brief design and analysis of discrete time robust kalman filters in this paper the problem of finite and infinite horizon robust kalman filtering for uncertain discrete time systems is studied the system under consideration is subject to time varying norm bounded parameter uncertainty in both the state and output matrices the problem addressed is the design of linear filters having an error variance with an optimized guaranteed upper bound for any allowed uncertainty a novel technique is developed for robust filter design this technique gives necessary and sufficient conditions to the design of robust quadratic filters over finite and infinite horizon in terms of a pair of parameterized riccati equations feasibility and convergence properties of the robust quadratic filters are also analyzed

limit cycles of planar quadratic differential equations abstract since hilbert posed the problem of systematically counting and locating the limite cycles of polynomial systems on the plane in 1900 much effort has been expended in its investigation a large body of literature chiefly by chinese and soviet authors has addressed this question in the context of differential equations whose field is specified by quadratic polynomials this paper considers the class of quadratic differential equations which admit a unique equilibrium state and establish sufficient conditions for the existence and uniqueness of limit cycles the work is based upon insights and techniques developed in an earlier analysis of such systems motivated by questions from mathematical control theory

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

the number of limit cycles of certain polynomial differential equations two dimensional differential systems are considered where p and q are polynomials the question of interest is the maximum possible numberof limit cycles of such systems in terms of the degree of p and q an algorithm is described for determining a so called focal basis this can be implemented on a computer estimates can then be obtained for the number of small amplitude limit cycles the technique is applied to certain cubic systems a class of examples with exactly five small amplitude limit cycles is constructed quadratic systems are also considered

nonsymmetric macdonald polynomials and demazure characters we establish a connection between a specialization of the nonsymmetric macdonald polynomials and the demazure characters of the corresponding affine kac moody algebra this allows us to obtain a representation theoretical interpretation of the coefficients of the expansion of the specialized symmetric macdonald polynomials in the basis formed by the irreducible characters of the associated finite lie algebra

nonuniform filter bank design with noises this work solves the signal reconstruction problem involving nonuniform filter bank systems with rational decimation factors and noise three main nonuniform filter bank systems i e filter block decimator fbd structure upsampler filter downsampler ufd structure and tree structure are included in this study according to different operating conditions two different signal reconstruction problems for nonuniform filter bank systems with noise under the unknown but identifiable input signal model and the unknown input signal model are discussed respectively at the first stage a unified block state space model for different nonuniform filter bank systems with noise is developed then by incorporating the identified input signal model with this unified state space model and appropriate choice of the augmented state vector the signal reconstruction problem is reduced to an equivalent state estimation problem for resulting augmented systems if the input signal is identifiable if the input signal is lacking in modeling the signal reconstruction is discussed from the minimax estimation point of view two state estimation techniques involving robust kalman filtering and h sub spl infin filtering are employed respectively to treat the signal reconstruction problem of nonuniform filter bank systems according to different a priori knowledge of the input signal finally several numerical examples are presented to illustrate the proposed algorithms and exhibit the performances

robust kalman filtering for discrete time varying uncertain systems with multiplicative noises in this paper a robust finite horizon kalman filter is designed for discrete time varying uncertain systems with both additive and multiplicative noises the system under consideration is subject to both deterministic and stochastic uncertainties sufficient conditions for the filter to guarantee an optimized upper bound on the state estimation error variance for admissible uncertainties are established in terms of two discrete riccati difference equations a numerical example is given to show the applicability of the presented method

robust filtering via semidefinite programming with applications to target tracking in this paper we propose a novel finite horizon discrete time time varying filtering method based on the robust semidefinite programming sdp technique the proposed method provides robust performance in the presence of norm bounded parameter uncertainties in the system model the robust performance of the proposed method is achieved by minimizing an upper bound on the worst case variance of the estimation error for all admissible systems our method is recursive and computationally efficient in our simulations the new method provides superior performance to some of the existing robust filtering approaches in particular when applied to the problem of target tracking the new method has led to a significant improvement in tracking performance our work shows that the robust sdp technique and the interior point algorithms can bring substantial benefits to practically important engineering problems

estimation of systems with statistically constrained inputs abstract this paper discusses the estimation of a class of discrete time linear stochastic systems with statistically constrained unknown inputs ui which can represent an arbitrary combination of a class of un modeled dynamics random ui with unknown covariance matrix and deterministic ui in filter design an upper bound filter is explored to compute recursively and adaptively the upper bounds of covariance matrices of the state prediction error innovation and state estimate error furthermore the minimum upper bound filter mubf is obtained via online scalar parameter convex optimization in pursuit of the minimum upper bounds two examples a system with multiple piecewise uis and a continuous stirred tank reactor cstr are used to illustrate the proposed mubf scheme and verify its performance

finite horizon robust kalman filter design we study the problem of finite horizon kalman filtering for systems involving a norm bounded uncertain block a new technique is presented for robust kalman filter design this technique involves using multiple scaling parameters that ran be optimized by solving a semidefinite program the use of optimized scaling parameters leads to an improved design a recursive design method that can be applied to real time applications is also proposed

robust finite horizon minimax filtering for discrete time stochastic uncertain systems we study a finite horizon robust minimax filtering problem for time varying discrete time stochastic uncertain systems the uncertainty in the system is characterized by a set of probability measures under which the stochastic noises driving the system are defined the optimal minimax filter has been found by applying techniques of risk sensitive lqg control the structure and properties of resulting filter are analyzed and compared to h and kalman filters

robust wiener filtering with non parametric spectral uncertainty in this article robust least squares filtering problems are considered for non parametric multivariate spectral uncertainty defined by the so called spectral band and generalised moment constraints its major aim is to provide a basis for computing approximate solutions to worst case wiener filtering optimisation problems involving causal filters and multivariate signals it hinges upon associating upper and lower bounds on the minimum worst case performance achievable with causal filters with linear cost linear matrix inequality lc lmi constraint optimisation problems on the basis of a lagrangean duality formulation for the worst case least squares performance of a given filter upper bounds on it are obtained as the optimal values of lc lmi problems then for linearly parameterised classes of filter transfer functions a causal filter which optimises such an upper bound on worst case performance can also be obtained from an lc lmi optimisation problem to estimate the amount of conservatism incur

robust mimo equalization for non parametric channel model uncertainty in this paper three mimo robust equalization problems are considered for non parametric classes of channel models defined by weighted h2 or h balls of frequency responses and performance criteria based on h2 variance or h norms of error signals the approach pursued here centers on characterizing the worst case performance of candidate equalizers or upper bounds on it by means of dual lagrangian functionals then for linearly parametrized finite dimensional classes of candidate equalizers the corresponding robust equalization problems are converted into semi definite linear programming problems for which approximate solutions can be effectively computed a simple numerical example is presented involving h2 model uncertainty and error variance performance to illustrate for various levels of uncertainty the changes in the worst case performances of the nominally optimal equalizer and of the one in a specific linear class which minimizes the worst case error variance

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

distributed recursive filtering for stochastic systems under uniform quantizations and deception attacks through sensor networks this paper is concerned with the distributed recursive filtering problem for a class of discrete time delayed stochastic systems subject to both uniform quantization and deception attack effects on the measurement outputs the target plant is disturbed by the multiplicative as well as additive white noises a novel distributed filter is designed where the available innovations are from not only the individual sensor but also its neighboring ones according to the given topology attention is focused on the design of a distributed recursive filter such that in the simultaneous presence of time delays deception attacks and uniform quantization effects an upper bound for the filtering error covariance is guaranteed and subsequently minimized by properly designing the filter parameters via a gradient based method at each sampling instant furthermore by utilizing the mathematical induction a sufficient condition is established to ensure the asymptotic boundedness of the sequence of the error covariance finally a simulation example is utilized to illustrate the usefulness of the proposed design scheme of distributed filters

robust reduced order nonstrictly proper state estimation via the optimal projection equations with petersen hollot bounds a state estimation design problem involving parametric plant uncertainties is considered an error bound suggested by recent work of petersen and hollot is utilized for guaranteeing robust estimation necessary conditions which generalize the optimal projection equations for reduced order state estimation are used to characterize the estimator which minimizes the error bound the design equations thus effectively serve as sufficient conditions for synthesizing robust estimators an additional feature is the presence of a static estimation gain in conjunction with the dynamic kalman estimator i e a nonstrictly proper estimator

state estimation for stochastic complex networks with switching topology this technical note studies the state estimation problem for stochastic complex networks with switching topology a set of bernoulli random variables are used to describe the switching behavior of the network by using the structure of the extended kalman filter ekf a recursive estimator is developed for each node to guarantee an optimized upper bound on the state estimation error covariance despite the switching coupling and linearization errors compared with the existing results on state estimation for stochastic complex networks a distinct feature for the proposed estimator is that the estimation errors for all nodes are not formulated in an augmented vector so that the gain matrix can be determined separately for each node by solving two riccati like difference equations based on the stochastic analysis theory it is shown that the estimation error is bounded in mean square under certain conditions simulation results are provided to verify the effectiveness of the proposed estimator

h 2 robust filter design with performance certificate via convex programming in this paper a new approach to h 2 robust filter design is proposed both continuous and discrete time invariant systems subject to polytopic parameter uncertainty are considered after a brief discussion on some of the most expressive methods available for h 2 robust filter design a new one based on a performance certificate calculation is presented the performance certificate is given in terms of the gap produced by the robust filter between lower and upper bounds of a minimax programming problem where the h 2 norm of the estimation error is maximized with respect to the feasible uncertainties and minimized with respect to all linear rational and causal filters the calculations are performed through convex programming methods developed to deal with linear matrix inequality lmi many examples borrowed from the literature to date are solved and it is shown that the proposed method outperforms all other designs

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

minimum variance distortionless response estimators for linear discrete state space models for linear discrete state space models under certain conditions the linear least mean squares filter estimate has a convenient recursive predictor corrector format aka the kalman filter the purpose of this paper is to show that the linear minimum variance distortionless response mvdr filter shares exactly the same recursion except for the initialization which is based on a weighted least squares estimator if the mvdr filter is suboptimal in mean squared error sense it is an infinite impulse response distortionless filter a deconvolver which does not depend on the prior knowledge first and second order statistics on the initial state in other words the mvdr filter can be pre computed and its behaviour can be assessed in advance independently of the prior knowledge on the initial state

discrete time robust iterative learning kalman filtering for repetitive processes a discrete time robust iterative learning kalman filter is proposed for state estimation on repetitive process systems with norm bounded uncertainties in both the state and output matrices the filter design combines iterative learning control and robust kalman filtering by exploiting process repetitiveness

robust discrete time minimum variance filtering the bounded variance filtered estimation of the state of an uncertain linear discrete time system with an unknown norm bounded parameter matrix is considered an upper bound on the variance of the estimation error is found for all admissible systems and estimators are derived that minimize the latter bound we treat the finite horizon time varying case and the infinite time case where the nominal system model is time invariant in the special stationary case where it is known that the uncertain system is time invariant we provide a robust filter for all uncertainties that still keep the system asymptotically stable

unified forms for kalman and finite impulse response filtering and smoothing the kalman filter and smoother are optimal state estimators under certain conditions the kalman filter is typically presented in a predictor corrector format but the kalman smoother has never been derived in that format we derive the kalman smoother in a predictor corrector format thus providing a unified form for the kalman filter and smoother we also discuss unbiased finite impulse response ufir filters and smoothers which can provide a suboptimal but robust alternative to kalman estimators we derive two unified forms for ufir filters and smoothers and we derive lower and upper bounds for their estimation error covariances

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

optimal filtering for rm it mathhat o stochastic continuous time systems with multiple delayed measurements this technical note focuses on optimal filtering for ito stochastic continuous time systems with multiple delayed measurements stochastic analysis and calculus of stochastic variables are the main tools employed for the analysis and design for an ito stochastic system its stochastic differential and integral have a significant place and are different from that for other stochastic systems owing to the wiener or the brownian process in this technical note an ito stochastic continuous time system with multiple delayed measurements is first reduced to an equivalent system with delay free measurements by solving stochastic equation via the non singularity of the transition matrix instead of reorganizing the innovation then based on the delay free measurements the optimal filter is derived through calculation of the conditional expectation it is should be stressed that the optimal filter follows directly from the manipulation of the performance finally a short interest rate model in mathematical finance is chosen to demonstrate the design of the optimal filter via the approach proposed in the technical note

robust h sub 2 and h sub spl infin filters for uncertain lft systems in this note robust h sub 2 and h sub spl infin filter design problems are considered the uncertainties unstructured or structured are norm bounded and represented by linear fractional transformation lft the main result is that after upper bounding the objectives the problems of minimizing the upper bounds are converted to finite dimensional convex optimization problems involving linear matrix inequalities lmis these are extensions of well known results for systems with polytopic uncertainty it is shown that for the unstructured norm bounded uncertainty case the upper bounds are directly minimized without further overbounding yielding less conservative results than previously available an elementary numerical example is given to illustrate the results

robust h2 filtering for uncertain linear systems lmi based methods with parametric lyapunov functions abstract this paper addresses the design of robust h 2 filters for linear continuous time systems subject to parameter uncertainty in the state space model the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain two methods based on parameter dependent lyapunov functions are proposed for designing linear stationary asymptotically stable filters that assure asymptotic stability and a guaranteed h 2 performance irrespective of the uncertain parameters the proposed filter designs are given in terms of linear matrix inequalities which depend on a scalar parameter that should be searched for in order to optimize the filter performance

delayed unknown input observers for discrete time linear systems with guaranteed performance abstract in this paper we propose a state and unknown input observer for discrete time linear systems with bounded unknown inputs and measurement disturbances the design procedure is formulated using a set of linear matrix inequalities and leverages delayed or fixed lag estimates the observer error states and or user defined performance outputs are guaranteed to operate at certain performance bounds furthermore by employing sufficiently large delays the observer is guaranteed to provide exact asymptotic state and input estimates for minimum phase systems we demonstrate via numerical examples that the proposed observer can be used for a wider class of systems than those satisfying matching conditions

extended kalman filtering with stochastic nonlinearities and multiple missing measurements in this paper the extended kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon both deterministic and stochastic nonlinearities are included in the system model where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances the phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval 0 1 such a probability distribution is allowed to be any commonly used distribution over the interval 0 1 with known conditional probability the aim of the addressed filtering problem is to design a filter such that in the presence of both the stochastic nonlinearities and multiple missing measurements there exists an upper bound for the filtering error covariance subsequently such an upper bound is minimized by properly designing the filter gain at each sampling instant it is shown that the desired filter can be obtained in terms of the solutions to two riccati like difference equations that are of a form suitable for recursive computation in online applications an illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme

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

a direct approach to h sub 2 optimal deconvolution of periodic digital channels this paper studies the h sub 2 optimal deconvolution problem for periodic finite impulse response fir and infinite impulse response iir channels it shows that the h sub 2 norm of a periodic filter can be directly quantified in terms of periodic system matrices and linear matrix inequalities lmis without resorting to the commonly used lifting technique the optimal signal reconstruction problem is then formulated as an optimization problem subject to a set of matrix inequality constraints under this framework the optimization of both the fir and iir periodic deconvolution filters can be made convex solved using the interior point method and computed by using the matlab lmi toolbox the robust deconvolution problem for periodic fir and iir channels with polytopic uncertainties are further formulated and solved also by convex optimization and the lmis compared with the lifting approach to the design of periodic filters the proposed approach is simpler yet more powerful in dealing with multiobjective deconvolution problems and channel uncertainties especially for iir deconvolution filter design the obtained solutions are applied to the design of an optimal filterbank yielding satisfactory performance

competitive robust estimation for uncertain linear dynamic models in this paper two types of robust linear estimation problems for dynamic channel model uncertainty are considered with the aim of characterizing in computationally effective ways competitive robust estimators i e robust estimators that improve on the pointwise performance of minimax mse mean squared error estimators over the uncertain model set at the expense of a moderate increase in the worst case mse the first one corresponds to the minimization of the worst case value of an approximate regret function defined by a quadratic approximation of the lower mse envelope on the uncertain model set the second one corresponds to minimizing the nominal mse error while ensuring that the worst case estimation error does not exceed a prescribed value for uncertain classes defined by h 2 norm balls it is shown that these two types of estimation problems can be recast as semidefinite programming problems sdps for short numerical examples are presented for both the case of linear finite dimensional model classes firs of a given length and the case of nonparametric uncertain sets of causal real rational frequency responses suggesting that these two types of estimators can be attractive alternatives to the min max mse estimator for the case of spectral norm in the finite dimensional case or h infty norm in the nonparametric case the worst case mse and approximate regret for each candidate estimator are replaced by upper bounds obtained by lagrangian relaxation and somewhat conservative versions of the estimation problems previously mentioned are posed it is shown that these problems can also be recast as sdps

brief robust h filtering with error variance constraints for discrete time varying systems with uncertainty the robust h filtering problem with error variance constraints is considered for discrete time varying systems subject to norm bounded parameter uncertainties in both the state and the output matrices of the state space model sufficient conditions for a finite horizon filter to satisfy state estimation error variance constraints as well as prescribed h performance for all admissible perturbations are given in terms of two discrete riccati difference equations which are of a form suitable for recursive computation the results are extended to cover the case of stationary filtering over an infinite horizon for uncertain time invariant systems

on the discrete time bounded real lemma with application in the characterization of static state feedback h controllers abstract this paper deals with the discrete time bounded real lemma and its application in the characterization of all static state feedback h controllers for discrete time systems we first present two versions of the discrete time bounded real lemma the results apply to non minimal stable state space realizations and are given in terms of either the positive semi definite strong solution or the positive semi definite stabilizing solution of a discrete algebraic riccati equation based on the discrete time bounded real lemma we obtain a characterization of all static state feedback h controllers for discrete time systems as an application of the parameterization of all static state feedback h controllers we develop a solution to the discrete time h control problem via static output feedback also a numerical procedure is proposed to determine an output feedback gain

james stein state filtering algorithms in 1961 james and stein discovered a remarkable estimator that dominates the maximum likelihood estimate of the mean of a p variate normal distribution provided the dimension p is greater than two this paper extends the james stein estimator and highlights the benefits of applying these extensions to adaptive signal processing problems the main contribution of this paper is the derivation of the james stein state filter jssf which is a robust version of the kalman filter the jssf is designed for situations where the parameters of the state space evolution model are not known with any certainty in deriving the jssf we derive several other results we first derive a james stein estimator for estimating the regression parameter in a linear regression a recursive implementation which we call the james stein recursive least squares js rls algorithm is derived the resulting estimate although biased has a smaller mean square error than the traditional rls algorithm finally several heuristic algorithms are presented including a james stein version of the yule walker equations for ar parameter estimation

a new method to h2 robust filter design abstract in this paper a new method to h 2 robust filter design is proposed both continuous and discrete time settings are considered for systems subject to polytopic parameter uncertainty lower and upper bounds of the true cost are determined in order to evaluate the degree of sub optimality of the proposed robust filter the design method is based on the parametrization of all robust filters as a convex combination of kalman filters associated to each vertex of the uncertainty domain among all feasible filters the one minimizing a guaranteed h 2 cost of the estimation error is determined by a pure convex programming problem expressed in terms of linear matrix inequalities lmis the order of the robust filter is generally greater than the order of the plant a fact that contributes to reduce conservatism the proposed design technique is compared with other methods available in the literature in several examples solved the proposed method outperforms all other designs

non autonomous equations related to polynomial two dimensional systems periodic solutions of certain one dimensional non autonomous differential equations are investigated equation 1 4 the independent variable is complex the motivation which is explained in the introductory section is the connection with certain polynomial two dimensional systems several classes of coefficients are considered in each case the aim is to estimate the maximum number of periodic solutions into which a given solution can bifurcate under perturbation of the coefficients in particular we need to know when there is a full neighbourhood of periodic solutions we give a number of sufficient conditions and investigate the implications for the corresponding two dimensional systems

a robust h sub 2 filtering approach and its application to equalizer design for communication systems in this paper we aim at developing a robust h sub 2 filtering approach to the design of robust equalizers for communication systems the contents of this paper mainly include two parts first we present a robust h sub 2 filter design method for general multi input multioutput linear systems with norm bounded uncertainties in the system matrices based on the linear matrix inequality technique the characteristics of the equalization problem are taken into account in the filtering model considered here the advantage of the proposed method is that we can find the optimal solution to robust h sub 2 filtering problem at a reasonable computational burden second we apply the above method to the design of robust equalizers two generic examples are studied one for a single transmit and receive antenna system and another for a multiple transmit and receive antenna system both analytical and simulation results show that robust h sub 2 equalizer outperforms the zero forcing equalizer in both bit error rate and mean square errors in the whole simulated range of the signal to noise ratio snr when the channel is perturbed from its nominal value while for the nominal channel the robust h sub 2 equalizer performs better than the zero forcing equalizer when the snr is lower but it performs worse than the zero forcing equalizer when the snr is higher

robust weighted fusion time varying kalman smoothers for multisensor system with uncertain noise variances this paper addresses the design of robust weighted fusion time varying kalman smoothers for multisensor time varying system with uncertain noise variances by the augmented state approach according to the minimax robust estimation principle and the unbiased linear minimum variance ulmv optimal estimation rule the six robust weighted fusion time varying kalman smoothers are presented based on the worst case conservative system with the conservative upper bounds of noise variances the actual smoothing error variances of each fuser are guaranteed to have a minimal upper bound for all admissible uncertainties their robustness is proved by the lyapunov equation approach their robust accuracy relations are analyzed and proved specially the corresponding steady state robust kalman smoothers are also presented for multisensor time invariant system and the convergence in a realization between the time varying and steady state robust kalman smoothers is proved by the dynamic error system analysis desa method and dynamic variance error system analysis dvesa method a simulation example is given to verify the robustness and robust accuracy relations

robust minimum variance filtering this paper deals with the robust minimum variance filtering problem for linear systems subject to norm bounded parameter uncertainty in both the state and the output matrices of the state space model the problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty two methods for designing robust filters are investigated the first one deals with constant parameter uncertainty and focuses on the design of steady state filters that yield an upper bound to the worst case asymptotic error variance this bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system and it can be made tighter if a tight bound on the latter power spectrum can be obtained the second method allows for time varying parameter uncertainty and for general time varying systems and is more systematic we develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems

an exponential formula for polynomial vector fields abstract the well known matrix exponentiation for linear first order systems of ode is generalised to polynomial vector fields the substitution process of our exponential formula is closely related to the usual iteration of polynomial mappings

robust ℋ2 filtering for lti systems with linear fractional representation this article introduces a new approach to 2 robust filtering design for continuous and discrete time lti systems subjected to linear fractional parameter uncertainty representation the novelty consists on the determination of a performance certificate in terms of the gap between lower and upper bounds of a minimax programming problem which defines the optimal robust filter and the associated equilibrium cost the calculations are performed through convex programming methods applying slack variables known as multipliers to handle the fractional dependence of the plant transfer function with respect to the parameter uncertainty the theory is illustrated by means of an example borrowed from the literature and a practical application involving the design of a robust filter for the load voltage estimation on a transmission line with a stub feeding an unknown resistive load