viscosity versus vorticity stretching global well posedness for a family of navier stokes alpha like models abstract we study global well posedness and regularity of solutions for a family of incompressible three dimensional navier stokes alpha like models that employ fractional laplacian operators this family of equations depends on two parameters 1 and 2 which affect the strength of non linearity vorticity stretching and the degree of viscous smoothing varying 1 and 2 interpolates between the incompressible navier stokes equations and the incompressible lagrangian averaged navier stokes model our main result which contains previously established results of j l lions and others provides a relationship between 1 and 2 that is sufficient to guarantee global existence uniqueness and regularity of solutions

h_ infty filtering for nonlinear discrete time systems subject to quantization and packet dropouts this paper investigates the problem of h filtering for a class of nonlinear discrete time systems with measurement quantization and packet dropouts each output is transmitted via an independent communication channel and the phenomenon of packet dropouts in transmission is governed by an individual random binary distribution while the quantization errors are treated as sector bound uncertainties based on a piecewise lyapunov function an approach to the design of h piecewise filter is pro posed such that the filtering error system is stochastically stable with a guaranteed h performance some slack matrices are introduced to facilitate the filter design procedure by eliminating the coupling between the lyapunov matrices and the system matrices the filter parameters can be obtained by solving a set of linear matrix inequalities lmis which are numerically tractable with commercially available software finally two illustrative examples are provided to show the effectiveness of the proposed method

note on solution regularity of the generalized magnetohydrodynamic equations with partial dissipation abstract in this brief note we study the n dimensional magnetohydrodynamic equations with hyper viscosity and zero resistivity we prove global regularity of solutions when the hyper viscosity is sufficiently strong

robust h sub spl infin and mixed h sub 2 h sub spl infin filters for equalization designs of nonlinear communication systems fuzzy interpolation approach generally it is difficult to design equalizers for signal reconstruction of nonlinear communication channels with uncertain noises in this paper we propose the h sub spl infin and mixed h sub 2 h sub spl infin filters for equalization detection of nonlinear channels using fuzzy interpolation and linear matrix inequality lmi techniques first the signal transmission system is described as a state space model and the input signal is embedded in the state vector such that the signal reconstruction estimation design becomes a nonlinear state estimation problem then the takagi sugeno fuzzy linear model is applied to interpolate the nonlinear channel at different operation points through membership functions since the statistics of noises are unknown the fuzzy h sub spl infin equalizer is proposed to treat the state estimation problem from the worst case robust point of view when the statistics of noises are uncertain but with some nominal or average information available the mixed h sub 2 h sub spl infin equalizer is employed to take the advantage of both h sub 2 optimal performance with nominal statistics of noises and the h sub spl infin robustness performance against the statistical uncertainty of noises using the lmi approach the fuzzy h sub 2 h sub spl infin equalizer detector design problem is characterized as an eigenvalue problem evp the evp can be solved efficiently with convex optimization techniques

on the global regularity of generalized leray alpha type models abstract we generalize leray alpha type models studied in cheskidov et al 2005 1 and linshiz and titi 2007 4 via fractional laplacians and employ besov space techniques to obtain global regularity results with the logarithmically supercritical dissipation

brief stochastic optimal control and analysis of stability of networked control systems with long delay in this paper stochastic optimal controllers of networked control systems whose network induced delay is longer than a sampling period are designed for the two cases of the system with either full state information or partial state information the controllers are shown to render corresponding networked control systems exponentially mean square stable the optimal estimator of the system state is presented when the system has partial state information and network induced delay is longer than a sampling period the separation theorem is proved to still hold in such networked control systems

brief paper h filtering for nonlinear discrete time stochastic systems with randomly varying sensor delays this paper is concerned with the h filtering problem for a general class of nonlinear discrete time stochastic systems with randomly varying sensor delays where the delayed sensor measurement is governed by a stochastic variable satisfying the bernoulli random binary distribution law in terms of the hamilton jacobi isaacs inequalities preliminary results are first obtained that ensure the addressed system to possess an l 2 gain less than a given positive scalar c next a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the h performance constraint for all nonzero exogenous disturbances under the zero initial condition such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation furthermore it is shown that our main results can be readily specialized to the case of linear stochastic systems finally a numerical simulation example is used to demonstrate the effectiveness of the results derived

the beale kato majda criterion for the 3d magneto hydrodynamics equations we study the blow up criterion of smooth solutions to the 3d mhd equations by means of the littlewood paley decomposition we prove a beale kato majda type blow up criterion of smooth solutions via the vorticity of velocity only namely sup j in mathbb z int 0 t delta j nabla times u infty dt where j is the frequency localization operator in the littlewood paley decomposition

optimal h filtering in networked control systems with multiple packet dropouts abstract this paper studies the problem of h filtering in networked control systems ncss with multiple packet dropouts a new formulation enables us to assign separate dropout rates from the sensors to the controller and from the controller to the actuators by employing the new formulation random dropout rates are transformed into stochastic parameters in the system s representation a generalized h norm for systems with stochastic parameters and both stochastic and deterministic inputs is derived the stochastic h norm of the filtering error is used as a criterion for filter design in the ncs framework a set of linear matrix inequalities lmis is given to solve the corresponding filter design problem a simulation example supports the theory

fuzzy model based piecewise mathscr h _ infty static output feedback controller design for networked nonlinear systems this paper investigates the problem of robust h output feedback control for a class of nonlinear systems under unreliable communication links the nonlinear plant is represented by a takagi sugeno t s uncertain fuzzy model and the communication links between the plant and controller are assumed to be imperfect i e data packet dropouts occur intermittently which is often the case in a network environment stochastic variables that satisfy the bernoulli random binary distribution are adopted to characterize the data missing phenomenon and the attention is focused on the design of a piecewise static output feedback sof controller such that the closed loop system is stochastically stable with a guaranteed h performance based on a piecewise lyapunov function combined with some novel convexifying techniques the solutions to the problem are formulated in the form of linear matrix inequalities lmis finally simulation examples are also provided to illustrate the effectiveness of the proposed approaches

generalized mhd equations abstract solutions of the d dimensional generalized mhd gmhd equations t u u u p b b u t b u b b u b are studied in this paper we pay special attention to the impact of the parameters and on the regularity of solutions our investigation is divided into three major cases 1 0 and 0 2 0 and 0 and 3 0 and 0 when 0 and 0 the gmhd equations with any 0 and 0 possess a global weak solution corresponding to any l2 initial data furthermore weak solutions associated with 1 2 d 4 and 1 2 d 4 are actually global classical solutions when their initial data are sufficiently smooth as a special consequence smooth solutions of the 3d gmhd equations with 5 4 and 5 4 do not develop finite time singularities the study of the gmhd equations with 0 and 0 is motivated by their potential applications in magnetic reconnection a local existence result of classical solutions and several global regularity conditions are established for this case these conditions are imposed on either the vorticity u or the current density j b but not both and are weaker than some of current existing ones when 0 and 0 the gmhd equations reduce to the ideal mhd equations it is shown here that the ideal mhd equations admit a unique local solution when the prescribed initial data is in a holder space cr with r 1

brief paper robust filtering with stochastic nonlinearities and multiple missing measurements this paper is concerned with the filtering problem for a class of discrete time uncertain stochastic nonlinear time delay systems with both the probabilistic missing measurements and external stochastic disturbances the measurement missing phenomenon is assumed to occur in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over the interval 01 such a probabilistic distribution could be any commonly used discrete distribution over the interval 01 the multiplicative stochastic disturbances are in the form of a scalar gaussian white noise with unit variance the purpose of the addressed filtering problem is to design a filter such that for the admissible random measurement missing stochastic disturbances norm bounded uncertainties as well as stochastic nonlinearities the error dynamics of the filtering process is exponentially mean square stable by using the linear matrix inequality lmi method sufficient conditions are established that ensure the exponential mean square stability of the filtering error and then the filter parameters are characterized by the solution to a set of lmis illustrative examples are exploited to show the effectiveness of the proposed design procedures

robust h control for a class of nonlinear discrete time delay stochastic systems with missing measurements this paper is concerned with the problem of robust h output feedback control for a class of uncertain discrete time delayed nonlinear stochastic systems with missing measurements the parameter uncertainties enter into all the system matrices the time varying delay is unknown with given low and upper bounds the nonlinearities satisfy the sector conditions and the missing measurements are described by a binary switching sequence that obeys a conditional probability distribution the problem addressed is the design of an output feedback controller such that for all admissible uncertainties the resulting closed loop system is exponentially stable in the mean square for the zero disturbance input and also achieves a prescribed h performance level by using the lyapunov method and stochastic analysis techniques sufficient conditions are first derived to guarantee the existence of the desired controllers and then the controller parameters are characterized in terms of linear matrix inequalities lmis a numerical example is exploited to show the usefulness of the results obtained

robust mixed h_2 h_infty filtering for time delay fuzzy systems in this paper a robust mixed h2 hinfin filtering problem for continuous time fuzzy systems subject to parameter uncertainties and multiple time varying delays in state variables is addressed the uncertain systems are expressed as takagi sugeno fuzzy models with linear nominal parts and norm bounded uncertainties the main objective is to design stable filters that minimize a guaranteed cost index and achieve a prescribed hinfin performance under worst case disturbance based on lyapunov theory both delay independent and delay dependent sufficient conditions guaranteeing stability and achieving prescribed performances are stated in terms of linear matrix inequalities therefore stable filters can be obtained easily with existing convex algorithms lastly two examples are given to illustrate the proposed design methodology

h sub spl infin fuzzy output feedback control design for nonlinear systems an lmi approach addresses the problem of stabilizing a class of nonlinear systems by using an h sub spl infin fuzzy output feedback controller first a class of nonlinear systems is approximated by a takagi sugeno ts fuzzy model then based on a well known lyapunov functional approach we develop a technique for designing an h sub spl infin fuzzy output feedback control law which guarantees the l sub 2 gain from an exogenous input to a regulated output is less or equal to a prescribed value a design algorithm for constructing an h sub spl infin fuzzy output feedback controller is given in contrast to the existing results the premise variables of the h sub spl infin fuzzy output feedback controller are not necessarily to be the same as the premise variables of the ts fuzzy model of the plant a numerical simulation example is presented to illustrate the theory development

h_ infty filter design for a class of networked control systems via t s fuzzy model approach this paper is concerned with h design for a class of networked control systems ncss with multiple state delays via the takagi sugeno t s fuzzy model the transfer delays and packet loss that are induced by the limited bandwidth of communication networks are considered the focus of this paper is on the analysis and design of a full order h filter such that the filtering error dynamics are stochastically stable and a prescribed h attenuation level is guaranteed sufficient conditions are established for the existence of the desired filter in terms of linear matrix inequalities lmis an example is given to illustrate the effectiveness and applicability of the proposed design method

on a leray α model of turbulence in this paper we introduce and study a new model for three dimensional turbulence the leray model this model is inspired by the lagrangian averaged navier stokes model of turbulence also known navier stokes model or the viscous camassa holm equations as in the case of the lagrangian averaged navier stokes model the leray model compares successfully with empirical data from turbulent channel and pipe flows for a wide range of reynolds numbers we establish here an upper bound for the dimension of the global attractor the number of degrees of freedom of the leray model of the order of l l d 12 7 where l is the size of the domain and l d is the dissipation length scale this upper bound is much smaller than what one would expect for three dimensional models i e l l d 3 this remarkable result suggests that the leray model has a great potential to become a good sub grid scale large eddy simulation model of turbulence we support this observation by studying analytically and computationally the energy spectrum and show that in addition to the usual k 5 3 kolmogorov power law the inertial range has a steeper power law spectrum for wavenumbers larger than 1 finally we propose a prandtl like boundary layer model induced by the leray model and show a very good agreement of this model with empirical data for turbulent boundary layers

h filtering of discrete time fuzzy systems via basis dependent lyapunov function approach this paper is concerned with the h filtering problem for a class of discrete time fuzzy systems attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the h sense by using basis dependent lyapunov functions sufficient conditions for the solvability of this problem are obtained it has been shown that the h filtering problem can be solved as a linear matrix inequality lmi optimization problem two examples are provided to demonstrate the applicability of the proposed approach

global regularity of logarithmically supercritical 3 d lamhd alpha system with zero diffusion abstract we study the three dimensional lagrangian averaged magnetohydrodynamics alpha system with zero diffusion despite the dissipation strength at the logarithmically supercritical level using dyadic decomposition techniques we show that given initial data sufficiently smooth the solution pair remains smooth for all time this settles the global regularity case suggested by the authors in 27

h_ bm infty fuzzy filtering of nonlinear systems with intermittent measurements this paper is concerned with the problem of h infin fuzzy filtering of nonlinear systems with intermittent measurements the nonlinear plant is represented by a takagi sugeno t s fuzzy model the measurements transmission from the plant to the filter is assumed to be imperfect and a stochastic variable satisfying the bernoulli random binary distribution is utilized to model the phenomenon of the missing measurements attention is focused on the design of an h infin filter such that the filter error system is stochastically stable and preserves a guaranteed h infin performance a basis dependent lyapunov function approach is developed to design the h infin filter by introducing some slack matrix variables the coupling between the lyapunov matrix and the system matrices is eliminated which greatly facilitates the filter design procedure the developed theoretical results are in the form of linear matrix inequalities lmis finally an illustrative example is provided to show the effectiveness of the proposed approach

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

static output feedback mathscr h _ bm infty control of continuous time t s fuzzy affine systems via piecewise lyapunov functions this paper investigates the problem of robust h output feedback control for a class of continuous time takagi sugeno t s fuzzy affine dynamic systems with parametric uncertainties and input constraints the objective is to design a suitable constrained piecewise affine static output feedback controller guaranteeing the asymptotic stability of the resulting closed loop fuzzy control system with a prescribed h disturbance attenuation level based on a smooth piecewise quadratic lyapunov function combined with s procedure and some matrix inequality convexification techniques some new results are developed for static output feedback controller synthesis of the underlying continuous time t s fuzzy affine systems it is shown that the controller gains can be obtained by solving a set of linear matrix inequalities lmis finally three examples are provided to illustrate the effectiveness of the proposed methods

parameterized linear matrix inequality techniques in fuzzy control system design this paper proposes different parameterized linear matrix inequality plmi characterizations for fuzzy control systems these plmi characterizations are in turn relaxed into pure lmi programs which provides tractable and effective techniques for the design of suboptimal fuzzy control systems the advantages of the proposed methods over earlier ones are then discussed and illustrated through numerical examples and simulations

logarithmically extended global regularity result of lans alpha mhd system in two dimensional space abstract we study the two dimensional generalized lans alpha magnetohydrodynamics system we show that the solution pairs of velocity and magnetic fields to this system preserve their initial regularity in two cases dissipation logarithmically weaker than a full laplacian and zero diffusion zero dissipation and diffusion logarithmically weaker than a full laplacian

delay dependent hbox h _ infty filter design for discrete time fuzzy systems with time varying delays this paper investigates delay dependent hinfin filter design problems for discrete time fuzzy systems with time varying delays first a novel delay dependent piecewise lyapunov krasovskii functional ddplkf is proposed in which both the upper bound of delays and the delay interval are considered based on this ddplkf the delay dependent stability criteria for discrete time systems with constant or time varying delays are obtained respectively then delay dependent full order and reduced order hinfin filter design approaches are proposed the filter parameters can be obtained by solving a set of linear matrix inequalities lmis simulation examples are also given to illustrate the performance of the proposed approaches it is shown that our approaches are less conservative and that the corresponding hinfin filters can achieve better performance than the existing approaches

tests for homogeneity of the risk difference when data are sparse summary test statistics for the homogeneity of the risk difference for a series of 2 x 2 tables when the data are sparse is proposed a weighted least squares statistic is commonly used to test for equality of the risk difference over the tables however when the data are sparse this statistic can have anticonservative type i error rates simulation is used to compare the proposed test statistics to the weighted least squares statistic the weighted least squares statistic has the most anticonservative type i error rates of all the statistics compared we suggest the use of one of our proposed test statistics instead of the weighted least squares statistic sets of 2 x 2 tables with sparse data occur often in biostatistics in this paper we consider sparse sets of 2 x 2 tables that arise in clinical trials clinical trials typically involve a comparison of a standard treatment versus a new treatment often the outcome for a subject is binary success failure patients enrolled in the trial are randomly assigned to one of these two treatment groups and the success rates on the treatments are compared to determine which treatment is more efficacious in many trials including those undertaken by large cooperative cancer groups the cancer and leukemia group b the eastern cooperative oncology group the southwestern oncology group patients are randomized to one of the two treatment groups within an institution i e a hospital with treatment allocation approximately balanced within institutions the interest in the clinical trial is in estimating the difference in the success rates of the two treatments sometimes called the risk difference or treatment difference the risk difference is often used as the measure of effect in practice and it has a nice interpretation in a clinical trial the risk difference measures the actual gains that can be expected in terms of percentage of patients treated because the randomization is within institution patients from the same institution often have similar treatment outcomes due possibly to unmeasured variables such as the skill of the staff or the quality of the hospital equipment in other words there may be an institution effect emerson hoaglin and mosteller unpublished manuscript use simulations to compare estimates of a common risk difference across institutions however before estimating a common risk difference and testing if it equals zero one may first want to test for no institution effect i e for equality of the risk difference over institutions in this setting each institution contributes a 2 x 2 table of treatment by binary response however the data in each table may be sparse since each institution may not accrue many patients for

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

global regularity for the 2d boussinesq equations with partial viscosity terms abstract in this paper we prove the global in time regularity for the 2d boussinesq system with either the zero diffusivity or the zero viscosity we also prove that as diffusivity viscosity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion viscosity equations our result for the zero diffusion system in particular solves the problem no 3 posed by moffatt in r l ricca ed kluwer academic publishers dordrecht the netherlands 2001 pp 3 10

a new design of delay dependent robust cal h _ bm infty filtering for discrete time t s fuzzy systems with time varying delay this paper investigates the problem of delay dependent robust h infin filtering design for a class of uncertain discrete time state delayed takagi sugeno t s fuzzy systems the state delay is assumed to be time varying and of an interval like type which means that both the lower and upper bounds of the time varying delay are available the parameter uncertainties are assumed to have a structured linear fractional form based on a novel fuzzy basis dependent lyapunov krasovskii functional combined with finsler s lemma and an improved free weighting matrix technique for delay dependent criteria a new sufficient condition for robust h infin performance analysis is first derived and then the filter synthesis is developed it is shown that by using a simple linearization technique incorporating a bounding inequality a unified framework can be developed such that both the full order and reduced order filters can be obtained by solving a set of linear matrix inequalities lmis which are numerically efficient with commercially available software finally simulation examples are provided to illustrate the advantages and less conservatism of the proposed approach

variance constrained filtering for uncertain stochastic systems with missing measurements in this note we consider a new filtering problem for linear uncertain discrete time stochastic systems with missing measurements the parameter uncertainties are allowed to be norm bounded and enter into the state matrix the system measurements may be unavailable i e missing data at any sample time and the probability of the occurrence of missing data is assumed to be known the purpose of this problem is to design a linear filter such that for all admissible parameter uncertainties and all possible incomplete observations the error state of the filtering process is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prescribed upper bound it is shown that the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like inequalities or linear matrix inequalities the explicit expression of the desired robust filters is parameterized and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

some mathematical questions related to the mhd equations some questions relating to the large time behavior of the solutions of mhd equations for a viscous incompressible resistive fluid are investigated the physical system is briefly described and the functional setting of the equations a flow in a bounded domain or in whole space with a space periodicity property in all directions the main existence and uniqueness results for weak and strong solutions of the mhd equations are recalled regularity properties and bounds on the solutions to the equations which are valid for all time are established and the concept of functional invariant sets is introduced which is contained in the space of smooth functions if the data are sufficiently regular the squeezing property of the trajectories are stated and it is shown that any functional invariant set for the mhd equations and in particular any attractor has a finite haussdorf dimension the flow is found to be totally determined for large dimensions by a finite number of parameters 26 references

approaches to robust filtering design of discrete time fuzzy dynamic systems this paper presents two filter design methods for discrete time fuzzy dynamic systems based on a piecewise quadratic lyapunov function it is shown that the resulting filtering error system is globally stable with guaranteed hinfin or generalized h2 performance and the filter gains can be obtained by solving a set of linear matrix inequalities two simulation examples are also given to illustrate the performance of the proposed approaches