h sub infinity optimal control with state feedback a h sub infinity optimal control problem in which the measured outputs are the states of the plant is considered the main result shows that the infimum of the norm of the closed loop transfer function using linear static state feedback equals the infimum of the norm of the closed loop transfer function over all stabilizing dynamic even nonlinear time varying state feedback controllers

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

notions of stabilizability and controllability for a class of uncertain linear systems abstract this paper investigates the relationship between stabilizability and certain notions of controllability for a class of uncertain linear systems containing time varying unknown but bounded uncertain parameters the paper introduces a notion of controllability invariance roughly speaking an uncertain system is controllability invariant if it is controllable in the usual sense for each fixed value of the uncertain parameters the paper describes a class of uncertain systems for which controllability invariance implies stabilizability

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

internal positivity preserved model reduction this article studies model reduction of continuous time stable positive linear systems under the hankel norm h norm and h 2 norm performance the reduced order systems preserve the stability as well as the positivity of the original systems this is achieved by developing new necessary and sufficient conditions of the model reduction performances in which the lyapunov matrices are decoupled with the system matrices in this way the positivity constraints in the reduced order model can be imposed in a natural way as the model reduction performances are expressed in linear matrix inequalities with equality constraints the desired reduced order positive models can be obtained by using the cone complementarity linearisation iterative algorithm a numerical example is presented to illustrate the effectiveness of the given methods

robust stabilization of linear systems with norm bounded time varying uncertainty abstract in this paper robust stabilization of a class of linear systems with norm bounded time varying uncertainties is considered it is shown that for this class of uncertain systems quadratic stabilizability via linear control is equivalent to the existence of a positive definite symmetric matrix solution to a parameter dependent riccati equation also a construction for the stabilizing feedback law is given in terms of the solution to the riccati equation

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

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

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

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

frequency weighted optimal hankel norm approximation of stable transfer functions abstract this paper shows how to introduce arbitrary frequency weighting into the optimal hankel norm approximation problem for scalar finite dimensional linear time invariant systems the procedure has applications to the closed form design of reduced order controllers

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

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

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

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

exact calculation of the multiloop stability margin a mapping theorem by l a zadeh and c a desoer 1963 serves as the basis for an algorithm that computes the stability margin k sub m of diagonally perturbed multivariable feedback systems without conservatism the stability margin determination not only verifies system stability but also quantifies how much further the plan uncertainties can be extended before instability occurs the essence of the computational approach is the realization that the true image of a given domain can be approximated with arbitrary accuracy by first subdividing the domain into the requisite number of subdomains and then forming the union of the convex hulls of their images the technique is illustrated in an example with a plant model having three uncertainties in general the method is applicable to either siso or mimo lti systems whose uncertainties can be modeled with noninteracting coefficients in the open loop transfer function representations

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

unstable rational function approximation the problem is considered of approximating a transfer function with stable and unstable poles by a lower order transfer function with the same number of unstable poles a method is suggested and compared with alternative known methods based on hankel norm approximation examples suggest that no one method always outperforms other methods in terms of minimizing the approximation error

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

sample size tables for exact single stage phase ii designs tables for single phase ii trials based on the exact binomial distribution are presented these are preferable to those generated using fleming s design which are based on the normal approximation and can give rise to anomalous results for example if the upper success rate is accepted the lower success rate which the trial is designed to reject may be included in the final confidence interval for the proportion being estimated

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

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

nonlinear filtering for discrete time linear systems with non gaussian initial data the optimal minimum mean square error filtering problem is discussed for a linear system with non gaussian initial distribution an input output realization is derived using an absolutely continuous change of probability measure a representation result is presented which facilitates the derivation of optimal filter realization

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

a generalization of the routh hurwitz stability criteria and an application to a problem in robust controller design the classical results of routh and hurwitz on the stability of polynomials are generalized from the open left half plane to certain other subregions g of the complex plane by our method arbitrary conic sections can be handled the results are interpreted as criteria for g stability of linear systems a numerical algorithm to compute the criteria is given an application to a problem in robust controller design is outlined

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

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

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

frequency weighted model reduction with l error bounds abstract this paper considers frequency weighted model reduction the explicit lower and upper approximation error bounds are derived for certain classes of weighted model reduction problems the approximation is based on some unweighted approximations and the error bounds are given in terms of the hankel singular values of the weighted model

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

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

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

laguerre methods and h identification of continuous time systems abstract h identification of stable continuous time systems is studied using generalized laguerre series methods the theoretical basis of generalized laguerre series methods in h identification is established by giving several results on frequency unweighted and frequency weighted approximations of different classes of infinite dimensional systems an h identification technique based on step response data and laguerre methods is given and analysed generalized laguerre series methods are shown to provide h identification techniques which allow for frequency weighting furthermore it is demonstrated that the theory of generalized laguerre polynomials solves certain approximation problems in an analytical fashion for a class of delay systems

a structured approximation problem with applications to frequency weighted model reduction the authors consider the problem of finding necessary and sufficient conditions for the existence of a q with no more than k poles in the closed left half plane such that the norm of a certain matrix

effects of using observers on stabilization of uncertain linear systems the effects of observers on robust linear feedback controllers are studied sufficient conditions are obtained that guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback the effects of the resulting high gain observers on the disturbance rejection bounds are also studied it is shown that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection however if there is only additive plant disturbance and no measurement disturbance this degradation can be prevented

model reduction for discrete unstable systems based on generalized normal representations the input and output normal representations of stable systems are generalized for unstable systems these are then used to reduce the order of unstable discrete time linear multivariable systems resulting in reduced order models with the same number of unstable poles as the full order model and with an a priori upper bound on the reduction error the generalized normal representations are then modified to include a frequency weighting resulting in frequency weighted generalized normal representations these are used to derive frequency weighted reduced order models for unstable discrete systems with the same number of unstable poles as the full order model and with an a priori upper bound on the frequency weighted reduction error

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

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

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

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

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

truncated balanced realization of a stable non minimal state space system in this paper we present a numerically reliable algorithm to compute the balanced realization of a stable state space system that may be arbitrarily close to being unobservable and or uncontrollable the resulting realization which is known to be a good approximation of the original system must be minimal and therefore may contain a reduced number of states depending on the choice of partitioning of the hankel singular values this algorithm can be used either as a form of minimal realization or of model reduction this illustrates that in finite precision arithmetic these two procedures are closely related in addition to real matrix multiplication the algorithm only requires the solution of two lyapunov equations and one singular value decomposition of an upper triangular matrix

the constrained lyapunov problem and its application to robust output feedback stabilization given a dynamical system whose description includes time varying uncertain parameters it is often desirable to design an output feedback controller leading to asymptotic stability of a given equilibrium point when designing such a controller one may consider static i e memoryless or dynamic compensation in this paper we show that solvability of various output feedback design problems is implied by existence of a solution to a certain constrained lyapunov problem clp the clp can be stated in purely algebraic terms once the clp is described we provide necessary and sufficient conditions for its solution to exist subsequently we consider application of the clp to a number of robust stabilization problems involving static output feedback and observer based feedback

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

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

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

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

combined l2 h model reduction abstract a model reduction problem is considered which involves both l 2 quadratic and h worst case frequency domain aspects specifically the goal of the problem is to minimize an l 2 model reduction criterion subject to a prespecified h constraint on the model reduction error the principal result is a sufficient condition for characterizing reduced order models with bounded l 2 and h approximation error the sufficient condition involves a system of modified riccati equations coupled by an oblique projection i e idempotent matrix when the h constraint is absent the sufficient condition specializes to the l 2 model reduction result given by hyland and bernstein 1985

robust observers for systems with parameters abstract in many cases linear multivariable models which describe physical systems contain structured parametric type uncertainties specifically it may be that the state space model is expressed in a form which involves parameters we first consider circumstances in which a parameter independent observer can be constructed for the system and suggest conditions that guarantee its existence we also give conditions under which such a robust observer can be subsequently used with additional dynamics in a parameter free configuration for regulation

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

optimal three stage designs for phase ii cancer clinical trials the objective of a phase ii cancer clinical trial is to screen a treatment that can produce a similar or better response rate compared to the current treatment results this screening is usually carried out in two stages as proposed by simon for ineffective treatment the trial should terminate at the first stage ensign et al extended two stage optimal designs to three stages however they restricted the rejection region in the first stage to be zero response and the sample size to at least 5 this paper extends simon s two stage to a three stage design without these restrictions and provides tables for both optimal and minimax designs one can use the three stage design to reduce the expected sample size when the treatment is not promising a priori and when the accrual rate is slow the average reduction in size from a two stage to three stage design is 10 per cent

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

minimization of sample size when comparing two small probabilities in a non inferiority safety trial in clinical trials success rates of two treatments to be compared often range from 10 to 90 per cent when the comparison probabilities are much smaller than 10 per cent standard methods for sample size and power calculations may provide invalid results this situation may occur when there is interest in safety rather than in efficacy in such trials no more patients should be included than strictly necessary we compared the results of maximum likelihood methods for the computation of sample sizes in a non inferiority trial including exact procedures and considered unequal sample sizes for experimental and reference treatment an exact unequal sample size maximum likelihood procedure is advocated when the specified non zero risk difference under the null hypothesis is not too large such a procedure is also indicated when the parameter of interest is the relative risk rather than the risk difference

the algorithms for studying the trade offs between h attenuation and uncertainty tolerance uncertainty tolerance and h attenuations are two important concerns in feedback control design it is therefore important to develop effective methods to compute the trade off between these two objectives using a quasiconvex optimization approach this paper develops algorithms for two problems in this regard 1 given the uncertainty size of the system compute the minimum h norm bound of the closed loop system reachable by state feedback control and 2 given the required maximum acceptable h norm bound of the closed loop system compute the maximum uncertainty size which can be tolerated when state feedback control is applied a numerical example is included to show the trade off between uncertainty tolerance and h attenuations and the effectiveness of the algorithms

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

frequency weighted spl lscr sub spl infin norm and optimal hankel norm model reduction a new relative error model reduction method is proposed using frequency weighted balanced realization and explicit spl lscr sub spl infin norm error bounds are also derived for the relative error and multiplicative error the method only needs to solve two lyapunov equations it is further shown that this method is equivalent to the balanced stochastic truncation if the plant is square and minimum phase this paper also gives a complete solution to the frequency weighted hankel norm approximation with antistable weighting these results are then applied to spl lscr sub spl infin norm model reduction and several numerically effective algorithms are proposed it is shown through many numerical examples that these algorithms work very well and in many cases produce almost optimal solutions

hankel norm model reduction with fixed modes a constrained hankel norm approximation problem is considered the reduced order model is required to retain as a subset of its poles some prescribed eigenvalues from the original system the constraint approximation problem is solved with an optimal hankel norm criterion and an l sup infinity error bound for the approximation error is provided the proposed method for model reduction can be described as a partial eigenvalue preservation method the reduced order model is allowed to have a set of free poles in addition to eigenvalues which are preserved from the original system because of physical considerations although the method can be used in conjunction with the dominant mode concept it is equally feasible to retain some eigenvalues of particular interest but otherwise nondominant and let the free poles take care of the dominant characteristics of the system

an algebraic riccati equation approach to h optimization abstract this paper considers the general so called four block h optimal control problem with the assumption that system states are available for feedback it is shown that infimization of the h norm of the closed loop transfer function over all linear constant i e nondynamic stabilizing state feedback laws can be completely characterized via an algebraic riccati equation it is further shown that the optimal norm is not improved by allowing feedback to be dynamic thus the general state feedback h optimal control problem can be solved by iteratively solving one are and the controller can be chosen to be static gain

on the stability of projections of balanced realizations abstract this paper generalizes a stability property concerning the state matrix of a balanced realization established by pernebo and silverman it is shown that stability is preserved under a general projection of the state matrix provided that the hankel singular values of the realization are distinct a necessary and sufficient condition for the case with nondistinct hankel singular values is also established

optimal hankel norm approximation for stable systems with first order stable weighting functions abstract given a stable rational transfer function g s and weighting function w s the problem of finding g s of macmillan degree k so as to minimise w g g h is considered this problem is solved for w s s s with no assumptions on the signs of and this gives rise to approximations where w g g can be accurately bounded from above and below in terms of the hankel singular values of wg when 0

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

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

an l convergent method to reduce frequency weighted infinite dimensional discrete time systems abstract in this paper we present a method based on balanced realizations truncations to reduce frequency weighted infinite dimensional discrete time systems the method is shown to be l convergent for a subclass of the nuclear systems class as its numerical computation is not easy we propose a practical method to reduce frequency weighted infinite dimensional systems and prove that it is l convergent for the class of systems whose transfer function has its derivative in the wiener algebra

robust schur stability of a polytope of polynomials the main objective of the authors is to provide a necessary and sufficient condition for a polytope of polynomials to have all its zeros inside the unit circle the criterion obtained serves as a discrete time counterpart for results in s bialas 1985 and f fu and b r barmish 1987 for the continuous case also the results are reduced to operations on n 1 n 1 matrices it is concluded that by the edge result of a c bartlett et al 1987 it suffices to check the exposed edges in order to determine whether a polytope of polynomials has all its zeros in a simply connected region d

stabilization of an uncertain linear system in which uncertain parameters enter into the input matrix this paper presents a procedure for stabilizing a class of uncertain linear systems the uncertain systems under consideration are described by state equations in which the input matrix depends on a matrix of uncertain parameters this matrix of uncertain parameters may be time varying however it is constrained by a bound on its induced norm the stabilization procedure presented involves the repeated solution of an algebraic riccati equation when a positive definite solution to this riccati equation is obtained this solution is used to construct a stabilizing linear control law another important result contained in this paper can be stated roughly as follows for the class of uncertain systems under consideration if a system can be stabilized via nonlinear control then it is also possible to stabilize the system via linear control

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

the optimal projection equations for reduced order state estimation first order necessary conditions for optimal steady state reduced order state estimation for a linear time invariant plant in the presence of correlated disturbance and nonsingular measurement noise are derived in a new and highly simplified form in contrast to the lone matrix riccati equation arising in the full order kalman filter case the optimal steady state reduced order estimator is characterized by three matrix equations one modified riccati equation and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the estimator and which determines the optimal estimator gains this coupling is a graphic reminder of the suboptimality of proposed approaches involving either model reduction followed by full order estimator design or full order estimator design followed by estimator reduction techniques the results given here complement recently obtained results which characterize the optimal reduced order model by means of a pair of coupled modified lyapunov equations 7 and the optimal fixed order dynamic compensator by means of a coupled system of two modified riceati equations and two modified lyapunov equations 6

an optimal three stage design for phase ii clinical trials a phase ii clinical trial in cancer therapeutics is usually a single arm study to determine whether an experimental treatment e holds sufficient promise to warrant further testing when the criterion of treatment efficacy is a binary endpoint response no response with probability of response p we propose a three stage optimal design for testing h0 p p0 versus h1 p p1 where p1 and p0 are response rates such that e does or does not merit further testing at given levels of statistical significance and power 1 the proposed design is essentially a combination of earlier proposals by gehan and simon the design stops with rejection of h1 at stage 1 when there is an initial moderately long run of consecutive treatment failures otherwise there is continuation to stage 2 and possibly stage 3 which have decision rules analogous to those in stages 1 and 2 of simon s design thus rejection of h1 is possible at any stage but acceptance only at the final stage the design is optimal in the sense that expected sample size is minimized when p p0 subject to the practical constraint that the minimum stage 1 sample size is at least 5 the proposed design has greatest utility when the true response rate of e is small it is desirable to stop early if there is a moderately long run of early treatment failures and it is practical to implement a three stage design compared to simon s optimal two stage design the optimal three stage design has the following features stage 1 is the same size or smaller and has the possibility of stopping earlier when 0 successes are observed the expected sample size under the null hypothesis is smaller stages 1 and 2 generally have more patients than stage 1 of the two stage design but a higher probability of early termination under h0 and the total sample size and criteria for rejection of h1 at stage 3 are similar to the corresponding values at the end of stage 2 in the two stage optimal design

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

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

stability radius for structured perturbations and the algebraic riccati equation abstract in this paper we generalize the notion of stability radius introduced in 1 to allow for structured perturbations we then relate the stability radius to the existence of hermitian solutions of an algebraic riccati equation and give some applications of this result

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

robust reduced order modeling via the optimal projection equations with peterson hollot bounds an optimal reduced order modeling problem with parametric plant uncertainty is considered a model reduction bound suggested by recent work of i r petersen and c v hollot is utilized for guaranteeing robust reduced order modeling over a specified range of uncertain parameters necessary conditions which generalize the optimal projection equations for model reduction are used to characterize the reduced order model which minimizes the model reduction bound the optimality equations thus effectively serve as sufficient conditions for characterizing robust reduced order models