discontinuous galerkin methods for friedrichs systems i general theory this paper presents a unified analysis of discontinuous galerkin methods to approximate friedrichs systems an abstract set of conditions is identified at the continuous level to guarantee existence and uniqueness of the solution in a subspace of the graph of the differential operator then a general discontinuous galerkin method that weakly enforces boundary conditions and mildly penalizes interface jumps is proposed all the design constraints of the method are fully stated and an abstract error analysis in the spirit of strang s second lemma is presented finally the method is formulated locally using element fluxes and links with other formulations are discussed details are given for three examples namely advection reaction equations advection diffusion reaction equations and the maxwell equations in the so called elliptic regime

finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information this paper studies the problem of finite time l 2 l tracking control for markov jump repeated scalar nonlinear systems with partly usable model information the partly usable model information is considered following a certain bernoulli distributed white noise sequence the objective of the study is to design a state feedback controller such that the augmented closed loop system is mean square stochastically finite time bounded and a tracking performance level is achieved over a finite time interval by using the mode dependent diagonally dominant lyapunov function approach some sufficient conditions are established for the existence of an admissible state feedback controller based on these a state feedback controller can be constructed by using a simple matrix decoupling approach two numerical examples and a modified general economic model are presented to demonstrate the effectiveness of our proposed approach

reliable asynchronous sampled data filtering of t s fuzzy uncertain delayed neural networks with stochastic switched topologies abstract this paper investigates the issue of the reliable asynchronous sampled data filtering of takagi sugeno t s fuzzy delayed neural networks with stochastic intermittent faults randomly occurring time varying parameters uncertainties and controller gain fluctuation the asynchronous phenomenon occurs between the system modes and controller modes first in order to reduce the utilization rate of communication bandwidth a novel alterable sampled data terminal method is considered via variable sampling rates second based on the fuzzy model based control approach improved reciprocally convex inequality and new parameter time dependent discontinuous lyapunov approach several relaxed conditions are derived and compared with the existing work third the intermittent fault tolerance scheme is also taken into fully account in designing a reliable asynchronous sampled data controller which ensures such that the resultant neural networks is asymptotically stable finally two numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results

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

finite time asynchronous h control for markov jump repeated scalar non linear systems with input constraints finite time control issue for a quite comprehensive class of system model that is markov jump repeated scalar nonlinear systems mjrsnss has been addressed an asynchronous controller is first proposed in mjrsnss which has less conservatism than mode dependent when the partly available mode information is encountered the input constraints associated with physical limitations in some practical applications have been fully considered which make our model more realistic this paper is concerned with the problem of finite time h control for markov jump repeated scalar nonlinear systems mjrsnss with input constraints the jumps between mjrsnss and desired mode dependent controllers are considered to be nonsynchronous the mode transition of the controllers is governed by a nonstationary markov chain which can model the different degrees of asynchronous jumps between mjrsnss and controllers with the aid of lyapunov krasovskii methodology some h performance criteria for the mjrsnss are proposed based on these criteria sufficient conditions on the existence of the desired controllers are established and then the gains of the controllers can be obtained by solving a convex optimization problem finally an example is presented to illustrate the effectiveness of our method

energy to peak state estimation for markov jump rnns with time varying delays via nonsynchronous filter with nonstationary mode transitions in this paper the problem of energy to peak state estimation for a class of discrete time markov jump recurrent neural networks rnns with randomly occurring nonlinearities rons and time varying delays is investigated a practical phenomenon of nonsynchronous jumps between rnns modes and desired mode dependent filters is considered and a nonstationary mode transition among the filters is used to model the nonsynchronous jumps to different degrees that are also mode dependent the rons are used to model a class of sector like nonlinearities that occur in a probabilistic way according to a bernoulli sequence the time varying delays are supposed to be mode dependent and unknown but with known lower and upper bounds a priori sufficient conditions on the existence of the nonsynchronous filters are obtained such that the filtering error system is stochastically stable and achieves a prescribed energy to peak performance index further to the recent study on the class of nonsynchronous estimation problem a monotonicity is observed in obtaining filtering performance index while changing the degree of nonsynchronous jumps a numerical example is presented to verify the theoretical findings

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 finite horizon filtering with randomly occurred nonlinearities and quantization effects in this paper the robust h finite horizon filtering problem is investigated for discrete time varying stochastic systems with polytopic uncertainties randomly occurred nonlinearities as well as quantization effects the randomly occurred nonlinearity which describes the phenomena of a nonlinear disturbance appearing in a random way is modeled by a bernoulli distributed white sequence with a known conditional probability a new robust h filtering technique is developed for the addressed ito type discrete time varying stochastic systems such a technique relies on the forward solution to a set of recursive linear matrix inequalities and is therefore suitable for on line computation it is worth mentioning that in the filtering process the information of both the current measurement and the previous state estimate is employed to estimate the current state finally a simulation example is exploited to show the effectiveness of the method proposed in this paper

robust h control of descriptor discrete time markovian jump systems this paper considers the stochastic stability and the robust control of descriptor discrete time systems with markovian jumping parameters in terms of linear matrix inequalities a necessary and sufficient condition is proposed which ensures a discrete time descriptor markovian jump system to be regular causal and stochastically stable a robust admissibility condition and a robust bounded real lemma are also developed based on these a sufficient condition on the existence of a state feedback controller which guarantees the robust admissibility and the performance is also given by employing the linear matrix inequality technique a robustly stabilizing state feedback controller can be constructed through the numerical solutions of linear matrix inequalities finally an example is provided to demonstrate the effectiveness of the proposed approach

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

brief paper design of h filter for markov jumping linear systems with non accessible mode information for markov jumping linear systems mjls it is often encountered that the jumping mode cannot be accessible for filtering therefore it is strongly desirable to design a filter which is independent of the jumping model in this paper a new deterministic filter design procedure is proposed which shows less conservatism than existing results the whole design procedure can be accomplished by solving a set of linear matrix inequalities lmis finally numerical examples are given to illustrate the effectiveness of the proposed approach

a finite frequency approach to control of markov jump linear systems with incomplete transition probabilities this paper is concerned with the state feedback control of continuous markov jump linear systems with incomplete transition probabilities in finite frequency domain by developing a new technique to handle the coupling among lyapunov variable system matrix and controller parameter new sufficient conditions for the closed loop system to be stochastically stable with the required finite frequency performance are established in terms of linear matrix inequalities meanwhile the finite frequency state feedback controller is also obtained by the proposed conditions directly the validity of the proposed method is demonstrated by a numerical example

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

h control of 2 d continuous markovian jump delayed systems with partially unknown transition probabilities abstract this study focuses on stochastic stability and h control of two dimensional 2 d continuous delayed markovian jump systems mjss with partial information on transition probability at first a sufficient condition for the stochastic stability of 2 d mjss is proposed by choosing an appropriate lyapunov krasovskii functional then the results are developed by designing a state feedback controller that guarantees the stochastic stability of the resultant closed loop system with a prescribed h performance level finally the proposed results are validated with the help of examples

delay dependent synchronization for non diffusively coupled time varying complex dynamical networks this paper investigates the delay dependent synchronization schemes for the non diffusively coupled time varying complex dynamical networks the outer coupling configuration matrix in our network model may be non diffusive time varying uncertain asymmetric and irreducible different time varying coupling delays for different nodes are also put into consideration in this paper besides the nodes may have different state dimensions furthermore only the common bound of the outer coupling coefficients cbocc is used to design the synchronization controllers if the cbocc is known our delay dependent synchronization scheme can guarantee the network achieving exponential synchronization and when the cbocc is uncertain the adaptive synchronization scheme where only one adaptive law is needed is proposed to guarantee the network realizing asymptotic synchronization simulation examples are provided to verify the effectiveness and feasibility of our theoretical results

friedrichs systems in a hilbert space framework solvability and multiplicity abstract the friedrichs 1958 theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics irrespective of their type this theory was recast in an abstract hilbert space setting by ern guermond and caplain 2007 and by antonic and burazin 2010 in this work we make a further step presenting a purely operator theoretic description of abstract friedrichs systems and proving that any pair of abstract friedrichs operators admits bijective extensions with a signed boundary map moreover we provide sufficient and necessary conditions for existence of infinitely many such pairs of spaces and by the universal operator extension theory grubb 1968 we get a complete identification of all such pairs which we illustrate on two concrete one dimensional examples

h_ infty state estimation for discrete time complex networks with randomly occurring sensor saturations and randomly varying sensor delays in this paper the state estimation problem is investigated for a class of discrete time delay nonlinear complex networks with randomly occurring phenomena from sensor measurements the randomly occurring phenomena include randomly occurring sensor saturations rosss and randomly varying sensor delays rvsds that result typically from networked environments a novel sensor model is proposed to describe the rosss and the rvsds within a unified framework via two sets of bernoulli distributed white sequences with known conditional probabilities rather than employing the commonly used lipschitz type function a more general sector like nonlinear function is used to describe the nonlinearities existing in the network the purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that for all probabilistic sensor saturations and sensor delays the dynamics of the estimation error is guaranteed to be exponentially mean square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an h norm in terms of a novel lyapunov krasovskii functional and the kronecker product sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method a simulation example is provided to show the usefulness of the proposed state estimation conditions

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

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

optimal time weighted h 2 model reduction for markovian jump systems this article addresses the optimal time weighted h 2 model reduction problem for markovian jump linear systems that is for a given mean square stable markovian jump system our aim is to find a mean square stable jump system of lower order such that the time weighted h 2 norm of the corresponding error system is minimised the time weighted h 2 norm of the system is first defined and then a computational method is constructed the computation requires the solution of two sets of recursive lyapunov type linear matrix equations associated with the markovian jump system to solve the optimal time weighted h 2 model reduction problem we propose a gradient flow method for its solution a necessary condition for minimality is derived and a computational procedure is provided to obtain the minimising reduced order model the necessary condition generalises the standard result for systems when markov jumps and the time weighting term do not appear finally two numerical examples are given to demonstrate the

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

boundary operator from matrix field formulation of boundary conditions for friedrichs systems abstract following the recent progress in understanding the abstract setting for friedrichs symmetric positive systems by ern guermond and caplain 2007 8 as well as antonic and burazin 2010 3 an attempt is made to relate these results to the classical friedrichs theory a comparison of two approaches via the trace operator and the boundary operator has been made favouring the latter finally a particular set of sufficient conditions for a boundary matrix field to define a boundary operator in that case is given and the applicability of this procedure in realistic situations is shown by examples

parabolic h measures abstract classical h measures introduced by tartar 1990 and independently by gerard 1991 are not well suited for the study of parabolic equations recently several parabolic variants have been proposed together with a number of applications we introduce a new parabolic variant and call it the parabolic h measure which is suitable for these known applications moreover for this variant we prove the localisation and propagation principle establishing a basis for more demanding applications of parabolic h measures similarly as it was the case with classical h measures in particular the propagation principle enables us to write down a transport equation satisfied by the parabolic h measure associated to a sequence of solutions of a schrodinger type equation some applications to specific equations are presented illustrating the possible use of this new tool a comparison to similar results for classical h measures has been made as well

mathcal h_ infty control for 2 d markov jump systems in roesser model this paper considers the problem of asynchronous mathcal h infty control for two dimensional 2 d markov jump systems the underlying system is described based upon the roesser model especially the hidden markov model is employed when dealing with the asynchronization between a controlled system and a controller and the relation between them is constructed through a conditional probability matrix based on the lyapunov function technique the asymptotic mean square stability and mathcal h infty noise attenuation performance are investigated for the closed loop 2 d system moreover the controller gain can be obtained by solving a convex optimization problem an example is presented to show the effectiveness and potential of the proposed new design technique

stochastic stabilization of singular systems with markovian switchings this paper studies the stochastic stabilization problem for a class of singular markovian jump system the aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular markovian jump system smjs a new kind of stochastic controller only in the diffusion part is proposed such that the closed loop system has a unique solution and is almost surely exponentially admissible new sufficient condition for the existence of such a controller is given as linear matrix inequalities lmis based on this more extensions to transition probability matrix tpm with elements partially unknown and system states partially observable are developed a numerical example is used to demonstrate the effectiveness of the proposed methods

isogeometric analysis on implicit domains using weighted extended pht splines abstract the urging quest for diminishing the gap between finite element methods and computer aided design is growing every day isogeometric analysis is driving that search a step forward in contrast with traditional finite element methods one of the areas that need more investigation is using isogeometric analysis on domains that contain singularities in this case the parameterization process is occasionally non trivial and some of the inherited basis functions are not well defined producing rough solutions moreover nurbs basis functions are not the best choice to perform local refinement since adaptivity is indispensable in this study a new approach that serves as a generalization for some of the ideas in both the isogeometric analysis and the web method is introduced isogeometric analysis on implicit domains replaces mesh generation with implicit spline weight function generation and construct weighted extended pht splines for analysis the geometry and the analysis both are built starting from the same function space avoiding parameterization the pht splines are adaptive and allow local refinement naturally leading to a higher accuracy while dealing with singularities an illustration with numerical examples demonstrates the efficiency and performance of the proposed method

probability guaranteed h finite horizon filtering for a class of nonlinear time varying systems with sensor saturations in this paper the probability guaranteed h finite horizon filtering problem is investigated for a class of nonlinear time varying systems with uncertain parameters and sensor saturations the system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges attention is focused on the construction of a time varying filter such that the prescribed h performance requirement can be guaranteed with probability constraint by using the difference linear matrix inequalities dlmis approach sufficient conditions are established to guarantee the desired performance of the designed finite horizon filter the time varying filter gains can be obtained in terms of the feasible solutions of a set of dlmis that can be recursively solved by using the semi definite programming method a computational algorithm is specifically developed for the addressed probability guaranteed h finite horizon filtering problem finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme 2012 elsevier b v all rights reserved

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

robust estimation for neural networks with randomly occurring distributed delays and markovian jump coupling this paper studies the issue of robust state estimation for coupled neural networks with parameter uncertainty and randomly occurring distributed delays where the polytopic model is employed to describe the parameter uncertainty a set of bernoulli processes with different stochastic properties are introduced to model the randomly occurrences of the distributed delays novel state estimators based on the local coupling structure are proposed to make full use of the coupling information the augmented estimation error system is obtained based on the kronecker product a new lyapunov function which depends both on the polytopic uncertainty and the coupling information is introduced to reduce the conservatism sufficient conditions which guarantee the stochastic stability and the l 2 l infty performance of the augmented estimation error system are established then the estimator gains are further obtained on the basis of these conditions finally a numerical example is used to prove the effectiveness of the results

a unified discontinuous petrov galerkin method and its analysis for friedrichs systems we propose a unified discontinuous petrov galerkin dpg framework with optimal test functions for friedrichs like systems which embrace a large class of elliptic parabolic and hyperbolic partial differential equations pdes the well posedness i e existence uniqueness and stability of the dpg solution is established on a single abstract dpg formulation and two abstract dpg methods corresponding to two different but equivalent norms are devised we then apply the single dpg framework to several linear ized pdes including but not limited to scalar transport laplace diffusion convection diffusion convection diffusion reaction linear ized continuum mechanics e g linear ized elasticity a version of linearized navier stokes equations etc time domain acoustics and a version of the maxwell s equations the results show that we not only recover several existing dpg methods but also discover new dpg methods for both pdes currently considered in the dpg community and new ones as

finite time h asynchronous state estimation for discrete time fuzzy markov jump neural networks with uncertain measurements abstract this paper is concerned with the problem of the h asynchronous state estimation for fuzzy markov jump neural networks fmjnns with uncertain measurements over a finite time interval in terms of a bernoulli distributed white sequence the phenomenon of the randomly occurring uncertainties in the output equation is represented by exploiting a random variable with known occurrence probabilities the main focus of this paper is to present a state estimator such that the resulting error system is finite time bounded and satisfies an h performance requirement then by employing the stochastic analysis technique sufficient conditions are provided to ensure that the state estimator is designed by means of solving a convex optimization problem an example is finally given to explain the effectiveness and potentiality of the proposed design method

model reduction of markovian jump systems with uncertain probabilities this paper studies the problem of model reduction for nonhomogeneous markovian jump systems the transition probability matrix of the nonhomogeneous markovian chain has the characteristic of a polytopic structure an asynchronous reduced order model is considered and the asynchronization is modeled by a hidden markov model with a partially unknown conditional probability matrix under this framework a new sufficient condition is proposed to ensure that the augmented system is stochastically mean square stable with a specified level of h infty performance finally a numerical example is provided to show the effectiveness and advantages of the theoretic results obtained

extended dissipativity based non fragile sampled data control of fuzzy markovian jump systems with incomplete transition rates abstract this article addresses the topic of extended dissipative analysis and non fragile sampled data control for fuzzy markovian jump systems with incomplete transition rates where the extended dissipative analysis unifies the l 2 l h passivity q s r dissipativity performance in a framework first by making the best of the information in the sampling interval an appropriate closed loop function dependent sampling interval is constructed then with the addition of free weighting matrices approach and improved integral inequality technique sufficient conditions are obtained to ensure the considered systems are stochastically stable and extended dissipative respectively furthermore the corresponding two form of non fragile mode dependent sampled data controllers are also designed finally a simulation example is offered to verify the feasibility of the results

h measures and variants applied to parabolic equations since their introduction h measures have been mostly used in problems related to propagation effects for hyperbolic equations and systems in this study we give an attempt to apply the h measure theory to other types of equations through a number of examples we present how do the differences between parabolic and hyperbolic equations reflect in the properties of h measures corresponding to the solutions secondly we apply the h measures to the schrodinger equation where we succeed in proving a propagation property however our conclusion is that a variant of h measures should be sought which would be better suited to parabolic problems we propose such a variant show some fundamental properties and illustrate its applicability by some examples in particular we show that the variant provides new information in a number of situations where the original h measures did not finally we describe how the new variant can be used in small amplitude homogenisation of parabolic equations

input output finite time mean square stabilization of nonlinear semi markovian jump systems this paper is concerned with the input output finite time mean square stabilization problem for a class of nonlinear semi markovian jump systems smjss with time varying delay both time varying factors of transition rates and states delay are considered to be bounded our main purpose is to derive some parameter dependent sufficient criteria by designing a state feedback controller to guarantee the input output finite time mean square stabilization for the underlying systems where the nonlinear term satisfies the conic sector constraint then the stabilization conditions are obtained by employing a novel lyapunov krasovskii functional differential form gronwall s inequality and an extra slack variable which is composed of the time varying transition rates finally a simulation example is provided to illustrate the effectiveness and merits of the proposed method

heat equation as a friedrichs system abstract inspired by recent advances in the theory of friedrichs symmetric positive systems we apply newly developed results to the heat equation by showing how the intrinsic theory of ern guermond and caplain 2007 can be used in order to get a well posedness result for the dirichlet initial boundary value problem we also demonstrate the application of the two field theory with partial coercivity of ern and guermond 2008 originally developed for elliptic problems and also discuss different possibilities for the construction of the appropriate boundary operator

a novel approach to stability and stabilization of fuzzy sampled data markovian chaotic systems abstract this paper studies the problems of stability and stabilization of a class of markovian chaotic systems via fuzzy sampled data control different from some existing results the markovian jumping with general uncertain transition rates is considered for such systems a novel approach i e input delay dependent vector approach is proposed for the first time based on this approach an input delay dependent lyapunov krasovskii functional lkf with cubic function of input delay is successfully constructed and the convex combination technique is used with ease to derive stability and stabilization criteria compared with some existing stability and stabilization criteria for chaotic systems our results are not only less conservative but also with reduced calculation complexity finally the superiorities of proposed results are illustrated by two numerical examples

stability analysis of continuous time switched systems with a random switching signal this technical note is concerned with the stability analysis of continuous time switched systems with a random switching signal the switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part and a random part the stochastic stability of such switched systems is studied using a lyapunov approach a necessary and sufficient condition is established in terms of linear matrix inequalities the effect of the random switching signal on system stability is illustrated by a numerical example and the results coincide with our intuition

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

sliding mode control of mimo markovian jump systems this paper addresses the sliding mode control problem for uncertain mimo linear markovian jump systems firstly by using the linear matrix inequality approach sufficient conditions are proposed to guarantee the stochastically asymptotical stability of the system on the sliding surfaces secondly an equivalent control based sliding mode control is proposed such that the closed loop system can be driven onto the desired sliding surfaces in a finite time finally combining with multi step state transition probability the reaching and sliding probabilities are derived for situations where the control force may not be strong enough to ensure the fully asymptotical stability simulation results are presented to illustrate the effectiveness of the proposed design method

a delay dependent approach to h filtering for stochastic delayed jumping systems with sensor non linearities in this paper a delay dependent approach is developed to deal with the stochastic h filtering problem for a class of ito type stochastic time delay jumping systems subject to both the sensor non linearities and the exogenous non linear disturbances the time delays enter into the system states the sensor non linearities and the external non linear disturbances the purpose of the addressed filtering problem is to seek an h filter such that in the simultaneous presence of non linear disturbances sensor non linearity as well as markovian jumping parameters the filtering error dynamics for the stochastic time delay system is stochastically stable with a guaranteed disturbance rejection attenuation level by using ito s differential formula and the lyapunov stability theory we develop a linear matrix inequality approach to derive sufficient conditions under which the desired filters exist these conditions are dependent on the length of the time delay we then characterize the expression of the fi

technical communique resilient linear filtering of uncertain systems the problem of resilient linear filtering for a class of linear continuous time systems with norm bounded uncertainties is investigated we have considered additive filter gain variations to reflect the imprecision in filter implementation the design problem of resilient linear filter is formulated as a convex optimization problem over linear matrix inequalities as a limiting procedure the case of resilient kalman filter is derived all the developed results are conveniently extended to the case of multiplicative filter gain variations simulation studies are carried out to support the theoretical findings

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

cal h _ infty filtering of discrete time markov jump linear systems through linear matrix inequalities this technical note addresses the discrete time markov jump linear systems h infin filtering design problem first under the assumption that the markov parameter is measurable the main contribution is the linear matrix inequality lmi characterization of all linear filters such that the estimation error remains bounded by a given h infin norm level yielding the complete solution of the mode dependent filtering design problem based on this result a robust filter design able to deal with polytopic uncertainty is considered second from the same lmi characterization a design procedure for mode independent filtering is proposed some examples are solved for illustration and comparisons

robust and non fragile finite time h control for uncertain markovian jump nonlinear systems this paper investigates the non fragile and robust finite time h control problem for a class of uncertain markovian jump nonlinear systems with bounded parametric uncertainties and norm bounded disturbance by employing stochastic analysis and linear matrix inequality techniques sufficient criteria of stochastic finite time boundedness and stochastic h finite time boundedness are first provided for the class of stochastic jump systems then a controller is designed such that the class of stochastic nonlinear dynamics are stochastically finite time bounded and have an h attention performance level by utilizing matrix decomposition approach furthermore the analysis and design of non fragile and robust finite time controller are provided to guarantee that the class of uncertain stochastic systems are stochastically finite time boundeded with a prescribed attention index by using non fragile control technique in addition we also deal with the analysis and design of stochastic finite time stability and stochastic finite time stabilization all criterions can be characterized in terms of linear matrix inequalities finally two examples are also given to illustrate the effectiveness of obtained results

h filtering with randomly occurring sensor saturations and missing measurements in chap 5 the h filtering problem is studied for a class of nonlinear systems with randomly occurring incomplete information where the considered incomplete information includes both the sensor saturations and the missing measurements a new phenomenon of sensor saturation namely randomly occurring sensor saturation ross is first put forward in order to better reflect the reality in a networked environment then a novel sensor model is established to account for both the ross and missing measurement in a unified representation based on this sensor model a regional h filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean square asymptotically stable and the h norm requirement is satisfied

exponential stability criterion for interval neural networks with discrete and distributed delays abstract this paper investigates the global exponential stability of neural networks with discrete and distributed delays a new criterion for the exponential stability of neural networks with mixed delays is derived by using the lyapunov stability theory homomorphic mapping theory and matrix theory the obtained result is easier to be verified than those previously reported stability results finally some illustrative numerical examples are given to show the effectiveness of the proposed result

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

filtering for discrete fuzzy stochastic systems with sensor nonlinearities this paper deals with the filtering problem for discrete time fuzzy stochastic systems with sensor nonlinearities there exist time varying parameter uncertainties and random noise depending on state and external disturbance the characteristic of nonlinear sensor is handled by a decomposition method by means of the parallel distributed compensation technique the design method of the robust h filter is presented sufficient conditions for the stochastic stability of the filtering error systems are derived such that the filter parameters can be explicitly obtained simulation results are given to illustrate the proposed method

complex friedrichs systems and applications recently there has been a significant development of the abstract theory of friedrichs systems in hilbert spaces ern a guermond j l and caplain g commun partial differ equations 32 317 341 2007 and antonic n and burazin k commun partial differ equations 35 1690 1715 2010 and its applications to specific problems in mathematical physics however these applications were essentially restricted to real systems we check that the already developed theory of abstract friedrichs systems can be adjusted to the complex setting with some necessary modifications which allows for applications to partial differential equations with complex coefficients we also provide examples where the involved hilbert space is not the space of square integrable functions as it was the case in previous studies but rather its closed subspace or the space hs rd cr for real s this setting appears to be suitable for particular systems of partial differential equations such as the dirac system the di

brief paper static output feedback stabilization of discrete time markovian jump linear systems a system augmentation approach this paper studies the static output feedback sof stabilization problem for discrete time markovian jump systems from a novel perspective the closed loop system is represented in a system augmentation form in which input and gain output matrices are separated by virtue of the system augmentation a novel necessary and sufficient condition for the existence of desired controllers is established in terms of a set of nonlinear matrix inequalities which possess a monotonic structure for a linearized computation and a convergent iteration algorithm is given to solve such inequalities in addition a special property of the feasible solutions enables one to further improve the solvability via a simple d k type optimization on the initial values an extension to mode independent sof stabilization is provided as well compared with some existing approaches to sof synthesis the proposed one has several advantages that make it specific for markovian jump systems the effectiveness and merit of the theoretical results are shown through some numerical examples

synchronization for complex dynamical networks with time delay and discrete time information the synchronization problem is studied for complex dynamical networks cdns with time delay based on discrete time communication pattern a new lyapunov functional is proposed which is positive definite at communication instants but not necessarily positive definite inside the communication intervals and can make full use of the available information about the discrete time communication pattern based on the lyapunov functional an exponential synchronization criterion is proposed to ensure the synchronization of the considered cdns the effectiveness of the developed results are shown by the numerical simulation

almost sure estimation and synthesis of ultimate bounds for discrete time markov jump linear systems this paper is concerned with the problems of almost sure ultimate bound estimation and controller design for markov jump linear systems with bounded stochastic disturbances by utilising a lyapunov based scheme proposed in this paper an almost sure estimation of ellipsoidal ultimate bound eub of the system is obtained through tractable matrix inequalities on the basis of the estimation results the problem of designing mode dependent state feedback controllers that make the closed loop system admit a prescribed ellipsoid as an eub is considered the obtained results on estimation and synthesis are then extended to the case of systems with deficient mode information finally a practical example in dc motor devices is presented to demonstrate the applicability of the obtained results

the mean square stability probability of h_ infty control of continuous markovian jump systems in this technical note h infty control problem of continuous markovian jump systems is investigated a linear feedback control scheme combined with a state observer design is proposed in the form of linear matrix inequalities which can ensure the systems mean square stability with h infty performance then a multi step state transition conditional probability function is introduced for the continuous markovian process which is used to define the system s mean square stability probability furthermore the formulas for calculating the mean square stability probability are derived for situations where the control force may not be strong enough to ensure the full stability simulation results are presented to show the effectiveness of the theoretical results

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

exponential synchronization of delayed markovian jump complex networks with generally uncertain transition rates this paper investigates the exponential synchronization problem for a class of markovian jump complex networks mjcns with generally uncertain transition rates gutrs in this gutr neural network model each transition rate can be completely unknown or only its estimate value is known this new uncertain model could be applied to many practical cases based on the lyapunov functional method and kronecker product technique a sufficient condition on the exponentially synchronization in mean square is derived in terms of linear matrix inequalities lmis which can be easily solved by using the matlab lmi toolbox finally one numerical example is well studied to illustrate the effectiveness of the developed method

stabilization of stochastic delay systems via a disordered controller abstract in this paper the stabilization for stochastic delay systems is achieved by a disordered controller different from the traditionally stabilizing controllers the controller designed here experiences a disorder between control gains and system states by exploiting the robust method the above disorder is described as a controller having special uncertainties moreover the probability distribution of such uncertainties is embodied by a bernoulli variable a sufficient condition for the existence of such a disordered controller is given with lmis where the probability is considered in its design procedure based on this description a more general but complicated case where the corresponding probability is not exact but has a uncertainty is further studied whose lmi conditions are presented too finally a numerical example is exploited to demonstrate the effectiveness and superiority of the proposed methods

decentralized adaptive fuzzy control for nonlinear large scale systems with random packet dropouts sensor delays and nonlinearities abstract this paper investigates the adaptive fuzzy decentralized control problem for a class of uncertain nonlinear large scale systems different from the conventional backstepping based adaptive output feedback control technique the output measurements are imperfect and considered to suffer random packet dropouts rpds random sensor delays rsds and random sensor nonlinearities rsns which result typically from a network environment such as sensor networks a novel sensor model is established for describing the random phenomena within a unified representation by introducing a multi markovian variable based on this sensor model two main difficulties arise first is that the system output cannot be used directly for controller design due to the randomly occurring phenomena second is how to deal with the complex nonlinear stochastic terms with unknown interconnections unknown time varying delays and unknown sensor nonlinearities entangled together with the help of new coordinate transformations and mean value theorem by using appropriate lyapunov krasovskii functionals a new adaptive decentralized memoryless output feedback controller is designed it is proved that the constructed controller ensures the boundedness in probability of all the closed loop signals in presence of rpds rsds and rsns the simulation results are presented to show the effectiveness of the proposed scheme