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

reliable guaranteed variance filtering against sensor failures this paper presents a solution to a reliable filtering problem with error variance specifications for both continuous and discrete time systems the filtering error variance in the sensor failure cases is guaranteed to be less than a given upper bound while the performance in the nominal case is optimized a convergent iterative algorithm based on linear matrix inequality lmi is given to obtain the solution the algorithm solves the problem without introducing additional conservativeness and it is shown to get better performance and be less conservative compared with traditional lmi approaches a numerical example is given to show the advantages of our approach over existing techniques

simultaneous stabilization using evolutionary strategies in this work a new procedure is presented for the simultaneous stabilization of linear time invariant siso plants evolutionary strategies and substitutions by polynomials and rational functions are used the algorithm presented requires minimal computational resources for its execution in addition it is possible to work with some types of plants that could not be simultaneously stabilized until now and there are many more of these than is described in the literature the restrictions are minimal and the method can be extended with little difficulty to mimo plants moreover a mechanism of substitutions by polynomials and rational function is presented and this mechanism preserves simultaneously stabilizable plants and their controllers several examples are given showing the advantages of these procedures

transcendental and interpolation methods in simultaneous stabilization and simultaneous partial pole placement problems in this paper we investigate the existence of a compensator which simultaneously renders a given r tuple of multiinput multioutput p times m linear dynamical systems internally stable in particular we parametrize a set of simultaneously stabilizable r tuples of plants and show that provided r leqq max m p the above set is semialgebraic and dense in the space sigma of r tuples of plants furthermore we also consider an extension of the classical pole placement and stabilization problems and investigate the simultaneous partial pole placement problem consequently we consider a suitable topology in and obtain a necessary condition and a sufficient condition for the generic partial pole placement problem surprisingly enough the problem of simultaneously stabilizing a triplet of m times m plants chosen generically is shown equivalent to the problem of partially pole placing a single m times m plant by a stable minimum phase compensator on the other hand the problem of simultaneous

a condition for robust stabilizability a family of linear time invariant finite dimensional plants is called robustly stabilizable if there exists a single controller that stabilizes each plant in the family a condition for robust stabilizability is given that requires the plant transmission zeros to remain in the left half complex plane and moreover imposes a restriction on the high frequency behavior of the plant transfer matrix

simultaneous stabilization via static output feedback and state feedback in this paper the simultaneous stabilization problem is considered using the matrix inequality approach some necessary and sufficient conditions for simultaneous stabilizability of strictly proper multi input multi output mimo plants via static output feedback and state feedback are obtained in the form of coupled algebraic riccati inequalities it is shown that any such stabilizing feedback gain is the solution of some coupled linear quadratic control problems where every cost functional has a suitable cross term a heuristic iterative algorithm based on the linear matrix inequality technique is presented to solve the coupled matrix inequalities the effectiveness of the approach is illustrated by numerical examples

robust h observer design of linear time delay systems with parametric uncertainty abstract this paper deals with the problem of h observer design for a class of uncertain linear systems with delayed state and parameter uncertainties this problem aims at designing the linear state observers such that for all admissible parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint independently of the time delay the time delay is assumed to be unknown and the parameter uncertainties are allowed to be norm bounded and appear in all the matrices of the state space model an effective matrix inequality methodology is developed to solve the proposed problem we derive the conditions for the existence of the desired robust h observers and then characterize the analytical expression of these observers in terms of some free parameters a numerical example demonstrates the validity and applicability of the present approach

an iterative design procedure for simultaneous stabilization of mimo systems this paper considers the problem of finding one compensator which simultaneously stabilizes a family of mimo plants the family of plants bdp s q q q represented by their transfer function matrices may be uncountable thus allowing for the possibility of a continuum of variations in plant parameters a hermite invariant factorization of the plant is introduced and shown to be quite useful as far as stabilization is concerned to obtain the desired results a number of assumptions describing the set of allowable plants are imposed these assumptions include some regularity conditions on the plant and mimo versions of minimum phase and one sign high frequency gain requirements the satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator c s guaranteeing simultaneous stabilization the algorithm used for controller design has one most attractive feature namely it is recursive in nature and allows the designer to select one compensator coefficient at a time

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

on similarity invariants of matrix commutators and jordan products abstract denote by x y the additive commutator xy yx of two square matrices x y over a field f in a previous paper the possible eigenvalues ranks and numbers of nonconstant invariant polynomials of a x 1 x 2 x k when a is a fixed matrix and x 1 x k vary were studied moreover given any expression g x 1 x k obtained from distinct noncommuting variables x 1 x k by applying recursively the lie product and without using the same variable twice the possible eigenvalues ranks and numbers of nonconstant invariant polynomials of g x 1 x k when one of the variables x 1 x k takes a fixed value in f n n and the others vary were studied the purpose of the present paper is to show that analogous results can be obtained when additive commutators are replaced with multiplicative commutators or jordan products

adaptive reliable h_ infty filtering against sensor failures this paper is concerned with the adaptive reliable hinfin filtering problem against sensor failures for continuous time linear systems an adaptive hinfin performance index is defined to describe the disturbance attenuation performance of systems with time varying parameter estimations by combining the linear matrix inequality lmi approach for hinfin filter design and adaptive method a method of designing adaptive reliable hinfin filters is proposed where the filter parameter matrices are updated automatically to compensate the sensor failures effects on systems based on the online estimations of eventual faults it is shown that the design condition for the newly proposed adaptive hinfin filtering is more relaxed than that for the traditional fixed gain filter design based on lmi approach an illustrative example and its simulation results are given to illustrate the effectiveness of the proposed design method

recursive state estimation for two dimensional shift varying systems with random parameter perturbation and dynamical bias abstract in this paper the state estimation problem is investigated for a class of two dimensional 2 d stochastic systems with shift varying parameters the stochasticity with the underlying system comes from three sources namely random parameter perturbations dynamical biases and additive white noises the measurement output is subject to the uniform quantization as a result of communication constraints on the sensors the purpose of the addressed problem is to recursively estimate the system states with prescribed estimation performance in spite of the stochastic disturbances and the uniform quantizations an augmented model is first constructed to combine the information about the state and the bias and the dynamical evolution is subsequently discussed furthermore through stochastic analysis and mathematical induction the estimator design algorithm is developed to acquire certain upper bound on the estimation error variance and such an upper bound is then minimized in the matrix trace sense moreover the boundedness issue of the estimation errors is investigated via matrix inversion lemma and inductive analysis technique finally the effectiveness of the proposed state estimation algorithm is validated on a typical 2 d system modeled by the well known darboux equation with extensive application potentials in industrial processes

on the number of invariant polynomials of the matrix xax 1 b abstract let f be a field if a is an n n matrix over f we denote by i a the number of invariant polynomials of a different from 1 we shall prove that if a b are n n matrices over f and t 1 n then i a i b n t if and only if there exists a nonsingular matrix x over f such that i xax 1 b t except in a few cases

simultaneous stabilization of single input single output discrete time systems the problem of finding one compensator which simultaneously stabilizes a family of single input single output siso discrete time plants is considered the family of plants is described by the transfer functions pz q q in q which are generated via a z transformation a number of assumptions describing the set of allowable plants are then given these assumptions include some regularity conditions on the plants and a minimum phase requirement the satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator c z for simultaneous stabilization an iterative computation method is provided for control design

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

technical communique robust state prediction for descriptor systems this paper deals with the problem of state prediction for descriptor systems subject to bounded uncertainties the problem is stated in terms of the optimization of an appropriate quadratic functional this functional is well suited to derive not only the robust predictor for descriptor systems but also that for usual state space systems numerical examples are included in order to demonstrate the performance of this new filter

simultaneous stabilization using stable system inversion abstract this paper investigates the use of stable system inversion to design controllers for the simultaneous stabilization of multi input multi output systems a parametrization of all simultaneously stabilizing controllers for systems admitting a stable inverse is developed the controller is shown to have the structure of a generalized observer for strictly proper systems an intermediate step of the design requires solving a sequence of strong stabilization subproblems for systems with components having identical stable minimum phase transfer functions the design requires only a single model of the component in the controller in systems where a stable inverse fails to exist an interpolation scheme is proposed to develop a stabilizing controller

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

brief on simultaneous h control and strong h stabilization in this note the simultaneous h control problem is addressed it is first shown that the existence of a single controller which simultaneously stabilizes two systems with a given h norm level is equivalent to that of a strong h stabilization controller of an associated system moreover the result is extended to the case involving r 2 systems then a sufficient condition for the strong h stabilization is proposed based on the bounded real lemma finally a simple numerical example is presented to show the effectiveness of the result

simultaneous partial pole placement a new approach to multimode system design simultaneous partial pole placement of a family of single input single output plants is proposed as a generalization of the classical pole placement and stabilization problems this problem finds application in the design of a compensator for a family of linear dynamical systems in this note we show that the proposed problem is equivalent to a new class of transcendental problem using stable minimum phase rational functions with real coefficients a necessary condition for the solvability of the associated transcendental problem is obtained finally a counterexample to the following conjecture is obtained pairs of simultaneously stabilizable plants of bounded mcmillan degree have simultaneously stabilizing compensators of bounded mcmillan degree

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 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

stabilization of a linear plant via a stable compensator having no real unstable zeros abstract this paper studies the following problem under what conditions can a linear plant be stabilized by a stable compensator having no real zeros in the closed right half plane solving this problem is an important step towards to solving the problems of stabilization of linear systems via stable minimum phase compensation and simultaneous stabilization of n n 2 plants in the paper necessary and sufficient conditions are derived these conditions are completely general and therefore encompass unstable nonminimum phase plants as well it is shown that the stabilizability solely depends on the locations of real zeros and real poles of a given plant for a plant satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is also provided and illustrated via an example

optimal robust filtering for systems subject to uncertainties in this paper we deal with an optimal filtering problem for uncertain discrete time systems parametric uncertainties of the underlying model are assumed to be norm bounded we propose an approach based on regularization and penalty function to solve this problem the optimal robust filter with the respective recursive riccati equation is written through unified frameworks defined in terms of matrix blocks these frameworks do not depend on any auxiliary parameters to be tuned simulation results show the effectiveness of the robust filter proposed

simultaneous pole placement of m discrete time plants using a m periodic controller a generic procedure for designing a m periodic controller sought in the controller canonical form for the simultaneous placement of the closed loop poles of m 2 3 4 discrete time invariant plants is presented the procedure is a two stage one first a set of m simultaneous linear polynomial equations arising out of the m given plants and the corresponding desired closed loop pole locations are solved via a generalized sylvester matrix approach to obtain a set of m 1 intermediate polynomials and next the controller parameters are obtained solving another set of simultaneous linear polynomial equations that involve the above intermediate polynomials thus both the computational steps are linear algebraic in nature a list of the isolated plant configurations for which solutions do not exist is given an example illustrates the procedure

an approach to simultaneous system design part 11 nonswitching gain and dynamic feedback compensation by algebraic geometric methods this paper studies structured uncertainty problems in feedback system design considers a compact parameterization of the space of linear dynamical systems and introduces base points and critical points as two algebraic geometric objects that have significance in sensitivity and robustness studies respectively using the nevanlinna pick interpolation theory the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one parameter family of plants a recent result due to kharitonov on the simultaneous stability of a parameterized family of polynomials leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants furthermore the author considers simultaneous pole placement of an r tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system the concept of nondegenerate and twisted r tuples of plants is introduced as the pole placement problem is studie

on the eigenvalues of jordan products abstract this paper studies the possible eigenvalues of the jordan product xa ax when a is fixed and x varies

finite escapes and convergence properties of guaranteed cost robust filters the design of robust filters for linear time varying systems subject to parameter perturbations is considered the design is based on the minimization of an upper bound for the error covariance the computation of the filter matrices calls for the solution of a pair of differential riccati equations parameterized by a scalar design parameter the main results of the paper concern the asymptotic properties of the filter when it is applied to time invariant systems differently from the standard kalman filter the robust filter may abruptedly cease to exist owing to the presence of finite escape times in the associated riccati equations nevertheless provided that the parameter perturbations do not affect the unstable dynamics convergence to a stable steady state filter can always be ensured by properly adjusting the scalar design parameter since such an adjustment might deteriorate the steady state performance a time varying strategy for the tuning of the scalar parameter is developed in order to guarantee both convergence and performance

robust h sub 2 filtering for uncertain systems with measurable inputs this paper deals with the robust minimum variance filtering problem for linear time varying systems subject to a measurable input and to norm bounded parameter uncertainty in the state and or 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 and any input of bounded energy three types of input signals are considered a signal that is a priori known for the whole time interval an unknown signal of very large bandwidth that is perfectly measured on line and a large bandwidth signal that is measured ahead of time in a fixed preview time interval both the time varying finite horizon and stationary infinite horizon cases are treated

on the order of simultaneously stabilizing compensators in this paper simultaneous strong stabilization problem is considered and it is shown that there is no upper bound for the minimal order of a simultaneously strongly stabilizing compensator in terms of the plant orders a similar problem was also considered by smith et al 1986 where it was shown that such a bound does not exist for the strong stabilization problem of a single plant but the examples given in the article were forcing an approximate unstable pole zero cancellation or forcing the distance between two distinct unstable zeros to go to zero in this paper it is shown that 1 if approximate unstable pole zero cancellation does not occur and the distances between distinct unstable zeros are bounded below by a positive constant then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator and 2 for the simultaneous strong stabilization problem even for the two plant case such a bound cannot be found

h sub 2 and h sub spl infin robust filtering for convex bounded uncertain systems investigates robust filtering design problems in h sub 2 and h sub spl infin spaces for continuous time systems subjected to parameter uncertainty belonging to a convex bounded polyhedral domain it is shown that by a suitable change of variables both designs can be converted into convex programming problems written in terms of linear matrix inequalities the results generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured then assuming the order of the uncertain system is known the optimal guaranteed performance h sub 2 and h sub spl infin filters are proven to be of the same order as the order of the system a numerical example illustrate the theoretical results

characterization of controllers in simultaneous stabilization this paper gives a convenient parametrization for the class of all stabilizing controllers for two or more plants the result represent a generalization of the youla parametrization of the class of all stabilizing controllers in terms of an arbitrary stable proper transfer function although as expected the additional constraints for simultaneous stabilization are not readily incorporated into h h2 optimization procedures as in the standard case there is immediate application of the theory for reduction of controllers which simultaneously stabilize two or more plants

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

on the simultaneous stabilization of three or more plants in this note the problem of the simultaneous stabilization of three multivariable plants is addressed we consider the general case where the existence of a unit controller cannot be used as a sufficient condition to guarantee the existence of a simultaneous controller for three multivariable plants the sufficient conditions given in this note lead to a constructive controller design to stabilize simultaneously three multivariable plants a generalization is proposed for stabilizing simultaneously n multivariable plants

robust kalman filtering for continuous time lag systems the linear continuous time kalman filter for a class of time lag systems with norm bounded uncertain parameters is considered we investigate the conditions for linear delayless state estimator such that the estimation error covariance is guaranteed to lie within a prescribed bound for all admissible uncertainties it is proven that a robust kalman filter algorithm can be determined in terms of two riccati equations involving scalar parameters the developed theory is illustrated by numerical simulation

robust kalman filtering for uncertain systems abstract this paper studies the problem of kalman filter design for uncertain systems the system under consideration is subjected to time varying norm bounded parameter uncertainties in both the state and measurement matrices the problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties a riccati equation approach is proposed to solve the above problem furthermore a suboptimal covariance upper bound can be computed by a convex optimization

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

technical communique robust h2 optimal filtering for continuous time stochastic systems with polytopic parameter uncertainty in this paper robust h 2 optimal filtering is addressed for continuous time stochastic systems with polytopic parameter uncertainty a new robust stability condition is presented a continuous time robust h 2 optimal filter is obtained by solving a sufficient linear matrix inequality condition characterizing a solution of a robust minimum variance filtering problem which takes into account the polytopic type of model uncertainties the proposed approach is demonstrated through numerical examples

reducing the sensitivity to parameter variations of a minimum order reduced order observer a quantitative upper hound is established which defines the extent to which a minimum order reduced order non adaptive observer may be rendered insensitive to parameter variations that upper bound depends on the number of measurements and the location of questionable parameters within the system matrices an integral squared error objective function is explicitly solved that objective function may be used to assess the sensitivity of the system to parameter errors a numerical example is presented for a continuous observer the results are extended to the discrete ease

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

minimum variance unbiased fir filter for discrete time variant systems this paper is concerned with the minimum variance unbiased mvu finite impulse response fir filtering problem for linear system described by discrete time variant state space models an mvu fir filter is derived by minimizing the variance from the unbiased fir ufir filter the relationship between the filter gains of mvu fir ufir and optimal fir ofir filters is derived analytically and the mean square errors mses of different fir filters are compared to provide an insight into the estimation performance simulations provided verify that errors in the mvu fir filter are in between the ufir and ofir filters it is also shown that the mvu fir filter can offer optimal estimates without a prior knowledge of the initial state and exhibits better robustness against temporary modeling uncertainties than the kalman filter

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

on the invariant polynomials of jordan products let f be an algebraically closed field this paper describes the possible numbers of nonconstant invariant polynomials of the jordan product xa ax when a is fixed and x varies

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

optimal linear filtering under parameter uncertainty this paper addresses the problem of designing a guaranteed minimum error variance robust filter for convex bounded parameter uncertainty in the state output and input matrices the design procedure is valid for linear filters that are obtained from the minimization of an upper bound of the error variance holding for all admissible parameter uncertainty the results provided generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured assuming the order of the uncertain system is known the optimal robust linear filter is proved to be of the same order as the order of the system in the present case of convex bounded parameter uncertainty the basic numerical design tools are linear matrix inequality lmi solvers instead of the riccati equation solvers used for the design of robust filters available in the literature to date the paper that contains the most important and very recent results on robust filtering is used for comparison purposes in particular it is shown that under the same assumptions our results are generally better as far as the minimization of a guaranteed error variance is considered some numerical examples illustrate the theoretical results

technical communique resilient linear filtering of uncertain systems the problem of resilient linear filtering for a class of linear continuous time systems with norm bounded uncertainties is investigated we have considered additive filter gain variations to reflect the imprecision in filter implementation the design problem of resilient linear filter is formulated as a convex optimization problem over linear matrix inequalities as a limiting procedure the case of resilient kalman filter is derived all the developed results are conveniently extended to the case of multiplicative filter gain variations simulation studies are carried out to support the theoretical findings

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

brief condition and algorithm for simultaneous stabilization of linear plants this paper is devoted to the problem of simultaneous stabilization of linear plants it is shown that four given plants p i s i 1 2 3 4 are simultaneously stabilizable if and only if there exist four stable polynomials h i s i 1 2 3 4 which simultaneously satisfy two polynomial equations if we can only find four stable h i s i 1 2 3 4 to satisfy one of the two polynomial equations then two controllers c 1 s and c 2 s having a common denominator or numerator can be obtained such that c 1 s simultaneously stabilizes p 1 s and p 3 s and c 2 s simultaneously stabilizes p 2 s and p 4 s which is called the simultaneous stabilization in groups based on such two controllers a design algorithm for the simultaneous stabilization of three plants is induced

simultaneous stabilization of two discrete time plants using a 2 periodic controller a generic method for designing a 2 periodic controller for the simultaneous placement of the closed loop poles of two single input single output discrete shift invariant plants at the origin is presented the method consists of first recasting the simultaneous pole placement problem as one of solving a coupled pair of linear polynomial equations involving three unknown polynomials and then obtaining the controller parameters in terms of the coefficients of these polynomials the isolated cases for which such pole placement is not possible have been listed simulation results show that the performances of systems thus compensated are superior to their performances when compensated using the higher periodicity controllers suggested in literature

a pole placement design approach for systems with multiple operating conditions the author proposes design procedures based on state space pole placement techniques for systems with multiple operating conditions this is the so called simultaneous pole placement problem first the full state feedback problem is studied in which a nonlinear local pole placement solution is proposed the design condition is formulated in terms of the rank condition of a multimode controllability matrix then the output feedback problem is approached using a multimodel controller design which is an extension of the observer design to multimode systems the design is decomposed into separated global pole placement subproblems and a local pole placement subproblem for a system with some operating conditions having modes on the j omega axis but no modes at the origin in the open right half of the complex plane stabilizability and detectability conditions for the design of an asymptotically stabilizing control are established without any restriction on the number of inputs or outputs relations of this approach to other simultaneous control design approaches are pointed out

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

brief paper distribution function tracking filter design using hybrid characteristic functions a new tracking filtering algorithm for a class of multivariate dynamic stochastic systems is presented the system is expressed by a set of time varying discrete systems with non gaussian stochastic input and nonlinear output a new concept such as hybrid characteristic function is introduced to describe the stochastic nature of the dynamic conditional estimation errors where the key idea is to ensure the distribution of the conditional estimation error to follow a target distribution for this purpose the relationships between the hybrid characteristic functions of the multivariate stochastic input and the outputs and the properties of the hybrid characteristic function are established a new performance index of the tracking filter is then constructed based on the form of the hybrid characteristic function of the conditional estimation error an analytical solution which guarantees the filter gain matrix to be an optimal one is then obtained a simulation case study is included to show the effectiveness of the proposed algorithm and encouraging results have been obtained

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

some new results on the simultaneous stabilizability of a family of single input single output systems abstract in this paper we obtain sufficiency conditions on the problem of simultaneous stabilization of a parameterized family of single input single output plants by a non switching compensator the sufficiency conditions include simultaneous stabilization and simultaneous pole assignment of a finite number of plants

matrices with prescribed submatrices and number of invariant polynomials abstract we give necessary and sufficient conditions for the existence of a matrix a b over a field where a is a square matrix such that a b has a prescribed submatrix and the pencil xi a b has a prescribed number of invariant factors different from 1 as a corollary we give a necessary and sufficient condition for the existence of a completely controllable pair a b such that a b has a prescribed submatrix

a robust reliable stabilization scheme for single input single output systems using transcendental methods abstract a stabilization scheme reliable against a single controller failure originally proposed by vidyasagar and viswanadham is analysed a connection between the problem of robust reliable stabilization and the problem of stabilization by a stable minimum phase compensator is established via interpolation theory

an approach to simultaneous system design i semialgebraic geometric methods this paper introduces semialgebraic parameterization as an approach to analyze simultaneous stabilization and pole placement problems rational families of plants of a given mcmillan degree that are simultaneously stabilizable by a fixed family of compensators are parameterized for a discrete family of plants the parameterization problem reduces to the simultaneous stabilization or the pole placement problem of a r tuple of multi input multi output plants by a nonswitching compensator it is shown that by removing a semialgebraic subset of a proper algebraic set the space of plants can be decomposed into components that are either simultaneously stabilizable or simultaneously unstabilizable under special cases explicit parameterization of the semialgebraic set is obtained finally a necessary condition for the simultaneous stabilization of single input or single output plants is obtained

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

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

simultaneous stabilization with fixed closed loop characteristic polynomial a solution is given to the problem of simultaneously stabilizing m single input single output plants by one dynamic compensator with the constraint that each closed loop system has the same characteristic polynomial

robust nonfragile kalman filtering for uncertain linear systems with estimator gain uncertainty the note is concerned with the problem of a robust nonfragile kalman filter design for a class of uncertain linear systems with norm bounded uncertainties the designed state estimator can tolerate multiplicative uncertainties in the state estimator gain matrix the robust nonfragile state estimator designs are given in terms of solutions to algebraic riccati equations the designs guarantee known upper bounds on the steady state error covariance a numerical example is given to illustrate the results

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

the solution of a transcendental problem and its applications in simultaneous stabilization problems a complete solution for a special transcendental problem in system theory is given one of the interpretations of this transcendental problem is the following simultaneous stabilization problem under what conditions can two linear plants be simultaneously stabilized by a single compensator having no real poles in the closed right half of the complex plane these conditions are completely general and therefore encompass unstable non minimum phase plants as well it is shown that the simultaneous stabilizability of two given plants via such a restricted compensator depends solely on the locations of the real zeros of the two plants and their difference plant in the closed right half of the complex plane for two plants satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is provided and illustrated a computationally checkable necessary condition for simultaneous stabilization of three plants is also given

robust reduced order unbiased filtering for uncertain systems this paper presents a simple solution to the robust unbiased functional reduced order filtering problem in the case of uncertain systems described by integral quadratic constraint iqc the existence condition of the unbiased filter is expressed through a rank relation then the filter is designed via linear matrix inequalities coupled with an equality constraint the results obtained in this paper are applicable to unstable systems the approach is illustrated by a numerical example

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

on the number of invariant polynomials of matrix commutators we study the possible numbers of noneonstant invariant polynomials of the matrix commutator xa ax when x varies elsevier science inc 1997

non euclidian metrics and the robust stabilization of systems with parameter uncertainty this paper considers from a complex function theoretic point of view certain kinds of robust synthesis problems in particular we use a certain kind of metric on the disk the hyperbolic metric which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non euclidian geometry it is shown that several apparently different problems can be treated in a unified general framework a new result on the gain margin problem for multivariable plants is also given finally we apply our methods to systems with real zero or pole variations

robust filtering for a class of stochastic uncertain nonlinear time delay systems via exponential state estimation we investigate the robust filter design problem for a class of nonlinear time delay stochastic systems the system under study involves stochastics unknown state time delay parameter uncertainties and unknown nonlinear disturbances which are all often encountered in practice and the sources of instability the aim of this problem is to design a linear delayless uncertainty independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances the dynamics of the estimation error is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are proposed to guarantee the existence of desired robust exponential filters which are derived in terms of the solutions to algebraic riccati inequalities the developed theory is illustrated by numerical simulation