vibration analysis of a circular arch with variable cross section using differential transformation and generalized differential quadrature vibration analysis of circular arches is an important subject in mechanics due to its various applications in particular circular arches with variable cross section have been widely used to satisfy modern architectural and structural requirements recently the generalized differential quadrature method gdqm and differential transformation method dtm were proposed by shu and zhou respectively in this study gdqm and dtm are applied to vibration analysis of circular arches with variable cross section the governing equation of motion is derived and the non dimensional natural frequencies are obtained for various boundary conditions the concepts of differential transformation and generalized differential quadrature are briefly introduced the results obtained by these methods are compared with previously published works gdqm and dtm showed fast convergence accuracy and validity in solving the vibration problem for circular arches with variable cross sections

out of plane vibrations of curved non uniform beams of constant radius the governing differential equations for out of plane vibrations of curved non uniform beams of constant radius are derived two physical parameters are introduced to simplify the analysis the explicit relations between the flexural displacement its first three order derivatives and the torsional displacement are derived with these explicit relations the two coupled governing characteristic differential equations can be decoupled and reduced to a sixth order ordinary differential equation with variable coefficients in the torsional displacement it is shown that if the material and geometric properties of the beam are in arbitrary polynomial forms of spatial variable then exact solutions for the out of plane vibrations of the beam can be obtained the derived explicit relations can also be used to reduce the difficulty in experimental measurements finally the influence of taper ratio center angle and arc length on the first two natural frequencies of the beams is illustrated

analytical and numerical approaches to nonlinear galloping of internally resonant suspended cables a study is carried out on nonlinear multimodal galloping of suspended cables a consistent model of a curved cable beam geometrically nonlinear and able to torque recently formulated by the authors is used the model accounts for quasi steady aerodynamic forces including the effect of static swing of the cable and dynamic twist of the cross section complementary solution methods are employed namely finite difference and galerkin spatial discretization followed by numerical time integration or galerkin spatial discretization in conjunction with multiple scale perturbation analysis the different techniques are applied to a cable close to the first cross over point at which a number of internal resonances exist branches of periodic solutions and their stability are evaluated as functions of wind velocity the existence of branches of quasi periodic solutions originating from narrow unstable intervals and propagating elsewhere is also proved qualitative and quantitative results furnished by the different investigation tools are compared among them and the importance of the various components of motion accounted or neglected in the reduced models is discussed

on construction of sampling patterns for preserving observability controllability of linear sampled data systems in this paper we design a new nonequidistant sampling pattern such that the property of controllability and observability of the linear continuous time systems is preserved during the procedure of

the non linear equations of motion of pipes conveying fluid abstract the non linear equations of motion of pipes conveying fluid are derived in simple and accessible terms by energy and newtonian methods different derivations are made for cantilevered pipes where the centreline is assumed inextensible and for pipes with both ends fixed it is shown that the derivations the origin of the various terms and the structure of the equations are distinctly different in these two cases the equations of motion are then compared with those already in existence e g by holmes rousselet and herrmann and lundgren sethna and bajaj at the same time clarifying the derivations and assumptions made and discussing the validity and completeness of the final equations some of the equations are found to be fully correct indeed superior to those derived here while others are found to be deficient because of assumptions made or inconsistencies in the derivations for pipes with both ends fixed the equations given in this paper are considered to be the most complete and correct

analytical and numerical study on spatial free vibration of non symmetric thin walled curved beams for spatial free vibration of non symmetric thin walled circular curved beams an accurate displacement field is introduced by defining all displacement parameters at the centroidal axis and three total potential energy functionals are consistently derived by degenerating the potential energy for the elastic continuum to that for thin walled curved beams the closed form solutions are newly obtained for in plane and out of plane free vibration analysis of monosymmetric curved beams respectively also two thin walled curved beam elements are developed using the third and fifth order hermitian polynomials in order to illustrate the accuracy and the practical usefulness of the present method analytical and numerical solutions by this study are presented and compared with previously published results or solutions by abaqus the shell element particularly effects of the thickness curvature as well as the inextensional condition are investigated on free vibration of curved beams with monosymmetric and non symmetric cross sections

technical communique sliding mode control of singular stochastic hybrid systems this paper is concerned with the sliding mode control smc of nonlinear singular stochastic systems with markovian switching an integral sliding surface function is designed and the resulting sliding mode dynamics is a full order markovian jump singular stochastic system by introducing some specified matrices a new sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic stability of the sliding mode dynamics then a smc law is synthesized for reaching motion moreover when there exists an external disturbance the 2 disturbance attenuation performance is analyzed for the sliding mode dynamics some related sufficient conditions are also established

a new approach for displacement functions of a curved timoshenko beam element in motions normal to its initial plane summary in existing literature either analytical methods or numerical methods the formulations for free vibration analysis of circularly curved beams normal to its initial plane are somewhat complicated particularly if the effects of both shear deformation sd and rotary inertia ri are considered it is hoped that the simple approach presented in this paper may improve the above mentioned drawback of the existing techniques first the three functions for axial or normal to plane displacement and rotational angles about radial and circumferential or tangential axes of a curved beam element were assumed since each function consists of six integration constants one has 18 unknown constants for the three assumed displacement functions next from the last three displacement functions the three force displacement differential equations and the three static equilibrium equations for the arc element one obtained three polynomial expressions equating to zero the coefficients of the terms in each of the last three expressions respectively one obtained 17 simultaneous equations as functions of the 18 unknown constants excluding the five dependent ones among the last 17 equations one obtained 12 independent simultaneous equations solving the last 12 independent equations one obtained a unique solution in terms of six unknown constants finally imposing the six boundary conditions at the two ends of an arc element one determined the last six unknown constants and completely defined the three displacement functions by means of the last displacement functions one may calculate the shape functions stiffness matrix mass matrix and external loading vector for each arc element and then perform the free and forced vibration analyses of the entire curved beam good agreement between the results of this paper and those of the existing literature confirms the reliability of the presented theory copyright 2005 john wiley sons ltd

stochastic h filtering for neural networks with leakage delay and mixed time varying delays abstract this paper deals with the problem of h filtering for stochastic neural networks snns with a mixed of time varying interval delays time varying distributed delays and leakage delays a novel quintuple integral lyapunov krasovskii functional lkf is constructed to improve the performance of the snn sufficient criteria can be obtained by applying the linear matrix inequality lmi approach and developing a new mathematical analysis which ensures the filtering error system is asymptotically stable in the mean square finally simulation results are provided to show the superiority and usefulness of the proposed method

three dimensional free vibrations of a circular arch using the theory of a cosserat point small deformation three dimensional free vibrations of a circular arch with uniform rectangular cross section have been investigated by using different theoretical approaches and by experimental verification special emphasis has been focused on a numerical formulation which models each element of the arch using the theory of a cosserat point comparison has been made with accurate three dimensional numerical modeling of the arch using the computer program ansys also three dimensional beam elements in the computer programs ansys and i deas have been considered along with an exact solution of approximate model equations of the arch the results indicate that appropriate modeling of rotary inertia is necessary to predict accurate frequencies associated with torsional out of plane modes moreover in its general form the theory of a cosserat point is a fully nonlinear theory that has already been tested for buckling of beams and arches therefore the success of the cosserat theory for the dynamic problem considered in this paper suggests that the theory of a cosserat point can be used for more complicated nonlinear dynamic problems of thin rod like structures

brief paper sliding mode control for ito stochastic systems with markovian switching this paper deals with the problem of sliding mode control smc for a class of nonlinear uncertain stochastic systems with markovian switching by introducing some specified matrices the connections among the designed sliding surfaces corresponding to every mode are established furthermore the present sliding mode controller including the transition rates of modes can cope with the effect of markovian switching by means of linear matrix inequalities lmis with equality constraint sufficient conditions are derived such that the sliding motions on the specified sliding surfaces are stochastically stable with c disturbance attenuation level finally a numerical example is given to illustrate the applicability of the present method

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

distributed fusion estimation with square root array implementation for markovian jump linear systems with random parameter matrices and cross correlated noises the distributed fusion estimation is presented for markovian jump linear systems with random parameter matrices and cross correlated noises in sensor networks the lmmse estimator is derived based on gram schmidt orthogonal innovation sequence under a centralized framework the square root array implementation is further presented by recursively triangularizing the square roots of related positive semidefinite matrices in the lmmse estimator via the information filter form the distributed fusion estimation with square root array implementation is proposed incorporated with consensus strategy the convergent condition and the convergence point are also discussed with respect to consensus strategy this study presents the distributed fusion estimation of discrete time markovian jump linear systems with random parameter matrices and cross correlated noises in sensor networks the recursive linear minimum mean square error estimator is proposed based on the gram schmidt orthogonalization procedure under a centralized framework in order to avoid the loss of positive semidefiniteness and reduce dynamical range its square root array implementation is presented by recursively triangularizing the square roots of relevant positive semidefinite matrices furthermore via the information filter form the distributed fusion estimation with square root array implementation is derived from the centralized fusion structure incorporated with consensus strategy a maneuvering target tracking simulation in a sensor network validates the proposed method

low frequency mode transition in the free in plane vibration of curved beams the low frequency mode transition in the free in plane vibration of beams with varying curvature and cross section is examined by using perturbation analysis a simplified zeroth order equation for beam vibration in the region of the mode transition is derived this equation shows explicitly which modes undergo a transition for a particular type of beam curvature and cross section analytic approximations for frequency and mode shape are derived by the cases of beam curvature represented by symmetric and antisymmetric polynomials and their validity is illustrated by comparison with numerical solutions many features of mode transition phenomenon are revealed analytically including the effect of beam curvature on mode shape during the transition stage the similarities and distinctions between the low mode and the high mode number transitions are discussed

new fluid velocity expression in an extensible semi circular pipe conveying fluid a new expression for fluid velocity is presented for a fluid conveying semi circular pipe with an extensible centreline the proposed fluid velocity expression is obtained from the material derivative while the previous velocity expressions are from love s kinematical relations in order to show that the new fluid velocity expression is more reasonable than the previous velocity expressions the equations of in plane motion derived with the new expression are compared to the equations derived with the previous expressions furthermore the equilibrium positions natural frequencies and mode shapes obtained with both the new and previous expressions are analysed and discussed

the dynamics of a piping system with internal unsteady flow abstract the dynamics of a pipeline conveying one dimensional unsteady flow is considered the dynamics of the fluid pipe system is represented by a set of partial differential equations which consists of the axial and transverse equations of motion of the pipeline and the equations of momentum and continuity of the internal flow the vibration equations of the pipeline are derived by use of newton s law of motion while the fluid equations are derived based on the concept of a deformable moving control volume the equations are fully coupled to each other and thus can be applied to various fluid pipe interaction problems which can be generated by the diverse operations of valves and pumps attached to the pipeline the equations are applied to a simply supported inclined straight pipeline to investigate the stabilities and dynamic responses of the pipeline the stability analysis is conducted by use of bolotin s method the dynamic responses are numerically investigated for both stable and unstable conditions it is observed that unstable regions in the stability chart expand as the flow velocity and the mass density of the fluid increase and that natural frequencies of the pipeline increase as the fluid friction acting on the inner surface of pipeline increases

vibration of a flexible pipe conveying viscous pulsating fluid flow abstract the non linear equations of motion of a flexible pipe conveying unsteadily flowing fluid are derived from the continuity and momentum equations of unsteady flow these partial differential equations are fully coupled through equilibrium of contact forces the normal compatibility of velocity at the fluid pipe interfaces and the conservation of mass and momentum of the transient fluid poisson coupling between the pipe wall and fluid is also incorporated in the model a combination of the finite difference method and the method of characteristics is employed to extract displacements hydrodynamic pressure and flow velocities from the equations a numerical example of a pipeline conveying fluid with a pulsating flow is given and discussed

l2 l filter design for discrete time singular markovian jump systems with time varying delays the problem of l 2 l filter design for discrete time singular systems with markovian jump and time varying delays is investigated in this paper by using the delay partitioning technique a delay dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed l 2 l performance index based on the derived condition the full order and reduced order filters with mode independent characterization are designed in a unified framework the corresponding filter parameters can be obtained by solving a set of linear matrix inequalities the reported results not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism two numerical examples are provided to illustrate the effectiveness of the proposed methods

robust sliding mode control for uncertain time delay systems an lmi approach this note is devoted to robust sliding mode control for time delay systems with mismatched parametric uncertainties a delay independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities based on which the corresponding reaching motion controller is also developed the results are illustrated by an example

necessary and sufficient conditions for analysis and synthesis of markov jump linear systems with incomplete transition descriptions this technical note is concerned with exploring a new approach for the analysis and synthesis for markov jump linear systems with incomplete transition descriptions in the study not all the elements of the transition rate matrices trms in continuous time domain or transition probability matrices tpms in discrete time domain are assumed to be known by fully considering the properties of the trms and tpms and the convexity of the uncertain domains necessary and sufficient criteria of stability and stabilization are obtained in both continuous and discrete time numerical examples are used to illustrate the results

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

brief paper h estimation for discrete time piecewise homogeneous markov jump linear systems this paper concerns the problem of h estimation for a class of markov jump linear systems mjls with time varying transition probabilities tps in discrete time domain the time varying character of tps is considered to be finite piecewise homogeneous and the variations in the finite set are considered to be of two types arbitrary variation and stochastic variation respectively the latter means that the variation is subject to a higher level transition probability matrix the mode dependent and variation dependent h filter is designed such that the resulting closed loop systems are stochastically stable and have a guaranteed h filtering error performance index using the idea in the recent studies of partially unknown tps for the traditional mjls with homogeneous tps a generalized framework covering the two kinds of variations is proposed a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

in plane and out of plane free vibrations of curved beams with variable sections we present an approximate method to study the analysis for both the in plane and out of plane free vibration of horizontally curved beams with arbitrary shapes and variable cross sections the characteristic equation for free vibration can be derived by applying the green function which is obtained as a discrete type solution of differential equations governing the flexural behaviour of the curved beam under the action of a concentrated load

free vibrations of non circular arches with non uniform cross section abstract the differential equations governing free in plane vibrations of linearly elastic non circular arches with non uniform cross section are derived and solved numerically to obtain frequencies and mode shapes numerical results are presented for the quadratic parabolic catenary and elliptic arches with hinged hinged hinged clamped and clamped clamped end constraints three general taper types for a rectangular section are considered experimental measurements of frequencies and their corresponding mode shapes agree closely with those predicted by theory

robust h_ infty control for nonlinear stochastic systems a sliding mode approach this paper considers the sliding mode control for nonlinear stochastic systems modeled by ito stochastic differential equations it is noted that there exist state and exogenous disturbance dependent noise in the controlled systems by utilizing h infin disturbance attenuation technique a novel sliding mode control method is proposed such that the resultant system is asymptotically stable in probability with a prescribed h infin performance sufficient conditions for the solvability of these problems are derived via nonlinear hamilton jacobi hj type inequalities moreover it is shown that for a class of special nonlinear stochastic systems the h infin sliding mode control design can be obtained by solving linear matrix inequalities lmis finally a numerical simulation example is given

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

observability under sampling for bilinear system this work is a continuation of the study of the problem of the preservation of the observability under sampling in this paper we establish that for a bilinear system the property of observability is preserved after sampling provided that the controls take their values in a compact space of rm and do not vary too quickly

in plane and out of plane motions of an extensible semi circular pipe conveying fluid abstract in plane and out of plane motions of a semi circular pipe conveying fluid are analyzed in this paper assuming that the centerline of the semi circular pipe is extensible nonlinear equations of in plane and out of plane motions are derived according to the extended hamilton principle the lagrange nonlinear strain theory and the euler bernoulli beam theory are used to derive the equations the derived equations of motion are discretized by applying the galerkin method linearized equations around the equilibrium position are obtained from the discretized equations and then the dynamic characteristics of the pipe are investigated in addition some modelling issues which are related to the nonlinearity of the circumferential strain and stress are discussed this study finds that a semi circular pipe conveying fluid does not lose stability even at a high fluid velocity although a model using the lagrange nonlinear strain and the corresponding nonlinear stress yields the most accurate computational results of the natural frequencies a model using the lagrange strain and a linearized stress is recommended to compute the natural frequencies efficiently while still maintaining accuracy

on input to state stability of stochastic retarded systems with markovian switching this note develops a razumikhin type theorem on pth moment input to state stability of hybrid stochastic retarded systems also known as stochastic retarded systems with markovian switching which is an improvement of an existing result an application to hybrid stochastic delay systems verifies the effectiveness of the improved result

tecchnical communique robust stability and stabilization of linear delayed systems with structured uncertainty this paper shows criteria for robust stability and stabilization of linear state delayed systems with structured uncertainty we consider the structured uncertainty composed of repeated scalar block and full block forms and a time varying state delay delay dependent methods for robust stability and stabilization are provided in terms of linear matrix inequalities for linear systems with structured uncertainty and a time varying state delay the proposed methods give less conservative results than those obtained via the methods accounting for only norm boundedness of the uncertainty

in plane free vibration of a single crystal silicon ring in this paper the natural frequencies and the associated mode shapes of in plane free vibration of a single crystal silicon ring are analyzed it is found that the si 1 1 1 ring is two dimensionally isotropic in the 1 1 1 plane for elastic constants but three dimensionally anisotropic while the si 1 0 0 ring is fully anisotropic hamilton s principle is used to derive the equations of vibration which is a set of partial differential equations with coefficients being periodic in polar variable expressing the radial and tangential displacements in sinusoidal form with non predetermined amplitudes and through the integration with respect to the circumferential variable the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form the exact expressions for frequencies and mode shapes are obtained it is found that for si 1 0 0 rings the frequencies of a pair of modes which are equal for an isotropic ring split due to the anisotropic effect only for the second in plane vibration mode the phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups when the single crystal silicon is replaced by the polycrystalline silicon which is isotropic in elastic constants the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting

free non linear vibration of a rotating thin ring with the in plane and out of plane motions free non linear vibration of a rotating thin ring with a constant speed is analyzed when the ring has both the in plane and out of plane motions the geometric non linearity of displacements is considered by adopting the lagrange strain theory for the circumferential strain instead of the infinitesimal strain theory by using hamilton s principle the coupled non linear partial differential equations are derived which describe the out of plane bending and torsional motions as well as the in plane bending and extensional motions during deriving the equations of motion we discuss how to model the circumferential stress and strain in order to consider the geometric non linearity four models are established three non linear models and one linear model for the four models the linearized equations of motion are obtained in the neighbourhood of the steady state equilibrium position based on the linearized equations of the four cases the natural frequencies are computed at various rotational speeds and then they are compared through the comparison this study recommends which model is appropriate to describe the non linear behaviour more precisely

stabilization of singular markovian jump systems with generally uncertain transition rates this note is devoted to investigating the stability and stabilization problems for continuous time singular markovian jump systems smjss with generally uncertain transition rates gutrs in this gutr singular model each transition rate can be completely unknown or only its estimate value is known in terms of a set of coupled linear matrix inequalities lmis a sufficient condition is established to ensure the systems to be regular impulse free and stochastically stable moreover the corresponding sufficient condition on the existence of a mode dependent state feedback controller is derived to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method

out of plane free vibrations of curved beams with variable curvature abstract the differential equations governing out of plane free vibrations of the elastic horizontally curved beams with variable curvature are derived and solved numerically to obtain natural frequencies and mode shapes for parabolic sinusoidal and elliptic beams with hinged hinged hinged clamped and clamped clamped end constraints in which the effects of the rotatory and torsional inertias and shear deformation are included experimental measures of frequencies for several laboratory scale parabolic models serve to validate the theoretical results

reliable state estimation of switched neutral system with nonlinear actuator faults via sampled data control this paper aims to solve the reliable state estimation problem of an uncertain switched neutral system subject to nonlinear actuator faults and time varying delay by using sampled data approach to be precise the well known luenberger estimator is constructed to determine the immeasurable states of the addressed system and a general actuator fault model is employed to describe the nonlinearities encountering in the control design after that by defining an error variable the corresponding estimation error system is formulated by the virtue of lyapunov krasovskii stability theory and average dwell time method a new delay dependent sufficient criterion is established to guarantee the existence of the desired estimator and sampled data gains and subsequently the explicit expression of those gains is presented by means of the solution to a set of linear matrix inequalities moreover two numerical examples are given to show the efficiency of the proposed estimator design schemes where it is shown that the estimator gains can ensure the exponential stability of the considered switched neutral systems

free vibrations of circular arches a review abstract in this paper a critical brief review of the free dynamics of circular arches is presented under the classical hypotheses that 1 the dimensions of the cross section are small in comparison with the radius 2 the axis is inextensible and 3 shear forces and rotatory inertia are neglected a simple yet efficient method is proposed which allows one to take into account quite naturally the cross section variations and the presence of flexible supports a number of other approaches are also briefly illustrated from the ritz and galerkin methods to the finite element techniques and their numerical performances are compared for a wide range of examples uniform arches with rotationally flexible and axially flexible supports have been extensively examined together with three different kinds of stepped arches and two different arches with linearly varying cross section whenever possible a comparison with available exact solutions is also performed the agreement among all these methods is generally good even if there are some theoretical discrepancies to be pointed out

sliding mode control for stochastic systems subject to packet losses this paper investigates the problem of sliding mode control for stochastic system under the effect of packet dropout in this work a new sliding function dependent on the probability of packet dropout is constructed by means of a lyapunov function involved in sliding mode variable and system state both the reachabiltiy and the stability are analyzed simultaneously and the sufficient condition is derived via linear matrix inequalities finally numerical simulation results are given

robust stochastic stabilization and h control of uncertain neutral stochastic time delay systems this paper investigates the problems of robust stochastic stabilization and robust h control for uncertain neutral stochastic time delay systems with time varying norm bounded parameter uncertainties appearing in both the state and input matrices the time delay is assumed to be unknown sufficient conditions for the existence of state feedback controllers are proposed which ensure mean square asymptotic stability of the resulting closed loop system and reduce the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties a linear matrix inequality approach is employed to design the desired state feedback controllers furthermore in the case when time delays appear in both the state and control input results on the robust stochastic stabilization and robust h control are also presented an illustrative example is provided to show the potential of the proposed techniques

analysis and synthesis of markov jump linear systems with time varying delays and partially known transition probabilities in this note the stability analysis and stabilization problems for a class of discrete time markov jump linear systems with partially known transition probabilities and time varying delays are investigated the time delay is considered to be time varying and has a lower and upper bounds the transition probabilities of the mode jumps are considered to be partially known which relax the traditional assumption in markov jump systems that all of them must be completely known a priori following the recent study on the class of systems a monotonicity is further observed in concern of the conservatism of obtaining the maximal delay range due to the unknown elements in the transition probability matrix sufficient conditions for stochastic stability of the underlying systems are derived via the linear matrix inequality lmi formulation and the design of the stabilizing controller is further given a numerical example is used to illustrate the developed theory

a concept of local observability abstract a notion of local observability which is natural in the context of nonlinear input output regulation is introduced a simple characterization is provided a comparison is made with other local nonlinear observability definitions and its behavior under constant rate sampling is analyzed

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

sliding mode filter design for nonlinear polynomial systems with unmeasured states this paper addresses the mean square and mean module filtering problems for a nonlinear polynomial stochastic system with gaussian white noises the obtained solutions contain a sliding mode term signum of the innovations process it is shown that the designed sliding mode mean square filter generates the mean square estimate which has the same minimum estimation error variance as the estimate given by the conventional mean square polynomial filter basin et al 2008 8 although the gain matrices of both filters are different the designed sliding mode mean module filter generates the mean module estimate which yields a better value of the mean module criterion in comparison to the conventional mean square polynomial filter the theoretical result is complemented with an illustrative example verifying performance of the designed filters it is demonstrated that the estimates produced by the designed sliding mode mean square filter and the conventional mean square polynomial filter yield the same estimation error variance and there is an advantage in favor of the designed sliding mode mean module filter

sliding mode control of quantized systems against bounded disturbances abstract this paper investigates the sliding mode control problem of quantized systems with simultaneous input and output disturbances in a network environment the output measurements are supposed to be quantized with a logarithmic strategy before transmitting over the digital channels the main difficulties in this design are as follows 1 there exists input output disturbances and state time delay in the plant under consideration such that model discretization is difficult to be implemented the design work is therefore forbidden to be considered in continuous time domain 2 the quantized signals piecewise constants cannot be used to synthesize a continuous time sliding mode surface 3 traditional observer technique is not effective to handle output disturbances in this paper a filtering based technique is proposed to solve these difficulties based on which a sliding mode observer based control scheme is developed to stabilize the resulting closed loop systems finally the effectiveness of the proposed methodology is illustrated via a numerical example

in plane free vibration and stability of loaded and shear deformable circular arches the first known equations governing vibrations of preloaded shear deformable circular arches are derived according to a variational principle for dynamic problems concerning an elastic body under equilibrium initial stresses the equations are three partial differential equations with variable coefficients the governing equations are solved for arches statically preloaded with a uniformly distributed vertical loading by obtaining a static closed form solution and an analytical dynamic solution from series solutions and dynamic stiffness matrices convergence to accurate results is obtained by increasing the number of elements or by increasing both the number of terms in the series solution and the number of terms in the taylor expansion of the variable coefficients graphs of non dimensional frequencies and buckling loads are presented for preloaded clamped arches they clarify the effects of opening angle and thickness to radius ratio on vibration frequencies and buckling loads the effects of static deformations on vibration frequencies are also investigated this work also compares the results obtained from the proposed governing equations with those obtained from the classical theory neglecting shear deformation

brief paper mode dependent h filtering for discrete time markovian jump linear systems with partly unknown transition probabilities in this paper the problem of h filtering for a class of discrete time markovian jump linear systems mjls with partly unknown transition probabilities is investigated the considered systems are more general which cover the mjls with completely known and completely unknown transition probabilities as two special cases a mode dependent full order filter is constructed and the bounded real lemma brl for the resulting filtering error system is derived via lmi formulation then an improved version of the brl is further given by introducing additional slack matrix variables to eliminate the cross coupling between system matrices and lyapunov matrices among different operation modes finally the existence criterion of the desired filter is obtained such that the corresponding filtering error system is stochastically stable with a guaranteed h performance index a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

observability and observateur under sampling this work is a continuation of s ammar and j c vivalda on the preservation of observability under sampling systems and control letters 52 pp 7 15 2004 in which the authors showed the preservation of the observability under sampling in the first step of this paper by removing the assumption of infinitesimal observability and by adding the analyticity of the continuous system we show the conservation of the observability under sampling almost everywhere in the second step we discuss the problem of the observateur under sampling

non linear vibration of a flexible spinning disc with angular acceleration non linear dynamic responses are analyzed for a flexible spinning disc with angular acceleration based on the kirchhoff plate theory and the von karman strain theory non linear equations of motion are derived which are coupled equations between the radial tangential and transverse displacements the equations of motion are discretized by using the galerkin method from the discretized equations the dynamic responses are computed by the generalized time integration method the analysis results show the effects of angular acceleration on the dynamic responses

analytical and differential quadrature results for vibration analysis of damaged circular arches the present paper focuses on in plane linear free vibrations of circular arches in undamaged and damaged configurations for the model herein utilized the equations of motion in terms of displacements and rotation take into account shearing and axial deformations and rotary inertia the cracked section of the arch is modeled with an elastic spring an exact analytical method of solution and an approximate numerical one are presented the first method solves the fundamental system in closed form by means of a characteristic polynomial the second one is based on a simple and efficient differential quadrature and domain decomposition technique natural frequencies and mode shapes are computed for some significant cases showing very good agreement between the two approaches

lmi based sliding surface design for integral sliding mode control of mismatched uncertain systems we propose a linear matrix inequality lmi based sliding surface design method for integral sliding mode control of mismatched uncertain systems the uncertain system under consideration may have mismatched norm bounded uncertainties in the state matrix as well as the input matrix we give a sufficient condition for the existence of a sliding surface guaranteeing asymptotic stability of the full order sliding mode dynamics we also give an lmi characterization of the sliding surface together with an integral sliding mode control law guaranteeing the existence of a sliding mode from the initial time additionally we give an lmi condition of sliding surfaces guaranteeing the alpha stability constraint finally we give a simulation result to show the effectiveness of our method

out of plane dynamic analysis of beams with arbitrarily varying curvature and cross section by dynamic stiffness matrix method abstract the first known dynamic stiffness matrix for noncircular curved beams with variable cross section is developed with which an exact solution of the out of plane free vibration of this type of beam is derived by using the laplace transform technique and the developed dynamic stiffness matrix and equivalent nodal force vector the highly accurate dynamic responses including the stress resultants of the curved beams subjected to various types of loading can be easily obtained the dynamic stiffness matrix and equivalent nodal force vector are derived based on the general series solution of the differential equations for the out of plane motion of the curved beams with arbitrary shapes and cross sections the validity of the present solution for free vibration is demonstrated through comparison with published data the accuracy of the present solution for transient response is also confirmed through comparison with the modal superposition solution for a simply supported circular beam subjected to a moving load with the proposed solution both the free vibration and forced vibration of non uniform parabolic curved beams with various ratios of rise to span are carried out nondimensional frequency parameters for the first five modes are presented in graphic form over a range of rise to span ratios 0 05 h l 0 75 with different variations of the cross section dynamic responses of the fixed fixed parabolic curved beam subjected to a rectangular pulse are also presented for different rise to span ratios

on the stability of a differential riccati equation for continuous discrete observers abstractthis article deals with the stability properties of a continuous discrete riccati differential equation the main motivation comes from the theory of kalman filters for continuous time nonlinear systems with sampled measurements where this type of equation often arises stability is to be understood in the following sense under appropriate hypotheses the solution matrix is always symmetric positive definite and bounded from above and below no uniformity is expected from the sampling procedure only an upper bound on the elapsed time between consecutive samples is needed the exposition consists of two parts first the stability properties are proven and second by means of three examples it is shown how the article s main result applies

stochastic nicholson type delay differential system focusing on nicholson type delay differential system in random environments we introduce the stochastic system to model the dynamics of nicholson s blowflies population sizes with mortality rates

exact dynamic stiffness matrix of non symmetric thin walled curved beams subjected to initial axial force abstract an improved numerical method to exactly evaluate the dynamic element stiffness matrix is proposed for the spatially coupled free vibration analysis of non symmetric thin walled curved beams subjected to uniform axial force for this purpose firstly equations of motion boundary conditions and force deformation relations are rigorously derived from the total potential energy for a curved beam element next systems of linear algebraic equations with non symmetric matrices are constructed by introducing 14 displacement parameters and transforming the fourth order simultaneous differential equations into the first order simultaneous equations and then explicit expressions for displacement parameters are numerically evaluated via eigensolutions and the exact 14 14 element stiffness matrix is determined using force deformation relations in order to demonstrate the validity and the accuracy of this study the spatially coupled natural frequencies of non symmetric thin walled curved beams subjected to uniform compressive and tensile forces are evaluated and compared with analytical and finite element solutions using hermitian curved beam elements or abaqus s shell element in addition some results by the parametric study are reported

free in plane vibration of general curved beams using finite element method the governing differential equations for the free in plane vibration of uniform and non uniform curved beams with variable curvatures including the effects of the axis extensibility shear deformation and the rotary inertia are derived using the extended hamilton principle these equations were then solved numerically utilizing the galerkin finite element method and the curvilinear integral taken along the central line of the curvilinear beam based on the proposed finite element formulation one can easily study curved beams having different geometrical and boundary conditions furthermore those curved beams excluding the effects of the axis extensibility shear deformation and the rotary inertia are modeled and then solved utilizing the finite element method using a new non isoparametric element the results for the natural frequencies modal shapes and the deformed configurations are presented for different types of the curved beams with various geometrical properties and boundary conditions and in order to illustrate the validity and accuracy of the presented methodology they are compared with those published in literature

h sliding mode control for uncertain neutral type stochastic systems with markovian jumping parameters this paper is devoted to the investigation of h sliding mode control smc for uncertain neutral stochastic systems with markovian jumping parameters and time varying delays a sliding surface functional is firstly constructed then the sliding mode control law is designed to guarantee the reachability of the sliding surface in a finite time interval the sufficient conditions for asymptotically stochastic stability of sliding mode dynamics with a given disturbance attenuation level are presented in terms of linear matrix inequalities lmis finally an example is provided to illustrate the efficiency of the proposed method

h sub spl infin filtering for singular systems this note considers the h sub spl infin filtering problem for linear continuous singular systems the purpose is the design of a linear filter such that the resulting error system is regular impulse free and stable while the closed loop transfer function from the disturbance to the filtering error output satisfies a prescribed h sub spl infin norm bound constraint without decomposing the original system matrices a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given finally an illustrative example is presented to demonstrate the applicability of the proposed approach

free vibrations of spatial timoshenko arches abstract this paper addresses the evaluation of the exact natural frequencies and vibration modes of structures obtained by assemblage of plane circular arched timoshenko beams the exact dynamic stiffness matrix of the single circular arch in which both the in plane and out of plane motions are taken into account is derived in an useful dimensionless form by revisiting the mathematical approach already adopted by howson and jemah 1999 18 for the in plane and the out of plan natural frequencies of curved timoshenko beams the knowledge of the exact dynamic stiffness matrix of the single arch makes the direct evaluation of the exact global dynamic stiffness matrix of spatial arch structures possible furthermore it allows the exact evaluation of the frequencies and the corresponding vibration modes for the distributed parameter model through the application of the wittrick and williams algorithm consistently with the dimensionless form proposed in the derivation of the equations of motion and the dynamic stiffness matrix an original and extensive parametric analysis on the in plane and out of plane dynamic behaviour of the single arch for a wide range of structural and geometrical dimensionless parameters has been performed moreover some numerical applications relative to the evaluation of exact frequencies and the corresponding mode shapes in spatial arched structures are reported the exact solution has been numerically validated by comparing the results with those obtained by a refined finite element simulation

observability and observers for nonlinear systems this paper deals with observability and observers for general nonlinear systems in the non control affine case we characterize systems that are observable independently of the inputs an exponential observer for these systems is also exhibited

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

exact and approximate dynamic analysis of circular arches using dqm abstract a modified version of the differential quadrature method is applied to two versions of the sixth order differential equation of motion governing free in plane inextensional vibrations of circular arches see henrych 1981 all the boundary conditions can be imposed exactly without introducing points see e g bert and malik 1996 consequently the results are calculated with high precision and a comparison between exact and approximate frequencies becomes possible the convergence rate of the discretization method is shown to be very fast even for the higher eigenvalues so that a small number of lagrangian coordinates permits a good approximation to the true results it is shown that the approximate formulation leads to noticeable errors for the first frequencies of deep arches whereas shallow arches and higher order frequencies can be safely calculated with the simplified approach the paper ends with some tables in which the first ten free vibrations frequencies for clamped arches two hinged arches and cantilever arches are compared with some known results from the literature

spatial free vibration of shear deformable circular curved beams with non symmetric thin walled sections abstract for spatial free vibration of shear deformable circular curved beams with non symmetric thin walled cross sections an improved vibration theory is proposed the elastic strain and kinetic energies are first derived by considering constant curvature effects and shear deformation effects due to shear forces and restrained warping torsion next equilibrium equations and force deformation relations are obtained using a stationary condition of total potential energy and then the closed form solution for out of plane vibration of curved beam is newly derived in addition f e procedures are developed by using isoparametric curved beam element with arbitrary thin walled sections in order to illustrate the accuracy and the practical usefulness of this study closed form and numerical solutions for spatial free vibration are compared with results by available references and abaqus s shell element particularly not only shear deformation and thickness curvature effects on vibration behaviors of curved beams but also mode transition and crossover phenomena with change in curvatures and the length of beams are parametrically investigated

state estimation on positive markovian jump systems with time varying delay and uncertain transition probabilities investigate the positive discrete time mjs with disturbance input time varying delay and uncertain transition probabilities together for the first time where the transition probability matrix is described by a polytope set provide a necessary and sufficient condition of stochastic stability with regard to the resulting error dynamic system present the exact computation of l gain index for the resulting stochastically stable error dynamic systems firstly and derive a necessary and sufficient condition of the l gain performance correspondingly provide a sufficient condition on the existence of a desired observer to solve the state estimation problem such that the error dynamic system is stochastically stable with a prescribed l gain performance all the proposed conditions are expressed in linear programming forms which can be solved effectively by using some existing softwares and the observer gain matrices can be directly obtained by an effective algorithm this paper is concerned with the state estimation problem based on an l observer for a class of positive discrete time markovian jump systems mjss the system under consideration consists of time varying delay and uncertain transition probabilities where the transition probability matrix is described by a polytope set necessary and sufficient conditions are presented in linear programming lp form for the resulting error dynamic system to be stochastically stable and stochastically stable with an l gain performance respectively furthermore an l observer design scheme is presented to solve the state estimation problem such that the resulting error dynamic system is stochastically stable and achieves a prescribed l gain performance all the proposed conditions are solvable in terms of lp with additional parameters finally some examples are given to demonstrate the validity of the developed technique

in plane free vibration analysis of circular arches with varying cross sections using differential quadrature method abstract a differential quadrature dq methodology recently developed by the authors is used to obtain a general and a computationally efficient and accurate dq solution for free vibration of variable cross section circular thin arches as an improvement to the classical theory and in order to evaluate the higher order natural frequencies more accurately the commonly used hypothesis of the inextensibility of the central axis is removed this enables one to study the effects of slenderness ratio on the natural frequencies especially at higher order modes rotary inertia is included in the formulation and its influence on natural frequencies is studied arches with different types of boundary conditions including those with elastic constraint against rotation at their ends are considered for the cases where a change in the cross sectional or material properties of the arch occurs a numerical domain decomposition technique in conjunction with dq methodology is developed and incorporated to verify the accuracy of the methodology the results are compared with those of exact solutions and or other approaches such as finite elements rayleigh ritz galerkin cell discretization methods and other dq methodologies in particular excellent solution agreements are achieved with those of exact solutions the generalized differential quadrature rule and the optimized rayleigh ritz method solutions