogies between the two the formulation of the theory is closely connected to the representation theory of the rotation group the concept of the stochastic spherical harmonics associated with the rotation group and their several formulas are introduced and discussed at the beginning for the plane wave incident on a random spherical surface the scattered random wave field can be expanded systematically in terms of the stochastic spherical harmonics in much the same way as the nonrandom case and several formulas are derived for the coherent scattering amplitude the coherent and incoherent power flows and the coherent and incoherent scattering cross sections the power flow conservation law is cast into the stochastic version of the optical theorem stating that the total scattering cross section consisting of the coherent and incoherent power flow is equal to the imaginary part of the coherent forward scattering amplitude approximate solutions are obtained for the mie scattering with a slightly random spherical surface where the single scattering approximation is valid due to the absence of a real resonance as shown in the previous work on the two dimensional case some numerical calculations are made for the coherent and incoherent scattering cross sections

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

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 results on dissipativity analysis of singular systems with time varying delay abstract this paper focuses on the dissipativity analysis of singular systems with time varying delay the objective is to obtain a less conservative criterion with less computational demand based on the state decomposition method singular systems are rewritten as differential subsystems and algebraic ones first of all the components of state vectors are applied to design a novel lyapunov krasovskii functional lkf for the differential subsystems then in the derivative of the lkf the algebraic ones are introduced and the wirtinger based integral inequality together with the extended reciprocally convex matrix inequality is adopted to estimate the single integral term therefore a new dissipativity criterion is obtained which realizes both less conservativeness and less computational demand finally two numerical examples are given to verify the superiority of the proposed method

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

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

on equivalence and efficiency of certain stability criteria for time delay systems in recent years there have been a number of new delay dependent stability criteria based on linear matrix inequalities published in the literature this note aims to theoretically establish the equivalence of seven of these stability criteria moreover the efficiency of these stability criteria is assessed based on the number of unknowns in the linear matrix inequalities

delay variation dependent stability of delayed discrete time systems this note is concerned with the stability analysis of linear discrete time system with a time varying delay a generalized free weighting matrix gfwm approach is proposed to estimate summation terms in the forward difference of lyapunov functional and theoretical study shows that the gfwm approach encompasses several frequently used estimation approaches as special cases moreover an augmented lyapunov functional with a delay product type term is constructed to take into account delay changing information as a result the proposed gfwm approach together with the augmented lyapunov functional leads to a less conservative delay variation dependent stability criterion finally numerical examples are given to illustrate the advantages of the proposed criterion

technical communique stability and robust stability for systems with a time varying delay to concern the stability and robust stability criteria for systems with time varying delays this note uses not only the time varying delayed state x t h t but also the delay upper bounded state x email protected to exploit all possible information for the relationship among a current state x t an exactly delayed state x t h t a marginally delayed state x email protected and the derivative of the state email protected t when constructing lyapunov krasovskii functionals and some appropriate integral inequalities originally suggested by park 1999 a delay dependent stability criterion for systems with uncertain time invariant delays ieee transactions on automatic control 44 4 876 877 two fundamental criteria are provided for the cases where no bound of delay derivative is assumed and where an upper bound of delay derivative is assumed examples show the resulting criteria outperform all existing ones in the literature

stability of time delay systems via wirtinger based double integral inequality based on the wirtinger based integral inequality a double integral form of the wirtinger based integral inequality hereafter called as wirtinger based double integral inequality is introduced in this paper to show the effectiveness of the proposed inequality two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities lmis the advantage of employing the proposed inequalities is illustrated via two numerical examples

event based h filtering for sampled data systems this paper is concerned with event based h filtering for sampled data systems first an event based data packet processor is introduced to release sampled measurement outputs only if an event condition is violated as a result communication resources can be saved significantly while preserving the desired h performance second the resulting filtering error system is modeled as a system with an interval time varying delay by employing the lyapunov krasovskii functional approach a new bounded real lemma brl is established such that the filtering error system is asymptotically stable with the prescribed h performance third by performing an invertible linear transformation on the filtering error system a linear matrix inequality lmi based sufficient condition which is equivalent to the condition in the brl is obtained on the feasibility of the event based h filtering problem consequently suitable h filters and the event parameters in the event condition can be co designed provided that a set of lmis are satisfied finally a mechanical system with two masses and two springs is given to show the effectiveness of the proposed method

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

technical communique new stability criteria for linear systems with interval time varying delay this paper investigates robust stability of uncertain linear systems with interval time varying delay the time varying delay is assumed to belong to an interval and is a fast time varying function the uncertainty under consideration includes polytopic type uncertainty and linear fractional norm bounded uncertainty a new lyapunov krasovskii functional which makes use of the information of both the lower and upper bounds of the interval time varying delay is proposed to drive some new delay dependent stability criteria in order to obtain much less conservative results a tighter bounding for some term is estimated moreover no redundant matrix variable is introduced finally three numerical examples are given to show the effectiveness of the proposed stability criteria

further improvement of free weighting matrices technique for systems with time varying delay a novel method is proposed in this note for stability analysis of systems with a time varying delay appropriate lyapunov functional and augmented lyapunov functional are introduced to establish some improved delay dependent stability criteria less conservative results are obtained by considering the additional useful terms which are ignored in previous methods when estimating the upper bound of the derivative of lyapunov functionals and introducing the new free weighting matrices the resulting criteria are extended to the stability analysis for uncertain systems with time varying structured uncertainties and polytopic type uncertainties numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

summation inequalities to bounded real lemmas of discrete time systems with time varying delay summation inequality is an important technique for analysis of discrete time systems with a time varying delay it seems that from the literature a tighter inequality usually leads to a less conservative criterion based on h infty performance analysis problem this note presents different findings on the relationship between the conservatism of bounded real lemma brl and the tightness of summation inequality firstly the brl obtained by the wirtinger based inequality wbi is not always less conservative than the one by the jensen based inequality although the wbi is tighter secondly the wbi is tighter than a general free matrix based inequality gfmbi developed in this note while the brl obtained via the gfmbi is less conservative than the wbi based brl finally a numerical example is given to demonstrate those findings

note on stability of linear systems with time varying delay this note considers the stability of linear systems with a time varying delay we are interested in a simple lyapunov krasovskii functional lkf approach without delay decomposition in this category all recent tractable results had a fixed bound on the allowable maximum size of the delay for years we propose a new simple lkf including the cross terms of variables and quadratic terms multiplied by a higher degree scalar function and present a new result expressed in the form of lmis we show by two well known examples that our result overcomes the previous allowable maximum size of delay and it is less conservative than the previous results having a relatively small upper bound in the derivative of time delay

a note on equivalence between two integral inequalities for time delay systems jensen s inequality and extended jensen s inequality are two important integral inequalities when problems of stability analysis and controller synthesis for time delay systems are considered the extended jensen s inequality introduces two additional free matrices and is generally regarded to be less conservative than jensen s inequality the equivalence between jensen s inequality and extended jensen s inequality in bounding the quadratic term h t h t x t s z x s d s in lyapunov functional of time delay systems is presented and theoretically proved it is shown that the extended jensen s inequality does not decrease the lower bound of this quadratic term obtained using jensen s inequality and then it does not reduce the conservativeness though two additional free matrices m 1 and m 2 are involved

stability analysis for linear delayed systems via an optimally dividing delay interval approach this paper addresses the problem of stability for linear systems with time varying delay a novel augmented lyapunov krasovskii functional is constructed by using the idea of optimally dividing the delay interval 0 t into some variable sub intervals and line integral technology using the novel augmented functional the new delay dependent stability criteria are proposed for linear systems with time varying delay the gain is that this stability criterion can lead to much less conservative stability results compared to other methods for linear systems with delay two numerical examples are provided to verify the effectiveness of the proposed criteria

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

h state estimation for neural networks with general activation function and mixed time varying delays this article deals with h state estimation of neural networks with mixed delays in order to make full use of delay information novel delay product lyapunov krasovskii functional lkf by using parameterized delay interval is first constructed then generalized free weighting matrix integral inequality is used to estimate the derivative of lkf to reduce the conservatism also a more general activation function is further applied by combining with parameterized delay interval in order to obtain a more accurate estimator model finally sufficient conditions are derived to confirm that the estimation error system is asymptotically stable with a prescribed h performance numerical examples are simulated to show the benefits of our proposed method