on stabilization of bilinear uncertain time delay stochastic systems with markovian jumping parameters in this paper we investigate the stochastic stabilization problem for a class of bilinear continuous time delay uncertain systems with markovian jumping parameters specifically the stochastic bilinear jump system under study involves unknown state time delay parameter uncertainties and unknown nonlinear deterministic disturbances the jumping parameters considered here form a continuous time discrete state homogeneous markov process the whole system may be regarded as a stochastic bilinear hybrid system that includes both time evolving and event driven mechanisms our attention is focused on the design of a robust state feedback controller such that for all admissible uncertainties as well as nonlinear disturbances the closed loop system is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are established to guarantee the existence of desired robust controllers which are given in terms of the solutions to a set of either linear matrix inequalities lmis or coupled quadratic matrix inequalities the developed theory is illustrated by numerical simulation

optimal quadratic filtering of linear discrete time non gaussian systems in this work the state estimation problem for linear discrete time systems with non gaussian state and output noises is dealt with by following a geometric approach an optimal recursive second order polynomial estimate is proposed which actually improves the widely used optimal linear one

observer design for stochastic parameter systems constant gain linear observer design is utilized to reconstruct the state vector of stochastic systems with both multiplicative and additive noises it is shown that if the system model is mean square stable then it is very easy to design an effective estimation scheme

polynomial filtering for linear discrete time non gaussian systems in this work we propose a new filtering approach for linear discrete time non gaussian systems that generalizes a previous result concerning quadratic filtering a de santis a germani and m raimondi ieee trans automat control 40 1995 pp 1274 1278 a recursive nu th order polynomial estimate of finite memory delta is achieved by defining a suitable extended state which allows one to solve the filtering problem via the classical kalman linear scheme the resulting estimate will be the mean square optimal one among those estimators that take into account nu polynomials of the last delta observations numerical simulations show the effectiveness of the proposed method

linear state estimators for non linear stochastic systems with noisy non linear observations the design of linear filters is considered for reconstructing the state of a class of discrete time non linear stochastic systems using noise corrupted measurements it is shown that for systems with mean square stable dynamics it is always possible to guarantee stable estimation schemes this result is used to prove that a mean square optimal one step predictor has stable error dynamics and also to generate other stable predictors

linear estimation for networked control systems with random transmission delays and packet dropouts in networked control systems random delays and packet dropouts are inevitable during data transmissions due to the limited communication capacity the phenomena of random delays and packet dropouts of both sides from a sensor to an estimator and from a controller to an actuator are modeled via employing two groups of bernoulli random variables by defining some new variables the original system with random delays and packet dropouts is equivalently transformed into a stochastic parameterized system the optimal linear filter predictor and smoother in the linear minimum variance sense are presented via the orthogonality projection approach they depend on the probabilities of the stochastic parameters the solutions to the optimal linear estimators are given by three equations including a riccati a lyapunov and a simple difference the stability of the proposed estimators is analyzed at last a sufficient condition for the existence of the steady state estimators is given for time invariant systems two examples are provided to verify the effectiveness of the proposed algorithms

kalman filtering with random coefficients and contractions the riccati transformation of linear filtering control theory is shown to be a contraction on the space of positive symmetric matrices this is used to describe the asymptotic behavior of the filter for systems with stochastic stationary parameters

compensatability and optimal compensation of systems with white parameters the optimal compensation problem is considered in the case of linear discrete time systems with stationary white parameters and quadratic criteria a generalization of the notion of mean square stabilizability namely mean square compensatability is introduced it is shown that suitable mean square compensatability and detectability conditions are sufficient and necessary in general for the existence of a unique optimal mean square stabilizing compensator tests are given to determine whether or not a system is mean square compensatable it is indicated how to calculate numerically the tests and the optimal mean square stabilizing compensator the results are illustrated with examples

a new recursive filter for systems with multiplicative noise an optimal linear recursive minimum mean square error estimator was previously developed by the authors see ieee trans autom control vol 34 no 5 p 568 74 may 1989 for a zero mean signal corrupted by multiplicative noise in its measurement model this recursive filter cannot be obtained by the recursive structure of a conventional kalman filter where the new estimate is a linear combination of the previous estimate and the new data instead the recursive structure was achieved by combining the previous estimate with recursive innovation a linear combination of the most recent two data samples and the previous estimate in this work the signal is extended to be nonzero mean in the conventional kalman filter the superposition principle can be applied to both the signal and the measurement models for this nonzero mean extension however when multiplicative noise exists the measurement model becomes nonlinear therefore a new recursive structure for the innovation process needs to be developed to achieve a recursive filter

implications of a result on observer design for stochastic parameter systems an earlier result on observer design for stochastic parameter systems is utilized to show that optimal one step predictors for such systems are mean square stable and to propose a new class of stable estimation schemes

modeling and estimation for networked systems with multiple random transmission delays and packet losses abstract in networked systems data packets are transmitted through networks from a sensor to a data processing center due to the unreliability of communication channels a packet may be delayed even lost during the transmission at each moment the data processing center may receive one or multiple data packets or nothing at all a novel model is developed to describe the possible multiple random transmission delays and data packet losses by employing a group of bernoulli distributed random variables it is transformed to a measurement model with multiple random delayed states and noises based on the model an optimal linear filter in the linear minimum variance sense is proposed by using the orthogonal projection approach which is a universal tool to find the optimal linear estimate it does not have a steady state performance since it depends on the values of random variables that depict the phenomena of delays and losses at each moment so it needs to be computed online to reduce the online computational cost a suboptimal linear filter dependent on the probabilities of random variables is also proposed however it is worth noting that it is linearly optimal among all the linear filters dependent on the probabilities it can be computed offline since it has the steady state performance a sufficient condition of existence for the steady state performance is given a simulation example shows the effectiveness

reducibility and unobservability of markov processes the linear system case a vector markov process will be called stochastically unobservable by the measurement process if there exists an initial distribution such that some marginal conditional distributions equal the corresponding unconditional ones it will be called reducible if there exists an invertible transformation such that the transformed process is stochastically unobservable necessary and sufficient conditions are derived in the context of linear diffusions it is also shown that reducibility can be regarded as a natural extension of the concept of estimability defined for linear stochastic systems

the p variation of partial sum processes and the empirical process the p variation of a function f is the supremum of the sums of the p th powers of absolute increments of f over nonoverlapping intervals let f be a continuous probability distribution function dudley has shown that the p variation of the empirical process is bounded in probability as n to infty if and only if p 2 and for 1 leq p leq 2 the p variation of the empirical process is at least n 1 p 2 and is at most of the order n 1 p 2 log log n p 2 in probability in this paper we prove that the exact order of the 2 variation of the empirical process is log log n in probability and for 1 leq p 2 the p variation of the empirical process is of exact order n 1 p 2 in expectation and almost surely let s j x 1 x 2 dots x j then the p variation of the partial sum process for x 1 x 2 dots x n is defined as that of f on 0 n where f t s j for j 1 t leq j j 1 2 dots n bretagnolle has shown that the expectation of the p variation for independent centered random variables x i with bounded p th moments is of order n for 1 leq p 2 we prove that for p 2 the 2 variation of the partial sum process of i i d centered nonconstant random variables with finite 2 delta moment for some delta 0 is of exact order n log log n in probability

optimal linear estimation with square based sampling this paper is concerned with the problem of event based sampling for the purpose of reducing the number of data transferred in control systems and the corresponding modified kalman filter a mathematical description based upon square based sampling is proposed in which the sampling occured when the accumulated difference between two adjacent sampling points satisfies the specified event condition then by utilizing the square based sampling method a modified kalman filter algorithm is adopted in which the measurement is sent when the output exceeds a given event the simulation results illustrate the advantage of the new event based sampling scheme and the effectiveness of modified kalman filter

robust filtering for bilinear uncertain stochastic discrete time systems this paper deals with the robust filtering problem for uncertain bilinear stochastic discrete time systems with estimation error variance constraints the uncertainties are allowed to be norm bounded and enter into both the state and measurement matrices we focus on the design of linear filters such that for all admissible parameter uncertainties the error state of the bilinear stochastic system is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prespecified value it is shown that the design of the robust filters can be carried out by solving some algebraic quadratic matrix inequalities in particular we establish both the existence conditions and the explicit expression of desired robust filters a numerical example is included to show the applicability of the present method

frisch scheme identification for dynamic diagonal bilinear models the article addresses the problem of dynamic system identification in the errors in variables framework for a class of discrete time time invariant input output bilinear models when subjected to a white input signal the proposed algorithm is based on an extension of the bias compensated least squares method and utilises the frisch scheme equations to determine the parameter vector together with the variances of the input and output noise sequences the appropriateness of the approach is analysed and its performance evaluated when compared to other errors in variables identification techniques by means of a monte carlo simulation the results obtained demonstrate the accuracy of the proposed method and the performance in terms of noise robustness is also observed

robust kalman filtering for uncertain discrete time systems with probabilistic parameters bounded within a polytope we consider the problem of finite horizon discrete time kalman filtering for systems with parametric uncertainties specifically we consider unknown but deterministic uncertainties where the uncertain parameters are assumed to lie in a convex polyhedron with uniform probability density the condition and a procedure for the construction of a suboptimal filter that minimizes an expected error covariance over bound are derived

infinite horizon optimal control of linear discrete time systems with stochastic parameters the infinite horizon optimal control problem is considered in the general case of linear discrete time systems and quadratic criteria both with stochastic parameters which are independent with respect to time a stronger stabilizability property and a weaker observability property than usual for deterministic systems are introduced it is shown that the infinite horizon problem has a solution if the system has the first property if in addition the problem has the second property the solution is unique and the control system is stable in the mean square sense a simple necessary and sufficient condition explicit in the system matrices is given for the system to have the stronger stabilizability property this condition also holds for deterministic systems to be stabilizable in the usual sense the stronger stabilizability and weaker observability properties coincide with the usual ones if the parameters are deterministic

optimal filtering for discrete time linear systems with time correlated multiplicative measurement noises in this note the filtering problem for discrete time linear systems with time correlated multiplicative measurement noises is considered where the vector consisting of all the multiplicative measurement noises can be described by a linear system model with white noise by introducing several new recursive terms a novel algorithm for optimal filtering of the system under consideration is proposed in the sense of linear minimum mean square error the proposed algorithm is recursive and has time independent complexity computer simulations are provided to illustrate the performance of the proposed algorithm

optimal estimation for discrete time linear systems in the presence of multiplicative and time correlated additive measurement noises in this paper the state estimation problem for discrete time linear systems influenced by multiplicative and time correlated additive measurement noises is considered where the multiplicative noises are zero mean white noise sequences and the time correlated additive noise is described by a linear system model with white noise an optimal linear estimator for the system under consideration is proposed which does not require computing the inverse of state transition matrix the proposed estimator has a recursive structure and has time independent computation and storage load computer simulations are carried out to demonstrate the performance of the proposed estimator the simulation results show the superiority of the proposed estimator

optimal full order and reduced order estimators for discrete time systems with multiple packet dropouts this paper is concerned with the estimation problem for discrete time stochastic linear systems with multiple packet dropouts based on a recently developed model for multiple packet dropouts the original system is transferred to a stochastic parameter system by augmentation of the state and measurement the optimal full order linear filter of the form of employing the received outputs at the current and last time instants is investigated the solution to the optimal linear filter is given in terms of a riccati difference equation governed by packet arrival rate the optimal filter is reduced to the standard kalman filter when there are no packet dropouts the steady state filter is also studied a sufficient condition for the existence of the steady state filter is given and the asymptotic stability of the optimal filter is analyzed at last a reduced order filter is investigated

quadratic estimation problem in discrete time stochastic systems with random parameter matrices this paper addresses the least squares quadratic filtering problem in discrete time stochastic systems with random parameter matrices in both the state and measurement equations defining a suitable augmented system this problem is reduced to the least squares linear filtering problem of the augmented state based on the augmented observations under the assumption that the moments up to the fourth order one of the original state and measurement vectors are known a recursive algorithm for the optimal linear filter of the augmented state is designed from which the optimal quadratic filter of the original state is obtained as a particular case the proposed results are applied to multi sensor systems with state dependent multiplicative noise and fading measurements and finally a numerical simulation example illustrates the performance of the proposed quadratic filter in comparison with the linear one and also with other filters in the existing literature

state estimators for systems with random parameter matrices stochastic nonlinearities fading measurements and correlated noises using the innovation analysis approach the optimal linear state estimators including the filter predictor and smoother in the linear minimum variance lmv sense are presented for a class of nonlinear discrete time stochastic uncertain systems with fading measurements and correlated noises stochastic uncertainties of parameter matrices are depicted by correlated multiplicative noises stochastic nonlinearities are characterized by a known conditional mean and covariance different sensor channels have different fading measurement rates the process and measurement noises are finite step auto and or cross correlated with each other two simulation examples verify the effectiveness of the proposed algorithms

recursive filtering with random parameter matrices multiple fading measurements and correlated noises this paper is concerned with the recursive filtering problem for a class of discrete time nonlinear stochastic systems with random parameter matrices multiple fading measurements and correlated noises the phenomenon of measurement fading occurs in a random way and the fading probability for each sensor is governed by an individual random variable obeying a certain probability distribution over the known interval b k c k such a probability distribution could be any commonly used discrete distribution over the interval b k c k that covers the bernoulli distribution as a special case the process noise and the measurement noise are one step autocorrelated respectively the process noise and the measurement noise are two step cross correlated the purpose of the addressed filtering problem is to design an unbiased and recursive filter for the random parameter matrices stochastic nonlinearity and multiple fading measurements as well as correlated noises intensive stochastic analysis is carried out to obtain the filter gain characterized by the solution to a recursive matrix equation the proposed scheme is of a form suitable for recursive computation in online applications a simulation example is given to illustrate the effectiveness of the proposed filter design scheme

stability of optimum linear estimators of stochastic signals in white multiplicative noise conditions for uniform asymptotic stability in the large of the optimal minimum mean square error linear filter are developed for linear systems whose observations are corrupted by white multiplicative noise in addition to white additive noise both discrete time as well as continuous time systems are considered the multiplicative noise model may be useful in problems associated with phenomena such as fading or reflection of the transmitted signal from the ionosphere and also certain situations involving sampling gating or amplitude modulation conditions for existence uniqueness and stability of the steady state optimal filter are also considered for time invariant systems

full and reduced order observer design for discrete stochastic bilinear systems the author considers a general discrete time stochastic bilinear system model and derives the mean square optimal linear unbiased observer equations to be used in reconstructing a prespecified linear combination of state variables based on noisy output measurements

on the almost sure and mean square exponential convergence of some stochastic observers it is pointed out that linear observers used for estimating the state of the discrete time stochastic parameter systems are both almost surely and mean square ms exponentially convergent under the same conditions guaranteeing mean square convergence in addition to the mean square convergence properties of linear observers constructed for mean square stable stochastic parameter systems they also possess an almost sure exponential convergence property and the rate of ms convergence is exponential this rate depends on the parameters used in the design

the accurate dynamic modelling of contaminant dispersion in channels throw some dye into a flowing river how is the dye going to disperse along the river the dynamics may be modelled by taylor s one dimensional model of shear dispersion we discuss the creation and utility of models of the dispersion of the dye using invariant manifold theory the models are effective exponentially quickly we describe a one mode centre manifold and a two mode and a three mode invariant manifold model from the analysis we decide under what conditions these three models are valid using the geometric picture provided by the theory of invariant manifolds we find a complete set of initial conditions for the models so that the evolution of the full and approximate systems are identical after a short time throughout a comparison of the three models is made to identify the practical situations when each model will be preferred

detectability of linear discrete time systems with stochastic parameters abstract the paper introduces the concept of mean square detectability and relates this to the recently introduced concept of mean square observability it is shown that under appropriate mean square detectability and stabilizability conditions the infinite horizon optimal control problem for the general case of linear discrete time systems and quadratic criteria both with stochastic parameters which are statistically independent of time has a unique solution when the control system is mean square stable a simple necessary and sufficient condition explicit in the system matrices is given to determine if a system is mean square detectable this condition also holds for deterministic systems to be detectable in the usual sense the mean square detectability property coincides with the usual one if the parameters are deterministic

minimax robust deconvolution filters under stochastic parametric and noise uncertainties the author consider the design of robust deconvolution filters for linear discrete time systems with stochastic parameter and noise uncertainties it is assumed that some large but bounded uncertainties exist in the driving and measurement noise covariances as well as the second order statistics of stochastic parameters and initial conditions three kinds of minimax sensitivity criteria are used to develop the techniques to the synthesis of minimax deconvolution filters under uncertain linear stochastic systems their approach is based on saddle point theory and the sensitivity analysis of kalman filters the design algorithms give the recursive realization of the minimax deconvolution filters for the time varying uncertain systems under fairly general conditions for the time invariant uncertain case the existence and solutions of steady state deconvolution filters are further developed finally the utility of the minimax design approaches and the properties of the resulting minimax deconvolution filters are illustrated by a numerical example

a new structure of recursive estimator a novel structure of a linear recursive estimator minimizing the mean square error is derived for a system with a multiplicative noise in the measurement model the conventional form of a recursive estimator the new estimate is a linear combination of the new data and the previous estimate is not appropriate for the above system in contrast according to presented form of estimator the new estimate and the new innovation which is recursively obtained by a linear combination of the new data the previous data and the previous innovation

linear estimation of continuous discrete linear state space models with multiplicative noise this paper deals with the estimation of the state variable of continuous discrete linear state space models with multiplicative noise specifically the optimal minimum variance linear filter for that class of models is constructed moreover the solutions of the differential equations that describe the evolution of the two first conditional moments between observations are obtained and an algorithm for their numerical computation is also given the performance of the linear filter is illustrated by means of numerical experiments

polynomial filtering of discrete time stochastic linear systems with multiplicative state noise the problem of finding an optimal polynomial state estimate for the class of stochastic linear models with a multiplicative state noise term is studied for such models a technique of state augmentation is used leading to the definition of a general polynomial filter the theory is developed for time varying systems with nonstationary and non gaussian noises moreover the steady state polynomial filter for stationary systems is also studied numerical simulations show the high performances of the proposed method with respect to the classical linear filtering techniques

brief paper optimal linear estimation for systems with multiple packet dropouts this paper is concerned with the optimal linear estimation problem for linear discrete time stochastic systems with multiple packet dropouts based on a packet dropout model the optimal linear estimators including filter predictor and smoother are developed via an innovation analysis approach the estimators are computed recursively in terms of the solution of a riccati difference equation of dimension equal to the order of the system state plus that of the measurement output the steady state estimators are also investigated a sufficient condition for the convergence of the optimal linear estimators is given simulation results show the effectiveness of the proposed optimal linear estimators

variance constrained filtering for uncertain stochastic systems with missing measurements in this note we consider a new filtering problem for linear uncertain discrete time stochastic systems with missing measurements the parameter uncertainties are allowed to be norm bounded and enter into the state matrix the system measurements may be unavailable i e missing data at any sample time and the probability of the occurrence of missing data is assumed to be known the purpose of this problem is to design a linear filter such that for all admissible parameter uncertainties and all possible incomplete observations the error state of the filtering process is mean square bounded and the steady state variance of the estimation error of each state is not more than the individual prescribed upper bound it is shown that the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like inequalities or linear matrix inequalities the explicit expression of the desired robust filters is parameterized and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach

brief paper optimal estimation of linear discrete time systems with stochastic parameters this paper considers optimal linear state estimation in the general case of linear discrete time systems with stochastic parameters which are statistically independent with respect to time the estimator is derived by transforming the system to one with deterministic parameters and state dependent additive system and observation noise it is shown that mean square stability of the system is a sufficient and almost necessary condition for the existence uniqueness and stability of the time invariant estimator