delay dependent h filtering for singular markovian jump systems with general uncomplete transition probabilities this paper is devoted to the investigation of the delay dependent h filtering problem for a kind of singular markovian jump time delay systems with general unknown transition probabilities in this model the transition rates of the jumping process are assumed to be partly available that is some elements have been exactly known some ones have been merely known with lower and upper bounds others may have no information to use using the lyapunov functional theory a stochastically stable filter is designed to guarantee both the mean square exponential admissibility and a prescribed level of h performance for the singular markovian jump time delay systems with general unknown transition probabilities a sufficient condition is derived for the existence of such a desired filter in terms of linear matrix inequalities lmis a numerical example is provided to demonstrate the effectiveness of the proposed theory

h control of markov jump systems with time varying delay and incomplete transition probabilities this paper addresses the h control of continuous markov jump systems with interval time varying delay and incomplete transition probabilities a linearization method is used to handle unknown transition probabilities meanwhile the wirtinger based integral inequality and the reciprocally convex technique are adopted to deal with the time varying delay additionally a separating technique is employed to tackle the coupling among lyapunov variable system matrix and controller parameter based on these strategies new sufficient conditions for the closed loop system to be stochastically stable are formulated in the framework of linear matrix inequalities finally numerical examples are provided to demonstrate the effectiveness of the proposed method

delay independent stability test for systems with multiple time delays delay independent stability dis of a general class of linear time invariant lti multiple time delay system mtds is investigated in the entire delay parameter space stability of such systems may be lost only if their spectrum lies on the imaginary axis for some delays we build an analytical approach that requires the inspection of the roots of finite number of single variable polynomials in order to detect if the spectrum ever lies on the imaginary axis for some delays excluding infinite delays the approach enables to test the necessary and sufficient conditions of dis of lti mtds technically known as weak dis as well as the robust stability of single delay systems against all variations in delay ratios the proposed approach which does not require any parameter sweeping and graphical display becomes possible by establishing a link between the infinite spectrum and algebraic geometry case studies are provided to show the effectiveness of the approach

modeling fractures and barriers as interfaces for flow in porous media we consider a fractured porous medium that is studied at a scale such that the fractures can be modeled individually models for flow in which the fractures are interfaces between subdomains are presented these models take into account interactions between the fractures and the surrounding porous medium existence and uniqueness of the solution to the model problem are proved error estimates show convergence as mathcal o max h d in the l2 norm where h is the mesh size and d the fracture width numerical experiments confirm the theoretical results

admissibility and dissipativity analysis for discrete time singular systems with mixed time varying delays abstract the problems of admissibility and dissipativity are studied for discrete time singular systems with mixed time varying delays the mixed time delays consist of both discrete and distributed delays by taking advantage of the delay partitioning technique a criterion that warrants the admissibility of the considered systems is established based on the criterion a dissipativity condition is also given all the results presented depend upon not only discrete delay and distributed delay but also depend upon the number of delay partitions some numerical examples are included to demonstrate the improvement and effectiveness of the proposed methods

robust exponential h control for uncertain time varying delay systems with input saturation a markov jump model approach abstract this paper is concerned with the state feedback stabilization problem for uncertain time varying delay systems with input saturation based on the stochastic property of time varying delay the considered system can be transformed into a continuous markov jump system with stochastic delays where the growth trend and the maximum value of the time varying delay are limited the problem we address is to design a robust state feedback controller which can switch with time varying delay in terms of markov process such that the system is exponentially mean square stable with disturbance attenuation conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities lmis when these lmis are feasible the desired robust controller is given finally two examples are provided to demonstrate the effectiveness of the proposed approach

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

robust h sup spl infin filtering for uncertain markovian jump systems with mode dependent time delays this paper considers the problem of robust h sup spl infin filtering for uncertain markovian jump linear systems with time delays which are time varying and depend on the system mode the parameter uncertainties are time varying norm bounded the aim of this problem is to design a markovian jump linear filter that ensures robust exponential mean square stability of the filtering error system and a prescribed l sub 2 induced gain from the noise signals to the estimation error for all admissible uncertainties a sufficient condition for the solvability of this problem is obtained the desired filter can be constructed by solving a set of linear matrix inequalities an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

unbiased h filtering for neutral markov jump systems abstract the unbiased h filtering problem is studied for stochastic markov jump system with constant and neutral time delays by re constructing the system the dynamic filtering error characteristics of unknown inputs and time delays are obtained a sufficient condition is initially established on the existence of mode dependent unbiased h filter of constant time delay system using stochastic lyapunov krasovskii function then the unbiased h filter is also designed for the jump system with constant and neutral time delays the design criterions are presented in the form of linear matrix inequality finally the unbiased h filtering problems are described as optimization algorithms numerical examples illustrate the effectiveness of the developed techniques

passivity based sliding mode control of uncertain singular markovian jump systems with time varying delay and nonlinear perturbations in this paper a sliding mode control smc with passivity of uncertain singular markovian jump systems smjs with time varying delay and nonlinear perturbations is investigated firstly a new integral type switching surface is designed secondly by introducing free matrix method and lyapunov functionals a delay dependent sufficient condition in terms of strict linear matrix inequalities lmi is derived for the resulting sliding mode dynamics such that the closed loop system is stochastically admissible and robustly passive for all admissible uncertainties thirdly a smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally numerical examples are provided to demonstrate the effectiveness of the proposed method

controller design for markov jumping systems subject to actuator saturation in this paper the stochastic stabilization problem for a class of markov jumping linear systems mjls subject to actuator saturation is considered the concept of domain of attraction in mean square sense is used to analyze the closed loop stability when the jumping mode is available a mode dependent state feedback controller is developed otherwise we give a less conservative approach to design the mode independent state feedback controller both design procedures can be converted into a set of linear matrix inequalities lmis finally a numerical example is provided to show the effectiveness of the techniques

asynchronous h filtering for 2d discrete markovian jump systems with sensor failure this paper investigates the problem of the asynchronous h filtering for a class of two dimensional 2d markovian jump systems with sensor failure the asynchronous phenomenon is considered to be random mismatch between system modes and candidate filters the mismatch behavior is assumed to be stochastic with a certain probability and a new markov chain is proposed to model the jumping process of the filtering error system besides a switching method is proposed to dealing with the sensor failure sufficient conditions for the existence of a desired filter such that the filtering error system is stochastically stable with a guaranteed h performance index are obtained in the form of linear matrix inequalities lmis two examples are provided to illustrate the effectiveness and advantage of the proposed method

an asynchronous operation approach to event triggered control for fuzzy markovian jump systems with general switching policies this paper investigates the problem of event triggered control for a class of fuzzy markov jump systems with general switching policies a novel event triggered scheme is proposed to improve the transmission efficiency at each sampling instance each transition rate allows to be unknown known or only its uncertain domains value is known with the help of a tailored technique to bind the uncertain terms and an asynchronous operation approach to tackle the fuzzy system and fuzzy controller sufficient conditions for the resulting fuzzy markovian jump systems are established in terms of coupled linear matrix inequalities finally an example is given to illustrate the validity of the developed technique

mode independent cal h _ infty filters for markovian jump linear systems this note addresses the problem of hinfin filtering for continuous time linear systems with markovian jumping parameters the main contribution of the note is to provide a method for designing an asymptotically stable linear time invariant hinfin filter for systems where the jumping parameter is not accessible the cases where the transition rate matrix of the markov process is either exactly known or unknown but belongs to a given polytope are treated the robust hinfin filtering problem for systems with polytopic uncertain matrices is also considered and a filter design method based on a lyapunov function that depends on the uncertain parameters is developed the proposed filter designs are given in terms of linear matrix inequalities

finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching an extension of fixed transition probability markovian switching model to combine time varying transition probabilities has offered another set of useful regime switching models this paper investigated the problem of finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching based on the results of finite time boundness and average dwell time a novel sufficient condition for finite time bounded of h filtering is derived and the system trajectory stays within a prescribed bound finally an example is provided to illustrate the usefulness and effectiveness of the proposed method

decomposition of some hankel matrices generated by the generalized rencontres polynomials abstract using the algebraic techniques of formal series we obtain a combinatorial decomposition of some matrices generated by the generalized rencontres polynomials specifically for the complete matrix and the hankel matrix we obtain an ldu decomposition r d s t where d is a diagonal matrix and r and s are two sheffer matrices then for the shifted matrices we obtain an ltu decomposition r t s t where t is a tridiagonal matrix and r and s are two sheffer matrices furthermore we give an algebraic characterization of the generalized rencontres numbers and polynomials in terms of hankel determinants finally we determine a relation between the complete matrices and the hankel matrices

l2 l filtering for neutral markovian switching system with mode dependent time varying delays and partially unknown transition probabilities this paper investigates the problem of l 2 l filtering for neutral markovian switching systems with partially unknown transition probabilities for different system mode and delay mode the system under consideration involves discrete and mode dependent time varying delays based on the lyapunov krasovskii functional an approach to design a filter such that the filtering error system is stochastically stable with a prescribed l 2 l performance by using free weighting matrices free connection weighting matrix method and convex combination approach sufficient conditions for the existence of l 2 l filters are expressed in terms of linear matrix inequalities lmis which can be solved by using matlab lmi control toolbox a numerical example is given to illustrate the effectiveness and potential of the proposed method

finite differences and determinant identities determinants of higher derivatives of composite functions are evaluated as limits of the corresponding ones concerning finite differences as examples several interesting identities of wronskian and hankel determinants are consequently derived

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

further results on h control for discrete time markovian jump time delay systems abstractthis paper studies the problem of h control for a class of discrete time markovian jump systems with time delay the purpose is to improve the existing results on h controller design for markovian jump systems a novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality which is proved to be less conservative than most results in the literature then the state feedback controller is designed which guarantees the stochastic stability of the closed loop system with a given disturbance attenuation numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques

state estimation for discrete time markov jump linear systems with time correlated and mode dependent measurement noise abstract the state estimation problem for discrete time markov jump linear systems corrupted by time correlated and mode dependent measurement noise is considered where the time correlated and mode dependent measurement noise is described via a discrete time stochastic system with markov parameter and kronecker delta function by defining the measurement noise in this manner both time correlation and periodic step change caused by the change of system environment or structure can be embodied in the measurement noise a novel distributed measurement differencing method is applied to the problem of state estimation under consideration so that two algorithms are obtained using some results presented in this paper the first algorithm is optimal in the sense of minimum mean square error which can exactly compute the minimum mean square error estimate of system state the second algorithm is suboptimal and the suboptimality of the algorithm is caused by using some gaussian hypotheses the two proposed algorithms are recursive and the proposed suboptimal algorithm has a time independent complexity the performance of the proposed suboptimal algorithm is illustrated using computer simulations

two dimensional peak to peak filtering for stochastic fornasini marchesini systems this paper is concerned with the problem of two dimensional 2 d stochastic peak to peak filter design for fornasini marchesini local state space fm lss systems with state multiplicative noise first a novel sufficient condition is established which guarantees that the underlying fm lss system is stochastically mean square stable with 2 d stochastic peak to peak performance a deterministic fm lss system case is also discussed subsequently based on the result a new 2 d stochastic peak to peak filter of general form is designed for fm lss systems with state multiplicative noise finally a numerical example is presented to show the effectiveness of the proposed 2 d stochastic peak to peak filter

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

numerical analysis of a two phase flow discrete fracture matrix model we present a new model for two phase darcy flows in fractured media in which fractures are modelled as submanifolds of codimension one with respect to the surrounding domain matrix fractures can act as drains or as barriers since pressure discontinuities at the matrix fracture interfaces are permitted additionally a layer of damaged rock at the matrix fracture interfaces is accounted for the numerical analysis is carried out in the general framework of the gradient discretisation method compactness techniques are used to establish convergence results for a wide range of possible numerical schemes the existence of a solution for the two phase flow model is obtained as a byproduct of the convergence analysis a series of numerical experiments conclude the paper with a study of the influence of the damaged layer on the numerical solution

passivity analysis for discrete time stochastic markovian jump neural networks with mixed time delays in this paper passivity analysis is conducted for discrete time stochastic neural networks with both markovian jumping parameters and mixed time delays the mixed time delays consist of both discrete and distributed delays the markov chain in the underlying neural networks is finite piecewise homogeneous by introducing a lyapunov functional that accounts for the mixed time delays a delay dependent passivity condition is derived in terms of the linear matrix inequality approach the case of markov chain with partially unknown transition probabilities is also considered all the results presented depend upon not only discrete delay but also distributed delay a numerical example is included to demonstrate the effectiveness of the proposed methods

state estimation and sliding mode control of markovian jump singular systems this paper is concerned with the state estimation and sliding mode control problems for continuous time markovian jump singular systems with unmeasured states firstly a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic admissibility of the unforced markovian jump singular system then the sliding mode control problem is considered by designing an integral sliding surface function an observer is designed to estimate the system states and a sliding mode control scheme is synthesized for the reaching motion based on the state estimates it is shown that the sliding mode in the estimation space can be attained in a finite time some conditions for the stochastic admissibility of the overall closed loop system are derived finally a numerical example is provided to illustrate the effectiveness of the proposed theory

a multi layer extension of the stochastic heat equation motivated by recent developments on solvable directed polymer models we define a multi layer extension of the stochastic heat equation involving non intersecting brownian motions by developing a connection with darboux transformations and the two dimensional toda equations we conjecture a markovian evolution in time for this multi layer process as a first step in this direction we establish an analogue of the karlin mcgregor formula for the stochastic heat equation and use it to prove a special case of this conjecture

analysis on robust h performance and stability for linear systems with interval time varying state delays via some new augmented lyapunov krasovskii functional in this paper the problem of h performance and stability analysis for linear systems with interval time varying delays is considered first by constructing a newly augmented lyapunov krasovskii functional which has not been proposed yet an improved h performance criterion with the framework of linear matrix inequalities lmis is introduced next the result and method are extended to the problem of a delay dependent stability criterion finally numerical examples are given to show the superiority of proposed method

brief paper stability and stabilization of markovian jump linear systems with partly unknown transition probabilities in this paper the stability and stabilization problems of a class of continuous time and discrete time markovian jump linear system mjls with partly unknown transition probabilities are investigated the system under consideration is more general which covers the systems with completely known and completely unknown transition probabilities as two special cases the latter is hereby the switched linear systems under arbitrary switching moreover in contrast with the uncertain transition probabilities studied recently the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements the sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via lmis formulation and the relation between the stability criteria currently obtained for the usual mjls and switched linear systems under arbitrary switching are exposed by the proposed class of hybrid systems two numerical examples are given to show the validity and potential of the developed results

robust kalman filtering for uncertain discrete time systems this paper is concerned with the problem of a kalman filter design for uncertain discrete time systems the system under consideration is subjected to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of a linear filter such that the variance of the filtering error is guaranteed to be within a certain bound for all admissible uncertainties furthermore the guaranteed cost can be optimized by appropriately searching a scaling design parameter

h filtering for nonuniformly sampled systems a markovian jump systems approach abstract this paper is concerned with the design of an h filter for a sampled data system where the measurement is sampled nonuniformly and randomly but the input is updated uniformly at a fast rate the process of nonuniform measurement sampling is modeled using a markov chain therefore the discrete time system together with the markov chain is a markovian jump system a mode dependent full order h filter is constructed sufficient lmi conditions are derived to ensure stochastic stability and h disturbance attenuation for the error system the case of unknown measurement sampling probabilities is also considered finally the effectiveness of the proposed approach is demonstrated through simulation results and a comparison with a general time varying h filter

hybrid projective synchronization and control of the baier sahle hyperchaotic flow in arbitrary dimensions with unknown parameters the problem of hybrid projective synchronization hps strategies and control for the baier sahle hyperchaotic flow in arbitrary dimensions with unknown parameters is considered based on the lasalle invariance principle and adaptive control method adaptive controllers and parameters update laws are given for the hps between two identical hyper chaotic systems with fully unknown parameters using this method the baier sahle hyperchaotic flow in arbitrary dimensions is controlled to the unsteady equilibrium points the baier sahle hyperchaotic flow is a useful choice for this analysis since it is a standard model of hyperchaos yet it is simple enough to be analytically tractable in particular the baier sahle hyperchaotic flow has been proposed as an n dimensional nonlinear system model giving the maximal number of positive lyapunov exponents n 2 both a rigorous theoretical analysis and direct numerical simulations are provided to demonstrate the control of hyperchaos in this model the results suggest that the methods used here can be applied to more complicated models from which hyperchaos arises

event triggered h control for networked discrete time markov jump systems with repeated scalar nonlinearities this paper investigates the event triggered h control problem for networked discrete time markov jump systems subject to repeated scalar nonlinearities an event triggered communication transmission scheme is adopted and an event generator is presented between the controller and sensor our aim is to design a controller such that although the unavoidable phenomenon of network induced delays is fully considered the resulting closed loop system is stochastically stable with a prescribed h performance level by employing a diagonally dominant type lyapunov functional a co design method is established for the existence of an admissible controller and some available mode dependent event triggered parameters finally the effectiveness of our proposed control design method is shown by a numerical example

traces extensions and co normal derivatives for elliptic systems on lipschitz domains this is the post print version of the article the official published version can be accessed from the link below copyright 2011 elsevier

generalised nonlinear l 2 l filtering of discrete time markov jump descriptor systems this paper is devoted to the l2 l filter design problem for nonlinear discrete time markov jump descriptor systems subject to partially unknown transition probabilities the partially unknown transition probabilities are modelled via the polytopic uncertainties the objective is to propose a generalised nonlinear full order filter design method such that the resulting filtering error system is regular casual and stochastically stable and a prescribed l2 l attenuation level is satisfied for the autonomous discrete time descriptor system subject to lipschitz nonlinear condition by introducing some slack matrix variables a mode dependent stability criterion is established it cannot only ensure the regularity casuality and stochastic stability of system but also guarantee the considered system has a unique solution based on this obtained criterion a sufficient condition in terms of linear matrix inequalities lmis is derived such that the resulting filtering error system is regular casual s

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

global stabilization of a chain of integrators with input saturation and disturbances a new approach in this article we solve the problem of global stabilization for a chain of integrators in the presence of input saturation and disturbances a novel and elegant approach to solve this problem in the absence of disturbances was proposed by teel 1992 using saturation functions and coordinate transformation with teel s work as a foundation many results have been proposed to improve the performance of controllers for a chain of integrators naturally all such approaches also inherited the limitations of teel s approach most importantly in the presence of uncertainties and disturbances the transformation introduced in teel 1992 would considerably shrink the region where the controller is unsaturated and severely limit the level of uncertainties and disturbances which can be tolerated in order to overcome these difficulties a conceptually different approach which does not rely on the coordinate transformation is presented in this work specifically modified saturation functions are directly applied to the tracking error of actual states as opposed to transformed fictitious states to develop a globally stable controller the proposed controller is less conservative in terms of the level of uncertainties and disturbances which can be handled in addition arbitrarily good disturbance rejection in the unsaturated region can be achieved theoretically comparative simulation studies performed on a third order integrator chain verified the effectiveness of the proposed scheme

finite time h static output control of markov jump systems with an auxiliary approach this paper considers the finite time h static output feedback control of markov jump systems with the help of introducing two new variables related to the original system state and output sufficient conditions for the closed loop system to be stochastic finite time boundedness with the prescribed h performance level are proposed in terms of linear matrix inequalities lmis meanwhile the static output control gains are solved explicitly by the proposed conditions it is shown that the proposed method is less or at least the same conservative than the existing result lastly a numerical example is given to demonstrate the effectiveness of the proposed method

further refinements in stability conditions for time varying delay systems abstract this paper addresses the problem of assessing the stability of linear time invariant lti systems with time varying delay the first contribution is a new stability criterion specified as a negativity condition for a quadratic function parameterized by the delay this result mainly follows from an augmented affine parameter dependent lyapunov krasovskii functional which in turn takes advantages of convexity properties then as a second contribution we invoke a result from robust control literature to show how the proposed stability condition can be checked exactly in terms of linear matrix inequality lmi conditions the improvements obtained by the proposed refinements are illustrated via numerical examples drawn from the literature

gradient discretization of hybrid dimensional darcy flows in fractured porous media this article deals with the discretization of hybrid dimensional darcy flows in fractured porous media these models couple the flow in the fractures represented as surfaces of codimension one with the flow in the surrounding matrix the convergence analysis is carried out in the framework of gradient schemes which accounts for a large family of conforming and nonconforming discretizations the vertex approximate gradient scheme and the hybrid finite volume scheme are extended to such models and are shown to verify the gradient scheme framework our theoretical results are confirmed by numerical experiments performed on tetrahedral cartesian and hexahedral meshes in heterogeneous isotropic and anisotropic porous media

an efficient multi point flux approximation method for discrete fracture matrix simulations we consider a control volume discretization with a multi point flux approximation to model discrete fracture matrix systems for anisotropic and fractured porous media in two and three spatial dimensions inspired by a recently introduced approach based on a two point flux approximation we explicitly account for the fractures by representing them as hybrid cells between the matrix cells as well as simplifying the grid generation our hybrid approach excludes small cells in the intersection of the fractures and hence avoids severe time step restrictions associated with small cells excluding the small cells also reduces the condition number of the discretization matrix for examples involving realistic anisotropy ratios in the permeability numerical results show significant improvement compared to existing methods based on two point flux approximations we also investigate the hybrid method by studying the convergence rates for different apertures and fracture matrix permeability ratios finally the effect of removing the cells in the intersections of the fractures are studied together these examples demonstrate the efficiency flexibility and robustness of our new approach

parallel numerical modeling of hybrid dimensional compositional non isothermal darcy flows in fractured porous media this paper introduces a new discrete fracture model accounting for non isothermal compositional multiphase darcy flows and complex networks of fractures with intersecting immersed and non immersed fractures the so called hybrid dimensional model using a 2d model in the fractures coupled with a 3d model in the matrix is first derived rigorously starting from the equi dimensional matrix fracture model then it is dis cretized using a fully implicit time integration combined with the vertex approximate gradient vag finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media the fully coupled systems are assembled and solved in parallel using the single program multiple data spmd paradigm with one layer of ghost cells this strategy allows for a local assembly of the discrete systems an efficient preconditioner is implemented to solve the linear systems at each time step and each newton type iteration of the simulation the numerical efficiency of our approach is assessed on different meshes fracture networks and physical settings in terms of parallel scalability nonlinear convergence and linear convergence

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

robust cal h _ infty filtering for markovian jump systems with randomly occurring nonlinearities and sensor saturation the finite horizon case this paper addresses the robust h filtering problem for a class of discrete time varying markovian jump systems with randomly occurring nonlinearities and sensor saturation two kinds of transition probability matrices for the markovian process are considered namely the one with polytopic uncertainties and the one with partially unknown entries the nonlinear disturbances are assumed to occur randomly according to stochastic variables satisfying the bernoulli distributions the main purpose of this paper is to design a robust filter over a given finite horizon such that the h disturbance attenuation level is guaranteed for the time varying markovian jump systems in the presence of both the randomly occurring nonlinearities and the sensor saturation sufficient conditions are established for the existence of the desired filter satisfying the h performance constraint in terms of a set of recursive linear matrix inequalities simulation results demonstrate the effectiveness of the developed filter design scheme

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

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 new method for stabilization of networked control systems with random delays we consider the stabilization problem for a class of networked control systems in the discrete time domain with random delays the sensor to controller and controller to actuator delays are modeled as two markov chains and the resulting closed loop systems are jump linear systems with two modes the necessary and sufficient conditions on the existence of stabilizing controllers are established it is shown that state feedback gains are mode dependent an iterative linear matrix inequality lmi approach is employed to calculate the state feedback gains

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

brief paper 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

h control for discrete time markov jump systems with uncertain transition probabilities in this technical note the h control problem for a class of discrete time markov jump systems mjss with uncertain transition probabilities tps is investigated the uncertain information of transition probabilities is quantized by gaussian transition probability density function pdf in light of the proposed descriptions the mjss with gaussian pdf of tps cover the systems with precisely known and partially known tps as two special cases sufficient conditions for the existence of h controller of the underlying systems are derived in term of linear matrix inequalities a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

filtering design for two dimensional markovian jump systems with state delays and deficient mode information this paper is concerned with the problem of h filtering for a class of two dimensional markovian jump linear systems described by the fornasini marchesini local state space model the systems under consideration are subject to state delays and deficient mode information in the markov chain the description of deficient mode information is comprehensive that simultaneously includes the exactly known partially unknown and uncertain transition probabilities by invoking the properties of the transition probability matrix together with the convexification of uncertain domains a new h performance analysis criterion for the filtering error system is firstly derived then via some matrix inequality linearisation procedures two approaches for the filter synthesis are proposed it is shown that both the full order and reduced order filters can be constructed by solving a set of linear matrix inequalities finally simulation studies are provided to illustrate the effectiveness of the proposed design methods

non fragile h control for markovian jump fuzzy systems with time varying delays abstract this paper focuses on the non fragile h control of markovian jump fuzzy systems with time varying delays in order to obtain less conservatism an improved delay partitioning method is introduced which divides the delay interval into multiple segments with a geometric sequence a modified lyapunov krasovskii functional is constructed and some less conservative delay dependent stability criteria are derived by using linear matrix inequalities technique then a non fragile controller is designed finally two numerical examples are given to show the effectiveness of the obtained results

hybrid dimensional modelling of two phase flow through fractured porous media with enhanced matrix fracture transmission conditions in this work we extend to two phase flow the single phase darcy flow model proposed in 26 12 in which the d 1 dimensional flow in the fractures is coupled with the d dimensional flow in the matrix three types of so called hybrid dimensional two phase darcy flow models are proposed they all account for fractures acting either as drains or as barriers since they allow pressure jumps at the matrix fracture interfaces the models also permit to treat gravity dominated flow as well as discontinuous capillary pressure at the material interfaces the three models differ by their transmission conditions at matrix fracture interfaces while the first model accounts for the nonlinear two phase darcy flux conservations the second and third ones are based on the linear single phase darcy flux conservations combined with different approximations of the mobilities we adapt the vertex approximate gradient vag scheme to this problem in order to account for anisotropy and heterogeneity aspects as well as for applicability on general meshes several test cases are presented to compare our hybrid dimensional models to the generic equi dimensional model in which fractures have the same dimension as the matrix leading to deep insight about the quality of the proposed reduced models

partially mode dependent design of h filter for stochastic markovian jump systems with mode dependent time delays abstract this paper is concerned with the h filtering problem for stochastic delay systems with markovian jump parameters where both the state dynamics and measurements of systems are corrupted by wiener process in contrast with traditional mode dependent and mode independent filtering methods a new partially mode dependent filter is established via using a mode dependent lyapunov function where the system mode available to filter implementation is transmitted through an unreliable network and the stochastic property of mode available to a filter is considered sufficient conditions for the existence of h filters are obtained as linear matrix inequalities finally an example is used to show the effectiveness of the given theoretical results

addition formulas for polynomials built on classical combinatorial sequences abstract we prove addition formulas for some polynomials built on combinatorial sequences catalan numbers bell numbers or related to classical polynomials hermite these relations give also an explicit computation of several hankel determinants

loop erased walks and random matrices it is well known that there are close connections between non intersecting processes in one dimension and random matrices based on the reflection principle there is a generalisation of the reflection principle for more general e g planar processes due to fomin in which the non intersection condition is replaced by a condition involving loop erased paths in the context of independent brownian motions in suitable planar domains this also has close connections to random matrices an example of this was first observed by sato and katori phys rev e 83 041127 2011 we present further examples which give rise to various cauchy type ensembles we also extend fomin s identity to the affine setting and show that in this case by considering independent brownian motions in an annulus one obtains a novel interpretation of the circular orthogonal ensemble

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

an unfitted finite element method for the darcy problem in a fracture network abstract the paper develops an unfitted finite element method for solving the darcy system of equations posed in a network of fractures embedded in a porous matrix the approach builds on the hughes masud stabilized formulation of the darcy problem and the trace finite element method the system of fractures is allowed to cut through the background mesh in an arbitrary way moreover the fractures are not triangulated in the common sense and the junctions of fractures are not fitted by the mesh to couple the flow variables at multiple fracture junctions we extend the hughes masud formulation by including penalty terms to handle interface conditions one observation made here is that by over penalizing the pressure continuity interface condition one can avoid including additional jump terms along the fracture junctions this simplifies the formulation while ensuring the optimal convergence order of the method the application of the trace finite element method allows to treat both planar and curvilinear fractures with the same ease the paper presents convergence analysis and assesses the performance of the method in a series of numerical experiments for the background mesh we use an octree grid with cubic cells the flow in the fracture can be easily coupled with the flow in matrix but we do not pursue the topic of discretizing such coupled system here

a novel approach for static anti windup compensation of one sided lipschitz systems under input saturation abstract this paper illustrates a new strategy for designing the local static anti windup aw compensator for nonlinear systems with one sided lipschitz osl nonlinearities under saturating actuators and exogenous disturbances the static aw strategy is designed such that the resulting closed loop system with osl nonlinearity actuator saturation and exogenous disturbance is stable and the region of attraction can be maximized inequalities based conditions are formulated for the static aw gain design by using lyapunov stability theory sector condition l2 gain reduction osl inequality and quadratic inner bounded qib condition the proposed aw technique is simpler to design straightforward to implement and deals with a broader class of systems in contrast to conventional methods an application example demonstrates that the proposed static aw can successfully mitigate the saturation consequences in osl nonlinear systems

stabilisation of mode dependent singular markovian jump systems with generally uncertain transition rates this paper is devoted to investigating the stability and stabilisation problems for continuous time mode dependent singular markovian jump systems smjss with generally uncertain transition rates gutrs first we establish a sufficient condition in terms of a set of coupled linear matrix inequalities lmis to ensure the systems to be regular impulse free and stochastically stable then we design a mode dependent state feedback controller 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