existence of solutions for integral inclusions this paper presents sufficient conditions for the existence of solutions to a nonlinear integral inclusion being a volterra counterpart of an integral inclusion arising in traffic theory our results are obtained via a martelli type fixed point theorem and lead to new existence principles

stubborn state observers for linear time invariant systems for the purpose of estimating the state of a linear time invariant system with measurements subject to outliers we propose an observer with a saturated output injection in such a way to mitigate the effect of abnormal and isolated measurement noise on the error dynamics stability conditions in both the continuous time and the discrete time cases are derived which ensure global exponential stability to the origin for the error dynamics such conditions can be expressed in terms of linear matrix inequalities allowing for a viable design by using convex optimization the effectiveness of the approach is illustrated by means of simulations in comparison with the luenberger observer

robust kalman filter based on a generalized maximum likelihood type estimator a new robust kalman filter is proposed that detects and bounds the influence of outliers in a discrete linear system including those generated by thick tailed noise distributions such as impulsive noise besides outliers induced in the process and observation noises we consider in this paper a new type called structural outliers for a filter to be able to counter the effect of these outliers observation redundancy in the system is necessary we have therefore developed a robust filter in a batch mode regression form to process the observations and predictions together making it very effective in suppressing multiple outliers a key step in this filter is a new prewhitening method that incorporates a robust multivariate estimator of location and covariance the other main step is the use of a generalized maximum likelihood type gm estimator based on schweppe s proposal and the huber function which has a high statistical efficiency at the gaussian distribution and a positive breakdown point in regression the latter is defined as the largest fraction of contamination for which the estimator yields a finite maximum bias under contamination this gm estimator enables our filter to bound the influence of residual and position where the former measures the effects of observation and innovation outliers and the latter assesses that of structural outliers the estimator is solved via the iteratively reweighted least squares irls algorithm in which the residuals are standardized utilizing robust weights and scale estimates finally the state estimation error covariance matrix of the proposed gm kalman filter is derived from its influence function simulation results revealed that our filter compares favorably with the h filter in the presence of outliers

nonlinear boundary value problems for multivalued differential equations in banach spaces with f j x x 0 xmultivalued map j a b compact real interval x banach space a t x is a continuous operator on x for each t x e j x x l c j x x is a linear continuous operator from the space of all continuous functions x j x whose range is contained in x h c j x x is a continuous operator nonlinear in general such problems have been studied repeatedly in the literature with different hypotheses on a f l h the pioneering work with conditions similar to the ones used in the present paper but for ordinary differential equations is the note by scrucca l where the operator a was independent from the state variable x e x anichini 2 has studied analogous problems in the context of ordinary differential systems in ir in which the operator a also depends on x e ir in the case of multivalued differential systems kartsatos 3 has also considered boundary value problems for v valued differential equations but over an unbounded time interval zecca and zezza 4 have extended the work of kartsatos to differential equations in banach spaces in both 3 and 4 the operator a is dependent only on t e j recently papageorgiu 5 has established the existence of mild solutions on a compact interval with the operator a depending only on t e j but in general is unbounded the fundamental tools used in the existence proofs of all above mentioned works are essentially fixed point theorems schauder s theorem in 11 eilenberg montgomery s theorem in 2 ky fan s theorem in 3 4 5 here we use a fixed point theorem due to martelli 6 the idea of the present paper has originated from the study of an analogous problem examined by anichini and conti 7 for ordinary differential systems in m and carbone et al 8 for multivalued differential systems again in ir

robust h sup spl infin filtering for uncertain markovian jump systems with mode dependent time delays this paper considers the problem of robust h sup spl infin filtering for uncertain markovian jump linear systems with time delays which are time varying and depend on the system mode the parameter uncertainties are time varying norm bounded the aim of this problem is to design a markovian jump linear filter that ensures robust exponential mean square stability of the filtering error system and a prescribed l sub 2 induced gain from the noise signals to the estimation error for all admissible uncertainties a sufficient condition for the solvability of this problem is obtained the desired filter can be constructed by solving a set of linear matrix inequalities an illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach

multiple positive solutions for a class of integral inclusions this paper deals with sufficient conditions for the existence of at least two positive solutions for a class of integral inclusions arising in the traffic theory to show our main results we apply a norm type expansion and compression fixed point theorem for multivalued map due to agarwal and o regan a note on the existence of multiple fixed points for multivalued maps with applications j differential equation 160 2000 389 403

brief an analysis and design method for linear systems subject to actuator saturation and disturbance we present a method for estimating the domain of attraction of the origin for a system under a saturated linear feedback a simple condition is derived in terms of an auxiliary feedback matrix for determining if a given ellipsoid is contractively invariant this condition is shown to be less conservative than the existing conditions which are based on the circle criterion or the vertex analysis moreover the condition can be expressed as linear matrix inequalities lmis in terms of all the varying parameters and hence can easily be used for controller synthesis this condition is then extended to determine the invariant sets for systems with persistent disturbances lmi based methods are developed for constructing feedback laws that achieve disturbance rejection with guaranteed stability requirements the effectiveness of the developed methods is illustrated with examples

robust estimation in multiple linear regression model with non gaussian noise the traditional least squares estimators used in multiple linear regression model are very sensitive to design anomalies to rectify the situation we propose a reparametrization of the model we derive modified maximum likelihood estimators and show that they are robust and considerably more efficient than the least squares estimators besides being insensitive to moderate design anomalies

controllability observability and discrete time markovian jump linear quadratic control this paper is concerned with the controllability and observability of discrete time linear systems that possess randomly jumping parameters described by finite stale markov processes and the relationship between these properties and the solution of the infinite time jump linear quadratic jlq optimal control problem the solution of the markovian jlq problem with finite or infinite time horizons is known necessary and sufficient conditions for the existence of optimal constant control laws that lead to finite optimal expected costs as the time horizon becomes infinite are also known sufficient conditions for these steady state control laws to stabilize the controlled system are also available chizeck et al 1986 these conditions are not easy to test however various definitions of controllability and observability for stochastic systems exist in the literature these definitions are unfortunately not related to the steady state jlq control problem in a manner that is analogous to the role of deter

hybrid fixed points of multivalued operators in metric spaces with applications abstract this paper deals with the existence of hybrid fixed points involving two multivalued operators in a complete metric space our claim is also illustrated with applications to a class of integral inclusions for proving the existence results

on existence and asymptotic stability of solutions of a nonlinear integral equation we prove an existence theorem for a nonlinear integral equation being a volterra counterpart of an integral equation arising in the traffic theory the method used in the proof allows us to obtain additional characterization in terms of asymptotic stability of solutions of an equation in question

new kalman filter and smoother consistency tests abstract we derive three new tests that can be applied to a kalman filter to check for inconsistencies the filter residual test can detect observations that are outliers but would be missed by a basic residual test because the uncertainty of the expected observation is large relative to the uncertainty of the observation the smoother residual test uses the output from a modified bryson frazier mbf smoother to detect observations that are outliers the smoother state test compares the state estimates from the filter and mbf smoother to detect model inconsistencies in particular insufficient process noise

an algebraic approach to bounded controllability of linear systems in this paper we present an algebraic approach to the proof that a linear system with matrices a b is null controllable using bounded inputs if and only if it is null controllable with unbounde

brief paper anti windup synthesis for linear control systems with input saturation achieving regional nonlinear performance in this paper we present lmi based synthesis tools for regional stability and performance of linear anti windup compensators for linear control systems we consider both static and dynamic compensators algorithms are developed that minimize the upper bound on the regional l 2 gain for exogenous inputs with l 2 norm bounded by a given value and that minimize this upper bound with a guaranteed reachable set or domain of attraction based on the structure of the optimization problems it is shown that for systems whose plants have poles in the closed left half plane plant order dynamic anti windup can achieve semiglobal exponential stability and finite l 2 gain for exogenous inputs with l 2 norm bounded by any finite value the problems are studied in a general setting where the only requirement on the linear control system is well posedness and internal stability the effectiveness of the proposed techniques is illustrated with an example

linear discrete time global and regional anti windup an lmi approach in this article we address linear anti windup design for linear discrete time control systems guaranteeing regional and global stability and performance the techniques that we develop are the discrete time counterpart of existing techniques for anti windup augmentation which lead to convex constructions by way of linear matrix inequalities lmis when adopting static and plant order anti windup augmentation interesting system theoretic interpretations of the performance bounds for the non linear closed loop can also be given we show here that parallel results apply to the discrete time case we derive the corresponding conditions and prove their effectiveness by adapting the continuous time approaches to the discrete time case

system identification in the presence of outliers and random noises in this paper we consider robust system identification of fir systems when both sparse outliers and random noises are present we reduce this problem of system identification to a sparse error correcting problem using a toeplitz structured real numbered coding matrix and prove the performance guarantee thresholds on the percentage of correctable errors for toeplitz structured matrices are established when both outliers and observation noise are present we have shown that the estimation error goes to 0 asymptotically as long as the probability density function for observation noise is not vanishing around origin no probabilistic assumptions are imposed on the outliers

h model reduction of markovian jump linear systems abstract in this paper the h model reduction problem for linear systems that possess randomly jumping parameters is studied the development includes both the continuous and discrete cases it is shown that the reduced order models exist if a set of matrix inequalities is feasible an effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the model reduction solutions using the numerical solutions of the matrix inequalities the reduced order models can be obtained an example is given to illustrate the proposed model reduction method

iterative least squares solutions of coupled sylvester matrix equations abstract in this paper we present a general family of iterative methods to solve linear equations which includes the well known jacobi and gauss seidel iterations as its special cases the methods are extended to solve coupled sylvester matrix equations in our approach we regard the unknown matrices to be solved as the system parameters to be identified and propose a least squares iterative algorithm by applying a hierarchical identification principle and by introducing the block matrix inner product the star product for short we prove that the iterative solution consistently converges to the exact solution for any initial value the algorithms proposed require less storage capacity than the existing numerical ones finally the algorithms are tested on computer and the results verify the theoretical findings

iterative solutions of coupled discrete markovian jump lyapunov equations in this paper two iterative methods are given to solve coupled discrete markovian jump lyapunov equations arising from the stability analysis of discrete time markovian jump systems when such equations have unique positive definite solutions a sufficient condition for the convergence of iterates for one iterative method is derived when such equations only have unique solutions but not necessarily positive definite the above iterative method may fail and an alterative iterative method is provided by using the solutions of discrete time lyapunov equations as its intermediate steps a sufficient condition is also presented for the convergence of the iterates

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

antiwindup design with guaranteed regions of stability an lmi based approach this note addresses the design of antiwindup gains for obtaining larger regions of stability for linear systems with saturating inputs considering that a linear dynamic output feedback has been designed to stabilize the linear system without saturation a method is proposed for designing an antiwindup gain that maximizes an estimate of the basin of attraction of the closed loop system it is shown that the closed loop system obtained from the controller plus the antiwindup gain can be modeled by a linear system with a deadzone nonlinearity a modified sector condition is then used to obtain stability conditions based on quadratic lyapunov functions differently from previous works these conditions are directly in linear matrix inequality form some numerical examples illustrate the effectiveness of the proposed design technique when compared with the previous ones

brief paper a continuous optimization framework for hybrid system identification we propose a new framework for hybrid system identification which relies on continuous optimization this framework is based on the minimization of a cost function that can be chosen as either the minimum or the product of loss functions the former is inspired by traditional estimation methods while the latter is inspired by recent algebraic and support vector regression approaches to hybrid system identification in both cases the identification problem is recast as a continuous optimization program involving only the real parameters of the model as variables thus avoiding the use of discrete optimization this program can be solved efficiently by using standard optimization methods even for very large data sets in addition the proposed framework easily incorporates robustness to different kinds of outliers through the choice of the loss function

parameter and state estimation of nonlinear systems using a multi observer under the supervisory framework we present a hybrid scheme for the parameter and state estimation of nonlinear continuous time systems which is inspired by the supervisory setup used for control state observers are synthesized for some nominal parameter values and a criterion is designed to select one of these observers at any given time instant which provides state and parameter estimates assuming that a persistency of excitation condition holds the convergence of the parameter and state estimation errors to zero is ensured up to a margin which can be made as small as desired by increasing the number of observers to reduce the potential computational complexity of the scheme we explain how the sampling of the parameter set can be dynamically updated using a zoom in procedure this strategy typically requires a fewer number of observers for a given estimation error margin compared to the static sampling policy the results are shown to be applicable to linear systems and to a class of nonlinear systems we illustrate the applicability of the approach by estimating the synaptic gains and the mean membrane potentials of a neural mass model

parallel algorithm for solving coupled algebraic lyapunov equations of discrete time jump linear systems abstract a parallel iterative scheme for solving coupled algebraic lyapunov equations of discrete time jump linear systems with markovian transitions is introduced the algorithm is computationally efficient since it operates on reduced order decoupled algebraic discrete lyapunov equations furthermore the solutions at every iteration are computed by elementary matrix operations hence the number of operations is minimal monotonicity of convergence is established under the existence conditions of unique positive solutions