robust kalman bucy filter development of a robust estimator for uncertain stochastic systems under persistent excitation is presented the given continuous time stochastic formulation assumes norm bounded parametric uncertainties and excitations when there are no system uncertainties the performance of the proposed robust estimator is similar to that of the kalman bucy filter and the proposed approach asymptotically recovers the desired optimal performance in the presence of uncertainties and or persistent excitation

finite horizon ℋ 2 ℋ control for a class of nonlinear markovian jump systems with probabilistic sensor failures this article is concerned with the mixed 2 control problem over a finite horizon for a class of nonlinear markovian jump systems with both stochastic nonlinearities and probabilistic sensor failures the stochastic nonlinearities described by statistical means could cover several types of well studied nonlinearities and the failure probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over a given interval the purpose of the addressed problem is to design state feedback controllers such that the closed loop system achieves the expected 2 performance requirement with a guaranteed disturbance attenuation level the solvability of the addressed control problem is expressed as the feasibility of certain coupled matrix equations the controller gain at each time instant k can be obtained by solving the corresponding set of matrix equations a numerical example is given to illustrate the effectiveness and applicability of the proposed al

discrete time nonlinear h control with measurement feedback abstract this paper deals with the problem of h control via measurement feedback with internal stability for discrete time nonlinear systems using the theory of discrete time dissipative systems and differential game we first present a parameterization of a family of static state feedback h nonlinear controllers then we provide sufficient conditions for the existence of a dynamic output compensator which solves the problem of disturbance attenuation with internal stability for discrete time nonlinear systems the theory developed in this paper incorporates the well known results for discrete time linear systems and generalizes some recent advances in h control of continuous time nonlinear systems to their discrete time counterparts

robust h control for linear markovian jump systems with unknown nonlinearities this paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous time uncertain systems with markovian jumping parameters the uncertainties are assumed to be nonlinear and state control and external disturbance dependent a sufficient condition is provided to solve the above problem an h controller is designed such that the resulting closed loop system is stochastically stable and has a disturbance attenuation for all admissible uncertainties it is shown that the control law is in terms of the solutions of a set of coupled riccati inequalities a numerical example is included to demonstrate the potential of the proposed technique

mathcal l _ 2 mathcal l _ infty output feedback controller design for fuzzy systems over switching parameters this paper focuses on the problem of mathcal l 2 mathcal l infty dynamic output feedback controller dofc design for nonlinear switched systems with nonlinear perturbations in the takagi sugeno fuzzy framework first the average dwell time approach is used to stabilize a nonlinear switched system exponentially under an arbitrary switching law then based on the technique of piecewise lyapunov functions a fuzzy rule dependent dofc is designed to ensure that the overall closed loop system is exponentially stable with a weighted mathcal l 2 mathcal l infty performance level left gamma alpha right the solvability condition for the desired dofc is derived using a linearization technique it is shown that the controller parameters can be obtained as solutions to a set of strict linear matrix inequalities that are numerically solvable with available standard software finally two simulation examples illustrate effectiveness of the developed technique including cognitive radio systems

birkhoff formula for conformal compressions of symmetric cones in this paper we derive the birkhoff formula for conformal compressions on symmetric cones let v be a euclidean jordan algebra and let be the associated symmetric cone then admits a natural finsler metric contracted by any conformal compressions of we show that the lipschitz constant of a conformal compression of is equal to the hyperbolic tangent of one fourth of the diameter of the image this is the same relation which was obtained by birkhoff on positive reals and by liverani and wojtkowski on the space of positive definite real matrices

filtering on sampled data systems with parametric uncertainty the paper is concerned with the problem of robust h sub spl infin filtering for a class of systems with parametric uncertainties and unknown time delays under sampled measurements the parameter uncertainties considered are real time varying and norm bounded appearing in the state equation an approach has been proposed for the designing of h sub spl infin filters using sampled measurements which would guarantee a prescribed h sub spl infin performance in the continuous time context irrespective of the parameter uncertainties and unknown time delays both cases of finite and infinite horizon filtering are studied it has been shown that the above robust h sub spl infin filtering problem can be solved in terms of differential riccati inequalities with finite discrete jumps

new approaches to robust minimum variance filter design this paper is concerned with the design of robust filters that ensure minimum filtering error variance bounds for discrete time systems with parametric uncertainty residing in a polytope two efficient methods for robust kalman filter design are introduced the first utilizes a recently introduced relaxation of the quadratic stability requirement of the stationary filter design the second applies the new method of recursively solving a semidefinite program sdp subject to linear matrix inequalities lmis constraints to obtain a robust finite horizon time varying filter the proposed design techniques are compared with other existing methods it is shown via two examples that the results obtained by the new methods outperform all of the other designs

an alternative look at the constant gain kalman filter for state estimation over erasure channels this technical note studies state estimation problems subject to data loss we consider a class of switched estimators where missing data is replaced by optimal estimates the considered class of estimators encompasses a number of estimation schemes proposed in the literature we show that the estimator that minimizes the steady state estimation error covariance within that class is given by a constant gain kalman filter which was previously proposed as an alternative to the kalman filter with intermittent observations as a by product of our results we derive expressions that allow one to compare analytically popular suboptimal data dropout compensation mechanisms

stability of mmse state estimators over lossy networks using linear coding this paper studies the state estimation problem for a stochastic discrete time system over a lossy channel where the packet loss is modeled as an independent and identically distributed binary process to counter the effect of random packet loss we propose a linear coding method to preprocess the measured output and prove that the coded output is information preserving when packet loss is void and is information enhancing when packet loss is present an optimal state estimator under the minimum mean square error mmse criterion is derived for the coded output when subject to packet loss the maximum packet loss rate for ensuring a stable estimator is then derived and shown to be very close to a well known lower bound also considered is a compressed linear coding method where the measured output is first compressed onto a lower dimensional space before encoding and it is shown that the similar packet rate condition for stability holds

kalman filtering with intermittent observations tail distribution and critical value in this paper we analyze the performance of kalman filtering for discrete time linear gaussian systems where packets containing observations are dropped according to a markov process modeling a gilbert elliot channel to address the challenges incurred by the loss of packets we give a new definition of non degeneracy which is essentially stronger than the classical definition of observability but much weaker than one step observability which is usually used in the study of kalman filtering with intermittent observations we show that the trace of the kalman estimation error covariance under intermittent observations follows a power decay law moreover we are able to compute the exact decay rate for non degenerate systems finally we derive the critical value for non degenerate systems based on the decay rate improving upon the state of the art

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

weighted maximum likelihood for dynamic factor analysis and forecasting with mixed frequency data for the purpose of forecasting key macroeconomic or financial variables from a panel of time series variables we adopt the dynamic factor model and propose a weighted likelihood based method for parameter estimation the loglikelihood function is split into two parts that are weighted differently the first part is associated with the key variables while the second part is associated with the related variables which may contribute to the forecasting of key variables we derive asymptotic properties including consistency and asymptotic normality of the weighted maximum likelihood estimator we show that this estimator outperforms the standard likelihood based estimator in approximating the true unknown distribution of the data as well as in out of sample forecasting accuracy we verify the new estimation method in a monte carlo study and investigate the role of different weights in different settings in the context of forecasting gross domestic product growth this key variable is typically observed at a low quarterly frequency while the supporting variables are observed at a high monthly frequency we adopt a low frequency representation of the mixed frequency dynamic factor model and discuss the computational efficiencies of this approach in our empirical study for the u s economy we present improvements in nowcasting and forecasting accuracy when the weighted likelihood based estimation procedure is adopted

kalman filtering with intermittent observations weak convergence to a stationary distribution the paper studies the asymptotic behavior of discrete time random riccati equations rre arising in kalman filtering when the arrival of the observations is described by a bernoulli independent and identically distributed i i d process we model the rre as an order preserving strongly sublinear random dynamical system rds under a sufficient condition stochastic boundedness and using a limit set dichotomy result for order preserving strongly sublinear rds we establish the asymptotic properties of the rre the sequence of random prediction error covariance matrices converges weakly to a unique invariant distribution whose support exhibits fractal behavior for stabilizable and detectable systems stochastic boundedness and hence weak convergence holds for any nonzero observation packet arrival probability and in particular we can establish weak convergence at operating arrival rates well below the critical probability for mean stability the resulting invariant measure in that situation does not possess a first moment we apply the weak feller property of the markov process governing the rre to characterize the support of the limiting invariant distribution as the topological closure of a countable set of points which in general is not dense in the set of positive semi definite matrices we use the explicit characterization of the support of the invariant distribution and the almost sure a s ergodicity of the sample paths to easily compute statistics of the invariant distribution a one dimensional example illustrates that the support is a fractured subset of the non negative reals with self similarity properties

asymptotics for parametric garch in mean models abstract in this paper we develop an asymptotic theory for the quasi maximum likelihood estimator qmle of the parametric garch in mean model the asymptotics is based on a study of the volatility as a process of the model parameters the proof makes use of stochastic recurrence equations for this random function and uses exponential inequalities to localize the problem our results show why the asymptotics for this specification is quite complex although it is a rather standard parametric model nevertheless our theory does not yet treat all standard specifications of the mean function

recursive state estimation for uncertain systems with an integral quadratic constraint this paper considers a robust state estimation problem for a class of uncertain systems where the noise and uncertainty are modeled deterministically via an integral quadratic constraint the robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint

brief control of singularly perturbed systems with markovian jump parameters an h approach in this paper we study the problem of h control for singularly perturbed linear continuous time systems with markovian jump parameters the system under consideration is described by a state space model consisting of slow and fast dynamics with a continuous time discrete state markov process taking values on a finite set on the basis of reduced order technique our attention is focused on the designing of state feedback control such that both stochastic stability and a prescribed h performance for the full order system are achieved it has been shown that the above problem can be solved if a set of coupled riccati equations has solution furthermore the asymptotic structure of composite mode dependent controller is characterized which shows that the controller is independent of the singular perturbation e when e is sufficiently small

robust stability of a class of uncertain markov jump nonlinear systems this note addresses the problem of robust stability analysis for a class of markov jump nonlinear systems subject to polytopic type parameter uncertainty a condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed an estimate of a robust domain of attraction of the origin is also provided the approach is based on a stochastic lyapunov function with polynomial dependence on the system state and uncertain parameters a numerical example illustrates the proposed result

h sup infinity control for nonlinear systems with output feedback the basic question of nonlinear h sup infinity control theory is to decide for a given two port system when feedback that makes the full system dissipative and internally stable exists this problem can also be viewed as a question about circuits and after translation also has a game theoretic statement several necessary conditions for solutions to exist are presented and sufficient conditions for a certain construction to lead to a solution are given

sensitivity penalization based robust state estimation for uncertain linear systems this technical note deals with robust state estimation when parametric uncertainties nonlinearly affect a plant state space model based on a simultaneous minimization of nominal estimation errors and their sensitivities an analytic solution is derived for the optimal estimator which can be recursively realized this estimator has a form similar to the robust estimator of and its computational complexity is comparable to the kalman filter under certain conditions this robust estimator is proved to converge to a stable system its estimation errors have a bounded covariance matrix and the estimate is asymptotically unbiased numerical simulations show that the obtained estimator has nice estimation performances

conditional central algorithms for worst case set membership identification and filtering this paper deals with conditional central estimators in a set membership setting the role and importance of these algorithms in identification and filtering is illustrated by showing that problems like worst case optimal identification and state filtering in contexts in which disturbances are described through norm bounds are reducible to the computation of conditional central algorithms the conditional chebyshev center problem is solved for the case when energy norm bounded disturbances are considered a closed form solution is obtained by finding the unique real root of a polynomial equation in a semi infinite interval

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

kalman filtering with intermittent observations convergence for semi markov chains and an intrinsic performance measure this technical note shows that the stationary distribution for the covariance of kalman filtering with intermittent observations exists under mild conditions for a very general class of packet dropping models semi markov chain these results are proved using the geometric properties of riccati recursions with respect to a particular riemannian distance moreover the riemannian mean induced by that distance is always bounded therefore it can be used for characterizing the performance of the system for regimes where the moments of the covariance do not exist other interesting properties of that mean include the symmetry between covariance and information matrices averaging covariances or their inverse gives the same result and its interpretation in information geometry as the natural mean for the manifold of gaussian distributions

einstein solvmanifolds existence and non existence questions the aim of this paper is to study the problem of which solvable lie groups admit an einstein left invariant metric the space mathcal n of all nilpotent lie brackets on mathbb r n parametrizes a set of n 1 dimensional rank one solvmanifolds s mu mu in mathcal n containing the set of all those which are einstein in that dimension the moment map for the natural gl n action on mathcal n evaluated at mu in mathcal n encodes geometric information on s and suggests the use of strong results from geometric invariant theory for instance the functional on mathcal n whose critical points are precisely the einstein s s is the square norm of this moment map we use a gl n invariant stratification for the space mathcal n and show that there is a strong interplay between the strata and the einstein condition on the solvmanifolds s as an application we obtain criteria to decide whether a given nilpotent lie algebra can be the nilradical of a rank one einstein solvmanifold or not we find several examples of mathbb n graded even 2 step nilpotent lie algebras which are not a classification in the 7 dimensional 6 step case and an existence result for certain 2 step algebras associated to graphs are also given

technical communique robust state estimation for uncertain discrete time stochastic systems with missing measurements in this paper results of robust estimation of zhou 2010a are extended to state estimation with missing measurements a new procedure is derived which inherits the main properties of that of zhou 2010a in this extension a covariance matrix used in the recursions is replaced by its estimate which makes its asymptotic property investigation mathematically difficult though introducing a monotonic function and using the so called squeeze rule this new robust estimator is proved to converge to a stable system numerical simulation results indicate that the proposed estimator may have an estimation accuracy better than the estimator of wang yang daniel and liu 2005

trivial central extensions of lie bialgebras abstract from a lie algebra g satisfying z g 0 and 2 g g 0 in particular for g semisimple we describe explicitly all lie bialgebra structures on extensions of the form l g k in terms of lie bialgebra structures on g not necessarily factorizable nor quasi triangular and its biderivations for any field k of characteristic different form 2 3 if moreover g g g then we describe also all lie bialgebra structures on extensions l g k n in interesting cases we characterize the lie algebra of biderivations

disturbance attenuation and h sub infinity control via measurement feedback in nonlinear systems a solution to the problem of disturbance attenuation via measurement feedback with internal stability is presented for an affine nonlinear system it is shown that the concept of disturbance attenuation in the sense of truncated l sub 2 norms can be given an interpretation in terms of the response to periodic inputs in the sense of rms amplitude even in the nonlinear setup in the case of state feedback a family of controllers is also provided the proofs of all these results are simple and provide deeper insight even in the analysis of the corresponding linear control problem

robust filtering for linear systems with convex bounded uncertain time varying parameters this note addresses the design of robust h2 filters for linear systems with a state space model subject to time varying uncertain parameters with limited variation the uncertain parameters and their rate of variation are assumed to belong to a given convex bounded polyhedral domain a method based on a parameter dependent lyapunov function is proposed for designing a linear stationary asymptotically stable filter with a guaranteed average error variance irrespective of the uncertain parameters the proposed design is formulated in terms of linear matrix inequalities

robust h_ infty fuzzy control approach for a class of markovian jump nonlinear systems this paper addresses the problem of stabilizing a class of nonlinear systems subject to markovian jump parameters using a robust stochastic fuzzy controller with hinfin performance the class of jump nonlinear systems considered is described by a fuzzy model composed of two levels a crisp level which represents the jumps and a fuzzy level which represents the system nonlinearities considering the approximation error between the fuzzy model and the jump nonlinear system as norm bounded uncertainties we develop a systematic technique based on a coupled lyapunov function to obtain a robust stochastic fuzzy controller which guarantees the l2 gain of the closed loop system in respect to external inputs to be equal to or less than a prescribed value a simulation example on an industrial power plant operating in a cogeneration scheme is presented to illustrate the effectiveness of the proposed stabilizing controller in reducing oscillations as well as maintaining a desired operation condition in the presence of fluctuations in the local load

l sub 2 gain analysis of nonlinear systems and nonlinear state feedback h sub infinity control previously obtained results on l2 gain analysis of smooth nonlinear systems are unified and extended using an approach based on hamilton jacobi equations and inequalities and their relation to invariant manifolds of an associated hamiltonian vector field on the basis of these results a nonlinear analog is obtained of the simplest part of a state space approach to linear h sub infinity control namely the state feedback h sub infinity optimal control problem furthermore the relation with h sub infinity control of the linearized system is dealt with

lie bialgebra structures on 2 step nilpotent graph algebras abstract we generalize a result on the heisenberg lie algebra that gives restrictions to possible lie bialgebra cobrackets on 2 step nilpotent algebras with some additional properties for the class of 2 step nilpotent lie algebras coming from graphs we describe these extra properties in a very easy graph combinatorial way we exhibit applications for f n the free 2 step nilpotent lie algebra

nonlinear state estimation for uncertain systems with an integral constraint this paper considers a problem of robust filtering for a class of uncertain nonlinear systems the solution involves a set valued state estimate that is obtained by solving a hamilton jacobi bellman equation in addition a less computationally intensive approximate solution to the problem is obtained for filtering problems defined over a large time interval the paper also presents an approximate solution to the robust filtering problem which leads to a robust version of the extended kalman filter

asymptotic behavior of recursive state estimations with intermittent measurements convergence rate and stationary distribution approximation are investigated in this paper for both the covariance matrix of the kalman filter and the pseudo covariance matrix of a robust recursive state estimator developed by us when the measurement dropping process is described by a markov chain and an associated plant is both controllable and observable it is proved that if the dropping probability is less than 1 these two matrices converge exponentially to a stationary distribution independent of its initial values moreover when they are initialized with the stabilizing solution of an associated algebraic riccati equation both of them are shown to converge to an ergodic process based on these results two approximations are derived for their stationary probability distributions as well as a bound of approximation errors it has been made clear that rather than the delta function suggested by kar and moura a series of delta functions give a more accurate approximation and replacement of these estimators update gain by a constant matrix usually deteriorates their steady estimation accuracy a numerical example is provided to illustrate the obtained theoretical results

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

diversity effects in kalman filtering over rayleigh fading channels a scalar first order gauss markov signal is sent over d parallel i i d rayleigh fading channels using uncoded transmission assuming perfect channel estimation at the receiver the optimal mmse estimator is the kalman filter with random instantaneous estimation error variance statistical characteristics of the instantaneous estimation error variance are studied to characterize the estimation quality one such characteristic is the estimation error outage which probabilistically depicts how often the value of the instantaneous estimation error variance exceeds a certain threshold in this paper we study the effect of channel diversity on the estimation error outage probability we show that for a certain range of outage thresholds the estimation error outage probability decreases with inverse of d th power of the average signal to noise ratio at the receiver side this means that analogous to the context of digital communication over fading channels our result implies a diversity order of d in estimating the input process

moderate deviations of a random riccati equation the paper characterizes the invariant filtering measures resulting from kalman filtering with intermittent observations in which the observation arrival is modeled as a bernoulli process with packet arrival probability our prior work showed that for 0 the sequence of random conditional error covariance matrices converges weakly to a unique invariant distribution this paper shows that as approaches one the family 0 satisfies a moderate deviations principle with good rate function i 1 as 1 the family converges weakly to the dirac measure p concentrated on the fixed point of the associated discrete time riccati operator 2 the probability of a rare event an event bounded away from p under decays to zero as a power law of 1 as 1 and 3 the best power law decay exponent is obtained by solving a deterministic variational problem involving the rate function i for specific scenarios the paper develops computationally tractable methods that lead to efficient estimates of rare event probabilities under

robust recursive state estimation with random measurement droppings a recursive state estimation procedure is derived for a linear time varying system with both parametric uncertainties and stochastic measurement droppings this estimator has a similar form as that of kalman filter with intermittent observations but its parameters should be adjusted when a plant output measurement arrives a new recursive form is derived for the pseudo covariance matrix of estimation errors based on a riemannian metric for positive definite matrices some necessary and sufficient conditions have been obtained for the strict contractiveness of this recursion it has also been proved that under some controllability and observability conditions as well as some weak requirements on measurement arrival probability the update gain of this recursive robust state estimator and the mean of its squared estimation errors converge in probability one respectively to a corresponding stationary distribution numerical simulation results show that estimation accuracy of the suggested procedure is more robust against parametric modelling errors than kalman filter

kalman filtering with intermittent observations motivated by navigation and tracking applications within sensor networks we consider the problem of performing kalman filtering with intermittent observations when data travel along unreliable communication channels in a large wireless multihop sensor network the effect of communication delays and loss of information in the control loop cannot be neglected we address this problem starting from the discrete kalman filtering formulation and modeling the arrival of the observation as a random process we study the statistical convergence properties of the estimation error covariance showing the existence of a critical value for the arrival rate of the observations beyond which a transition to an unbounded state error covariance occurs we also give upper and lower bounds on this expected state error covariance

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

asymptotic normality of the quasi maximum likelihood estimator for multidimensional causal processes strong consistency and asymptotic normality of the quasi maximum likelihood estimator qmle are given for a general class of multidimensional causal processes for particular cases already studied in the literature for instance univariate or multivariate garch arch arma garch processes the assumptions required for establishing these results are often weaker than existing conditions the qmle asymptotic behavior is also given for numerous new examples of univariate or multivariate processes for instance tarch or nlarch processes

convergence of nonlinear observers on bbr n with a riemannian metric part i we study how convergence of an observer whose state lives in a copy of the given system s space can be established using a riemannian metric we show that the existence of an observer guaranteeing the property that a riemannian distance between system and observer solutions is nonincreasing implies that the lie derivative of the riemannian metric along the system vector field is conditionally negative moreover we establish that the existence of this metric is related to the observability of the system s linearization along its solutions moreover if the observer has an infinite gain margin then the level sets of the output function are geodesically convex conversely we establish that if a complete riemannian metric has a lie derivative along the system vector field that is conditionally negative and is such that the output function has a monotonicity property then there exists an observer with an infinite gain margin

intrinsically bayesian robust kalman filter an innovation process approach in many contemporary engineering problems model uncertainty is inherent because accurate system identification is virtually impossible owing to system complexity or lack of data on account of availability time or cost the situation can be treated by assuming that the true model belongs to an uncertainty class of models in this context an intrinsically bayesian robust ibr filter is one that is optimal relative to the cost function in the classical sense and the prior distribution over the uncertainty class in the bayesian sense ibr filters have previously been found for both wiener and granulometric morphological filtering in this paper we derive the ibr kalman filter that performs optimally relative to an uncertainty class of state space models introducing the notion of bayesian innovation process and the bayesian orthogonality principle we show how the problem of designing an ibr kalman filter can be reduced to a recursive system similar to the classical kalman recursive equations except with effective counterparts such as the effective kalman gain matrix after deriving the recursive ibr kalman equations for discrete time we use the limiting method to obtain the ibr kalman bucy equations for continuous time finally we demonstrate the utility of the proposed framework for two real world problems sensor networks and gene regulatory network inference

h filtering for linear periodic systems with parameter uncertainty abstract this paper focuses on h filtering for a class of linear periodic systems with a certain type of norm bounded time varying parameter uncertainty which appears in both the state and output matrices the problem addressed is the design of a linear periodic estimator that guarantees both the quadratic stability and and prescribed h performance on infinite horizon for the estimation error for all admissible parameter uncertainties a solution to this problem is obtained via a riccati equation approach

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

optimal filtering with random sensor delay multiple packet dropout and uncertain observations this paper studies the problem of optimal filtering of discrete time systems with random sensor delay multiple packet dropout and uncertain observation the random sensor delay multiple packet dropout or uncertainty in observation is transformed to a stochastic parameter in the system representation a new formulation enables us to design an optimal filter for a system with multiple packet dropout in sensor data based on a stochastic definition of the norm of a system with a stochastic parameter new relations for stochastic norm are derived the stochastic norm of the estimation error is used as a criterion for the filter design the relations derived for the new norm definition are used to obtain a set of linear matrix inequalities lmis to solve the filter design problems simulation examples show the effectiveness of the proposed method

mixed norm h 2 h regulation and estimation the discrete time case abstract a discrete time h2 static output feedback design problem involving a constraint on h disturbance attenuation is addressed and state space formulae are derived the dual problem of discrete time dynamic estimation with an h error bound is also addressed these results are analogous to results obtained previously for the continuous time problem

a framework for state space estimation with uncertain models develops a framework for state space estimation when the parameters of the underlying linear model are subject to uncertainties compared with existing robust filters the proposed filters perform regularization rather than deregularization it is shown that under certain stabilizability and detectability conditions the steady state filters are stable and that for quadratically stable models the filters guarantee a bounded error variance moreover the resulting filter structures are similar to various time and measurement update prediction and information forms of the kalman filter albeit ones that operate on corrected parameters rather than on the given nominal parameters simulation results and comparisons with spl hscr sub spl infin guaranteed cost and set valued state estimation filters are provided

set membership filtering for discrete time systems with nonlinear equality constraints in this technical note the problem of set membership filtering is considered for discrete time systems with nonlinear equality constraint between their state variables the nonlinear equality constraint is first linearized and transformed into a state linear equality constraint with two uncertain quantities related to linearizing truncation error and base point error s procedure method is then applied to merge all inequalities into one inequality and the solution to the unconstrained set membership filtering problem is provided the set membership filter with state constraint is finally derived from projecting the unconstrained set membership filter onto the constrained surface by using finsler s lemma a time varying linear matrix inequality optimization based approach is proposed to design the set membership filter with nonlinear equality constraint a recursive algorithm is developed for computing the state estimate ellipsoid that guarantees to contain the true state an illustrative example is provided to demonstrate the effectiveness of the proposed set membership filtering with nonlinear equality constraint

h control with transients in h infty or uniformly optimal control problems it is usually assumed that the system initial conditions are zero in this paper an h infty like control problem that incorporates uncertainty in initial conditions is formulated this is done by defining a worst case performance measure both finite and infinite horizon problems are considered necessary and sufficient conditions are derived for the existence of controllers that yield a closed loop system for which the above mentioned performance measure is less than a prespecified value state space formulae for the controllers are also presented

mean square stability for kalman filtering with markovian packet losses this paper studies the stability of kalman filtering over a network subject to random packet losses which are modeled by a time homogeneous ergodic markov process for second order systems necessary and sufficient conditions for stability of the mean estimation error covariance matrices are derived by taking into account the system structure while for certain classes of higher order systems necessary and sufficient conditions are also provided to ensure stability of the mean estimation error covariance matrices all stability criteria are expressed by simple inequalities in terms of the largest eigenvalue of the open loop matrix and transition probabilities of the markov process their implications and relationships with related results in the literature are discussed

nonexpansiveness of the resolvent average abstract we show that the resolvent average for positive definite matrices which interpolates between the harmonic and the arithmetic means contracts the thompson metric on the convex cone of positive definite matrices classical results depending on the nonexpansive property of the arithmetic average are considered in the context of the resolvent average in particular resolvent power mean approximation to the karcher mean and ferrante and levy like matrix equations are investigated

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

mutual information of wireless channels and block jacobi ergodic operators shannon s mutual information of a random multiple antenna and multipath time varying channel is studied in the general case where the process constructed from the channel coefficients is an ergodic and stationary process which is assumed to be available at the receiver from this viewpoint the channel can also be represented by an ergodic self adjoint block jacobi operator which is close in many aspects to a block version of a random schrodinger operator the mutual information is then related to the so called density of states of this operator in this paper it is shown that under the weakest assumptions on the channel the mutual information can be expressed in terms of a matrix valued stochastic process coupled with the channel process this allows numerical approximations of the mutual information in this general setting moreover assuming further that the channel coefficient process is a markov process a representation for the mutual information offset in the large signal to noise ratio regime is obtained in terms of another related markov process this generalizes previous results from levy et al it is also illustrated how the mutual information expressions that are closely related to those predicted by the random matrix theory can be recovered in the large dimensional regime

adaptive backstepping controller design for stochastic jump systems in this technical note we improve the results in a paper by shi et al in which problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps were considered however the system considered is switching stochastically between different subsystems the dynamics of the jump system can not stay on each sliding surface of subsystems forever therefore it is difficult to determine whether the closed loop system is stochastically stable in this technical note the backstepping techniques are adopted to overcome the problem in a paper by shi et al the resulting closed loop system is bounded in probability it has been shown that the adaptive control problem for the markovian jump systems is solvable if a set of coupled linear matrix inequalities lmis have solutions a numerical example is given to show the potential of the proposed techniques

multiobjective filter design for uncertain stochastic time delay systems this note addresses the problem of robust multiobjective filtering for discrete time delay systems with mixed stochastic and deterministic uncertainties in addition to unmodeled nonlinearities a procedure is developed for the design of linear and exponentially stable filters with a bounded error variance exponential rate of decay and robust performance for the error system

regularized robust filters for time varying uncertain discrete time systems this note develops robust filters for time varying uncertain discrete time systems the developed filters are based on a data regularization solution and they enforce a minimum state error variance property simulation results confirm their superior performance over other robust filter designs

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

performance of ensemble kalman filters in large dimensions contemporary data assimilation often involves more than a million prediction variables ensemble kalman filters enkf have been developed by geoscientists they are successful indispensable tools in science and engineering because they allow for computationally cheap low ensemble state approximation for extremely large dimensional turbulent dynamical systems the practical finite ensemble filters like enkf necessarily involve modifications such as covariance inflation and localization and it is a genuine mystery why they perform so well with small ensemble sizes in large dimensions this paper provides the first rigorous stochastic analysis of the accuracy and covariance fidelity of enkf in the practical regime where the ensemble size is much smaller than the large ambient dimension for enkfs with random coefficients a challenging issue overcome here is that enkf in huge dimensions introduces unavoidable bias and model errors that need to be controlled and estimated 2017 the authors communications on pure and applied mathematics is published by the courant institute of mathematics and wiley periodicals inc

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

solvable lie algebras and graphs abstract we define a solvable extension of the graph 2 step nilpotent lie algebras of 5 by adding elements corresponding to the 3 cliques of the graph we study some of their basic properties and we prove that two such lie algebras are isomorphic if and only if their graphs are isomorphic we also briefly discuss some metric properties providing examples of homogeneous spaces with nonpositive curvature operator and solvsolitons

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

robust h sub spl infin control for linear discrete time systems with norm bounded nonlinear uncertainties this paper studies the problem of robust control of a class of uncertain discrete time systems the class of uncertain systems is described by a state space model with linear nominal parts and norm bounded nonlinear uncertainties in the state and output equations the authors address the problem of robust h sub spl infin control in which both robust stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainties it has been shown that instead of the nonlinear uncertain system one may only consider a related linear uncertain system and thus a linear static state feedback control law is designed which is in terms of a riccati inequality

on asymptotic behaviors of a sensitivity penalization based robust state estimator abstract asymptotic properties are investigated in this paper for the robust state estimator derived by zhou 2008 11 a new formula is derived for the update of the pseudo covariance matrix of estimation errors in the case where plant nominal parameters are time invariant it is shown that in order to guarantee that this pseudo covariance matrix converges to a constant positive definite matrix it is necessary and sufficient that some stabilizability and detectability conditions are satisfied it is also proved that when these conditions are satisfied the robust estimator converges to a stable time invariant system moreover when the system is exponentially stable this estimate is asymptotically unbiased and its estimation errors are upper bounded

optimal linear state estimation over a packet dropping network using linear temporal coding we consider the problem of linear minimum mean square error estimation for a discrete time system over a packet dropping network in order to improve the estimation performance different from the standard approach of sending the current measurement data we choose sending a linear combination of the current measurement and the measurement collected at the previous time a method called linear temporal coding we assume the packet arrival sequence is unknown and the noise contained in the packet may come from sensor or communication channel in an effort to cope with colored noise caused by measurement combination after comparing with the classic state augmentation approach and measurement differencing approach we derive a recursive estimation algorithm by means of orthogonal projection principle and innovation sequence approach our algorithm consists of two parts smooth and estimate for large measurement noise case numerical example shows the benefit of using linear temporal coding strategy compared with directly sending the current data on the contrary when communication noise plays the dominating role for scalar system we prove there is no benefit to choose this scheme

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

bounded real lemma for linear systems with finite discrete jumps the problem of strict bounded realness for linear systems with finite discrete jumps is investigated in this paper several versions of the strict bounded real lemma for such systems in both the finite and infinite horizon cases are obtained in terms of either a riccati differential equation or riccati differential inequality with finite discrete jumps these results encompass both existing continuous time and discretetime strict bounded real lemmas

the contraction rate in thompson s part metric of order preserving flows on a cone application to generalized riccati equations abstract we give a formula for the lipschitz constant in thompson s part metric of any order preserving flow on the interior of a possibly infinite dimensional closed convex pointed cone this shows that in the special case of order preserving flows a general characterization of the contraction rate in thompson s part metric given by nussbaum leads to an explicit formula as an application we show that the flow of the generalized riccati equation arising in stochastic linear quadratic control is a local contraction on the cone of positive definite matrices and characterize its lipschitz constant by a matrix inequality we also show that the same flow is no longer a contraction in other invariant finsler metrics on this cone including the standard invariant riemannian metric this is motivated by a series of contraction properties concerning the standard riccati equation established by bougerol liverani wojtkowski lawson lee and lim we show that some of these properties do and that some other do not carry over to the generalized riccati equation

robust filtering for linear time invariant continuous systems the problem of robust filtering for linear time invariant lti continuous systems subject to parametric uncertainties is treated in this paper through transfer function and polynomial representations and then in the state space domain the basic idea consists of introducing the gradient of the estimation error with respect to the uncertain parameters in the optimization scheme via a epsiv contaminated model the general solution to the problem is given in the transfer function representation while in the polynomial framework the causal estimator is obtained by means of a spectral factorization and a diophantine equation the state space realization of the causal estimator is discussed examples show the ability of the proposed technique to provide a reliable estimation in presence of model uncertainty

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

optimal linear state estimator with multiple packet dropouts this technical note is concerned with the optimal linear estimation problem in the presence of multiple packet dropouts in both sensor to controller and controller to actuator channels the considered stochastic packet dropouts are independent and bernoulli distributed based on a linear packet dropout model with stochastic parameters a linear minimum variance lmv filter is proposed using the orthogonality principle a sufficient condition for convergence of the steady state lmv filter under a dc controller output is also given simulation results show the effectiveness of the proposed filter

robust h sub 2 h sub spl infin state estimation for systems with error variance constraints the continuous time case the paper is concerned with the state estimator design problem for perturbed linear continuous time systems with h sub spl infin norm and variance constraints the perturbation is assumed to be time invariant and norm bounded and enters into both the state and measurement matrices the problem we address is to design a linear state estimator such that for all admissible measurable perturbations the variance of the estimation error of each state is not more than the individual prespecified value and the transfer function from disturbances to error state outputs satisfies the prespecified h sub spl infin norm upper bound constraint simultaneously existence conditions of the desired estimators are derived in terms of riccati type matrix inequalities and the analytical expression of these estimators is also presented a numerical example is provided to show the directness and effectiveness of the proposed design approach

brief paper weighted h model reduction for linear switched systems with time varying delay this paper is concerned with model reduction for continuous time linear switched systems with time varying delay for a given stable switched system our attention is focused on construction of a reduced order model such that the error system is exponentially stable with a prescribed weighted performance by applying the average dwell time approach and the piecewise lyapunov function technique delay dependent deley independent sufficient conditions are proposed in terms of linear matrix inequality lmi to guarantee the exponential stability and the weighted performance for the error system the model reduction problem is solved by using the projection approach which casts the model reduction problem into a sequential minimization problem subject to lmi constraints by employing the cone complementary linearization algorithm a numerical example is provided to illustrate the effectiveness of the proposed theory

coordinated one step optimal distributed state prediction for a networked dynamical system a new recursive one step state prediction procedure is derived for a networked dynamic system under the coordination of a collaboration unit that provides optimal update gains for each individual subsystem utilizing merely system parameters this predictor estimates plant s local states based only on local system output measurements this estimator can be easily realized in a distributed way and can also be simply scaled to systems with a large amount of subsystems provided it has enough communication and storage capacities it is proved that when prediction error variances are adopted in performance comparisons the optimal gain matrix is usually unique recursive and explicit expressions are derived for both this optimal gain matrix and the covariance matrix of the corresponding prediction errors the optimal gain matrix for every subsystem in this distributed recursive predictor has been shown to be equal to that of the well known kalman filter utilizing only local system output measurements which makes it possible to robustify this state predictor using a sensitivity penalization approach numerical simulation results illustrate that prediction accuracy of the suggested procedure may sometimes be as good as that of the lumped kalman filter