moving horizon estimation for markov jump systems in this paper we study the state estimation problem for a class of nonlinear markov jump systems with the moving horizon estimation algorithm which is an optimization based filtering method the optimal estimate is obtained by minimizing a quadratic estimation cost function defined on fixed sliding horizon measurements for this purpose the quadratic estimation cost function is formulated from the negative logarithm of the joint states distribution whose particular factorization is represented by a bayesian network by analyzing the corresponding full information estimation as a basic problem for nonlinear markov jump systems the formulation of the moving horizon estimation is developed an example is presented to compare the proposed new estimation technique with classical interacting multiple model particle filtering and show the effectiveness and advantages of the new estimation scheme

on the hyers ulam rassias stability of approximately additive mappings abstract in this paper using an idea from the paper of p gvruta j math anal appl 184 1994 431 436 the results of th m rassias j math anal appl 158 1991 106 113 shall be generalized

mixed h2 h control of markovian jump time delay systems with uncertain transition probabilities this study addresses the robust stability problem of markovian jump time delay systems with mixed h2 and h control and uncertain transition probabilities in the discrete time domain the transition probabilities are considered to be uncertain but bounded by proposing a new lyapunov functional and applying the free weighting matrix technique we design the mode dependent mixed h2 h controller such that the resultant closed loop systems possess stochastic stability and are prescribed with h performance indices these results generalize several results reported in previous literature which consider the markovian transition probabilities to be known a priori or partially unknown transition probabilities numerical examples and a practical motion control system are presented to illustrate the effectiveness of this technique

some further generalizations of the hyers ulam rassias stability of functional equations abstract in this paper we study the hyers ulam rassias stability theory by considering the cases where the approximate remainder is defined by f x y f x f y x y x y g 1 f x y g x h y x y x y g 2 2f x y 1 2 f x f y x y x y g 3 where g is a certain kind of algebraic system e is a real or complex hausdorff topological vector space and f g h are mappings from g into e we prove theorems for the hyers ulam rassias stability of the above three kinds of functional equations and obtain the corresponding error formulas

on the stability of functional equations on a square symmetric groupoid abstract let x be a square symmetric groupoid and y d a complete metric divisible square symmetric groupoid in this paper we obtain the hyers ulam stability problem of the functional inequality d g x y g x g y e x y for approximate mapping g x y of the functional equation f x y f x f y differing by e x 2 0 in particular we have investigated the case of f x f y h f x 1 t f y 1 t on some set y

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

distributed model predictive control of linear systems with stochastic parametric uncertainties and coupled probabilistic constraints this paper investigates the distributed stochastic model predictive control dsmpc for multiple constrained dynamically decoupled subsystems subject to stochastic uncertainties in the parameters to obtain a computationally tractable formulation for real control applications a spectral method called generalized polynomial chaos expansions gpces is utilized to propagate the stochastic parametric uncertainties through the system model by using gpces combined with the probabilistic information on the uncertainties both local probabilistic constraints and coupled probabilistic constraints are converted explicitly into deterministic convex second order cone constraints the constraints can achieve satisfaction of coupled probabilistic constraints in a distributed way by permitting a single subsystem to optimize a local cost function at each time step while freezing the plans of others the proposed gpces based dsmpc algorithm guarantees recursive feasibility with respect to both local and coupled prob

a hidden markov model with dependence jumps for predictive modeling of multidimensional time series abstract hidden markov models hmms are a popular approach for modeling sequential data typically based on the assumption of a first or moderate order markov chain however in many real world scenarios the modeled data entail temporal dynamics the patterns of which change over time in this paper we address this problem by proposing a novel hmm formulation treating temporal dependencies as latent variables over which inference is performed specifically we introduce a hierarchical graphical model comprising two hidden layers on the first layer we postulate a chain of latent observation emitting states the temporal dependencies between which may change over time on the second layer we postulate a latent first order markov chain modeling the evolution of temporal dynamics dependence jumps pertaining to the first layer latent process as a result of this construction our method allows for effectively modeling non homogeneous observed data where the patterns of the entailed temporal dynamics may change over time we devise efficient training and inference algorithms for our model following the expectation maximization paradigm we demonstrate the efficacy and usefulness of our approach considering several real world datasets

addendum to on the stability of functional equations on square symmetric groupoid abstract let x be a square symmetric groupoid and y d a complete metric divisible square symmetric groupoid in this paper we obtain the hyers ulam stability problem of functional inequality d g x y g x g y e x y for approximate mapping g x y of functional equation f x y f x f y differing by e x 2 0 in particular we have investigated the case of f x f y h f x 1 t f y 1 t on some set y

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

adaptive tracking control for switched nonlinear systems with fuzzy actuator backlash abstract this paper concentrates on the adaptive tracking control problem for a class of switched nonlinear systems in nonstrict feedback form with uncertain actuator backlash the switching signal considered in our model is arbitrary the adaptive tracking controller design procedure is divided into three parts firstly a novel fuzzy backlash model is presented to describe the uncertain backlash then the fuzzy backlash is defuzzified and approximated by the linear combination of a linear term and a disturbance like term without constructing a backlash inverse finally an adaptive backstepping based tracking controller via common lyapunov function clf method is presented to guarantee the tracking error asymptotically converges to an adjustable region of zero the stability analysis and simulation examples are presented at the end of this paper to further verify effectiveness of our control scheme

on the general solution and hyperstability of the general radical quintic functional equation in quasi β banach spaces abstract the goal of this paper is to study the general solution of the following general radical quintic functional equation f a x 5 b y 5 5 r f x s f y for f a mapping from the field of real numbers into a vector space where a b r s are fixed nonzero reals also we prove the generalized hyperstability results for the general radical quintic functional equation by using the fixed point theorem cf dung and hang 2018 15 theorem 2 1 in quasi banach spaces namely we show under some weak natural assumptions functions satisfying the above equation approximately in some sense must be actually solutions to it

moving horizon estimation for switching nonlinear systems this paper is concerned with moving horizon estimation for a class of constrained switching nonlinear systems where the system mode is regarded as an unknown discrete state to be estimated together with the continuous state in this work we establish the observability framework of switching nonlinear systems by proposing a series of concepts about observability and analyzing the properties of such concepts by fully applying the observability properties we prove the stability of the proposed moving horizon estimators simulation results are reported to verify the derived results

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

further results on exponential estimates of markovian jump systems with mode dependent time varying delays this technical note studies the problem of exponential estimates for markovian jump systems with mode dependent interval time varying delays a novel lyapunov krasovskii functional lkf is constructed with the idea of delay partitioning and a less conservative exponential estimate criterion is obtained based on the new lkf illustrative examples are provided to show the effectiveness of the proposed results

moving horizon estimation for hybrid systems we propose a state smoothing algorithm for hybrid systems based on moving horizon estimation mhe by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems we provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the mhe scheme moreover we propose two practical algorithms for the computation of penalties that allow us to implement mhe by solving a mixed integer quadratic program

singular invariant tempered distributions on regular prehomogeneous vector spaces revue des espaces vectoriels prehomogenes distributions temperees invariantes distributions temperees avec un parametre meromorphe puissances complexes des invariants relatifs soit p x un polynome homogene irreductible a coefficients reels sur un espace vectoriel v soit s x v p x 0 se decompose en un nombre fini de g 1 orbites avec g 1 g gl v p g x p x on pose v 1 uv 2 u uv e v s la decomposition en composantes connexes on donne une condition necessaire et suffisante pour qu une distribution temperee g 1 invariante a support dans s puisse s obtenir comme une combinaison lineaire finie de coefficients de laurent negatifs de la distribution p x s vd i

novel neural control for a class of uncertain pure feedback systems this paper is concerned with the problem of adaptive neural tracking control for a class of uncertain pure feedback nonlinear systems using the implicit function theorem and backstepping technique a practical robust adaptive neural control scheme is proposed to guarantee that the tracking error converges to an adjusted neighborhood of the origin by choosing appropriate design parameters in contrast to conventional lyapunov based design techniques an alternative lyapunov function is constructed for the development of control law and learning algorithms differing from the existing results in the literature the control scheme does not need to compute the derivatives of virtual control signals at each step in backstepping design procedures furthermore the scheme requires the desired trajectory and its first derivative rather than its first n derivatives in addition the useful property of the basis function of the radial basis function which will be used in control design is explored simulation results illustrate the effectiveness of the proposed techniques

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

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

output feedback stabilization of networked control systems with random delays modeled by markov chains this note investigates the output feedback stabilization of networked control systems ncss the sensor to controller s c and controller to actuator c a random network induced delays are modeled as markov chains the focus is on the design of a two mode dependent controller that depends on not only the current s c delay but also the most recent available c a delay at the controller node the resulting closed loop system is transformed to a special discrete time jump linear system then the sufficient and necessary conditions for the stochastic stability are established further the output feedback controller is designed via the iterative linear matrix inequality lmi approach simulation examples illustrate the effectiveness of the proposed method

event triggered h filtering of markov jump systems with general transition probabilities abstract this paper investigates the h filtering of markov jump systems with general transition probabilities which are known uncertain and unknown the transmission from sensor to filter is determined by a mode dependent event triggered scheme the advantage of the scheme is that no restriction is imposed on a triggering scalar employing a zero order holder the resulting filtering error system is expressed by markov jump systems with time delay with the aid of a relaxed lyapunov krasovskii functional and the finlser lemma the desired h filter gains and the related triggering parameter are solved in a uniformed framework it is shown that the proposed approach is less conservative than the existing one numerical examples are given to verify the validity of the proposed method

a generalization of the hyers ulam rassias stability of the pexiderized quadratic equations abstract in this paper we prove the hyers ulam rassias stability by considering the cases that the approximate remainder is defined by f x y f x y 1 2g x 2g y x y f x y g x y 1 2h x 2k y x y where g is a group x is a real or complex hausdorff topological vector space and f g h k are functions from g into x

stability of a mixed functional equation in several variables on banach modules abstract in this paper we establish the general solution of the functional equation i 1 n f x i 1 n j 1 n x j i 1 n f x i n f 1 n i 1 n x i n 2 and use a fixed point method to prove its generalized hyers ulam stability in banach modules over a unital banach algebra

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

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed theory

hyers ulam rassias stability of a linear recurrence abstract in this paper we give a hyers ulam rassias stability result for the first order linear recurrence in banach spaces

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

a classification of 2 simple prehomogeneous vector spaces of type i let p g gl v be a rational representation of a connected linear algebraic group g on a finite dimensional vector space v all defined over an algebraically closed field k of characteristic zero if v has a zariskidense g orbit we call a triplet g p v a prehomogeneous oector space abbrev p v when p is irreducible such p v s have been classified in 11 since then it has turned out gradually that the complete classification of reductive p v s i e p v s with reductive groups g is an extremely laborious task therefore it is natural to classify some restricted class of p v s e g 2 to get some insight into the general situation a p v g p v is called a 2 simple p v when 1 g gl 1 x g x g with simple algebraic groups g and gz 2 p is the composition of a rational representation p of g x g of the form p p1 0 p pkol a a l l z t with k s t l where pi tv resp pi t are nontrivial irreducible representations of g resp g and the scalar multiplications gz 1 on each irreducible component v for i 1 f where v i v we say that a 2 simple p v g p v is of type zif k l and at least one of gl l xg xg pi pi i 1 k is a nontrivial p v see definition 5 p 43 in 11 on the other hand if k l and all gl l xg xg p op i l k are trivial p v s it is called a 2 simple p v of type ii in 3 all 2 simple p v s of type ii has been already classified in this paper we shall classify all 2simple p v s of type i thus together with 3 we complete a classification of all 2 simple p v s for example the fact that all irreducible p v s are castling equivalent to 2 simple p v s or to x m x y m x g 2 1 1 i i n 1 with m 2 3 see 1 indicates the importance of 2 simple p v s for simplicity we write g p v or g p instead of g p v

a new type of approximation for the radical quintic functional equation in non archimedean 2 β banach spaces abstract let r be the set of real numbers in this paper we first introduce the notions of non archimedean 2 normed spaces x and we will reformulate the fixed point theorem 10 theorem 1 in this space after it we introduce and solve the radical quintic functional equation f x 5 y 5 5 f x f y x y r also under some weak natural assumptions on the function r r x 0 we show that this theorem is a very efficient and convenient tool for proving the hyperstability results when f r x satisfy the following radical quintic inequality f x 5 y 5 5 f x f y z x y z x y r 0 z x with x y

etale representations for reductive algebraic groups with one dimensional center abstract a complex vector space v is a prehomogeneous g module if g acts rationally on v with a zariski open orbit the module is called etale if dim v dim g we study etale modules for reductive algebraic groups g with one dimensional center for such g even though every etale module is a regular prehomogeneous module its irreducible submodules have to be non regular for these non regular prehomogeneous modules we determine some strong constraints on the ranks of their simple factors this allows us to show that there do not exist etale modules for g gl 1 s s with s simple

a classification of the representations of reductive algebraic groups which admit only a finite number of orbits introduction let p g gl v be a finite dimensional rational representation of a semi simple algebraic group g all defined over c then we have p pi epe and v v1i d ve where pi is an irreducible representation of g on vi for i 1 f let p be the action of g gl 1 i x g on v which is the composition of p and scalar multiplications gl 1 ion each irreducible component vi i 1 f in this paper we shall classify all the triplet g p v such that v decomposes into a finite union of g orbits prof v g kac 3 4 and the first author 7 14 but only the necessary conditions are written in 14 have already completed independently the case when p is irreducible i e f 1 prof v g kac has also completed the case when each irreducible components are gl n x gl m al al v n v m see 5 which is the development of the results of prof p gabriel 1 note that if v decomposes into the finite union of g orbits then one of the orbits must be zariski dense and hence g p v must be a prehomogeneous vector space abbrev p v we call such a p v a finite prehomogeneous vector space abbrev f p this paper consists of the following sections

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

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

the space of psi gamma additive mappings on semigroups in this paper we introduce the concept of pseudoadditive mappings from a semigroup into a banach space and we provide a generalized solution of ulam s problem for approximately additive mappings

approximate kalman bucy filter for continuous time semi markov jump linear systems the aim of this paper is to propose a new numerical approximation of the kalman bucy filter for semi markov jump linear systems this approximation is based on the selection of typical trajectories of the driving semi markov chain of the process by using an optimal quantization technique the main advantage of this approach is that it makes pre computations possible we derive a lipschitz property for the solution of the riccati equation and a general result on the convergence of perturbed solutions of semi markov switching riccati equations when the perturbation comes from the driving semi markov chain based on these results we prove the convergence of our approximation scheme in a general infinite countable state space framework and derive an error bound in terms of the quantization error and time discretization step we employ the proposed filter in a magnetic levitation example with markovian failures and compare its performance with both the kalman bucy filter and the markovian linear minimum mean squares estimator

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

an improvement to the interacting multiple model imm algorithm computing the optimal conditional mean state estimate for a jump markov linear system requires exponential complexity and hence practical filtering algorithms are necessarily suboptimal in the target tracking literature suboptimal multiple model filtering algorithms such as the interacting multiple model imm method and generalized pseudo bayesian gpb schemes are widely used for state estimation of such systems we derive a reweighted interacting multiple model algorithm although the imm algorithm is an approximation of the conditional mean state estimator our algorithm is a recursive implementation of a maximum a posteriori map state sequence estimator this map estimator is an instance of a previous version of the em algorithm known as the alternating expectation conditional maximization aecm algorithm computer simulations indicate that the proposed reweighted imm algorithm is a competitive alternative to the popular imm algorithm and gpb methods

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

dissipativity based asynchronous filtering for periodic markov jump systems abstract this paper is devoted to developing a periodic and asynchronous filter for periodic markov jump systems a periodic and asynchronous filter means that the filter parameters are s periodic for a given operating mode and its operating modes are unnecessary to be identical but form a periodic hidden markov model together with the modes of the plant a sufficient condition is proposed to guarantee that the filtering error system is exponentially mean square stable and strictly q s r dissipative to realize this filter a slack matrix is introduced to deal with the nonlinearity and finsler s lemma is applied such that the decision variables are reduced finally a numerical simulation provides verification for the effectiveness of our designed filter

on commutative polarizations let l be a finite dimensional lie algebra over a field k of characteristic zero and let u l be its enveloping algebra with quotient division ring d l let p be a commutative lie subalgebra of l in o2 the necessary and sufficient condition on p was given in order for d p to be a maximal commutative subfield of d l in particular this condition is satisfied if p is a commutative polarization cp with respect to any regular f l and the converse holds if l is ad algebraic the purpose of this paper is to study lie algebras admitting these cp s and to demonstrate their widespread occurrence first we have the following characterisation if l is completely solvable p is a cp of l if and only if there exists a descending chain of lie subalgebras

stability problem of ulam for generalized forms of cauchy functional equation abstract let g 1 be a vector space and g 2 a banach space in this paper we solve the generalized hyers ulam rassias stability problem for a generalized form g i 1 n a i x i c i 1 n a i g x i c x i g 1 of cauchy functional equation f x y f x f y for a mapping f g 1 g 2 where a i a i are scalars for all i 1 n and c g 1 c g 2 are vectors

robust sliding mode control for uncertain discrete singular systems with time varying delays and external disturbances in this paper a sliding mode control smc of uncertain discrete singular systems with external disturbances and time varying delays is under consideration by use of the free weighting matrices and the lyapunov krasovskii functional a delay dependent sufficient condition is given in strict linear matrix inequality lmi format to guarantee the sliding mode dynamics to be admissible regular causal and stable furthermore a proposed smc law and an adaptive smc law are synthesized to make sure that the trajectories of system can be driven to a region near equilibrium point in finite time finally a numerical example is designed to display the effectiveness of the control scheme all these results are expected to propose a new approach for the research on smc of discrete time delay singular systems

stochastic stability of ito differential equations with semi markovian jump parameters in this note the problem of stochastic stability for linear systems with jump parameters being semi markovian rather than full markovian is further investigated in particular the system under consideration is described by ito type nonlinear stochastic differential equations with phase type semi markovian jump parameters stochastic stability conditions are presented

exponential stability analysis for delayed semi markovian recurrent neural networks a homogeneous polynomial approach this paper investigates the exponential stability analysis issue for a class of delayed recurrent neural networks rnns with semi markovian parameters by constructing a stochastic lyapunov functional and using some zoom techniques to estimate its weak infinitesimal operator the exponential mean square stability criteria have been proposed for the markovian neural networks with certain transition probabilities we then generalize the homogeneous polynomial approach for the delayed markovian rnns with uncertain transition probabilities during the stability analysis theoretical results have obtained by introducing an appropriate technique for dealing with a large number of complex homogeneous polynomial matrix inequalities finally numerical examples are provided to demonstrate the effectiveness of the proposed technique

robust h infinity control for a class of neutral type systems via sliding mode observer in this paper the problem of observer based h infinity integral sliding mode control ismc is investigated for a class of uncertain neutral type systems with time delay ntstd an ismc strategy is put forward based on the sliding mode observer a new sufficient condition of robust asymptotic stability for the overall systems composed of the error system and sliding mode dynamics with disturbance attenuation level is derived via linear matrix inequality lmi then a smc law is designed such that the reachability of the sliding surface defined in the state estimate space can be guaranteed finally a simulation example is presented to demonstrate the feasibility of the obtained result

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 finite time stability and stabilization of uncertain markovian jump systems with time varying delay this paper deals with the robust finite time stability and stabilization problems of uncertain stochastic delayed jump systems where the uncertainty is in the form of additive perturbations and exists in the drift and diffusion sections simultaneously though perturbation time varying delay and brownian motion existing at the same time two conditions checking its robust finite time stability are proposed by a mode dependent parameter approach which are different from some existing methods based on the proposed results sufficient conditions for the existence of the state feedback controller are provided with lmis which could be solved directly it is seen that all the features of the underlying system such as time varying delay perturbation diffusion mode dependent parameters and uncertain transition rate matrix play important roles in the system analysis and synthesis of finite time stability finally numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods

on the hyers ulam rassias stability of an additive functional equation in quasi banach spaces abstract in this paper we investigate the hyers ulam rassias stability of the following functional equation i 1 m f m x i j 1 j i m x j f i 1 m x i 2 f i 1 m m x i m n m 2 in quasi banach spaces

on the hyers ulam rassias stability of functional equations in n variables abstract in this paper we investigate a generalization of the hyers ulam rassias stability for a functional equation of the form f x x f x x and the stability in the sense of ger for the functional equation of the form f x x f x where x lie in n variables as a consequence we obtain a stability result in the sense of hyers ulam rassias g vruta and ger for some well known equations such as the gamma beta and g function type s equations

optimal mean variance control for discrete time linear systems with markovian jumps and multiplicative noises in this paper we consider the stochastic optimal control problem of discrete time linear systems subject to markov jumps and multiplicative noises under two criteria the first one is an unconstrained mean variance trade off performance criterion along the time and the second one is a minimum variance criterion along the time with constraints on the expected output we present explicit conditions for the existence of an optimal control strategy for the problems generalizing previous results in the literature we conclude the paper by presenting a numerical example of a multi period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor

some p v equivalences and a classification of 2 simple prehomogeneous vector spaces of type a classification of 2 simple prehomogeneous vector spaces is completed by using some p v equivalences together with 3 some part is very different from the previous classification of the irreducible or simple cases 1 2 and some new method is necessary this result shows the difficult point of a classification problem of reductive prehomogeneous vector spaces introduction in m sato and t kimura 1 all irreducible prehomogeneous vector spaces abbreviated irreducible p v s are classified up to castling equivalence and it is proved that any irreducible p v is castling equivalent to a 2 simple p v or to sl m x sl m x gl 2 a1 x a1 x a1 with m 2 3 therefore as a step to a classification of the general case it is natural to classify all nonirreducible 2 simple p v s in this paper we shall classify all 2 simple p v s of type ii and give the complete list of them up to strong equivalence in the sense of definition 4 p 36 in 1 however we need various p v equivalences cf propositions 1 7 1 12 1 34 1 36 1 37 theorem 1 16 and its corollary corollary 1 26 definition 1 31 remark 1 32 to carry out the classification and hence first we shall prove them we also investigate the regularity in some cases since all 2 simple p v s of type i are already classified in 3 this completes the classification of all 2 simple p v s here we say that g p v or simply g p is a 2 simple p v if it is a prehomogeneous vector space of the following form g gl 1 k s t xg x g2 where g1 and g2 are simple algebraic groups p the composition of the scalar multiplications gl l k s on each irreducible component and the representation p p1 p 1 pk p k a1 s 1 1 t1 t ofthegroupg1 x g2 where pi aj resp p tj are nontrivial irreducible representations of g1 resp g2 we write g p v instead of g p v for simplicity to avoid confusion we write instead of clearly each gl 1 x g1 x g2 pi p i 1 k is an irreducible 2 simple p v if at least one of them is a nontrivial p v see definition 1 1 we call it a 2 simple p v of type i on the other hand if all of them are trivial p v s we call it a 2 simple p v of type ii in this case we have g2 sl n received by the editors march 3 1986 and in revised form july 30 1986 1980 mathematics subject classification 1985 revision primary 11r20 11r29 secondary 11n25 11r18 01988 american mathematical society 0002 9947 88 1 00 25 per page

approximate solution of radical quartic functional equation related to additive mapping in 2 banach spaces abstract the aim of this paper is first to reformulate the fixed point theorem 4 theorem 1 in 2 banach spaces after it we introduce and solve the radical quartic functional equation f x 4 y 4 4 f x f y we also show that the fixed point methods allow to investigate ulam s type stability of radical quartic functional equation in 2 banach spaces

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

fuzzy stability of the jensen functional equation we establish a generalized hyers ulam rassias stability theorem in the fuzzy sense in particular we introduce the notion of fuzzy approximate jensen mapping and prove that if a fuzzy approximate jensen mapping is continuous at a point then we can approximate it by an everywhere continuous jensen mapping as a fuzzy version of a theorem of schwaiger we also show that if every fuzzy approximate jensen type mapping from the natural numbers into a fuzzy normed space can be approximated by an additive mapping then the fuzzy norm is complete

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

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

filtering of two dimensional periodic roesser systems subject to dissipativity abstract in this note the problem of dissipativity based filtering of two dimensional 2d periodic roesser systems is investigated a discrete time periodic roesser model extensively used in practical systems is introduced to describe 2d periodic systems moreover it is assumed that the periods of the augmented system in horizontal and vertical directions are the same which can greatly simplify stability analyses by resorting to the periodic lyapunov functional approach that depends on periodical property of the augmented system less conservative results for the existence of 2d periodic filter are presented to ensure the asymptotic stability and 2d q 1 q 2 q 3 dissipativity particularly the parameters of 2d periodic filter are derived with convex optimization method simulation results are provided to verify the effectiveness and merits of the theoretical findings in addition the correlation between optimal dissipative performance indices and different lyapunov functions is revealed

a cholesky factorization based approach for blind fir channel identification for blind channel identification various techniques including transmitter induced cyclostationarity based approaches have been proposed in literature to induce cyclostationarity at the transmitter zero padding to every symbol packet can be considered some subspace methods are proposed for the channel estimation by exploiting the induced cyclostationarity due to zero padding the covariance matrix of received signal vectors can have a special structure utilizing this structure we can estimate channel impulse responses through factorization in this correspondence we propose a factorization based approach to estimate channel impulse responses in general the proposed factorization based approach can work with a small number of samples and becomes much more computationally efficient than the subspace method when the length of packets is long

state estimation for asynchronous sensor systems with markov jumps and multiplicative noises abstract this paper is concerned with the asynchronous state estimation problem for sensor systems subject to markov jump parameters and multiplicative noises the asynchronous sensors considered can have arbitrary sampling rates and arbitrary initial sampling instants by transforming the asynchronous measurements within each fusion interval into an augmented measurement the equivalent measurement equation and state equation at the fusion time instant are constructed based on the two equations a linear minimum mean squared error lmmse estimator is developed using the orthogonality projection principle due to the existence of the common process noise in the equivalent process and measurement noises the equivalent process and measurement noises are cross correlated and the equivalent measurement noises are autocorrelated these correlations are taken into account in the estimator design the stationary case is also studied and the sufficient condition is established for the stability of the proposed estimator a target tracking example is provided to illustrate the effectiveness of the proposed estimator

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

input to state stability for nonlinear systems with stochastic impulses abstract in this study the problem of input to state stability iss is systematically investigated for nonlinear systems with stochastic impulses first the iss problem is considered for systems where impulsive strengths are assumed to be stochastic and impulsive intervals are confined by the average impulsive interval then the iss problem is analyzed for nonlinear systems with both stochastic impulsive intensity and density several different cases are considered i e cases where the impulsive instants are satisfied by a renewal process poisson process semi markov chain and markov chain an example of coordination of multi agent systems is provided to illustrate the effectiveness of the proposed new stability criteria

constrained state estimation for nonlinear discrete time systems stability and moving horizon approximations state estimator design for a nonlinear discrete time system is a challenging problem further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances one strategy for constrained state estimation is to employ online optimization using a moving horizon approximation we propose a general theory for constrained moving horizon estimation sufficient conditions for asymptotic and bounded stability are established we apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation examples are used to illustrate the benefits of constrained state estimation our framework is deterministic

moving horizon state estimation for nonlinear discrete time systems new stability results and approximation schemes a moving horizon state estimation problem is addressed for a class of nonlinear discrete time systems with bounded noises acting on the system and measurement equations as the statistics of such disturbances and of the initial state are assumed to be unknown we use a generalized least squares approach that consists in minimizing a quadratic estimation cost function defined on a recent batch of inputs and outputs according to a sliding window strategy for the resulting estimator the existence of bounding sequences on the estimation error is proved in the absence of noises exponential convergence to zero is obtained moreover suboptimal solutions are sought for which a certain error is admitted with respect to the optimal cost value the approximate solution can be determined either on line by directly minimizing the cost function or off line by using a nonlinear parameterized function simulation results are presented to show the effectiveness of the proposed approach in comparison with the extended kalman filter

generalized gelfand graev representations of exceptional simple algebraic groups over a finite field i introduction let ffi be an adjoint simple algebraic group of type e n 6 7 8 f 4 or g2 over an algebraically closed field k of characteristic p 0 we assume that 5 has a fixed fq rational structure for a finite subfield fq of k the purpose of this paper is to determine explicitly the values of the irreducible characters of g ffi fq at the unipotent elements when p is good 38 i 4 3 in this part i we shall do this only for large p and the full result will be proved in the forthcoming part ii after submitting the first version of the present paper the author was informed by lusztig that he solved analogous problems for classical groups using his theory of character sheaves and that he can also recover the result of this paper mentioned above our method depends upon 1 a parametrization of the irreducible characters of g and the determination of their multiplicities in deligne lusztig virtual representations lusztig 25 2 the computation of the green functions of g in large characteristic springer 36 7 1 shoji 33 beynon and spaltenstein 3 4 3 the determination of the values of generalized gelfand graev characters 20 of g in good characteristic see section 3 by 1 and 2 the uniform parts of the irreducible characters are already known explicitly in large characteristic this implies that in large characteristic our problem for groups of type e 6 o r e 7 has already been solved it should be mentioned here that the whole character table of the g2 group is also known by chang and ree 8 hence in the g2 case this paper gives just another approach to a part of the result of chang and ree if g is of type g2 f4 or e 8 the restriction of an irreducible character r of g to the set of unipotent elements can be written as a sum of its uniform part with a function of the form

a note on ulam stability of some fuzzy number valued functional equations abstract this note investigates the ulam stability of the following fuzzy number valued functional equations in banach spaces by using the metric defined on a fuzzy number space f x y 2 f x y 2 f x and f a x b y r f x s f y

uncertain jumping systems with strong and weak functional delays this paper provides complete results on the stability behavior of a class of uncertain dynamical systems with jumping parameters and functional time delays the jumping parameters are modeled as a continuous time discrete state markov process the parametric uncertainties are norm bounded appearing in all system matrices and the delay factor depends on the mode of operation notions of weak and strong stochastic stability for the jumping system are developed depending on the available information using a prescribed h performance memoryless and delayed state feedback are considered to guarantee the closed loop stability all the results are cast into linear matrix inequalities format a numerical example is given to illustrate the developed results

hyers ulam rassias stability of an equation of davison abstract in this work the hyers ulam rassias stability of the davison functional equation f xy f x y f xy x f y is proved

a generalization of the hyers ulam rassias stability of the pexider equation in this paper we prove a generalization of the stability of the pexider equation f x y g x h y in the spirit of hyers ulam rassias and g vruta

h2 filtering for discrete time hidden markov jump systems abstractin this paper we consider the h2 filtering problem for a discrete time markov jump linear systemin which the markov parameter is not available in the spirit of active fault tolerant control systems it is supposed that there is a discrete time hidden markov model k k in which the observable part k represents the information coming from a detector and available to the filter while the hidden part k of the process represents the dynamics of the real system several models found in the literature are encompassed by this framework like the complete observation case the clustering information case the mode independent case and markov models in fault tolerant control we start by analysing an auxiliary filtering problem in which it is assumed that both k k are available to the filter so that necessary and sufficient conditions in terms of lmi linear matrix inequalities for the existence of the optimal filter can be obtained in the sequel we consider the realistic case

adaptive tracking control for a class of stochastic switched systems the problem of adaptive tracking is considered for a class of stochastic switched systems in this paper as preliminaries the criterion of global asymptotical practical stability in probability i