a note on stabilization by dynamic high gain output feedback in this note we study the problem of stabilization by dynamic output feedback for a certain class of linear systems we establish the existence of pairs of subspaces im upsilon a where im is a minimum phase input subspace contained in an almost stabilizability snbspace upsilon a by applying a recent theorem by sehumacber this result leads to the existence of stabilizing high gain compensators for the linear systems under consideration in particular it will be shown that invertible minimum phase systems can always be stabilized by dynamic compensators of dynamic order equal to the excess of poles over zeros minus the number of inputs

the discrete time h control problem with measurement feedback this paper is concerned with the discrete time h infty control problem with measurement feedback it follows that as in the continuous time case the existence of an internally stabilizing controller that makes the h infty norm strictly less than 1 is related to the existence of stabilizing solutions to two algebraic riccati equations however in the discrete time case the solutions of these algebraic riccati equations must satisfy extra conditions

products in hochschild cohomology and grothendieck rings of group crossed products abstract we give a general construction of rings graded by the conjugacy classes of a finite group some examples of our construction are the hochschild cohomology ring of a finite group algebra the grothendieck ring of the drinfel d double of a group and the orbifold cohomology ring for a global quotient we generalize the first two examples by deriving product formulas for the hochschild cohomology ring of a group crossed product and for the grothendieck ring of an abelian extension of hopf algebras our results account for similarities in the product structures among these examples

nested generalized linear mixed models an orthodox best linear unbiased predictor approach summary we introduce a new class of generalized linear mixed models based on the tweedie exponential dispersion model distributions accommodating a wide range of discrete continuous and mixed data using the best linear unbiased predictor of random effects we obtain an optimal estimating function for the regression parameters in the sense of godambe allowing an efficient common fitting algorithm for the whole class although allowing full parametric inference our main results depend only on the first and second moment assumptions of unobserved random effects in addition we obtain consistent estimators for both regression and dispersion parameters we illustrate the method by analysing the epilepsy data and cake baking data along with simulations and asymptotic justifications this shows the usefulness of the method for analysis of clustered non normal data

a minimax approach to consistency and efficiency for estimating equations the consistency of estimating equations has been studied in the main along the lines of cramer s classical argument which only asserts the existence of consistent solutions the statement similar to that of doob and wald which identifies the consistent solutions has not yet been established the obstacle is that the solutions of estimating equations cannot in general be defined as the maximum of likelihood functions in this paper we demonstrate that the consistent solutions can be identified as the minimax of a function r whose properties resemble those of a log likelihood ratio but which exists in a much wider context furthermore since we do not need r to be differentiable the minimax is consistent even when the estimating equation does not exist in this respect the minimax is a new estimator we first convey the idea by focusing on the quasi likelihood estimate and then indicate its full generality by providing a set of sufficient conditions for consistency and studying a number of important cases efficiency will also be verified

on computing the stabilizing solution of the discrete time riccati equation abstract a necessary and sufficient condition is given for the existence of the stabilizing solution of the discrete time riccati equation without any invertibility or positivity assumptions the result involves a special associated matrix pencil

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

system structure and singular control the general continuous time linear quadratic control problem is considered it is shown that recently developed linear system theoretic properties and algorithms play an important role in solving this singular control problem

continuity properties of the cheap control problem without stability abstract an open problem concerning the convergence of the optimal cost for the cheap control problem without stability is solved it turns out that the definition of a new type of linear quadratic optimal control problems is necessary this new problem requires the infimization of the cost functional under the constraint that the state trajectory modulo a certain subspace vanishes as time goes to infinity the associated optimal cost turns out to be the limit of the optimal cost for the cheap control problem without stability moreover for left invertible systems the optimal control state and output for the perturbed problem tend to the optimal control state and output for the new problem also a characterization of the optimal cost for the latter problem is given in terms of the dissipation inequality

brief control relevant experiment design for multivariable systems described by expansions in orthonormal bases the problem of control relevant experiment design is considered we first develop the problem in abstract form as an optimization of an unspecified closed loop performance index then we make the problem specific by considering systems that can be described via a finite expansion of orthonormal bases and designing the controller by specifying the closed loop system s sensitivity function although the resulting optimization problem is nonconvex and may admit local solutions simulations of high purity binary distillation columns are presented to demonstrate that significant improvements in controller performance may be obtained even by using the local solution

on the perfect regulation of optimal regulators an alternative proof is provided for an earlier result of francis 1 on the perfect regulation of optimal regulators our proof shown in the present paper 1 is an interesting application of anderson s result on the spectral factorization and may be simpler and more transparent than the one in 1

spectral sequences for the cohomology rings of a smash product abstract stefan and guichardet have provided lyndon hochschild serre type spectral sequences which converge to the hochschild cohomology and ext groups of a smash product we show that these spectral sequences carry natural multiplicative structures and that these multiplicative structures can be used to calculate the cup product on hochschild cohomology and the yoneda product on an ext algebra

the h control problem with zeros on the boundary of the stability domain in this paper we study the discrete and continuous time h control problems without any assumptions on the system parameters our approach yields necessary and sufficient conditions for the existence of a suitable controller

the discrete time riccati equation related to the h sub spl infin control problem the h sub spl infin control problem has been solved recently with the use of discrete time algebraic riccati equations in this paper we investigate this riccati equation we derive recursive methods to find the stabilizing solution of this riccati equation moreover we derive several properties of the class of positive semi definite solutions of this equation

existence of minimum upcrossing controllers an optimal stochastic control problem that minimizes the probability that a signal upcrosses a level is solved by rewriting it as a one parametric optimization problem over a set of lqg control problem solutions finding the optimal controller can be interpreted as finding an optimal costing transfer function the existence of the optimal controller is investigated in a constructive way and it is shown that it is equivalent to the existence of a controller with sufficiently small closed loop variance of the controlled signal

lur e equations and even matrix pencils abstract in this work we consider the so called lur e matrix equations that arise e g in model reduction and linear quadratic infinite time horizon optimal control we characterize the set of solutions in terms of deflating subspaces of even matrix pencils in particular it is shown that there exist solutions which are extremal in terms of definiteness it is shown how these special solutions can be constructed via deflating subspaces of even matrix pencils

a note on families of linear quadratic problems continuity properties in the above mentioned paper by h l trentelman see ibid vol ac 32 pp 323 329 1987 one parameter epsilon families of these problems with stability are investigated it is shown that the set of invariant zeros of the epsilon problem is contained in the set of invariant zeros of the boundary problem the problem with epsilon 0 if the boundary system is left invertible this result is obtained by applying only the assumptions on the continuity and the monotonicity of the weighting matrices that are made in the above mentioned paper consequently one can replace the third assumption in that paper by a much weaker one

the first cohomology group of an algebra with coefficients in a bimodule after their introduction in the 1940s cf 18 the hochschild homology and cohomology groups of an algebra with coefficients in a bimodule have played a fundamental role given an algebra and a bimodule m and viewing both and m as left modules over the enveloping algebra e op the hochschild cohomology groups h m are the groups ext m while the homology groups h m are the corre sponding tor groups cf 5 chap ix the most studied case has been that in which m and more specifically when is a split basic finite dimensional algebra over a field k in that case the algebra is partially determined by combinatorial data namely its quiver with relations and it is a natural goal to obtain information about h m resp h m in terms of those combinatorial data that was the scheme of the initial attempts made by cibils 6 and happel 17 to give explicit formulae for the dimensions of the h in terms of computations the first natural situation to look at is that in which the algebra is monomial since

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

the singular h 2 control problem in this paper we discuss the standard h2 control problem for linear finite dimensional time invariant systems without any assumptions on the system parameters we give an explicit formula for the infimum over all internally stabilizing strictly proper compensators and give a characterization when the infimum is attained

hierarchical generalized linear models we consider hierarchical generalized linear models which allow extra error components in the linear predictors of generalized linear models the distribution of these components is not restricted to be normal this allows a broader class of models which includes generalized linear mixed models we use a generalization of henderson s joint likelihood called a hierarchical or h likelihood for inferences from hierarchical generalized linear models this avoids the integration that is necessary when marginal likelihood is used under appropriate conditions maximizing the h likelihood gives fixed effect estimators that are asymptotically equivalent to those obtained from the use of marginal likelihood at the same time we obtain the random effect estimates that are asymptotically best unbiased predictors an adjusted profile h likelihood is shown to give the required generalization of restricted maximum likelihood for the estimation of dispersion components a scaled deviance test for the goodness of fit a model selection criterion for choosing between various dispersion models and a graphical method for checking the distributional assumption of random effects are proposed the ideas of quasi likelihood and extended quasi likelihood are generalized to the new class we give examples of the poisson gamma binomial beta and gamma inverse gamma hierarchical generalized linear models a resolution is proposed for the apparent difference between population averaged and subject specific models a unified framework is provided for viewing and extending many existing methods

on the existence of a positive definite solution of the matrix equation x atx 1a i the question is raised under which conditions on the real square matrix a the matrix equation x atx 1a i has a real symmetric positive definite solution x both necessary and sufficient solvability conditions on a are derived moreover we give an algorithm to calculate the solution for a number of special cases we also present an analytic solution

on linear and quadratic estimating functions summary in some cases maximum quasi likelihood estimation which is at the core of glim can fail to give reasonable results a more general class of estimating functions is investigated which avoids such failure and also is not restricted to the particular forms of mean and variance function of glim

asymptotic orders of reachability in perturbed linear systems a framework for studying asymptotic orders of reachability in perturbed linear time invariant systems is developed the systems of interest are defined by matrices that have asymptotic expansions in powers of a perturbation parameter epsilon about the point 0 the reachability structure is exposed by means of the smith form of the reachability matrix this approach is used to provide insight into the kinds of inputs needed to reach weakly reachable target states into the structure of high gain feedback for pole placement and into the types of inputs that steer trajectories arbitrarily close to almost a b invariant subspaces and almost a b controllability subspaces

continuity properties of solutions to h 2 and h riccati equations in h2 and h optimal control semi stabilizing solutions of algebraic riccati equations play an essential role it is well known that these solutions might have discontinuities as a function of the system parameters the paper shows that these discontinuities are directly linked to non left invertibility and in contrast to what one might think unrelated to zeros on the imaginary axis

a unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback we study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties our approach relies on well known h sub spl infin linear control tools and allows one to recover and improve in the unifying framework of a semiglobal separation result existing results on the semiglobal stabilization via output feedback in particular we discuss the case of uncorrupted outputs input and output nonlinearities or model uncertainties which may include for example practical situations such as backlash hysteresis and saturations the key feature of our design procedure is given by the choice of two continuous functions the first one is instrumental in constructing a stabilizing controller the second one arises in the candidate lyapunov function for the closed loop system relying on our main theorem we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems

multiple time scale decomposition in cheap control problems singular control a linear quadratic regulator problem where a small parameter 2multiplies the control cost is considered as mu rightarrow 0 it exhibits a dynamic behavior with multiple time scales whereas for mu 0 it is a singular control problem at first a multiparameter singularly perturbed model of the given problem is constructed by transferring the singularity that exists in the performance index to the dynamic equations then the problem is decomposed into several subproblems of minimal order each pertaining to only one time scale the method developed permits under a single framework the characterization of asymptotic behavior of optimal closed loop poles state and control trajectories performance index and optimal transfer function as mu rightarrow 0 moreover the asymptotic solution brings into focus 1 the nature of singular control and its connection to transmission zeros and 2 the presence of various types of impulses and other higher order distributions in both state and control the approach unifies and extends significantly several ideas previously somewhat disjoint

efficiency of estimating equations and the use of pivots summary methods are proposed for deriving unbiased estimating equations for the parameters of interest in a statistical model which includes further incidental or nuisance parameters we start with pivot like quantities which eliminate the dependence on the incidental parameters and derive functions of these which give estimating equations which are most efficient in a certain sense these equations involve the incidental parameters which are then replaced by estimators the methods overcome some of the difficulties encountered in likelihood and least squares estimation when there are many incidental parameters and our theory reduces to likelihood and least squares estimation when there are none thus the optimality results apply to these methods too some examples are discussed

quasi likelihood for multiplicative random effects summary a quasi likelihood approach similar to that described by morton 1987 is found to be particularly simple in the case of measurements subject to two or more sources of multiplicative error still further simplification occurs when the effects of interest also are multiplicative the multiplicative analogue of the balanced split plot model is considered in detail an analysis of gamma deviance replaces the familiar analysis of variance the efficiency of the quasi likelihood method relative to a more conventional analysis of logarithms of the data is explored briefly

direct singular perturbation analysis of high gain and cheap control problems a new and direct approach to the analysis and design of high gain feedback and cheap control problems is developed transformation of such singular problems to singular perturbation models of conventional type early at the onset of analysis or design allows a direct application of the readily available singular perturbation literature the approach permits a simple characterization of a multivariable root loci under a high gain feedback and b asymptotic behavior of optimal closed loop poles state and control trajectories performance index and optimal transfer function as the control cost coefficient in the performance index goes to zero

the role of the dissipation matrix in singular optimal control the optimal cost in the regular stationary linear quadratic optimal control problem is given by the maximal solution of an algebraic riccati equation this solution minimizes the rank of a certain matrix which we call the dissipation matrix the rank minimization problem is also meaningful in the singular case does it provide the optimal cost for the singular control problem this question was posed by j c willems in 1971 the answer is yes

semi global stabilizability of linear null controllable systems with input nonlinearities an h sub spl infin based lyapunov proof is provided for a result established by lin and saberi 1993 if a linear system is asymptotically null controllable with bounded controls then when subject to input saturation it is semi globally stabilizable by linear state feedback a new result is that if the system is also detectable then it is semi global stabilizable by completely linear output feedback further an extension which relaxes the requirements on the input characteristic is obtained

the crossed burnside rings iii the dress construction for a tambara functor abstract we discuss the dress construction for a tambara functor associated to a finite commutative monoid with action of a finite group

algorithms for optimal control with invariant zeros on the extended imaginary axis abstract we transform an control problem with invariant zeros on the extended imaginary axis into a regular problem then using the nevanlinna pick theorem we find necessary and sufficient existence conditions for the original control problem an algorithm and examples with invariant zeros on the extended imaginary axis are given by the same approach we also solve the singular 2 control problem

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

crossed burnside rings ii the dress construction of a green functor abstract we present some results about the dress construction of green functor associated to a g monoid in particular we see that the crossed burnside rings the representation rings of quantum double and hochschild cohomology rings are constructed by the dress construction of some green functors

a geometric approach to the singular filtering problem we consider the least squares filtering problem for a stationary gaussian process when the observation is not fully corrupted by white noise the so called singular case an optimal estimator is constructed consisting of an integrating part which is as in the regular case computed from a spectral factorization or an equivalent matrix problem and a differentiating part whose parameters are computed from a single matrix equation this improves on older results which either work under restrictive assumptions or describe the solution only as the result of some nested algorithm

on a class of optimal control problems with an almost cost free solution for a class of linear singular optimal control problems with a nonunique singular arc the solution of the corresponding nearly singular problem is analyzed and a limit solution based on formal singular perturbations is derived a rigorous proof of the correctness of the result is given by constructing a convergent power series satisfying the riccati equation of the nearly singular problem

all controllers for the general h control problem lmi existence conditions and state space formulas this paper presents all controllers for the general h control problem with no assumptions on the plant matrices necessary and sufficient conditions for the existence of an h controller of any order are given in terms of three linear matrix inequalities lmis our existence conditions are equivalent to scherer s results but with a more elementary derivation furthermore we provide the set of all h controllers explicitly parametrized in the state space using the positive definite solutions to the lmis even under standard assumptions full rank etc our controller parametrization has an advantage over the q parametrization the freedom q a real rational stable transfer matrix with the h norm bounded above by a specified number is replaced by a constant matrix l of fixed dimension with a norm bound and the solutions x y to the lmis the inequality formulation converts the existence conditions to a convex feasibility problem and also the free matrix l and the pair x y define a finite dimensional design space as opposed to the infinite dimensional space associated with the q parametrization

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

almost disturbance decoupling with internal stability the almost disturbance decoupling problem with internal stability is solved in terms of the geometric concepts of linear systems theory the solution gives necessary and sufficient conditions for the existence of a dynamic output feedback controller such that in the closed loop system the disturbances are quenched say in the h sup infinity sense up to any degree of accuracy while maintaining a stable system matrix

continuous and discrete time riccati theory a popov function approach abstract necessary and sufficient conditions for the existence of the stabilizing solution of the algebraic riccati equation are derived for both the continuous and the discrete time case under the weakest possible assumptions imposed on the initial data both frequency domain conditions involving an associated popov function and time domain conditions involving an associated matrix pencil are investigated

identification of arx systems with non stationary inputs asymptotic analysis with application to adaptive input design a key problem in optimal input design is that the solution depends on system parameters to be identified in this contribution we provide formal results for convergence and asymptotic optimality of an adaptive input design method based on the certainty equivalence principle i e for each time step an optimal input design problem is solved exactly using the present parameter estimate and one sample of this input is applied to the system the results apply to stable arx systems with the input restricted to be generated by white noise filtered through a finite impulse response filter or a binary signal obtained from the latter by a static nonlinearity

a nine fold canonical decomposition for linear systems the zero structure for non minimal proper systems in state space form is investigated the approach is geometric and a complete characterization in geometric terms is given of the invariant decoupling system and transmission zeros as defined by rosenbrock the first main result is a formula for the transmission zeros second a canonical lattice diagram is presented of a decomposition of the state space which can be viewed as the product of the kalman canonical decomposition and the morse canonical decomposition this decomposition gives a straightforward characterization of all zeros just mentioned in terms of spectral properties of subspaces under a certain class of feedback and injection mappings via this diagram a number of equivalent formulae for the transmission zeros are derived the freedom in pole assignment leads to new characterizations for the invariant and system zeros in terms of greatest common divisors of characteristic polynomials finally the relation is demonstrated be

cohomological symmetry in triangulated categories abstract we give a criterion for cohomological symmetry in a triangulated category as an application we show that such cohomological symmetry holds for all pairs of modules over any exterior algebra

approximate likelihoods for generalized linear errors in variables models when measurement error is present in covariates it is well known that naively fitting a generalized linear model results in inconsistent inferences several methods have been proposed to adjust for measurement error without making undue distributional assumptions about the unobserved true covariates stefanski and carroll focused on an unbiased estimating function rather than a likelihood approach their estimating function known as the conditional score exists for logistic regression models but has two problems a poorly behaved wald test and multiple solutions they suggested a heuristic procedure to identify the best solution that works well in practice but has little theoretical support compared with maximum likelihood estimation to help to resolve these problems we propose a conditional quasi likelihood to accompany the conditional score that provides an alternative to wald s test and successfully identifies the consistent solution in large samples

the almost disturbance decoupling problem with internal stability for linear systems subject to input saturation state feedback case abstract we consider the almost disturbance decoupling problem addp and or almost d bounded disturbance decoupling problem addp d with internal stability for linear systems subject to input saturation and input additive disturbance via linear static state feedback we show that the almost d bounded disturbance decoupling problem with local asymptotic stability addp las d is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable no matter where the poles of the open loop system are and the locations of these poles play a role only in the solution of addp gas d addp sgas d or addp gas where semi global or global asymptotic stability is required

output regulation for linear systems subject to input saturation the purpose of this paper is to examine the problem of controlling a linear time invariant system subject to input saturation in order to have its output track or reject a family of reference or disturbance signals produced by some external generator it is shown that a semiglobal framework for this problem is a natural one within this framework a set of solvability conditions are given and feedback laws that solve the problem are constructed the theory developed in this paper incorporates earlier results established for linear systems without input saturation

reduced order controllers for the h control problem with unstable invariant zeros this paper addresses the existence and design methods of reduced order controllers for the h control problem with unstable invariant zeros in the state space realization of the transfer function matrix from the control input to the controlled error or from the exogenous input to the observation output where the realization is induced from a stabilizable and detectable realization of the generalized plant this paper presents a new controller degree bound for the h control problem in terms of the minimal rank of the system matrix pencils of these two transfer function matrices in the unstable region when the unstable invariant zero exists this paper shows that reduced order controllers with orders strictly less than that of the generalized plant exist if the h control problem is solvable moreover this paper shows that the computational problem of finding the controllers with the new degree bound is convex by providing two linear matrix inequality based design methods algorithms for constructing the reduced order controllers the results developed in this paper are valid both for the continuous and discrete time h control problems

approximate likelihood ratios for general estimating functions summary the method of estimating functions godambe 1991 is commonly used when one desires to conduct inference about some parameters of interest but the full distribution of the observations is unknown however this approach may have limited utility due to multiple roots for the estimating function a poorly behaved wald test or lack of a goodness of fit test this paper presents approximate likelihood ratios that can be used along with estimating functions when any of these three problems occurs we show that the approximate likelihood ratio provides correct large sample inference under very general circumstances including clustered data and misspecified weights in the estimating function two methods of constructing the approximate likelihood ratio one based on the quasi likelihood approach and the other based on the linear projection approach are compared and shown to be closely related in particular we show that quasi likelihood is the limit of the projection approach we illustrate the technique with two applications

relationship between three discrete time h algebraic riccati equation solutions this paper presents a proof of a connection between the strong solutions to three algebraic riccati equations which are associated with the solution of a discrete time h optimal control problem of these solutions denoted x y and z two parametrize a generator of all suboptimal output feedback controllers and one is associated with a dual state feedback problem the relationship is proved by establishing the existence of a similarity transformation between two symplectic matrix pencils which are associated with two of the riccati equations a similar result is known to exist in the continuous time setting

singular optimal control a geometric approach linear quadratic singular optimal control problem is solved for nonminimum phase and noninvertible systems a state space decomposition is obtained and a reduced order nonsingular subproblem is solved the optimal stabilizing input of the singular problem has been found when there are no transmission zeros on the imaginary axis

simultaneous l p stabilization and internal stabilization of linear systems subject to input saturation state feedback case abstract we consider the problem of simultaneous finite gain l p stabilization and internal stabilization of linear systems subject to input saturation via linear static state feedback we show that bounded input finite gain l p stabilization and local asymptotic stabilization can always be achieved simultaneously no matter where the poles of the open loop system are and the locations of these poles play a role only when bounded input finite gain l p stabilization and global or semi global stabilization are required simultaneously

bounds for hochschild cohomology of block algebras we show that for any block algebra b of a finite group over an algebraically closed field of prime characteristic the dimension of hh n b is bounded by a function depending only on the nonnegative integer n and the defect of b the proof uses in particular a theorem of brauer and feit which implies the result for n 0

h control problem with jω axis zeros abstract in this paper we discuss the so called one block h control problem in the case where the plant has j axis including infinity poles and zeros first we derive a necessary and sufficient condition for the h model matching problem to have a solution in the transfer function setting second we give a solvability condition which enables us to check the solvability by i examining matrix norm conditions related to j axis zeros and ii solving two generalized riccati equations finally we extend our result to the standard h problem

a generalized linear model with nested strata of extra poisson variation on etend la definition de quasivraisemblance pour tenir compte de plusieurs strates de variation emboitees dans un modele lineaire generalise

a complete and simple parametrization of controllers for a nonstandard h control problem abstract a complete and simple parametrization of all h controllers is derived for a class of nonstandard h control problems with d 12 and d 21 being of full row and column ranks respectively by making use of the youla parametrization and standard h control theory

input design via lmis admitting frequency wise model specifications in confidence regions a framework for reformulating input design problems in prediction error identification as convex optimization problems is presented for linear time invariant single input single output systems this framework unifies and extends existing results on open loop input design that are based on the finite dimensional asymptotic covariance matrix of the parameter estimates basic methods for parametrizing the input spectrum are provided and conditions on these parametrizations that guarantee that all possible covariance matrices for the asymptotic distribution of the parameter estimates can be generated are provided a wide range of model quality constraints can be handled in particular different frequency by frequency constraints can be used this opens up new applications of input design in areas such as robust control furthermore quality specifications can be imposed on all models in a confidence region thus allowing for statements such as with at least 99 probability the model quality specifications will be satisfied

h sub spl infin observer design for lipschitz nonlinear systems the problem of observer design for lipschitz nonlinear systems is considered a new dynamic framework which is a generalization of previously used lipschitz observers is introduced and the generalized sufficient condition that ensures asymptotic convergence of the state estimates is presented the equivalence between this condition and an h sub spl infin optimal control problem which satisfies the standard regularity assumptions in h sub spl infin optimization theory is shown and a parameterization of all possible observers is also presented a design procedure which is less restrictive than the existing design approaches is proposed and a simulation example is given to illustrate the observer design

solvability conditions and design for state synchronization of multi agent systems this paper derives conditions on the agents for the existence of a protocol which achieves synchronization of homogeneous multi agent systems mas with partial state coupling where the communication network is directed and weighted these solvability conditions are necessary and sufficient for single input agents and sufficient for multi input agents the solvability conditions reveal that the synchronization problem is primarily solvable for two classes of agents this first class consists of at most weakly unstable agents i e agents have all eigenvalues in the closed left half plane and the second class consists of at most weakly non minimum phase agents i e agents have all zeros in the closed left half plane under our solvability condition we provide in this paper a design utilizing h optimal control

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

quillen stratification for hochschild cohomology of blocks we decompose the maximal ideal spectrum of the hochschild cohomology ring of a block of a finite group into a disjoint union of subvarieties corresponding to elementary abelian p subgroups of a defect group these subvarieties are described in terms of group cohomological varieties and the alperin broue correspondence on blocks our description leads in particular to a homeomorphism between the hochschild variety of the principal block and the group cohomological variety the proofs require a result of stephen f siegel given in the appendix which states that nilpotency in hochschild cohomology is detected on elementary abelian p subgroups

families of linear quadratic problems continuity properties in this paper we investigate for given one parameter families of linear time invariant finite dimensional systems the parameter dependence of the linear quadratic optimal cost optimal control inputs optimal state trajectories and optimal outputs it is shown that results that have been obtained in the past in the context of the problem of cheap control can in fact be generalized to a much broader class of parameter dependent cost functionals including cost functionals in which for every parameter value the weighting matrix of the control inputs is singular essentially only two assumptions on the parameter dependence of the cost functionals are required in order to have continuity of the optimal cost and optimal control inputs with respect to the underlying parameter one assumption is concerned with the continuity of the weighting matrices with respect to this parameter the other with the monotonicy of the weighting matrices with respect to the parameter instrumental in our development is a characterization of the linear quadratic optimal cost in terms of the so called dissipation inequality the results obtained are applied to the problem of cheap control and to a problem of priority control the latter provides an example of a family of quadratic cosl functionals with a polynomial parameter dependence

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

the hochschild cohomology ring of a group algebra there is a standard additive decomposition of the hochschild cohomology ring of the group algebra of a finite group g as the direct sum of the cohomology rings of the centralizers of representatives of the conjugacy classes of g a special case of our main result describes the cup product in terms of this decomposition as applications we determine presentations for the hochschild cohomology rings of 1 the mod 3 group algebra of the symmetric group s 3 2 the mod 2 group algebra of the alternating group a 4 and 3 the mod 2 group algebras of the dihedral 2 groups

asymptotic properties of nonlinear least squares estimates in stochastic regression models stochastic regression models of the form y i f i e i where the random disturbances e i form a martingale difference sequence with respect to an increasing sequence of fields g i and f i is a random g i 1 measurable function of an unknown parameter cover a broad range of nonlinear and linear time series and stochastic process models herein strong consistency and asymptotic normality of the least squares estimate of in these stochastic regression models are established in the linear case f i t y i they reduce to known results on the linear least squares estimate 1 n y i y i t with stochastic g i 1 measurable regressors i

biometrika centenary theory and general methodology note reprinted in biometrika one hundred years edited by d m titterington and d r cox oxford university press 11 50 reference stat article 2001 002doi 10 1093 biomet 88 1 13view record in web of science record created on 2006 04 21 modified on 2017 05 12