brief paper an anti windup technique for lmi regions the anti windup problem seeks to minimize closed loop performance deterioration due to input nonlinearities such as saturation for a given linear time invariant plant and controller this paper presents a linear matrix inequality lmi based method that attempts to minimize performance deterioration while explicitly restricting the anti windup closed loop dynamics the restriction placed on the dynamics is described via lmi regions which is a form of regional pole placement finally the techniques discussed in this paper are demonstrated on an electro hydraulic testbed

synchronization of identical linear dynamic systems subject to input saturation abstract this paper investigates the synchronization problem for a group of agents with identical linear dynamics subject to input saturation two classes of linear systems asymptotically null controllable with bounded control ancbc systems and double integrator systems are studied for ancbc systems it is shown that a linear protocol with the control gain obtained via parametric lyapunov equations can semiglobally synchronize the undirected topology provided that its augmented directed topology has a spanning tree for a special case of ancbc the double integrator systems it is established that if the augmented directed topology has a spanning tree then in the presence of input saturation using linear protocols with positive control gains can achieve global synchronization two numerical examples are given to demonstrate the effectiveness of the theoretical results

on the spectral radius of trees with fixed diameter let t n d be the set of trees on n vertices with diameter d in this paper the first d2 1 spectral radii of trees in the set t n d 3 d n 4 are characterized

generalized sector synthesis of output feedback control with anti windup structure this paper considers the control synthesis problem for linear time invariant lti continuous time systems with actuator saturation nonlinearities the control architecture is standard a nominal lti output feedback with an anti windup aw mechanism traditional approaches have focused on aw synthesis where the nominal controller is first designed to achieve a local performance in the linear region of the actuators and then the aw compensator is added to guarantee stability performance properties when the actuators saturate in contrast this paper proposes a synthesis method to design both the nominal controller and the aw compensator simultaneously using the generalized sector gs approach in the multiplier setting a sufficient condition is given in terms of linear matrix inequalities so that a given ellipsoid is synthesized as a domain of attraction for the closed loop system our result is shown to include the existing results on the simultaneous circle synthesis and the anti windup gs synthesis as special cases this paper also shows that the direct feed through term in the aw compensator does not contribute to enlarging the achievable domain of attraction within the multiplier gs framework

global leader following consensus of a group of general linear systems using bounded controls this paper studies the global leader following consensus problem for a multi agent system with bounded controls the follower agents and the leader agent are all described by a general linear system both a bounded state feedback control law and a bounded output feedback control law are constructed for each follower agent in the group the feedback law for each input of an agent uses a multi hop relay protocol in which the agent obtains the information of other agents through multi hop paths in the communication network the number of hops each agent uses to obtain its information about other agents for an input is less than or equal to the sum of the number of eigenvalues at the origin and the number of pairs of non zero imaginary eigenvalues of the sub system corresponding to the input and the feedback gains are constructed from the adjacency matrix of the communication network it is shown that global leader following consensus is achieved under these feedback control laws when the communication topology among follower agents is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower

on constructing lyapunov functions for multi agent systems lyapunov equations that depend on communication graph topologies provide building blocks of lyapunov functions which play an important role in controller design and stability analysis of multi agent systems however construction of such a lyapunov equation in some published works has a flaw or requires unnecessarily strong graph conditions this paper presents several choices of lyapunov equations over various graph topologies

ordering of some uniform supertrees with larger spectral radii abstract a supertree is a connected and acyclic hypergraph we study some uniform supertrees with larger spectral radii we first define a new type of edge moving operation on hypergraphs and study its applications on the comparison of the spectral radii of hypergraphs by using this new operation on some supertrees together with the general edge moving operation introduced by li shao and qi in 2015 and using a result by zhou et al in 2014 about the relation between the spectral radii of an ordinary graph and its power hypergraph we are able to determine the first eight k uniform supertrees on n vertices with the largest spectral radii

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

a comparison of different matching designs in case control studies an empirical example using continuous exposures continuous confounders and incidence of myocardial infarction the paper presents a case control study involving a disease exposures and several continuous confounders the relative efficiency and validity of a fully matched design is compared with random sampling of controls we test a viable option of a partially matched design when inability to match all study subjects on all confounders occurs the degree of bias in the odds ratios introduced by the different designs and by the different analytic models is assessed in comparison with the estimates obtained from a total cohort from which both cases and controls were selected matched designs and analytic strategies are also evaluated in terms of the variances of the odds ratios the results indicate that matching on continuous variables may lead to a more precise estimate of odds ratio than statistical control of confounding in unmatched designs partial selection of controls by matching may be a useful strategy when complete matching cannot be achieved in practice partial matching achieves most of the benefits of full matching

a small gain condition for interconnections of iss systems with mixed iss characterizations we consider interconnected nonlinear systems with external inputs where each of the subsystems is assumed to be input to state stable iss sufficient conditions of small gain type are provided guaranteeing that the interconnection is iss with respect to the external input to this end we extend recently obtained small gain theorems to a more general type of interconnections the small gain theorem provided here is applicable to situations where the iss conditions are formulated differently for each subsystem and are either given in the maximization or the summation sense furthermore it is shown that the conditions are compatible in the sense that it is always possible to transform sum formulations to maximum formulations without destroying a given small gain condition an example shows the advantages of our results in comparison with the known ones

efficiency of age adjusted tests in animal carcinogenicity experiments based on asymptotic relative efficiency calculations ryan 1985 biometrics 41 525 531 concludes that in the analysis of animal carcinogenicity experiments age adjusted tests of tumor rates should be routinely preferred to simple proportions tests for both lethal and nonlethal tumors we recalculate the asymptotic efficiencies of the simple proportions test relative to the log rank test for the lethal tumor case for a simplified model it is shown that the relative efficiency may be easily computed as a function of the crude tumor rate and the survival rate at the time of terminal sacrifice more generally we calculate by numerical quadrature the asymptotic relative efficiency for all models considered by ryan and using simulations examine the relevance of asymptotic efficiencies to typical sample sizes contrary to the numerical results of ryan we find for experiments with good survival and typical tumor rates that the relative efficiencies are greater than 95 usually about 99 in the nonlethal tumor case similar results follow from ryan for tumor rates and survival rates typically encountered in practice as it is often difficult to determine whether or not a tumor is lethal we conclude for equal interim mortality rates that the simple proportions test is usually adequate in evaluating animal carcinogenicity experiments

linear lmi based external anti windup augmentation for stable linear systems we study linear anti windup augmentation for linear control systems with saturated linear plants in the special case when the anti windup compensator can only modify the input and the output of the windup prone linear controller we also measure the arising performance in terms of the finite l 2 gain from exogenous inputs to selected performance outputs our main results are a system theoretic feasibility characterization for fixed order anti windup design and a linear matrix inequality lmi formulation for optimal static and plant order anti windup design interpretations of lower bounds on the achievable performance are also given the effectiveness of the design procedure is demonstrated on a simulation example

on global leader following consensus of identical linear dynamic systems subject to actuator saturation abstract this paper studies the leader following consensus problem for a group of agents with identical linear systems subject to control input saturation we focus on two classes of linear systems neutrally stable systems and double integrator systems for neurally stable systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with proper choices of relative potential functions global consensus can also be achieved over a switching communication topology for double integrator systems we establish that global consensus can be achieved by linear local feedback laws over a fixed communication topology and with the help of a simple saturation function in the local feedback laws global consensus can also be achieved over a switching communication topology simulation results illustrate the theoretical results

required sample size for categorical matching abstract this article investigates the sampling effort required to obtain matches for all members of a given sample the exact distribution of the sample size required to complete the match quotas in all categories of the matching variable s is derived the first two moments are also derived recursively using a markov chain approach for problems with equal quotas in equiprobable categories these moments may be computed as functions of gamma and normal order statistic moments numerical results are given to characterize the feasibility of matching in relation to the study size the number of matching categories and the distributions of the category probabilities and quotas

the spectral radius of trees on k pendant vertices abstract in this paper we consider the following problem of all trees of order n with k pendant vertices n k fixed which achieves the maximal spectral radius we show that the maximal spectral radius is obtained uniquely at t n k where t n k is a tree obtained from a star k 1 k and k paths of almost equal lengths by joining each pendant vertex of k 1 k to an end vertex of one path we also discuss the spectral radius of t n k and get some results

a general result on the stabilization of linear systems using bounded controls we present two constructions of controllers that globally stabilize linear systems subject to control saturation we allow essentially arbitrary saturation functions the only conditions imposed on the system are the obvious necessary ones namely that no eigenvalues of the uncontrolled system have positive real part and that the standard stabilizability rank condition hold one of the constructions is in terms of a neural network type one hidden layer architecture while the other one is in terms of cascades of linear maps and saturations

saturated finite interval iterative learning for tracking of dynamic systems with hnn structural output this brief investigates the interval iterative learning problem for dynamic systems with hierarchical neural network hnn structural output the first objective is to design the output of a dynamic system with hnn structure a sufficient condition is obtained to achieve the interval tracking in a finite interval by applying iterative learning control ilc then the saturated ilc is considered into the discussed system and a less conservative criterion is obtained to achieve the tracking in a finite interval using a network structure decomposition technique finally simulation results are given to illustrate the usefulness of the developed criteria

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

coxeter energy of graphs abstract we study the concept of the coxeter energy of graphs and digraphs quivers as an analogue of gutman s adjacency energy which has applications in theoretical chemistry and is a recently widely investigated graph invariant coxeter energy ce g of a di graph g is defined to be the sum of the absolute values of all complex eigenvalues of the coxeter matrix associated with g our main inspiration for the study comes from the coxeter formalism appearing in group theory lie theory representation theory of algebras mathematical physics and other contexts we focus on the coxeter energy of trees and we prove that the path resp the maximal star has the smallest resp the greatest coxeter energy among all trees resp two large subclasses of trees with fixed number of vertices we provide several other related results as the characterization of trees with second smallest and second greatest coxeter energy bounds for coxeter energy and general facts on coxeter spectra of graphs extending known results e g for salem trees and for certain special real coxeter eigenvalues of trees additionally we discuss few other energy like quantities for the coxeter spectra of di graphs including coxeter energy normalized by the trace of the coxeter matrix and the quantities derived from variants of coulson integral formula

on the optimal parameter of the composite laplacian quadratics function abstract recently the composite quadratic lyapunov function has been extended to study of multi agent systems leading to the so called composite laplacian quadratics clqs function compared with quadratic lyapunov functions the clqs function can yield a larger convergence region and is particularly useful in stabilization of multi agent systems with complex dynamics such as differential inclusions in the definition of the clqs function an optimal vector parameter plays a critical role in determining the value of the clqs function and in constructing stabilization laws derived from the clqs function this paper focuses on the properties of the optimal parameter of the clqs function the uniqueness of the optimal parameter is established a distributed computation approach is further proposed which is useful in computing the optimal parameter the robustness issue of the optimal parameter is also investigated for a multi agent system described by linear differential inclusions finally a numerical example is provided to validate the proposed theoretical results

stability analysis for continuous systems with two additive time varying delay components this paper presents a new result of stability analysis for continuous systems with two additive time varying delay components which represent a general class of delay systems with strong application background in network based control systems this criterion is expressed as a set of linear matrix inequalities which can be readily tested by using standard numerical software a numerical example is provided to show the effectiveness and advantage of the proposed stability condition

finite time information consensus for multi agent systems with fixed and switching topologies in this paper we study the consensus problems for a group of interacting agents first we analytically establish the explicit expression of the consensus state for the entire group second we prove that the agents of the group under a particular type of nonlinear interaction can reach the consensus state in finite time in the scenarios with fixed and switching undirected topologies the results are also extended to the case where the topology of the group is directed and satisfies a detailed balance condition on coupling weights third some numerical examples are provided to analyze the influencing factors of the convergence time that is the parameter of the particular interaction function and the algebraic connectivity of graphs finally an application of the theoretical results in sensor networks is given namely computing the maximum likelihood estimate of unknown parameters

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

brief paper synchronization in networks of identical linear systems the paper investigates the synchronization of a network of identical linear state space models under a possibly time varying and directed interconnection structure the main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected the result can be interpreted as a generalization of classical consensus algorithms stronger conditions are shown to be sufficient but to some extent also necessary to ensure synchronization with the diffusive static output coupling often considered in the literature

an antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation the article considers linear systems subject to actuator saturation an antiwindup technique is used to enlarge the domain of attraction of the closed loop system under an a priori designed linear dynamic feedback law the design of the antiwindup compensation gain is formulated and solved as an iterative optimization problem with lmi constraints numerical examples are used to demonstrate the effectiveness of the proposed design technique

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

the second largest eigenvalue of a tree denote by 2 t the second largest eigenvalue of a tree t an easy algorithm is given to decide whether 2 t for a given number and a structure theorem for trees with 2 t is proved also it is shown that a tree t with n vertices has 2 t lsqb n 3 2rsqb12 this bound is best possible for odd n

stability analysis for high frequency networked control systems this note generalizes the stability analysis for a high frequency networked control system the high frequency networked control system is described by a delta operator system with a high frequency constraint stability conditions are given for the high frequency delta operator system furthermore by developing the generalized kalman yakubovic popov lemma improved stability conditions are also presented in terms of linear matrix inequalities some experiment results are presented to illustrate the effectiveness of the developed techniques

leader following consensus of multi agent systems under fixed and switching topologies the leader following consensus problem of higher order multi agent systems is considered in the system the dynamics of each agent and the leader is a linear system the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented for both fixed and switching interaction topologies which describe the information exchange between the multi agent systems the design technique is based on algebraic graph theory riccati inequality and lyapunov inequality simulations indicate the capabilities of the algorithms

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

finite time observers for multi agent systems without velocity measurements and with input saturations abstract this paper is devoted to the distributed finite time observers for multi agent systems where the control inputs are required to be bounded and the velocities are assumed to be not available for feedback an effective framework through defining a class of coordinated saturation functions is introduced under which both a first order finite time observer and a high order finite time observer are constructed by applying the homogeneous theory for stability analysis it is proven that all the states of the followers can converge to that of the leader in finite time under our proposed observers with mild modifications of our control strategies the foregoing results are then extended to the distributed finite time containment control problem where the states of the followers converge to the convex hull spanned by the multiple dynamic leaders numerical simulations are presented to demonstrate the efficiency of our methods

bounds on the largest eigenvalues of trees with a given size of matching very little is known about upper bound for the largest eigenvalue of a tree with a given size of matching in this paper we find some upper bounds for the largest eigenvalue of a tree in terms of the number of vertices and the size of matchings which improve some known results

on the spectral radii and the signless laplacian spectral radii of c cyclic graphs with fixed maximum degree if g is a connected undirected simple graph on n vertices and n c 1 edges then g is called a c cyclic graph specially g is called a tricyclic graph if c 3 let g be the maximum degree of g in this paper we determine the structural characterizations of the c cyclic graphs which have the maximum spectral radii resp signless laplacian spectral radii in the class of c cyclic graphs on n vertices with fixed maximum degree n c 12 moreover we prove that the spectral radius of a tricyclic graph g strictly increases with its maximum degree when g 1 6 2n32 and identify the first six largest spectral radii and the corresponding graphs in the class of tricyclic graphs on n vertices

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

exact characterization of invariant ellipsoids for single input linear systems subject to actuator saturation we present a necessary and sufficient condition for an ellipsoid to be an invariant set of a linear system under a saturated linear feedback the condition is given in terms of linear matrix inequalities lmis and can be easily used for optimization based analysis and design

covariance adjustment of relative risk estimates in matched studies the matched sample case control study is widely used by epidemiologists to estimate the relative incidence of disease among persons exposed to different levels of one or more risk factors an apparent limitation of such designs has been the necessity to control the effects of all potential confounding variables in the matching process conditional likelihood analyses based on the linear logistic equation enable one to model the effects of covariates while preserving the original matching this paper reviews the logical basis for this methodology and illustrates its value by application to a case control study of esophageal cancer

the effect of pooling across strata in perfectly balanced studies pair matching frequency matching and stratification are used to obtain perfect exposure balance within strata defined by levels of confounders we consider the consequences of pooling such balanced data across strata in the analysis we examine model based inference for a variety of response variables and generalized linear regressions as well as for the cox 1972 journal of the royal statistical society series b 34 187 220 model if the data are pooled so that stratum effects are omitted from the regression certain models retain nominal size including all poisson models and all normal models with known variance the model based tests have supranominal size for all exponential models and subnominal size for all bernoulli models and for the cox model these results contrast with a previous analysis of simple randomization which only ensures exposure balance on average with simple randomization omission of stratum effects from these models leads to model based significance tests with supranominal size except for the cox and bernoulli models which retain nominal size just as for simple randomization however it is wise to include stratum effects in the analysis of perfectly balanced data to avoid biased estimation of exposure effects and to increase the efficiency of the comparison though motivated by cohort data these results also apply to balanced case control data under the logistic model

global consensus for discrete time multi agent systems with input saturation constraints in this paper we consider the global consensus problem for discrete time multi agent systems with input saturation constraints under fixed undirected topologies we first give necessary conditions for achieving global consensus via a distributed protocol based on relative state measurements of the agent itself and its neighboring agents we then focus on two special cases where the agent model is either neutrally stable or a double integrator for the neutrally stable case any linear protocol of a particular form which solves the consensus problem for the case without input saturation constraints also solves the global consensus problem for the case with input saturation constraints for the double integrator case we show that a subset of linear protocols which solve the consensus problem for the case without saturation constraints also solve the global consensus problem for the case with input saturation constraints the results are illustrated by numerical simulations

anti windup control design for exponentially unstable lti systems with actuator saturation in this paper a new saturation control technique in the framework of anti windup compensation is developed for exponentially unstable linear time invariant systems subject to input nonlinearities the proposed control algorithm guarantees regional stability in the existence of input saturation and provides less conservative performance than most existing anti windup schemes moreover an explicit form of anti windup controller with its order no more than the order of the plant is derived an inverted pendulum example is used to demonstrate the advantages of the newly proposed anti windup control technique

semi global exponential stabilization of linear systems subject to input saturation via linear feedbacks abstract it is known that a linear time invariant system subject to input saturation can be globally asymptotically stabilized if it has no eigenvalues with positive real parts it is also shown by fuller 1997 and sussmann and yang 1991 that in general one must use nonlinear control laws and only some special cases can be handled by linear control laws in this paper we show the existence of linear state feedback and or output feedback control laws for semi global exponential stabilization rather than global asymptotic stabilization of such systems we explicitly construct linear static state feedback laws and or linear dynamic output feedback laws that semi globally exponentially stabilize the given system our results complement the negative result of fuller 1977 and sussmann and yang 1991

delay dependent robust stability and stabilization of uncertain linear delay systems a linear matrix inequality approach this paper considers the problems of robust stability analysis and robust control design for a class of uncertain linear systems with a constant time delay the uncertainty is assumed to be norm bounded and appears in all the matrices of the state space model we develop methods for robust stability analysis and robust stabilization the proposed methods are dependent on the size of the delay and are given in terms of linear matrix inequalities

on the largest eigenvalues of bipartite graphs which are nearly complete abstract for positive integers p q r s and t satisfying rt p and st q let g p q r s t be the bipartite graph with partite sets u 1 u p and v 1 v q such that u i and v j are not adjacent if and only if there exists a positive integer k with 1 k t such that k 1 r 1 i kr and k 1 s 1 j ks in this paper we study the largest eigenvalues of bipartite graphs which are nearly complete we first compute the largest eigenvalue and all other eigenvalues of g p q r s t and then list nearly complete bipartite graphs according to the magnitudes of their largest eigenvalues these results give an affirmative answer to 1 conjecture 1 2 when the number of edges of a bipartite graph with partite sets u and v having u p and v q for p q is pq 2 furthermore we refine 1 conjecture 1 2 for the case when the number of edges is at least pq p 1

matching and design efficiency in epidemiological studies summary for an observational study to compare two groups with respect to a dichotomous outcome variable the design strategy of matching observational units with respect to a potential confounding variable x is compared with the strategy of selecting independent samples with possible poststratification on x for bias control the comparison is based on asymptotic relative efficiencies of appropriate mantel haenszel chi squared tests it is found that proper understanding requires that the prospective and the retrospective study designs be separately considered and that in certain circumstances the effect of matching on design efficiency is entirely different for the two designs conditions are established under which matching is more efficient than poststratification for the control of confounding

ordering trees and graphs with few cycles by algebraic connectivity abstract several approaches for ordering graphs by spectral parameters are presented in the literature we can find graph orderings either by the greatest eigenvalue spectral radius or index or by the sum of the absolute values of the eigenvalues the energy of a graph or by the second smallest eigenvalue of the laplacian matrix the algebraic connectivity among others by considering the fact that the algebraic connectivity is related to the connectivity and shape of the graphs several structural properties of graphs relative to this parameter have been studied hence a large number of papers about ordering graphs by algebraic connectivity mainly about trees and graphs with few cycles have been published this paper surveys the significant results concerning these topics trying to focus on possible points to be investigated in order to understand the difficulties to obtain partial orderings via algebraic connectivity

antiwindup for stable linear systems with input saturation an lmi based synthesis this paper considers closed loop quadratic stability and l sub 2 performance properties of linear control systems subject to input saturation more specifically these properties are examined within the context of the popular linear antiwindup augmentation paradigm linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification called the unconstrained closed loop behavior building on known results on h sub spl infin and lpv synthesis the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem which has an attractive system theoretic interpretation the lower bound on the achievable l sub 2 performance is the maximum of the open and unconstrained closed loop l sub 2 gains in the special cases of zero order static and plant order antiwindup compensation the feasibility conditions become convex linear matrix inequalities it is shown that if and only if the plant is asymptotically stable plant order linear antiwindup compensation is always feasible for large enough l sub 2 gain and that static antiwindup compensation is feasible provided a quasi common lyapunov function between the open loop and unconstrained closed loop exists using the solutions to the matrix feasibility problems the synthesis of the antiwindup augmentation achieving the desired level of l sub 2 performance is then accomplished by solving an additional lmi

a switching anti windup design based on partitioning of the input space abstract this paper revisits the problem of enlarging the domain of attraction of a linear system with multiple inputs subject to actuator saturation by designing a switching anti windup compensator the closed loop system consisting of the plant the controller and the anti windup compensator is first equivalently formulated as a linear system with input deadzone we then partition the input space into several regions in one of these regions all inputs saturate with the time derivative of the saturated input being zero in each of the remaining regions there is a unique input that does not saturate the time derivative of the deadzone function associated with the unsaturating input is zero by utilizing these special properties of the inputs on an existing piecewise lyapunov function of the augmented state vector containing the deadzone function of inputs we design a separate anti windup gain for each region of the input space the switching from one anti windup gain to another is activated when the input signals leave one region for another which can be implemented online since only the measurement of the input signals is required simulation results indicate that the proposed approach has the ability to obtain a significantly larger estimate of the domain of attraction than the existing approaches

ordering trees by their largest eigenvalues abstract the set of trees with n vertices is denoted by t n hofmeister has determined the first five values of the largest eigenvalue of trees in t n and the corresponding trees for these values linear algebra appl 260 1997 43 in other words an order of the first five trees in t n by their largest eigenvalues has been given focus on the same purpose we shall give a partition for trees in t n first in the this paper and then extend this order to the eighth tree

ordering trees by their largest eigenvalues abstract let t and 1 t denote the maximum degree and the largest eigenvalue of a tree t respectively let t n be the set of trees on n vertices and t n t t n t in the present paper among the trees in t n n 4 we characterize the tree which alone minimizes the largest eigenvalue as well as the tree which alone maximizes the largest eigenvalue when n 2 2 n 1 furthermore it is proved that for two trees t1 and t2 in t n n 4 if t 1 2 n 3 1 and t1 t2 then 1 t1 1 t2 by applying this result we extend the order of trees in t n by their largest eigenvalues to the 13th tree when n 12 this extends the results of hofmeister linear algebra appl 260 1997 43 and chang et al linear algebra appl 370 2003 175

second order consensus of multi agent systems under limited interaction ranges this paper studies a distributed linear consensus protocol for second order multi agent systems under limited agent interaction ranges in particular two agents can interact with each other only if their distance is within a certain range under a linear consensus protocol with the relative state feedback we derive a sufficient condition on the initial states and the interaction range to achieve the second order consensus by using a lyapunov functional approach finally simulation examples are included to validate the theoretical result

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

adaptive periodic event triggered consensus for multi agent systems subject to input saturation abstractthis paper investigates the distributed adaptive event triggered consensus control for a class of nonlinear agents each agent is subject to input saturation two kinds of distributed event triggered control scheme are introduced one is continuous time based event triggered scheme and the other is sampled data based event triggered scheme compared with the traditional event triggered schemes in the existing literatures the parameters of the event triggered schemes in this paper are adaptively adjusted by using some event error dependent adaptive laws the problem of simultaneously deriving the controller gain matrix and the event triggering parameter matrix and tackling the saturation nonlinearity is cast into standard linear matrix inequalities problem a convincing simulation example is given to demonstrate the theoretical results

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

neural network based distributed attitude coordination control for spacecraft formation flying with input saturation this brief considers the attitude coordination control problem for spacecraft formation flying when only a subset of the group members has access to the common reference attitude a quaternion based distributed attitude coordination control scheme is proposed with consideration of the input saturation and with the aid of the sliding mode observer separation principle theorem chebyshev neural networks smooth projection algorithm and robust control technique using graph theory and a lyapunov based approach it is shown that the distributed controller can guarantee the attitude of all spacecraft to converge to a common time varying reference attitude when the reference attitude is available only to a portion of the group of spacecraft numerical simulations are presented to demonstrate the performance of the proposed distributed controller

distributed velocity constrained consensus of discrete time multi agent systems with nonconvex constraints switching topologies and delays in this technical note a distributed velocity constrained consensus problem is studied for discrete time multi agent systems where each agent s velocity is constrained to lie in a nonconvex set a distributed constrained control algorithm is proposed to enable all agents to converge to a common point using only local information the gains of the algorithm for all agents need not to be the same or predesigned and can be adjusted by each agent itself based on its own and neighbors information it is shown that the algorithm is robust to arbitrarily bounded communication delays and arbitrarily switching communication graphs provided that the union of the graphs has directed spanning trees among each certain time interval the analysis approach is based on multiple novel model transformations proper control parameter selections boundedness analysis of state dependent stochastic matrices1 exploitation of the convexity of stochastic matrices and the joint connectivity of the communication graphs numerical examples are included to illustrate the theoretical results

distributed h constrained consensus problem abstract this paper is concerned with the distributed h constrained consensus problem for multi agent systems the objective is to use local information to make all agents reach a consensus in a given convex set while satisfying a desired h performance index in the presence of external disturbances a nonlinear distributed algorithm is adopted to solve this constrained consensus problem to measure the effects of the disturbance on the consensus of all agents and the convergence of all agents to the convex set a nonlinear function is constructed as the h output function by analyzing the convexity of the convex set a sufficient condition is given to solve the constrained consensus problem with the desired h performance finally a numerical simulation example is provided to show the effectiveness of our theoretical results

on exploring the domain of attraction for bilateral teleoperator subject to interval delay and saturated p d control scheme the domain of attraction problem is investigated for networked teleoperation system subject to actuator saturation the forward and backward time varying communication delays are assumed to be interval and asymmetric which is the case for network based teleoperation system we propose a novel lyapunov krasovskii functional for the closed loop teleoperation system with the consideration of the interval values of the time delays the delay dependent estimation of the domain of attraction is presented using linear matrix inequality lmi technique the problem of designing mathrm p mathrm d control law such that the domain of attraction is enlarged is formulated and solved as an optimization problem with lmi constraints experiments are performed to verify the effectiveness of the proposed approach

on the two largest eigenvalues of trees abstract very little is known about upper bounds for the largest eigenvalues of a tree that depend only on the vertex number starting from a classical upper bound for the largest eigenvalue some refinements can be obtained by successively removing trees from consideration the results can be used to characterize those trees that maximize the second largest eigenvalue this corrects a result from the literature and it includes a proof of a conjecture of neumaier the main tool for this endeavor is the theory of partial engenvectors

brief multivariable anti windup controller synthesis using linear matrix inequalities we present a general formulation of the problem of multi variable anti windup bumpless transfer awbt controller synthesis which provides sufficient conditions for stability covering a large class of typical input nonlinearities such as saturation deadzone and switching override nonlinearities the resulting synthesis method demonstrates graceful performance degradation whenever input nonlinearities are active through minimization of a weighted l 2 gain the main contribution of the paper is that the awbt controller synthesis using static compensation is cast as a convex optimization over linear matrix inequalities

distributed consensus of second order multiagent systems with nonconvex velocity and control input constraints this paper is devoted to a distributed consensus problem for second order multiagent systems with nonconvex velocity and control input constraints a distributed control algorithm is introduced using local information it is shown that consensus can be achieved as long as the union of the communication graphs has directed spanning trees among each time interval of certain bounded length in the presence of arbitrarily bounded communication delays finally a numerical example is included to illustrate the theoretical results

a generalization of the scattering transformation for conic systems a generalized version of the scattering transformation is introduced which allows for rendering of the input output characteristics of a nonlinear conic system into an arbitrary prescribed conic sector the transformation is consequently applied to the problem of stabilization of conic systems interconnections the stability is achieved by rendering the input output characteristics of the subsystems into complementary cones such that the graph separation stability condition is satisfied in the presence of communication delays the scattering based technique for stabilization of feedback interconnections is generalized to the case of arbitrary conic subsystems

generalized kyp lemma unified frequency domain inequalities with design applications the celebrated kalman yakubovic spl caron popov kyp lemma establishes the equivalence between a frequency domain inequality fdi and a linear matrix inequality and has played one of the most fundamental roles in systems and control theory this paper first develops a necessary and sufficient condition for an s procedure to be lossless and uses the result to generalize the kyp lemma in two aspects the frequency range and the class of systems and to unify various existing versions by a single theorem in particular our result covers fdis in finite frequency intervals for both continuous discrete time settings as opposed to the standard infinite frequency range the class of systems for which fdis are considered is no longer constrained to be proper and nonproper transfer functions including polynomials can also be treated we study implications of this generalization and develop a proper interface between the basic result and various engineering applications specifically it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain phase properties in several frequency ranges the method is illustrated by numerical design examples of digital filters and proportional integral derivative controllers

design of saturation based switching anti windup gains for the enlargement of the domain of attraction this technical note proposes a saturation based switching anti windup design for the enlargement of the domain of attraction of the closed loop system a widely adopted method of dealing with an m dimensional saturated linear feedback is to express it as a linear combination of a set of 2m auxiliary linear feedbacks for each value of the state these auxiliary linear feedbacks form a convex polyhedron of 2m vertices in the input space we propose to divide this convex polyhedron into several convex sub polyhedrons each of which is defined as the convex hull of a subset of the auxiliary feedbacks whenever the value of the saturated linear feedback falls into a sub polyhedron it can be expressed as a linear combination of a subset of the 2m auxiliary linear feedbacks that define the sub polyhedron and thus a less conservative result can be expected a separate anti windup gain is designed for each sub polyhedron by using a common quadratic lyapunov function and implemented when the value of the saturated linear feedback falls into this sub polyhedron simulation results indicate that such a saturation based switching anti windup design has the ability to significantly enlarge the domain of attraction of the closed loop system

anti windup strategies for discrete time switched systems subject to input saturation this paper deals with the design of anti windup compensator for discrete time switched systems subject to input saturation the cases of static and dynamic anti windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed loop system two aspects of the switching law are taken into account during the design either it is arbitrary or it is a part of the complete control law theoretical conditions allowing to synthesise the anti windup compensator are mainly described through linear matrix inequalities computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution

on the spectral radius of trees abstract in this paper we investigated the spectral radius of trees and obtained the following result let t be a tree on n vertices let m t denote one maximum matching of t and m t i let t i be a tree as shown in fig 1 then t 1 2 n i 1 n i 1 2 4 n 2i 1 and equality holds if and only if t t i

nonlinear scheduled anti windup design for linear systems the nonlinear l sub 2 anti windup framework introduced in teel and kapor 1997 reduces the anti windup synthesis problem to a state feedback synthesis problem for linear systems with input saturation and input matched l sub 2 disturbances in this note based on the structure proposed in that previous paper we provide a linear matrix ineqaulity lmi formulation of high performance anti windup design for control systems with linear asymptotically stable plants in particular we first give a linear quadratic based formulation of linear anti windup compensation in terms of the solution of a set of always feasible lmi constraints then we propose a nonlinear scheduling technique where hysteresis switching among a family of linear gains is employed for performance improvement both design techniques are demonstrated on an academic example

simpson s paradox and related phenomena simpson s paradox is viewed as one of a natural and coherent collection of association reversal phenomena that are of fundamental importance in statistical practice association reversal means that the direction of association between two variables x and y is changed by collapsing unconditioning over a covariate z an example is simpson s paradox for contingency tables this article gives necessary and sufficient conditions for simpson s paradox and for more general forms of association reversal close connections are noted with amalgamation paradoxes defined as situations where an unconditional measure of association between x and y lies outside the range of the conditional on z measures emphasis throughout is on statistical interpretation and on commonalities and contrasts between the paradoxical phenomena in various settings

saturation based switching anti windup design for linear systems with nested input saturation this paper proposes a saturation based switching anti windup design for the enlargement of the domain of attraction of a linear system subject to nested saturation a nestedly saturated linear feedback is expressed as a linear combination of a set of auxiliary linear feedbacks which form a convex hull where the nestedly saturated linear feedback resides this set of auxiliary linear feedbacks is then partitioned into several subsets the auxiliary linear feedbacks in each of these subsets form a convex sub hull of the original convex hull when the value of the nestedly saturated linear feedback falls into a convex sub hull it can be expressed as a linear combination of the subset of all the auxiliary feedbacks that form the convex sub hull a separate anti windup gain is designed for each convex sub hull by using a common quadratic lyapunov function and is implemented when the value of the nestedly saturated linear feedback falls into this convex sub hull simulation results indicate that such a saturation based switching anti windup design has the ability to significantly enlarge the domain of attraction of the closed loop system