ℋ index for continuous time stochastic systems with markov jump and multiplicative noise this paper investigates the problem of index for stochastic linear continuous time systems involving markov jump and multiplicative noise a set of generalized differential riccati equations gdres are presented and it is shown that the solvability of gdres is necessary and sufficient for the feasibility of an index larger than 0 our results extend the corresponding deterministic cases to stochastic systems furthermore the infinite horizon index problem for square systems is considered finally the effectiveness of the obtained results is tested by two examples

ergodic properties of poissonian id processes we show that a stationary idp process i e an infinitely divisible stationary process without gaussian part can be written as the independent sum of four stationary idp processes each of them belonging to a different class characterized by its levy measure the ergodic properties of each class are respectively nonergodicity weak mixing mixing of all order and bernoullicity to obtain these results we use the representation of an idp process as an integral with respect to a poisson measure which more generally has led us to study basic ergodic properties of these objects

embedding of the lie superalgebra d 2 1 α into the lie superalgebra of pseudodifferential symbols on s1 2 we obtain an embedding of the one parameter family of exceptional simple lie superalgebras d 2 1 into the lie superalgebra of pseudodifferential symbols on the supercircle s1 2 correspondingly there is an embedding of d 2 1 into a nontrivial central extension of the derived contact superconformal algebra k 4 realized in terms of 4 4 matrices over a weyl algebra

fuzzy filter design for ito stochastic systems with application to sensor fault detection the paper deals with the robust fault detection problem for takagi sugeno t s fuzzy ito stochastic systems our aim is to develop a robust fault detection approach to the t s fuzzy systems with brownian motion by using a general observer based fault detection filter as a residual generator the robust fault detection is formulated as a filtering problem attention is focused on the design of both the fuzzy rule independent and the fuzzy rule dependent fault detection filters guaranteeing a prescribed noise attenuation level in an hinfin sense sufficient conditions are proposed to guarantee the mean square asymptotic stability with an hinfin performance for the fault detection system the corresponding solvability conditions for the desired fuzzy rule independent and fuzzy rule dependent fault detection filters are also established finally a numerical example is provided to illustrate the effectiveness of the proposed theory

null flows positive flows and the structure of stationary symmetric stable processes this paper elucidates the connection between stationary symmetric stable processes with 0 2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows we show that necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes

stationary min stable stochastic processes we consider the class of stationary stochastic processes whose margins are jointly min stable we show how the scalar elements can be generated by a single realization of a standard homogeneous poisson process on the upper half strip 0 1 x r and a group of l1 isometries we include a dobrushin like result for the realizations in continuous time

generalised finite frequency kyp lemma in delta domain and applications to fault detection this article generalises the kalman yakubovi cbreve popov kyp lemma in delta domain to treat some conditions on different restricted frequency ranges the frequency ranges are characterised by two quadratic forms this characterisation encompasses low middle high frequency conditions for delta operator systems by utilising the obtained delta domain generalised kyp lemma a fault detection filter design problem is dealt with for delta operator systems in finite frequency domain the fault detection filter design problem is formulated as a two objective optimisation algorithm with h and h performance indexes a numerical example is given to illustrate the effectiveness and potential for the developed techniques

pareto optimal strategy for linear stochastic systems with h constraint in finite horizon abstract in this paper we derive conditions for the existence of pareto efficient strategy and pareto solution under h constraint for the linear quadratic lq finite horizon cooperative differential game of stochastic systems with state control and disturbance multiplicative noise firstly we present a stochastic bounded real lemma sbrl with any initial condition for the considered stochastic system next a necessary and sufficient condition for pareto optimal strategy under the h constraint is researched by two cross coupled generalized differential riccati equations gdres which is the key contribution of this paper another contribution is that the pareto solution for every controller is given under the pareto efficient strategy and worst case external disturbance finally a practical example is given to illustrate the effectiveness of our results

an lmi approach to minimum sensitivity analysis with application to fault detection this paper systematically studies the minimum input sensitivity analysis problem the lowest level of sensitivity of system outputs to system inputs is defined as an h index a full characterization of the h index is given first in terms of matrix equalities and inequalities and then in terms of linear matrix inequalities lmis as a dual of the bounded real lemma a related problem of input observability is also studied with new necessary and sufficient conditions given which are necessary for a fault detection system to have a nonzero worst case fault sensitivity the above results are applied to the problem of fault detection filter analysis with numerical examples given to show the effectiveness of the proposed approaches

h_ infty unbiased filtering for linear descriptor systems via lmi this note concerns the optimal h infin unbiased filtering problem for linear descriptor systems it unifies the design of reduced order minimal order and full order filters for continuous and discrete time systems necessary and sufficient conditions for the solvability of the problem are obtained in terms of a set of linear matrix inequalities lmis the parametrization of all h infin unbiased filters is presented application to standard systems with or without unknown inputs is given a numerical example is given to show the applicability of the presented approach

extreme value theory ergodic theory and the boundary between short memory and long memory for stationary stable processes we study the partial maxima of stationary stable processes we relate their asymptotic behavior to the ergodic theoretical properties of the flow we observe a sharp change in the asymptotic behavior of the sequence of partial maxima as flow changes from being dissipative to being conservative and argue that this may indicate a change from a short memory process to a long memory process

existence conditions for unknown input functional observers this article presents necessary and sufficient conditions for the existence and design of an unknown input functional observer the existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions the existence of the observer does not require the satisfaction of the observer matching condition i e equation 16 in hou and muller 1992 design of observers for linear systems with unknown inputs ieee transactions on automatic control 37 871 875 is not limited to estimating scalar functionals and allows for arbitrary pole placement the proposed observer always exists when a state observer exists for the unknown input system and furthermore the proposed observer can exist even in some instances when an unknown input state observer does not exist

filtering and fault detection for nonlinear systems with polynomial approximation this paper is concerned with polynomial filtering and fault detection problems for a class of nonlinear systems subject to additive noises and faults the nonlinear functions are approximated with polynomials of a chosen degree different from the traditional methods the approximation errors are not discarded but formulated as low order polynomial terms with norm bounded coefficients the aim of the filtering problem is to design a least squares filter for the formulated nonlinear system with uncertain polynomials and an upper bound of the filtering error covariance is found and subsequently minimized at each time step the desired filter gain is obtained by recursively solving a set of riccati like matrix equations and the filter design algorithm is therefore applicable for online computation based on the established filter design scheme the fault detection problem is further investigated where the main focus is on the determination of the threshold on the residual due to the nonlinear and time varying nature of the system under consideration a novel threshold is determined that accounts for the noise intensity and the approximation errors and sufficient conditions are established to guarantee the fault detectability for the proposed fault detection scheme comparative simulations are exploited to illustrate that the proposed filtering strategy achieves better estimation accuracy than the conventional polynomial extended kalman filtering approach the effectiveness of the associated fault detection scheme is also demonstrated

ergodic properties of sum and max stable stationary random fields via null and positive group actions we establish characterization results for the ergodicity of sym metric stable ss and frechet max stable stationary random fields we first show that the result of samorodnitsky 35 remains valid in the multiparameter setting i e a stationary ss 0 2 random field is ergodic or equivalently weakly mixing if and only if it is generated by a null group action the similarity of the spectral representations for sum and max stable random fields yields paral lel characterization results in the max stable setting by establishing multiparameter versions of stochastic and birkhoff ergodic theorems we give a criterion for ergodicity of these random fields which is valid for all dimensions and new even in the one dimensional case we also prove the equivalence of ergodicity and weak mixing for the general class of positively dependent random fields ams 2000 subject classifications primary 60g10 60g52 60g60 secondary 37a40 37a50

on split leibniz superalgebras abstract we study the structure of arbitrary split leibniz superalgebras we show that any of such superalgebras l is of the form l u j i j with u a subspace of an abelian graded subalgebra h and any i j a well described graded ideal of l satisfying i j i k 0 if j k in the case of l being of maximal length the simplicity of l is also characterized in terms of connections of roots

note on spin modules associated to z graded lie superalgebras the aim of this note is to clarify what can be a correct analog of modules of semi infinite wedges over the virasoro algebra considered by feigin and fuchs invariant skew symmetric differential operators on the line and verma modules over the virasoro algebra funct anal appl 16 114 1982 for a certain class of lie superalgebras

enhancement of robustness in observer based fault detection a prerequisite for the feasibility of the technique of observer based fault detection and isolation fdi in dynamic systems is a satisfactory robustness with respect to modelling uncertainties this paper surveys the most relevant methods to increase the robustness in both the stage of residual generation and residual evaluation among these methods are the generalized observer scheme the robust parity space check the unknown input and h observer scheme the decorrelation filter and the concept of adaptive threshold selection it is pointed out that the unknown input observer concept which provides perfect decoupling from the modelling errors or its optimal approximation with the aid of h techniques constitutes a general framework of robust residual generation that generalizes and unifies numerous other approaches among them the parity space and detection filter approach it is further shown that this fdi method can even be applied to a certain class of nonlinear systems

decomposition of stationary alpha stable random fields this work is concerned with the structural analysis of stationary a stable random fields three distinct classes of such random fields are characterized and it is shown that every stationary a stable random field can be uniquely decomposed into the sum of three independent components belonging to these classes various examples of stationary a stable random fields are discussed in this context 1 preliminaries and introduction in this paper we study measurable stationary symmetric a stable sas random fields x xt ttd where t r or z and d 1 such processes can be represented in distribution by stochastic integrals

stable stationary processes related to cyclic flows we study stationary stable processes related to periodic and cyclic flows in the sense of rosinski ann probab 23 1995 1163 1187 these processes are not ergodic we provide their canonical representations consider examples and show how to identify them among general stationary stable processes we conclude with the unique decomposition in distribution of stationary stable processes into the sum of four major independent components 1 a mixed moving average component 2 a harmonizable or trivial component 3 a cyclic component 4 a component which is different from these

on split lie superalgebras we study the structure of arbitrary split lie superalgebras we show that any of such superalgebras l is of the form l u jij with u a subspace of the abelian graded subalgebra h and any ij a well described graded ideal of l satisfying ij ik 0 if j k under certain conditions the simplicity of l is characterized and it is shown that l is the direct sum of the family of its minimal graded ideals each one being a simple split lie superalgebra

stable mixed moving averages the class of non gaussian stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise leading to stable mixed moving averages their distribution determines a certain combination of the filter function and the mixing measure leading to a generalization of a theorem of kanter 1973 for usual moving averages stable mixed moving averages contain sums of independent stable moving averages are ergodic and are not harmonizable also a class of stable mixed moving averages is constructed with the reflection positivity property

quasifinite representations of the lie superalgebra of quantum pseudodifferential operators in this paper we extend general results obtained by kac and liberati lett math phys 53 11 2000 for quasifinite highest weight representations of z graded lie algebras to 12z graded lie superalgebras and we apply these to classify the irreducible quasifinite highest weight modules of the lie superalgebra of quantum pseudodifferential operators

ℋ ℋ fault detection filter for a class of nonlinear descriptor systems this article addresses the problem of designing a robust fault detection filter rfdf for a class of nonlinear descriptor systems whose nonlinear term is globally lipschitz and linear term is described by a linear parameter varying form the effect of perturbations on the residuals is minimised using the norm while the sensitivity performance is guaranteed using the index thanks to a particular lyapunov function which depends on the faults and the filter design problem is formulated as a convex optimisation problem solved via linear matrix inequality techniques performances of the proposed filter are shown through the application of an activated sludge process model

a new iterative approach for multi objective fault detection observer design and its application to a hypersonic vehicle abstractthis paper addresses the multi objective fault detection observer design problems for a hypersonic vehicle owing to the fact that parameters variations modelling errors and disturbances are inevitable in practical situations system uncertainty is considered in this study by fully utilising the orthogonal space information of output matrix some new understandings are proposed for the construction of lyapunov matrix sufficient conditions for the existence of observers to guarantee the fault sensitivity and disturbance robustness in infinite frequency domain are presented in order to further relax the conservativeness slack matrices are introduced to fully decouple the observer gain with the lyapunov matrices in finite frequency range iterative linear matrix inequality algorithms are proposed to obtain the solutions the simulation examples which contain a monte carlo campaign illustrate that the new methods can effectively reduce the design conservativeness compared with the existing methods

h h fault detection filter design for discrete time takagi sugeno fuzzy system abstract in this note a robust fault detection observer is designed for a t s takagi sugeno fuzzy model with sensor faults and unknown bounded disturbances the method applies the technique of descriptor systems by considering sensor faults as an auxiliary state variable the idea is to formulate the robust fault detection observer design as an h h problem based on nonquadratic lyapunov functions a solution of the considered problem is then given via a linear matrix inequality lmi formulation an example is proposed to illustrate the design conditions

robust h h fault detection observer design for descriptor lpv systems with unmeasurable gain scheduling functions this paper addresses a design of a fault detection observer fdo for descriptor linear parameter varying d lpv systems in contrast with the conventional approach for d lpv systems the gain scheduling functions gsf are considered unmeasurable the fdo is investigated in the h h index framework in order to minimise the effects of the disturbance and maximise the effect of faults on the residuals and minimise the error caused by the unmeasurable gsf the stability is guaranteed based on a lyapunov approach sufficient conditions for the existence of the fdo are established in terms of linear matrix inequalities the effectiveness of the proposed method is illustrated by means of a simulation example

generalized kyp lemma unified frequency domain inequalities with design applications the celebrated kalman yakubovic spl caron popov kyp lemma establishes the equivalence between a frequency domain inequality fdi and a linear matrix inequality and has played one of the most fundamental roles in systems and control theory this paper first develops a necessary and sufficient condition for an s procedure to be lossless and uses the result to generalize the kyp lemma in two aspects the frequency range and the class of systems and to unify various existing versions by a single theorem in particular our result covers fdis in finite frequency intervals for both continuous discrete time settings as opposed to the standard infinite frequency range the class of systems for which fdis are considered is no longer constrained to be proper and nonproper transfer functions including polynomials can also be treated we study implications of this generalization and develop a proper interface between the basic result and various engineering applications specifically it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain phase properties in several frequency ranges the method is illustrated by numerical design examples of digital filters and proportional integral derivative controllers

h h fault detection observer in finite frequency domain for linear parameter varying descriptor systems abstract this paper considers h h fault detection observer design in the finite frequency domain for a class of linear parameter varying lpv descriptor systems we propose a novel fault detection observer with a non singular structure to make the residual sensitive to faults and robust against disturbances we develop a finite frequency h h design method based on a generalized kalman yakubovich popov lemma for lpv descriptor systems design conditions for the proposed fault detection observer are derived and converted as linear matrix inequalities simulation studies are conducted to demonstrate the performance of the proposed method

on the structure of stationary stable processes a connection between structural studies of stationary non gaussian stable processes and the ergodic theory of nonsingular flows is established and exploited using this connection a unique decomposition of a stationary stable process into three independent stationary parts is obtained it is shown that the dissipative part of a flow generates a mixed moving average part of a stationary stable process while the identity part of a flow essentially gives the harmonizable part the third part of a stationary process is determined by a conservative flow without fixed points and by a related cocycle

on the structure of split lie color algebras abstract the class of lie color algebras contains the one of lie superalgebras and so the one of lie algebras in order to begin an approach to the structure of arbitrary lie color algebras with no restrictions neither on the dimension nor on the base field we introduce the class of split lie color algebras as the natural extension of the classes of split lie algebras and split lie superalgebras by developing techniques of connections of roots for this kind of algebra we show that any such algebra l is of the form l u j i j with u a subspace of the abelian graded subalgebra h and eachx i j a well described graded ideal of l satisfying i j i k 0 if j k under certain conditions the simplicity of l is characterized and it is shown that l is the direct sum of the family of its minimal graded ideals each one being a simple split lie color algebra

ergodic theory abelian groups and point processes induced by stable random fields we consider a point process sequence induced by a stationary symmetric stable 0 2 discrete parameter random field it is easy to prove following the arguments in the one dimensional case in stochastic process appl 114 2004 191 210 that if the random field is generated by a dissipative group action then the point process sequence converges weakly to a cluster poisson process for the conservative case no general result is known even in the one dimensional case we look at a specific class of stable random fields generated by conservative actions whose effective dimensions can be computed using the structure theorem of finitely generated abelian groups the corresponding point processes sequence is not tight and hence needs to be properly normalized in order to ensure weak convergence this weak limit is computed using extreme value theory and some counting techniques

statistical inference for max stable processes in space and time max stable processes have proved to be useful for the statistical modelling of spatial extremes several families of max stable random fields have been proposed in the literature one such representation is based on a limit of normalized and rescaled pointwise maxima of stationary gaussian processes that was first introduced by kabluchko and co workers this paper deals with statistical inference for max stable space time processes that are defined in an analogous fashion we describe pairwise likelihood estimation where the pairwise density of the process is used to estimate the model parameters for regular grid observations we prove strong consistency and asymptotic normality of the parameter estimates as the joint number of spatial locations and time points tends to furthermore we discuss extensions to irregularly spaced locations a simulation study shows that the method proposed works well for these models

brief an lmi approach to design robust fault detection filter for uncertain lti systems in this paper the robust fault detection filter design problem for uncertain linear time invariant lti systems with both unknown inputs and modelling errors is studied the basic idea of our study is to use an optimal residual generator assuming no modelling errors as the reference residual model of the robust fault detection filter design for uncertain lti systems with modelling errors and based on it to formulate the robust fault detection filter design as an h model matching problem by using some recent results of h optimization a solution of the optimization problem is then presented via a linear matrix inequality lmi formulation the main results include the development of an optimal reference residual model the formulation of robust fault detection filter design problem the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the lmi solution parameters the determination of adaptive threshold for fault detection an illustrative design example is employed to demonstrate the effectiveness of the proposed approach