improved linear matrix inequality approach to stability analysis of linear systems with interval time varying delays this paper investigates the problem of stability analysis for a class of linear systems with interval time varying delay in order to develop a less conservative stability condition a lyapunov krasovskii functional comprising novel integral terms is introduced convex combination idea is utilized to derive a stability criterion in terms of linear matrix inequalities lmis without any additional free weighting matrices which increase drastically the computational burden of the stability test numerical examples are presented to illustrate the superiority of the proposed approach compared to some existing ones in the literature

an improved result on reachable set estimation and synthesis of time delay systems in this paper the problems of reachable set estimation and synthesis of time delay systems are investigated by introducing the non uniform delay partitioning method and the triple integral technique an improved reachable set estimation condition is proposed in terms of linear matrix inequality based on the criterion a sufficient condition for the existence of a state feedback controller is established to render the reachable set of the closed loop system be bounded by a given ellipsoid two numerical examples are given to demonstrate the effectiveness of the obtained results

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

further improvement of jensen inequality and application to stability of time delayed systems this paper is concerned with the delay dependent stability for the linear systems with a time varying delay to get a result in the form of lmi from a lyapunov krasovskii functional an integral inequality is necessary and jensen inequality has been a most powerful inequality in the last few years recently based on wirtinger inequality an improved integral inequality encompassing jensen inequality was proposed and its application to the stability showed a quite improvement in this paper without using wirtinger inequality a further improved integral inequality in the form of infinite series is derived and based on this a delay dependent stability condition in the form of lmi is derived finally its contribution on the stability criterion is shown by well known two examples

the robust regulation problem with robust stability a subspace valued function approach among the most common purposes are the tracking of reference signals and the rejection of disturbance signals in the face of uncertainties the related design problem is called the robust regulation problem here we investigate the tradeoff between the robust regulation constraint and the requirement of robust stability with respect to perturbations in the normalized coprime factors of the plant we use an approach in terms of subspace valued functions associated to plant and controller in this way necessary and sufficient conditions for robust regulation with robust stability can be related to a simple geometric property

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

the performance of different propensity score methods for estimating marginal hazard ratios propensity score methods are increasingly being used to reduce or minimize the effects of confounding when estimating the effects of treatments exposures or interventions when using observational or non randomized data under the assumption of no unmeasured confounders previous research has shown that propensity score methods allow for unbiased estimation of linear treatment effects e g differences in means or proportions however in biomedical research time to event outcomes occur frequently there is a paucity of research into the performance of different propensity score methods for estimating the effect of treatment on time to event outcomes furthermore propensity score methods allow for the estimation of marginal or population average treatment effects we conducted an extensive series of monte carlo simulations to examine the performance of propensity score matching 1 1 greedy nearest neighbor matching within propensity score calipers stratification on the propensity score inverse probability of treatment weighting iptw using the propensity score and covariate adjustment using the propensity score to estimate marginal hazard ratios we found that both propensity score matching and iptw using the propensity score allow for the estimation of marginal hazard ratios with minimal bias of these two approaches iptw using the propensity score resulted in estimates with lower mean squared error when estimating the effect of treatment in the treated stratification on the propensity score and covariate adjustment using the propensity score result in biased estimation of both marginal and conditional hazard ratios applied researchers are encouraged to use propensity score matching and iptw using the propensity score when estimating the relative effect of treatment on time to event outcomes copyright 2012 john wiley sons ltd

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

estimation and synthesis of reachable set for switched linear systems this paper focuses on the problems of reachable set estimation and state feedback controller design for discrete time switched linear systems under bounded peak disturbances for the reachable set estimation problem a lyapunov based inequality is developed based on the multiple lyapunov strategy by choosing appropriate lyapunov functions the ellipsoidal reachable set estimation conditions of discrete time switched linear systems are obtained in order to make the estimated ellipsoids as small as possible three optimization approaches are proposed specifically the genetic algorithm is used to search for the optimal parameters satisfying the obtained reachable set estimation conditions in addition the state feedback controller design problem for discrete time switched linear systems is considered the function of the controller is to manipulate the reachable set of the closed loop system to lie within a given ellipsoid or make the reachable set small finally the effectiveness of the obtained results is verified through some numerical examples

technical communique reachable set bounding for delayed systems with polytopic uncertainties the maximal lyapunov krasovskii functional approach this paper deals with the problem of reachable set estimation for time delay systems subject to both polytopic parameter uncertainties and bounded peak inputs the maximal lyapunov krasovskii functional is constructed as the pointwise maximum of a family of lyapunov krasovskii functionals each functional corresponds to a vertex of uncertain polytope some criteria bounding the reachable set are derived this approach shows great advantages over the traditional methods based on the common lyapunov functionals by introducing a modified integral inequality the limitation imposed on the derivative of time delay being less than one is relaxed furthermore the obtained results involve less computational burden when the number of vertices of the polytope is small two examples are given to illustrate the theoretical results

stability and performance for saturated systems via quadratic and nonquadratic lyapunov functions in this paper we develop a systematic lyapunov approach to the regional stability and performance analysis of saturated systems in a general feedback configuration the only assumptions we make about the system are well posedness of the algebraic loop and local stability problems to be considered include the estimation of the domain of attraction the reachable set under a class of bounded energy disturbances and the nonlinear l2 gain the regional analysis is established through an effective treatment of the algebraic loop and the saturation deadzone function this treatment yields two forms of differential inclusions a polytopic differential inclusion pdi and a norm bounded differential inclusion ndi that contain the original system adjustable parameters are incorporated into the differential inclusions to reflect the regional property the main idea behind the regional analysis is to ensure that the state remain inside the level set of a certain lyapunov function where the pdi or the ndi is valid with quadratic lyapunov functions conditions for stability and performances are derived as linear matrix inequalities lmis to obtain less conservative conditions we use a pair of conjugate non quadratic lyapunov functions the convex hull quadratic function and the max quadratic function these functions yield bilinear matrix inequalities bmis as conditions for stability and guaranteed performance level the bmi conditions cover the corresponding lmi conditions as special cases hence the bmi results are guaranteed to be as good as the lmi results in most examples the bmi results are significantly better than the lmi results

technical communique improved ellipsoidal bound of reachable sets for time delayed linear systems with disturbances we consider the problem of finding an ellipsoidal reachable set that bounds the states of time delayed linear systems with bounded peak disturbances the considered time delay is time varying but it has an upper bound in magnitude and rate based on the modified lyapunov krasovskii l k type functional we derive a delay dependent result expressed in the form of matrix inequalities containing only one non convex scalar the result is extended to uncertain time delayed linear systems finally we show the usefulness of our result by a comparative numerical example

technical communique further result on reachable set bounding for linear uncertain polytopic systems with interval time varying delays the problem of reachable set estimation of linear uncertain polytopic time varying delay systems subject to bounded peak inputs is studied in this paper the delays considered in this paper are assumed to be non differentiable and vary within an interval where the lower and upper bounds are known based on the lyapunov krasovskii method and delay decomposition technique a sufficient condition for the existence of a ball that bounds the reachable set of the system is proposed in terms of matrix inequalities containing only one scalar which can be solved by using an one dimensional search method and matlab s lmi toolbox and allow us to find the smallest radius a numerical example is given to illustrate the effectiveness of the proposed result

robust regulation with h 2 performance abstract we consider the problem of minimizing the h 2 norm of a feedback system subject to the constraint that the controller robustly regulate against constants and sinusoids we show that for any 0 there exists a controller that both achieves robust regulation and renders the closed loop h 2 norm within of the optimal norm the norm achievable without the robust regulation constraint we also provide conditions that are both necessary and sufficient for there to exist a robustly regulating controller that achieves the optimal h 2 norm all proofs are constructive

new results on stability of discrete time systems with time varying state delay this note is concerned with the stability analysis of discrete time systems with time varying state delay by defining new lyapunov functions and by making use of novel techniques to achieve delay dependence several new conditions are obtained for the asymptotic stability of these systems the merit of the proposed conditions lies in their less conservativeness which is achieved by circumventing the utilization of some bounding inequalities for cross products between two vectors and by paying careful attention to the subtle difference between the terms sigmam k dk k 1 middot and sigma m k dm k 1 middot which is largely ignored in the existing literature these conditions are shown via several examples to be much less conservative than some existing result

technical communique on reachable sets for linear systems with delay and bounded peak inputs linear systems with constant coefficients and time varying delays are considered we address the problem of finding an ellipsoid that bounds the set of the states in the euclidean space that are reachable from the origin in finite time by inputs with peak value that is bounded by a prechosen positive scalar the system may encounter uncertainties in the matrices of its state space model and in the delay length the lyapunov razumikhin approach is applied and a bounding ellipsoid is obtained by solving a set of linear matrix inequalities that depend on the upper bound of the delay length

h suboptimal control problem with boundary constraints abstract a necessary and sufficient condition is derived for the existence of a stabilizing controller such that i a specified closed loop transfer function g er s has h norm less than one and ii g er s satisfies generalized boundary constraints on the j axis

a parameter dependent approach to robust h_ infty filtering for time delay systems this paper is concerned with the problem of robust h infin filtering for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state we utilize the polynomially parameter dependent idea to solve the robust h infin filtering problem with new linear matrix inequality conditions obtained for the existence of admissible filters these conditions are developed based on homogeneous polynomially parameter dependent matrices of arbitrary degree the delay dependence and polynomial parameter dependence guarantee the proposed approach to be potentially less conservative which is shown via a numerical example

wirtinger based integral inequality application to time delay systems in the last decade the jensen inequality has been intensively used in the context of time delay or sampled data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities lmis however it is also well known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature reducing this gap is a relevant issue and always an open problem in this paper we propose an alternative inequality based on the fourier theory more precisely on the wirtinger inequalities it is shown that this resulting inequality encompasses the jensen one and also leads to tractable lmi conditions in order to illustrate the potential gain of employing this new inequality with respect to the jensen one two applications on time delay and sampled data stability analysis are provided

on reachable set estimation of singular systems in this paper the problem of reachable set estimation of singular systems is investigated based on the lyapunov method a sufficient condition is established in terms of a linear matrix inequality lmi to guarantee that the reachable set of singular system is bounded by the intersection of ellipsoids then the result is extended to the problem for singular systems with time varying delay by utilizing the reciprocally convex approach the effectiveness of the obtained results in this paper is illustrated by numerical examples

on the stability of linear systems with uncertain delay this paper focuses on the stability of some class of delay systems including uncertainty in the delays more precisely we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system if the delay perturbation is constant necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some finite dimensional constant matrix pencil if the delay perturbation is time varying some sufficient stability conditions are derived using exact lyapunov krasovskii functionals illustrative examples are also included

a novel result on stability analysis for uncertain neutral stochastic time varying delay systems generalized finsler lemma is applied to deduce delay dependent stability conditions the case is considered that the discrete delay is different from the neutral delay model transformation cross terms estimation and free weighting matrices are avoided the conditions show less conservatism and involves fewer computational variables numerical examples show that the proposed approach improves some existing ones this paper is concerned with the mean square exponential stability analysis for uncertain neutral linear stochastic time varying delay systems by lyapunov krasovskii theory and linear matrix inequality method under the generalized finsler lemma gfl framework delay dependent mean square exponential stability criteria are established without involving model transformation cross terms bounding technique or additional free weighting matrix moreover gfl is also employed to obtain stability criteria for a class of uncertain linear stochastic neutral systems with different discrete and neutral delays numerical examples are presented to verify that the proposed approach is both less conservative and less computationally complex than the existing results

razumikhin type theorems for hybrid system with memory in this paper we address the stability problem of hybrid systems with memory which are newly developed to model hybrid dynamic systems affected by delays for such systems stability criteria are developed based on razumikhin type conditions which are usually applied in the delay systems we prove that the hybrid system with memory is uniformly globally pre asymptotically stable by small gain theorem besides a relaxed razumikhin type stability criterion is also proposed which does not require strict decrease of the lyapunov razumikhin function during jumps several examples are given to illustrate the effectiveness and generality of the proposed results

the robust inference for the cox proportional hazards model abstract we derive the asymptotic distribution of the maximum partial likelihood estimator for the vector of regression coefficients under a possibly misspecified cox proportional hazards model as in the parametric setting this estimator converges to a well defined constant vector in addition the random vector n 1 2 is asymptotically normal with mean 0 and with a covariance matrix that can be consistently estimated the newly proposed robust covariance matrix estimator is similar to the so called sandwich variance estimators that have been extensively studied for parametric cases for many misspecified cox models the asymptotic limit or part of it can be interpreted meaningfully in those circumstances valid statistical inferences about the corresponding covariate effects can be drawn based on the aforementioned asymptotic theory of and the related results for the score statistics extensive studies demonstrate that the proposed robust tests and interval estimation procedures

reachable set estimation of t s fuzzy systems with time varying delay in this paper the reachable set estimation problem is investigated for delayed discrete time takagi sugeno fuzzy systems with bounded input disturbances and nonzero initial conditions a reachable set estimation condition is derived by using the reciprocally convex combination approach to bound the forward difference of triple summable terms the derived condition guarantees that all the states of the system with the initial conditions from some domain are bounded in a compact set and all the states from other domain converge exponentially within another compact set moreover a less conservative stability condition is also obtained the effectiveness and the reduced conservatism of the proposed results are illustrated by numerical examples

stability analysis and controller synthesis for discrete time delayed fuzzy systems via small gain theorem this paper investigates the problems of stability analysis and controller synthesis of discrete time takagi sugeno t s fuzzy systems with time varying delay via an input output approach the original system is reformulated as a feedback subsystem and a forward subsystem with two constant time delays and a delay uncertainty satisfying the scaled small gain theorem the lifting method is employed to convert the forward subsystem to a delay free system where the main result concerning the stability analysis of the system is obtained based on the scaled small gain theorem the merit of the new stability condition lies in its reduced conservatism which is made possible by a more precise estimation of the time varying delay additionally a state feedback controller is designed through the lyapunov krasovskii functional approach combined with the utilization of the scaled small gain theorem two illustrative examples are given to demonstrate the less conservatism of the stability condition and the effectiveness of the controller design method

on h control for linear systems with interval time varying delay this paper deals with the problem of delay dependent robust h control for linear time delay systems with norm bounded and possibly time varying uncertainty the time delay is assumed to be a time varying continuous function belonging to a given interval which means that the lower and upper bounds for the time varying delay are available and no restriction on the derivative of the time varying delay is needed which allows the time delay to be a fast time varying function based on an integral inequality which is introduced in this paper and lyapunov krasovskii functional approach a delay dependent bounded real lemma brl is first established without using model transformation and bounding techniques on the related cross product terms then employing the obtained brl a delay dependent condition for the existence of a state feedback controller which ensures asymptotic stability and a prescribed h performance level of the closed loop systems for all admissible uncertainties is proposed in terms of a linear matrix inequality lmi a numerical example is also given to illustrate the effectiveness of the proposed method

an lmi approach to h synthesis subject to almost asymptotic regulation constraints a multi objective controller synthesis problem is considered in which an output is to be regulated approximately by assuring a bound on the steady state peak amplification in response to an infinite energy disturbance while also guaranteeing a desired level of performance measured in terms of the worst case energy gain from a finite energy input to a performance output relying on a characterization of the controllers with which almost asymptotic regulation is accomplished the problem of guaranteeing the desired level of performance is reduced to solving a system of linear matrix inequalities subject to a set of linear equality constraints based on the solution of this system a procedure is outlined for the construction of a suitable controller whose order is equal to the order of the plant plus the order of the exogenous system

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

terminating observation within matched pairs of subjects in a matched cohort analysis a monte carlo simulation study matched cohort analyses are becoming increasingly popular for estimating treatment effects in observational studies however in the applied biomedical literature analysts and authors are inconsistent regarding whether to terminate follow up among members of a matched set once one member is no longer under observation this paper focused on time to event outcomes and used monte carlo simulation methods to determine the optimal approach we found that the bias of the estimated treatment effect estimate was negligible under both approaches and that the percentage of censoring had no discernible effect on the magnitude of bias the mean model based standard error of the treatment estimate was consistently higher when we terminated observation within matched pairs furthermore the type 1 error rate was consistently lower when we did not terminate follow up within matched pairs in conclusion when the focus was on time to event outcomes we demonstrated that there was no advantage to terminating follow up within matched pairs continuing follow up on each subject until their observation was naturally complete was superior compared with terminating a subject s observation time once its matched pair had ceased to be under observation given the frequency with which these analyses are conducted in the applied literature our results provide important guidance to analysts and applied researchers as to the preferred analytic approach

brief paper algebraic and topological aspects of the regulator problem for lumped linear systems the regulator problem with robustness is solved for systems modelled by rational transfer matrices a topology for possibly unstable plants is presented a necessary and sufficient condition is derived for the existence of a proper controller which provides internal stability and output regulation throughout an open neighbourhood of the plant a characterization of all such controllers is determined

performance with regulation constraints we study the problem where we have a regulation asymptotic tracking requirement together with a performance requirement for continuous time systems typically we measure performance by the h 2 or h norm of a chosen transfer function matrix although any other norm such as the l 1 norm could be used in the case when the performance is measured by the h 2 norm there is no loss in performance due to the regulation constraint on the other hand when the performance is measured by the h norm there exists in general certain loss of performance due to the regulation constraint and we explicitly characterize such a loss determining suitable controllers for a given system with both regulation and performance constraints requires solving only an unconstrained optimization problem for an auxiliary system which is explicitly constructed here

an ultimate state bound for a class of linear systems with delay abstract a new method is given to estimate an ultimate state bound on a time varying linear system with delay and bounded disturbances by using some results on metzler matrices the effectiveness of the obtained results is illustrated by a numerical example

improved delay dependent stability criteria for time delay systems this note provides an improved asymptotic stability condition for time delay systems in terms of a strict linear matrix inequality unlike previous methods the mathematical development avoids bounding certain cross terms which often leads to conservatism when time varying norm bounded uncertainties appear in a delay system an improved robust delay dependent stability condition is also given examples are provided to demonstrate the reduced conservatism of the proposed conditions

parameter dependent lyapunov functional for stability of time delay systems with polytopic type uncertainties this note concerns the problem of the robust stability of a linear system with a time varying delay and polytopic type uncertainties in order to construct a parameter dependent lyapunov functional for the system we first devised a new method of dealing with a time delay system without uncertainties in this method the derivative terms of the state which is in the derivative of the lyapunov functional are retained and some free weighting matrices are used to express the relationships among the system variables and among the terms in the leibniz newton formula as a result the lyapunov matrices are not involved in any product terms of the system matrices in the derivative of the lyapunov functional this method is then easily extended to a system with polytopic type uncertainties numerical examples demonstrate the validity of the proposed criteria

brief paper exponential stability of singular systems with multiple time varying delays this paper deals with the class of continuous time singular linear systems with multiple time varying delays in a range the global exponential stability problem of this class of systems is addressed delay range dependent sufficient conditions such that the system is regular impulse free and a stable are developed in the linear matrix inequality lmi setting moreover an estimate of the convergence rate of such stable systems is presented a numerical example is employed to show the usefulness of the proposed results

robust regulation in the presence of norm bounded uncertainty we consider robust regulation against steps and sinusoids in the presence of unstructured uncertainty the unstructured uncertainty is norm bounded by a constant that is given a priori this problem is equivalent to a certain multiobjective problem where one objective is robust regulation and the other is the standard objective of h sub spl infin suboptimal control it is shown that a solution to this problem exists if and only if the standard h sub spl infin problem admits a solution and certain matrix inequalities are satisfied these solvability conditions are readily computable controller synthesis is also addressed

linear functional state bounding for positive systems with disturbances varying within a bounded set in most of the existing works on state bounding for perturbed dynamical systems the disturbance vector is only considered under the assumption that its norms components are bounded by known constant bounds this paper considers a more general case where the disturbance vector is assumed to vary within a known bounded set furthermore instead of finding bounds of the full system state vector this paper focuses on finding the smallest componentwise bound of a given linear function of the system state vector a class of perturbed positive systems is considered and a new method for deriving the smallest bound is presented our presented method is also extended to positive systems with time delays and to nonlinear systems which are bounded by positive systems a numerical example is given to illustrate the effectiveness of the obtained results

robust output regulation for a class of linear multivariable systems in the design of robust regulators the solution of anh norm optimization problem of the formmin q r h t11 t12qt21 is needed to get an optimal controller a difficulty in doing this is that t12 j will be singular at the poles of the external signals in 11 a lower bound for this norm has been found in this paper it will be shown that for stable plants this bound is an infimum and can be approximated as near as possible thus a necessary and sufficient condition for robust regulation is found for a class for a class of linear mimo systems moreover if the external signals are step functions an h optimal controller can be obtained

delay dependent robust stabilization of uncertain state delayed systems this paper concerns a problem of robust stabilization of uncertain state delayed systems a new delay dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities an algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties

a new approach to state bounding for linear time varying systems with delay and bounded disturbances abstract in this note the problem of state bounding for linear time varying systems with delay and bounded disturbances input is considered for the first time by using a novel approach which does not involve the lyapunov krasovskii functional method new explicit delay independent conditions are derived for the existence of a ball such that all the state trajectories of the system converge exponentially within it a numerical example is given to illustrate the effectiveness of the obtained result

on uniform ultimate boundedness of linear systems with time varying delays and peak bounded disturbances abstract this paper is devoted to a problem of uniform ultimate boundedness uub for a class of linear systems with interval time varying delays and peak bounded disturbances by using the lyapunov krasovskii functional method a general uub condition and an estimation of the ultimate bound on system trajectories are developed on the basis of the above results linear matrix inequality lmi conditions on uub of the perturbed systems under consideration are derived by constructing an appropriate lyapunov krasovskii functional meanwhile the ultimate bound for a prescribed disturbance attenuation level is given in the form of an ellipsoidal surface the feasibility and effectiveness of the derived results are illustrated by two numerical examples

a delay dependent stability criterion for systems with uncertain time invariant delays this paper provides a new stability criterion for systems with time invariant uncertain delays based on an improved upper bound for the inner product of two vectors a new delay dependent robust stability criterion is derived which is shown by an example less conservative than existing stability criteria

a new method of reachable set estimation for time delay systems with polytopic uncertainties we address the reachable set bounding problem of linear systems subject to both time varying delay and polytopic uncertainties a novel criterion is established to give a more accurate description of the set which bounds the states starting from the origin by inputs with peak values by combining the maximal lyapunov functional and the reciprocally convex approach we obtain a tighter reachable set estimation with lower computational complexity the corresponding reachable set condition for the common lyapunov functional can be obtained naturally as a special case of the above result finally two examples illustrate the advantages of our proposed method

stability of time delay systems via wirtinger based double integral inequality based on the wirtinger based integral inequality a double integral form of the wirtinger based integral inequality hereafter called as wirtinger based double integral inequality is introduced in this paper to show the effectiveness of the proposed inequality two stability criteria for systems with discrete and distributed delays are derived within the framework of linear matrix inequalities lmis the advantage of employing the proposed inequalities is illustrated via two numerical examples

new results on a delay derivative dependent fuzzy h infty filter design for t s fuzzy systems this paper focuses on the fuzzy h filter design problem for takagi sugeno t s fuzzy systems with interval time varying delays two cases of the time varying delays are considered 1 the delays are differentiable and have both the lower and upper bounds of the delay derivatives and 2 the delays are bounded but not necessary to be differentiable since we employ a new fuzzy lyapunov krasovskii functional lkf and estimate a tighter upper bound of its derivative the proposed delay derivative dependent bound real lemma brl condition has advantages over some previous results in that it enlarges the application scope but has less conservatism which is established theoretically the brl condition that depends on both the upper and lower bounds of the delay derivatives is derived then based on the aforesaid brl a new fuzzy h filter scheme is proposed and a sufficient condition for the existence of such a filter is established in terms of linear matrix inequalities lmis finally some numerical examples and an application to the truck trailer system are utilized to demonstrate the effectiveness and reduced conservatism of our results

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

delay dependent state feedback stabilization for a networked control model with two additive input delays this paper is centered on delay dependent state feedback stabilization for a networked control model with two additive input delays firstly delay dependent stability is investigated by splitting the whole delay interval into subintervals according to the delays a lyapunov functional is constructed to reduce conservatism we handle the lyapunov functional in two ways more specifically we take the lyapunov functional as a whole to examine its positive definite rather than restrict each term of it to positive definite as usual in addition when estimating the derivative of the lyapunov functional we manage to get a fairly tighter upper bound by introducing different slack variables for the different subintervals the resulting stability results turn out dependent on the two delays separately and less conservative than some existing ones then based on the stability results state feedback stabilization is studied delay dependent conditions are formulated for the controller such that the closed loop system is asymptotically stable finally examples are given to show the less conservatism of the stability results and the effectiveness of the proposed stabilization method

optimal matching for observational studies abstract matching is a common method of adjustment in observational studies currently matched samples are constructed using greedy heuristics or stepwise procedures that produce in general suboptimal matchings with respect to a particular criterion a matched sample is suboptimal if it could be improved by changing the controls assigned to specific treated units that is if it could be improved with the data at hand here optimal matched samples are obtained using network flow theory in addition to providing optimal matched pair samples this approach yields optimal constructions for several statistical matching problems that have not been studied previously including the construction of matched samples with multiple controls with a variable number of controls and the construction of balanced matched samples that combine features of pair matching and frequency matching computational efficiency is discussed extensive use is made of ideas from two essentially disjoint literatures namely st

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

improved delay dependent robust stability criteria for uncertain time delay systems abstract this paper deals with the robust stability analysis for uncertain systems with time varying delay new delay dependent robust stability criteria of uncertain time delay systems are proposed by exploiting appropriate lyapunov functional candidate these developed results have advantages over some previous ones in that they have fewer matrix variables yet less conservatism due to the introduction of a method to estimate the upper bound of the derivative of lyapunov functional candidate without ignoring the additional useful terms numerical examples are given to demonstrate the effectiveness and the advantage of the proposed method

h optimization without assumptions on finite or infinite zeros explicit algebraic conditions are presented for the suboptimality of some parameter in the h infty optimization problem by output measurement control apart from two strict properness conditions no artificial assumptions restrict the underlying system in particular the plant may have zeros on the imaginary axis or at infinity these suboptimality characterizations are applied to show how to compute the optimal value by quadratically convergent algorithms and to solve the almost disturbance decoupling problem with internal stability

brief paper generalized asymptotic regulation with guaranteed h2 performance an lmi solution a multi objective controller synthesis problem is considered in which a set of generalized asymptotic regulation constraints are to be satisfied while also guaranteeing a desired level of performance measured in terms of the asymptotic variance of a performance output in response to a white noise random process with zero mean and identity covariance matrix the generalized regulation constraints are expressed as bounds on the state steady peak in response to disturbances generated by an anti stable autonomous exogenous system with nonzero initial states the controllers that guarantee these constraints can be realized by replicating the dynamics of the exogenous system within a certain structure formed by gain matrices which are subject to convex constraints and an accompanying controller with which the feedback loop is to be stabilized formulating the design of the accompanying controller in a way to guarantee the additional performance objective the overall design is rendered tractable over a set of free variables in terms of which the synthesis of a suitable controller is also outlined the order of the controller is equal to the order of the plant plus the order of the exogenous system by an adaptation of the developed techniques a solution is also provided for the problem of generalized asymptotic regulation with suboptimal transient response

passive control for singular time delay system with actuator saturation this paper considers the problem of passivity controller design for singular time delay system with actuator saturation and nonlinear disturbance firstly by tuning the wirtinger based integral inequality a sufficient condition is derived to guarantee that the nonlinear singular time delay system is regular impulse free asymptotically stable with the dissipation performance then based on the derived condition and applying linear matrix inequalities lmis techniques the passive state feedback controller is synthesized moreover the maximal estimate of the domain of attraction is proposed by an optimization problem finally some numerical examples are given to illustrate the effectiveness of the obtained theoretic results

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

further results on the robust tracking problem in two degree of freedom control systems the robust tracking problem in two degree of freedom control systems is formulated in a general setting which includes the case where the controlled output is not available directly a complete solution of the problem which is an extension of previous results is derived in a considerably simplified and transparent manner furthermore we show what kind of information about the output is needed to achieve robust tracking

extended rm h _ 2 controller synthesis for continuous descriptor systems this technical note presents a complete solution to the nonstandard h2 output feedback control problem for continuous descriptor systems where unstable and nonproper weighting functions are used in such a problem the desired controller has to satisfy two conditions simultaneously i the closed loop is admissible and has a minimum h2 norm ii only the internal stability of a part of the closed loop is sought the condition of the existence of such a controller is deduced an explicit characterization of the optimal solution is also formulated based on two generalized algebraic riccati equations gares and two generalized sylvester equations a numerical example is included to illustrate the validity of the proposed results

h control by state feedback for plants with zeros on the imaginary axis algebraic tests are derived for the suboptimality of some parameter in the h infty optimization problem by state feedback where the finite zero structure of the plant is not restricted as an application of these characterizations a quadratically convergent algorithm for the computation of the optimal value is presented the suboptimality tests are based on new solvability criteria for general algebraic riccati inequalities that are of independent interest

exponential stabilization of linear systems with time varying delayed state feedback via partial spectrum assignment abstract we consider the problem of controlling a linear system when the state is available with a known time varying delay delayed state feedback control or the actuator is affected by a delay the solution proposed in this paper consists in partially assigning the spectrum of the closed loop system to guarantee the exponential zero state stability with a prescribed decay rate by means of a finite dimensional control law a non conservative bound on the maximum allowed delay for the prescribed decay rate is presented which holds for both cases of constant and time varying delays an advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required we compare the performance of our approach in terms of delay bound and input signal with another recent approach

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