improved estimation of the disturbance variance in a linear regression model abstract in this paper we consider estimation of the disturbance variance in a linear regression model a new class of improved estimators is obtained by extending results dating to stein 1964 these estimators dominate the ordinary least squares estimator under squared error loss

parametrization of all strictly causal stabilizing controllers within the framework of the factorization approach we present parametrizations of all strictly causal stabilizing controllers

on stabilization and the existence of coprime factorizations shows that any transfer function matrix whose elements belong to the quotient field of h sub infinity and which is stabilizable has a matrix fraction representation over h sub infinity which is coprime in the sense that a matrix bezout identity can be satisfied

semi cancellable fractions in system theory in this paper we propose to define the transfer function of a system in a new way namely as a semi cancellable fraction scf i e a fraction in which unstable pole zero cancellations are not allowed within this new framework it is possible to be rigorous and coherent in dealing with the stabilizability of a system from an input output viewpoint not focusing on the stabilizability of infinite dimensional input output systems

optimal critical values of pre tests when estimating the regression error variance analytical findings under a general loss structure this paper re visits the problem of estimating the regression error variance in a linear multiple regression model after preliminary hypothesis tests for either linear restrictions on the coefficients or homogeneity of variances there is an extensive literature that discusses these problems particularly in terms of the sampling properties of the pre test estimators using various loss functions as the basis for risk analysis in this paper a unified framework for analysing the risk properties of these estimators is developed under a general class of loss structures that incorporates virtually all first order differentiable losses particular consideration is given to the choice of critical values for the pre tests analytical results indicate that an level substantially higher than those normally used may be appropriate for optimal risk properties under a wide range of loss functions the paper also generalizes some known analytical results in the pre test literature and proves other results only previously shown numerically

solving linear systems via pfaffians abstract an explicit solution is given for the system of linear equations e e t where are alternating matrices of pfaffian 1 which at most differ in their first row and column and e is of the form i 2 2 r e 1 i x i if v v w r r 1 with v w 1 v w then a sequence of cohn transforms with respect to the fixed w which takes v w to v w is prescribed

a simple adaptive procedure leading to correlated equilibrium we propose a new and simple adaptive procedure for playing a game regret matching in this procedure players may depart from their current play with probabilities that are proportional to measures of regret for not having used other strategies in the past it is shown that our adaptive procedure guarantees that with probability one the empirical distributions of play converge to the set of correlated equilibria of the game

constrained traffic equilibrium in routing we study noncooperative routing in which each user is faced with a multicriterion optimization problem formulated as the minimization of one criterion subject to constraints on others we address the questions of existence and uniqueness of equilibrium we show that equilibria indeed exist but uniqueness may be destroyed due to the multicriteria nature of the problem we obtain uniqueness in some weaker sense under appropriate conditions we show that the link utilizations are uniquely determined at equilibrium we further study the normalized constrained equilibrium and apply it to pricing

i inverness for polynomial matrices of non constant rank abstract let p1 pt be polynomials in c n with a variety v of common zeros contained in a suitable open set u explicit formulas are provided to construct rational functions 1 s such that i 1spi i 1 and such that the singularities of the i are contained in u this result is applied to compute rational functions valued 1 inverses of matrices with polynomial coefficients which do not have constant rank while retaining control over the location of the singularities of the rational functions themselves

analysis of stability robustness for generalized state space systems with structured perturbations abstract a new approach is proposed to analyze the stability robustness of generalized state space systems with structured perturbations the presented method is computationally simple to use and can easily be calculated by computer as far as we are aware this paper seems to be the first one to solve the robust stability problems for generalized state space systems with structured uncertainties the robust stability problem of generalized state space systems is more complicated than that of regular state space systems because it needs consideration of not only stability robustness but also system regularity and impulse elimination the latter two ones need not be considered in regular state space systems

algebraic geometric aspects of feedback stabilization this paper develops a theory of feedback stabilization for siso transfer functions over a general integral domain which extends the well known coprime factorization approach to stabilization necessary and sufficient conditions for stabilizability of a transfer function in this general setting are obtained these conditions are then refined in the special cases of unique factorization domains ufds noetherian rings and rings of fractions it is shown that these conditions can be naturally interpreted geometrically in terms of the prime spectrum of the ring this interpretation provides a natural generalization to the classical notions of the poles and zeros of a plant the set of transfer functions is topologized so as to restrict to the graph topology of vidyasagar ieee trans automatic control ac 29 1984 pp 403 418 when the ring is a bezout domain it is shown that stability of a feedback system is robust in this topology when the ring is a ufd this theory is then applied to the problem of sta

feedback stabilization of mimo 3 d linear systems the authors solve the open problem of the existence of double coprime factorizations for a large class of multi input multi output mimo three dimensional 3 d linear systems it is proven that if all the unstable zeros of the contents associated with left and right matrix fraction descriptions of a given feedback stabilizable causal mimo 3 d plant are simple then the plant has a double coprime factorization the authors then give a parameterization of all stabilizing compensators for a mimo 3 d system in this class the key result developed in the paper is a novel and constructive technique of replacing an unstable polynomial with a stable polynomial step by step an illustrative example is also provided

on syzygy modules for polynomial matrices abstract in this paper we apply the theory of multivariate polynomial matrices to the study of syzygy modules for a system of homogeneous linear equations with multivariate polynomial coefficients several interesting structural properties of syzygy modules are presented and illustrated with examples

a behavioral approach to the pole structure of one dimensional and multidimensional linear systems we use the tools of behavioral theory and commutative algebra to produce a new definition of a finite pole of a linear system this definition agrees with the classical one and allows a direct dynamical interpretation it also generalizes immediately to the case of a multidimensional nd system we make a natural division of the poles into controllable and uncontrollable poles when the behavior in question has latent variables we make a further division into observable and unobservable poles in the case of a one dimensional 1d state space model the uncontrollable and unobservable poles correspond respectively to the input and output decoupling zeros whereas the observable controllable poles are the transmission poles most of these definitions can be interpreted dynamically in both the 1d and nd cases and some can be connected to properties of kernel representations we also examine the connections between poles transfer matrices and their left and right matrix fraction descriptions mfds we find behavioral results which correspond to the concepts that a controllable system is precisely one with no input decoupling zeros and an observable system is precisely one with no output decoupling zeros we produce a decomposition of a behavior as the sum of subbehaviors associated with various poles this is related to the integral representation theorem which describes every system trajectory as a sum of integrals of polynomial exponential trajectories

causal and stable input output structures on multidimensional behaviors in this work we study multidimensional nd linear differential behaviors with a distinguished independent variable called time we define in a natural way causality and stability of input output structures with respect to this distinguished direction we make an extension of some results in the theory of partial differential equations demonstrating that causality is equivalent to a property of the transfer matrix which is essentially hyperbolicity of the p c operator defining the behavior cal b c 0 y we also quote results which in effect characterize time autonomy for the general systems case stability is likewise characterized by a property of the transfer matrix we prove this result for the 2d case and for the case of a single equation for the general case it requires solution of an open problem concerning the geometry of a particular set in mathbb c n in order to characterize input output stability we also develop new results on inclusions of kernels freeness of variables and closure with respect to cal s cal s prime and associated spaces which are of independent interest we also discuss stability of autonomous behaviors which we believe to be governed by a corresponding condition

weak convergence and local stability properties of fixed step size recursive algorithms a recursive equation that subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation ode the odes describing the motion of several common adaptive filters are examined in some simple settings including the least mean square lms algorithm and all three of its signed variants the signed regressor the signed error and the sign sign algorithms stability and instability results are presented in terms of the eigenvalues of a correlation like matrix this generalizes known results for lms signed regressor lms and signed error lms and gives new stability criteria for the sign sign algorithm the ability of the algorithms to track moving parameterizations can be analyzed in a similar manner by relating the time varying system to a forced ode the asymptotic distribution about the forced ode is an ornstein uhlenbeck process the properties of which can be described in a straightforward manner

kolmogorov s contributions to mathematical statistics in this paper kolmogorov s work in mathematical statistics is reviewed the main areas under discussion are the idea of sufficiency linear models and unbiased estimators the relationship of kolmogorov s contributions with modern statistical theory in particular with bayesian analysis is analyzed

parameterization of stabilizing controllers with either right or left coprime factorization a parameterization method of stabilizing controllers that requires only one of right left coprime factorizations is presented as an illustrative model we will consider the multidimensional system with structural stability for which it is not yet known in general whether or not a doubly coprime factorization always exists a parameterization of stabilizing controllers for the model is presented

finite time stabilization and h control for a class of nonlinear hamiltonian descriptor systems with application to affine nonlinear descriptor systems abstract this paper studies the finite time stabilization and finite time h control problems of a class of nonlinear hamiltonian descriptor systems with applications to affine nonlinear descriptor systems via an appropriate state feedback an equivalent nonlinear dissipative hamiltonian differential algebraic system is first obtained with the obtained dissipative form a finite time stabilization control design procedure is then presented based on which a finite time h controller is designed for the system with external disturbances finally the obtained results for hamiltonian descriptor systems are applied to affine nonlinear descriptor systems simulation results on nonlinear circuit system show the effectiveness of the controllers proposed in this paper

stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple lyapunov functions this paper presents a general framework for analyzing stability of nonlinear switched systems by combining the method of multiple lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures for deterministic switched systems this leads to a unification of representative existing results and an improvement upon the current scope of the method of multiple lyapunov functions for switched systems perturbed by white noise we develop new results which may be viewed as natural stochastic counterparts of the deterministic ones in particular we study stability of deterministic and stochastic switched systems under average dwell time switching

generalized quadratic stability for continuous time singular systems with nonlinear perturbation this note considers the generalized quadratic stability problem for continuous time singular system with nonlinear perturbation the perturbation is a function of time and system state and satisfies a lipschitz constraint in this work a sufficient condition for the existence and uniqueness of solution to the singular system is firstly presented then by using s procedure and matrix inequality approach a necessary and sufficient condition is presented in terms of linear matrix inequality under which the maximal perturbation bound is obtained to guarantee the generalized quadratic stability of the system that is the system remains exponential stable and the nominal system is regular and impulse free furthermore robust stability for nonsingular systems with perturbation can be obtained as a special case finally the effectiveness of the developed approach for both singular and nonsingular systems is illustrated by numerical examples

stochastic optimization by simulation convergence proofs for the gi g 1 queue in steady state approaches like finite differences with common random numbers infinitesimal perturbation analysis and the likelihood ratio method have drawn a great deal of attention recently as ways of estimating the gradient of a performance measure with respect to continuous parameters in a dynamic stochastic system in this paper we study the use of such estimators in stochastic approximation algorithms to perform so called single run optimizations of steady state systems under mild conditions for an objective function that involves the mean system time in a gi g 1 queue we prove that many variant of these algorithms converge to the minimizer in most cases however the simulation length must be increased from iteration to iteration otherwise the algorithm may converge to the wrong value one exception is a particular implementation of infinitesimal perturbation analysis for which the single run optimization converges to the optimum even with a fixed and small number of ends of service per iteration as a by product of our convergence proofs we obtain some properties of the derivative estimators that could be of independent interest our analysis exploits the regenerative structure of the system but our derivative estimation and optimization algorithms do not always take advantage of that regenerative structure in a companion paper we report numerical experiments with an m m 1 queue which illustrate the basis convergence properties and possible pitfalls of the various techniques

relaxation labeling with learning automata relaxation labeling processes are a class of mechanisms that solve the problem of assigning labels to objects in a manner that is consistent with respect to some domain specific constraints we reformulate this using the model of a team of learning automata interacting with an environment or a high level critic that gives noisy responses as to the consistency of a tentative labeling selected by the automata this results in an iterative linear algorithm that is itself probabilistic using an explicit definition of consistency we give a complete analysis of this probabilistic relaxation process using weak convergence results for stochastic algorithms our model can accommodate a range of uncertainties in the compatibility functions we prove a local convergence result and show that the point of convergence depends both on the initial labeling and the constraints the algorithm is implementable in a highly parallel fashion

a behavioral approach to control of distributed systems this paper develops a theory of control for distributed systems i e those defined by systems of constant coefficient partial differential operators via the behavioral approach of willems the study here is algebraic in the sense that it relates behaviors of distributed systems to submodules of free modules over the polynomial ring in several indeterminates as in the lumped case behaviors of distributed arma systems can be reduced to ar behaviors this paper first studies the notion of ar controllable distributed systems following the corresponding definition for lumped systems due to willems it shows that as in the lumped case the class of controllable ar systems is precisely the class of ma systems it then shows that controllable 2 d distributed systems are necessarily given by free submodules whereas this is not the case for n d distributed systems n ge 3 this therefore points out an important difference between these two cases this paper then defines two notions of autonomous distributed systems which mimic different properties of lumped autonomous systems control is the process of restricting a behavior to a specific desirable autonomous subbehavior a notion of stability generalizing bounded input bounded output stability of lumped systems is proposed and the pole placement problem is defined for distributed systems this paper then solves this problem for a class of distributed behaviors

algebraic aspects of linear control system stability after formulating the problem of linear control system stability in very general terms the problem is resolved by 1 establishing a necessary and sufficient condition for stability 2 exploring in some detail the nature of this condition and 3 developing a parametric characterization of all controllers which stabilize a given plant the problem formulation is based on a ring theoretic setting for linear systems and is distinguished by the use of a novel control system configuration any interconnection of two distinct systems can be represented in terms of this configuration while preserving the distinction between the two systems furthermore no other configuration has this property several benefits and extensions are accrued as a result of using this configuration first a completely general yet physically meaningful problem formulation results consequently state space and operator theoretic approaches to linear control system stability are thoroughly reconciled this reconciliation embraces continuous time as well as discrete time systems lumped as well as distributed systems and 1 d as well as n d systems second the controller parametrization affords four degrees of freedom two more than any existing parametrization the additional degrees of freedom make explicit the design opportunity associated with controller implementation and thus determine several important control system characteristics this result is expected to provide a theoretical basis for the development of comprehensive control system design methodologies wherein design considerations related to controller implementation are addressed

nelder mead simplex modifications for simulation optimization when the nelder mead method is used to optimize the expected response of a stochastic system e g an output of a discrete event simulation model the simplex resizing steps of the method introduce risks of inappropriate termination we give analytical and empirical results describing the performance of nelder mead when it is applied to a response function that incorporates an additive white noise error and we use these results to develop new modifications of nelder mead that yield improved estimates of the optimal expected response compared to nelder mead the best performance was obtained by a modified method rs s9 in which a the best point in the simplex is reevaluated at each shrink step and b the simplex is reduced by 10 rather than 50 at each shrink step in a suite of 18 test problems that were adapted from the minpack collection of netlib the expected response at the estimated optimal point obtained by rs s9 had errors that averaged 15 less than at the original method s estimated optimal point at an average cost of three times as many function evaluations two well known existing modifications for stochastic responses the n 3 rule and the next to worst rule were found to be inferior to the new modification rs s9

estimating the error variance in regression after a preliminary test of restrictions on the coefficients abstract maximum likelihood estimation of the variance of the disturbances in a linear regression is considered in the context of exact linear restrictions on the coefficient vector the exact risk function for the associated preliminary test estimator of this variance is derived and evaluated numerically on the basis of relative quadratic loss our results indicate that in practical situations the risk of the pre test estimator differs only slightly from that of the naive estimator which ignores the restrictions without testing applying the coefficient restrictions without testing their validity is not recommended

variance estimation in a model with gaussian sub models this article considers the problem of estimating the dispersion parameter in a gaussian model that is intermediate between a model where the mean parameter is fully known fixed and a model where the mean parameter is completely unknown one of the goals is to understand the implications of the two step process of first selecting a model among a finite number of submodels then estimating a parameter of interest after the model selection but using the same sample data the estimators are classified into global two step and weighted estimators whereas the global type estimators ignore the model space structure the two step estimators explore the structure adaptively and can be related to pretest estimators and the weighted estimators are motivated by the bayesian approach their performances are compared theoretically and through simulations using their risk functions based on a scale invariant quadratic loss function it is shown that in the variance estimation problem efficiency gains arise by ex

corrigendum feedback stabilization over commutative rings the matrix case in a previous paper 1 certain arguments in the proofs of proposition 1 proposition 4 and subsection 4 4 are erroneous these errors are highly regretted by this author and are corrected as follows these corrections however do not affect the main results of the paper 1 in definition 1 of a strictly causal matrix the second sentence should be corrected as a causal matrix m is called strictly causal if all entries of m are in j 2 in the sufficiency part of the proof of proposition 1 the two sentences starting in line 3 of the paragraph since it n j using units of r 1a should be replaced by the following from ny i x d and the assumption that all entries of p are in j and hence that of n since d is nonzerodivisor it follows that all entries of i x are in j hence detx det i i x is of the form 1 j where j is in j this implies that detx is a unit of r 1a as j is the jacobson s radical 3 the proof of the necessity part of proposition 4 is erroneous since this result is not needed further in the paper we replace it with the following version stating only the sufficient condition proposition 4 a strictly causal p nd 1 in f n is stabilizable if a b a

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part ii internal stabilization in this second part of the paper a quadrat siam j control optim 40 2003 pp 266 299 we show how to reformulate the fractional representation approach to synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions for internal stabilizability moreover we characterize all the integral domains a of siso stable plants such that every mimo plant defined by means of a transfer matrix whose entries belong to the quotient field k q a of a is internally stabilizable finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 s shankar and v r sule siam j control optim 30 1992 pp 11 30 v r sule siam j control optim 32 1994 pp 1675 1695 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

stochastic approximations and differential inclusions part ii applications we apply the theoretical results on stochastic approximations and differential inclusions developed in benaim et al m benaim j hofbauer s sorin 2005 stochastic approximations and differential inclusions siam j control optim 44 328 348 to several adaptive processes used in game theory including classical and generalized approachability no regret potential procedures hart and mas colell s hart a mas colell 2003 regret based continuous time dynamics games econom behav 45 375 394 and smooth fictitious play d fudenberg d k levine 1995 consistency and cautious fictitious play j econom dynam control19 1065 1089

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

inadmissibility of the stein rule estimator under the balanced loss function in this paper the risk of the stein rule sr estimator is compared with that of the improved stein rule estimator using the stein variance srsv estimator under the balanced loss function it is shown that the srsv estimator dominates the sr estimator even if the loss function is extended to the blf also our numerical results show that the srsv estimator dominates the ols estimator when the weight of precision of estimation is larger than about half and vice versa

on the consistency of bayes estimates on etudie les proprietes de frequence des regles de bayes avec une attention particuliere a la consistence

feedback stabilization of multivariable two dimensional linear systems a constructive algorithm is presented for solving a two dimensional 2 d polynomial matrix equation that plays an important role in the output feedback stabilization of multivariable 2 d linear systems it is shown that this algorithm can have some computational advantages over the previous known ones based on the grobner basis approach as an application of the algorithm the class of all stabilizing strictly causal 2 d compensators is parametrized for a given stabilizable causal not necessarily strictly causal 2 d plant

nonparametric estimation for normalized coprime factors of a mimo system this paper extends to multi input multi output mimo systems the results on frequency response estimation for normalized coprime factors ncf under a stochastic framework from closed loop frequency domain experimental data under the condition that the covariance matrices are available for the external disturbances and measurement errors an analytic solution has been obtained for the maximum likelihood estimate mle on the basis of a linear fractional transformation lft representation for all the plant possible normalized right coprime factors nrcf it is proved that the estimate can be expressed by a linear combination of a normalized random matrix with all its columns having independent complex normal distributions some methods are suggested to reduce the estimation bias when high quality experimental data can be obtained a numerical example is included that confirms the theoretical results

a note on pooling variances abstract the estimation of variance in the normal distribution is studied under statistical inference based on conditional specification when there are two samples available for estimating the variance and it is not certain whether the two samples are from the same population the experimenter usually uses a test to resolve the uncertainty when the test is not significant the samples are pooled to obtain a pooled estimator otherwise the individual sample variance is used the bias and mean squared error of such a preliminary test estimator are studied it is shown that the preliminary test estimator has a smaller mean squared error than the usual unbiased estimator when the level of significance for the preliminary test is appropriately chosen

identification of normalized coprime factors through constrained curve fitting this paper deals with identifying finite dimensional normalized right coprime factors nrcfs under a stochastic framework from a sequence of their frequency response estimates a two step procedure is suggested for the estimation in which two cost functions are sequentially minimized these cost functions are constructed on the basis of weighted curve fitting and the conditions on nrcfs a numerical procedure is proposed for computing the estimate moreover it is proved that under some conditions the estimate converges with probability 1 w p 1 to its actual value with increasing the data length and in general the optimal estimate is asymptotically approximately gaussian the efficiency of the proposed method in nrcf identification is illustrated by numerical simulations

regime switching stochastic approximation algorithms with application to adaptive discrete stochastic optimization this work is devoted to a class of stochastic approximation problems with regime switching modulated by a discrete time markov chain our motivation stems from using stochastic recursive algorithms for tracking markovian parameters such as those in spreading code optimization in cdma code division multiple access wireless communication the algorithm uses constant step size to update the increments of a sequence of occupation measures it is proved that least squares estimates of the tracking errors can be developed assume that the adaptation rate is of the same order of magnitude as that of the time varying parameter which is more difficult to deal with than that of slower parameter variations due to the time varying characteristics and markovian jumps the usual stochastic approximation sa techniques cannot be carried over in the analysis by a combined use of the sa method and two time scale markov chains asymptotic properties of the algorithm are obtained which are distinct from the usual sa

theoremes de convergence presque sure pour une classe d algorithmes stochastiques a pas decroissant the paper studies the pathwise asymptotic behaviour of stochastic algorithms of the following general form theta n 1 theta n gamma n 1 f theta n y n 1 the hypotheses allowing discontinuities on the adaptation termf the process y n n 0 is a markov chain controlled by n for each fixed the markov chain y n n 0 is essentially of positive recurrent type

integral manifolds of slow adaptation conditions are given under which an integral manifold slow manifold exists for a nonlinear system representing a broad class of adaptive algorithms the parameter update equation restricted to the manifold is an exact description of the slow adaptation process which can be approximately analyzed by averaging stability properties of the slow motion in the manifold are extended off the manifold by a set of conditions under which the manifold is shown to be attractive this two time scale analysis provides a geometrical visualization of instability phenomena observed in adaptive systems and generalizes earlier local stability results

feedback stabilization over commutative rings further study of the coordinate free approach this paper is concerned with the coordinate free approach to control systems the coordinate free approach is a factorization approach but does not require the coprime factorizations of the plant we present two criteria for feedback stabilizability for multi input multi output mimo systems in which transfer functions belong to the total rings of fractions of commutative rings both of them are generalizations of sule s results in siam j control optim 32 1994 pp 1675 1695 the first criterion is expressed in terms of modules generated from a causal plant and does not require the plant to be strictly causal it shows that if the plant is stabilizable the modules are projective the other criterion is expressed in terms of ideals called generalized elementary factors this gives the stabilizability of a causal plant in terms of the coprimeness of the generalized elementary factors as an example a discrete finite time delay system is considered

multidimensional discrete stability by serre categories and the construction and parametrization of observers via gabriel localizations immediate predecessors of this work were a paper on two dimensional deadbeat observers by bisiacco and valcher multidimens systems signal process 19 2008 pp 287 306 and one on one dimensional functional observers by blumthaler linear algebra appl 432 2010 pp 1560 1577 compare also fuhrmann s comprehensive paper linear algebra appl 428 2008 pp 44 136 the present paper extends blumthaler s results to continuous or discrete multidimensional behaviors i e constructs and parametrizes all controllable observers of a given multidimensional behavior and for this purpose also discusses the required multidimensional stability such an observer produces a signal that approximates or estimates a desired component of the behavior such that the signal difference is negligible in a suitable sense this definition thus presupposes that of negligible or stable autonomous systems in the standard one dimensional case these are the asymptotically stable behaviors we define and investigate

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

on a generalization of the youla kucera parametrization part i the fractional ideal approach to siso systems abstract in this paper we show how to use the theory of fractional ideals in order to study the fractional representation approach to analysis and synthesis problems for siso systems within this mathematical framework we give necessary and sufficient conditions so that a plant is internally strongly bistably stabilizable or admits a weak coprime factorization moreover we show how to generalize the youla kucera parametrization of the stabilizing controllers to any stabilizable plant which does not necessarily admit a coprime factorization this parametrization is generally affine in two free parameters

finite time parameter estimation in adaptive control of nonlinear systems this note presents a parameter estimation routine that allows exact reconstruction of the unknown parameters in finite time provided a given excitation condition is satisfied the robustness of the routine to an unknown bounded disturbance or modeling error is also shown the result is independent of the control and identifier structures employed the true parameter value is obtained without requiring the measurement or computation of the velocity state vector moreover the technique provides a direct solution to the problem of removing auxiliary perturbation signals when parameter convergence is achieved

elementary proof of controller parametrization without coprime factorizability recently a controller parametrization method without coprime factorizability was presented by mori in this note we present this method using elementary matrix operations unlike in the earlier paper good knowledge of commutative algebra and module theory is not required

technical communique a note on the existence of a solution and stability for lipschitz discrete time descriptor systems this paper addresses the existence and uniqueness of a solution and stability for lipschitz discrete time descriptor systems by means of the fixed point principle a criterion is presented via a matrix inequality and the criterion guarantees the existence and uniqueness of a solution in addition a sufficient condition is also presented to ensure that the solution exists for any compatible initial condition and the system is globally exponentially stable simultaneously it is shown that the criterion presented in this paper is easy to verify and independent of the choices of decomposition matrices for the given system finally the approach is illustrated by a numerical example

relationship between standard control problem and model matching problem without coprime factorizability we present the equivalence between a standard control problem and a model matching problem without coprime factorizability of plants this equivalence is well known if every stabilizable plant admit a doubly coprime factorization the result of this note does not require the coprime factorizability of plants

the stability robustness of generalized eigenvalues the concept of stability radius is generalized to matrix pairs a matrix pair is said to be stable if its generalized eigenvalues are located in the open left half of the complex plane the stability radius of a matrix pair a b is defined to be the norm of the smallest perturbation delta a such that a delta a b is unstable the purpose is to estimate the stability radius of a given matrix pair depending on whether the matrices under consideration are complex or real the problem can be classified into two cases the complex case is easy and a complete solution is provided the real case is more difficult and only a partial solution is given

on stability of randomly switched nonlinear systems this note is concerned with stability analysis and stabilization of randomly switched systems these systems may be regarded as piecewise deterministic stochastic systems the discrete switches are triggered by a stochastic process which is independent of the state of the system and between two consecutive switching instants the dynamics are deterministic our results provide sufficient conditions for almost sure stability and stability in the mean using lyapunov based methods when individual subsystems are stable and a certain ldquoslow switchingrdquo condition holds this slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants this condition is shown to hold for switching signals coming from the states of finite dimensional continuous time markov chains our results therefore hold for markovian jump systems in particular for systems with control inputs we provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems

on the elementary factors of linear systems over unique factorization domains abstract the concept of elementary factors introduced by sule siam j control optim 32 1994 1675 1695 plays an important role in the output feedback stabilizability and stabilization of linear systems over unique factorization domains ufds this paper gives a simple proof that the elementary factors of t and w are identical where t and w are matrices associated with a right and a left matrix fraction description of a linear system over a ufd relationship between the reduced minors and the elementary factors is established an efficient method for computing the elementary factors based on the reduced minors is also proposed

robust stability analysis of linear continuous discrete time systems with output feedback controllers the robust stability of linear systems with output feedback controllers and time varying uncertain parameters is considered the robust stability bounds for time varying uncertain parameters are given using the lyapunov method when there are no uncertain parameters in the input and or output matrices it is shown that the result for continuous time systems is the same as that presented by k m zhou and p p khargonekar 1987 and the result for discrete time systems is better than that of s r kolla 1989 for the same example

robust control analysis and design for discrete time singular systems abstract in this paper we propose a simple approach to analyse stability robustness of discrete time singular systems under structured perturbations the developed robustness criteria are then applied to solve robust regional pole assignment problems of singular systems a robust control design algorithm via state feedback is also given the robust stability problem of singular systems is more complicated than that of regular systems not only stability robustness but system regularity and impulse elimination should be considered simultaneously since the results of robust control and analysis for singular systems is not available in the literature as much as other fields the paper may be viewed as a complementary result in this field although only discrete time case is discussed several results can be directly applied to continuous time systems as well

an invariant measure approach to the convergence of stochastic approximations with state dependent noise a new method is presented for quickly getting the ode ordinary differential equation associated with the asymptotic properties of the stochastic approximation x n 1 x n a n f x n zeta n or the projected algorithm for the constrained problem either a n to 0 or a n can be constant in which case the analysis is on the sequence obtained when a to 0 the method requires that x n zeta n 1 be markov with a feller transition function but little else the simplest result requires that if x n equiv x the corresponding noise process zeta n x n geqq 0 have a unique invariant measure but the nonunique case can also be treated no mixing condition is required nor the construction of averaged test functions and f cdot cdot need not be continuous a detailed analysis of the way that zeta n varies with x n is not required for the class of sequences treated the conditions seem easier to verify than for other methods there

on stabilization and the existence of coprime factorizations let k be an integral domain and f its quotient field we show there are plants over f which have no stable coprime factorizations but can be stabilized in a stable closed loop this answers a question posed by vidyasagar schneider and francis

on the existence of inferences which are consistent with a given model if p is a additive statistical model and a finitely additive prior then any statistic t is sufficient with respect to a suitable inference consistent with p and provided only that p t t 0 for all and t here sufficiency is to be intended in the bayesian sense and consistency in the sense of lane and sudderth as a corollary if p is additive and diffuse then whatever the prior there is an inference which is consistent with p and two versions of the main result are also obtained for predictive problems

feedback stabilization over commutative rings the matrix case this paper provides a solution of the feedback stabilization problem over commutative rings for matrix transfer functions stabilizability of a transfer matrix is realised as local stabilizability over the entire spectrum of the ring for stabilizable plants certain modules generated by its fractions and that of the stabilizing controller are shown to be projective compliments of each other in the case of rings with irreducible spectrum this geometric relationship shows that the plant is stabilizable if and only if the above modules of the plant are projective of ranks equal to the number of inputs and the outputs if the maxspectrum of the ring is noetherian and of zero krull dimension then this result shows that the stabilizable plants have doubly coprime fractions over unique factorization domains the above stabilizability condition is interpreted in terms of matrices formed by the fractions of the plant certain invariants of these matrices known as elementary factors are defined and it is shown that the plant is stabilizable if and only if these elementary factors generate the whole ring this condition thus provides a generalization of the coprime factorizability as a condition for stabilizabilty a formula for the class of all stabilizing controllers is then developed that generalizes the previous well known formula in factorization theory for multidimensional transfer functions these results provide concrete conditions for stabilizabilty finally it is shown that the class of polynomial rings over principal ideal domains is an additional class of rings over which stabilizable plants always have doubly coprime fractions

saturated feedback stabilization of discrete time descriptor bilinear systems this note addresses global asymptotic stabilization of a class of discrete time descriptor bilinear systems via a saturated state feedback controller based on lasalle invariance principle and the implicit function theorem sufficient conditions are presented to guarantee the uniqueness and existence of solution and the global asymptotic stability of the resulting closed loop systems simultaneously it is shown that the condition is independent of the state transformation for the given descriptor systems furthermore the effectiveness of the proposed design method is illustrated by a numerical example

stochastic approximation and large deviations upper bounds and w p 1 convergence with probability one convergence results are obtained for stochastic recursive approximation algorithms under very general conditions the gain sequence a n can go to zero very slowly and state dependent noise discontinuous dynamical equations and the projected or constrained algorithm are all treated the basic technique is the theory of large deviations prior results obtained via this theory are extended in many directions let dot x bar b x denote the mean equation for the algorithm let delta 0 be given and let g theta be a neighborhood of a stable point theta of that ordinary differential equation then asymptotic upper bounds to a n log p x n notin g theta n geqq n mid x n theta leqq delta are obtained these are often more informative than the usual classical rate of convergence results that use a local linearization and furthermore are obtained for the constrained and nonsmooth cases for which there are no rate of convergence

pre testing for linear restrictions in a regression model with spherically symmetric disturbances abstract in this paper we derive the exact risk under quadratic loss of pre test estimators of the prediction vector and of the error variance of a linear regression model with spherically symmetric disturbances the pre test in question is one of the validity of a set of exact linear restrictions on the model s coefficient vector we demonstrate how the known results for the model with normal disturbances can be extended to this broader case we also show that the critical value of unity results in a minimum of the risk of the pre test estimator of the error variance to illustrate the results we assume multivariate student t regression disturbances and numerically evaluate the derived expressions

analysis and applications of robust nonsingularity problem using the structured singular value this note uses the structured singular value technique to solve the robust nonsingularity analysis problem for matrices with unstructured and or quadratically coupled structured uncertainties with the ready spl mu analysis tools a new approach is proposed for finding a set of uncertainties within which the perturbed matrix keeps nonsingularity applications and examples in robust control theory are given to show the usefulness and the practicality of the proposed approach

controller parameterization of anantharam s example we consider the controller parameterization of anantharam s example 1985 it is shown that the parameterization is achieved by using only one parameter even though the plant does not have a coprime factorization

robustness of regional pole placement for uncertain continuous time implicit systems in this note under assumptions that the nominal linear implicit system is regular impulse free with all its generalized eigenvalues lying inside some specified regions sufficient conditions are proposed to preserve the assumed properties when structured perturbations are added into the nominal system explicit bounds on perturbations with different structures are given in terms of the spectral radii of some nonnegative matrices

robustness analysis of uncertain linear singular systems with output feedback control the robustness analysis for a linear singular system with uncertain parameters and static output feedback control is considered the problem is transformed into a robust nonsingularity problem based on the linear fractional transformation lft approach the robustness bounds to preserve regularity impulse immunity and stability are found in terms of the structured singular value spl mu with respect to parametric uncertainties the lft approach provides a unified framework for robustness analysis of both uncertain linear continuous discrete time singular systems

stable model reference adaptive fuzzy control of a class of nonlinear systems in this paper we propose a new adaptive fuzzy control scheme called model reference adaptive fuzzy control mrafc the mrafc scheme employs a reference model to provide closed loop performance feedback for generating or modifying a fuzzy controller s knowledge base the mrafc scheme grew from ideas in conventional model reference adaptive control mrac the mrafc scheme is developed to perform adaptive feedback linearization to a class of nonlinear systems a class of fuzzy controllers which can be expressed in an explicit form is used as the primary controller based on lyapunov s second method we have developed mrafc schemes and derived fuzzy rule adaptive laws hence not only the stability of the system can be assured but also the performance such as the issues of robustness and parameter convergence of the mrafc system can be analyzed explicitly we showed that in the case of no modeling error the state error converges to zero asymptotically in the case that persistent excitation is satisfied we showed that the mrafc system is asymptotically stable by considering the periodic signal as reference input signal we showed that the square wave can make the mrafc system be persistently excited the feasibility of applying these techniques has been demonstrated by considering the control of an inverted pendulum in following a reference model response

a convex characterization of multidimensional linear systems subject to sqi constraints this technical note proposes a convex characterization of the set of all stable closed loop linear systems that are obtained from a given plant which may be multidimensional by interconnecting it in feedback with controllers that satisfy a certain pre selected constraint we take an approach that is particularly useful when a doubly coprime factorization of the plant is difficult to obtain and a stable stabilizing controller may not exist the plant is not strongly stabilizable or when one may be difficult to find most related work requires one of these we adopt the so called coordinate free approach which unlike youla s parametrization does not rely on a doubly coprime factorization of the plant we show that if constraints which satisfy a condition called strong quadratic invariance sqi are imposed on the controllers then the set of all stable closed loop multidimensional linear systems has a convex representation and norm optimal control problems can be cast in convex form although the sqi condition is in general slightly stronger than quadratic invariance qi which was developed in related work they are equivalent for common classes of problems arising in decentralized control

stability and stabilization of multidimensional input output systems in this paper we discuss stability and stabilization of continuous and discrete multidimensional input output io behaviors of dimension r which are described by linear systems of complex partial differential resp difference equations with constant coefficients where the signals are taken from various function spaces in particular from those of polynomial exponential functions stability is defined with respect to a disjoint decomposition of the r dimensional complex space into a stable and an unstable region with the standard stable region in the one dimensional continuous case being the set of complex numbers with negative real part a rational function is called stable if it has no poles in the unstable region an io behavior is called stable if the characteristic variety of its autonomous part has no points in the unstable region this is equivalent to the stability of its transfer matrix and an additional condition the system is called stabilizable if there is a compensator io system such that the output feedback system is well posed and stable we characterize stability and stabilizability and construct all stabilizing compensators of a stabilizable io system parametrization the theorems and proofs are new but essentially inspired and influenced by and related to the stabilization theorems concerning multidimensional io maps as developed for instance by bose guiver shankar sule xu lin ying zerz and quadrat and of course the seminal papers of vidyasagar youla and others in the one dimensional case in contrast to the existing literature the theorems and proofs of this paper do not need or employ the so called fractional representation approach i e various matrix fraction descriptions of the transfer matrix thus avoiding the often lengthy matrix computations and seeming to be of interest even for one dimensional systems at least to the author an important mathematical tool new in systems theory is gabriel s localization theory which only in the case of ideal convex shankar sule unstable regions coincides with the usual one algorithmic tests for stability stabilizability and ideal convexity and the algorithmic construction of stabilizing compensators are addressed but still encounter many difficulties see in particular the open problems listed by xu e

a generalization of serre s conjecture and some related issues abstract several topics concerned with multivariate polynomial matrices like unimodular matrix completion matrix determinantal or primitive factorization matrix greatest common factor existence and subsequent extraction along with relevant primeness and coprimeness issues are related to a conjecture which may be viewed as a type of generalization of the original serre problem conjecture solved nonconstructively in 1976 and constructively more recently this generalized serre conjecture is proved to be equivalent to several other unsettled conjectures and therfore all these conjectures constitute a complete set in the sense that solution to any one also solves all the remaining

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

tracking a markov modulated stationary degree distribution of a dynamic random graph this paper considers a markov modulated duplication deletion random graph where at each time instant one node can either join or leave the network the probabilities of joining or leaving evolve according to the realization of a finite state markov chain two results are presented first motivated by social network applications the asymptotic behavior of the degree distribution is analyzed second a stochastic approximation algorithm is presented to track empirical degree distribution as it evolves over time the tracking performance of the algorithm is analyzed in terms of mean square error and a functional central limit theorem is presented for the asymptotic tracking error also a hilbert space valued stochastic approximation algorithm that tracks a markov modulated probability mass function with support on the set of nonnegative integers is analyzed

distributed nash equilibrium seeking this paper presents an asynchronous gossip based algorithm for finding a nash equilibrium ne of a game in a distributed multi player network the algorithm is designed in such a way that players make decisions based on estimates of the other players actions obtained from local neighbors using a set of standard assumptions on the cost functions and communication graph the paper proves almost sure convergence to a ne for diminishing step sizes for constant step sizes an error bound on expected distance from a ne is established the effectiveness of the proposed algorithm is demonstrated via simulation for both diminishing and constant step sizes

on second order optimality of the observed fisher information the realized error of an estimate is determined not only by the efficiency of the estimator but also by chance for example suppose that we have observed a bivariate normal vector whose expectation is known to be on a circle then intuitively the longer that vector happens to be the more accurately its angle is likely to be estimated yet this chance though its information is contained in the data cannot be accounted for by the variance of the estimate one way to capture it is by the direct estimation of the realized error in this paper we will demonstrate that the squared error of the maximum likelihood estimate to the extent to which it can be estimated can be most accurately estimated by the inverse of the observed fisher information in relation to this optimality we will also study the properties of several other estimators including the inverse of the expected fisher information the sandwich estimators the jackknife and the bootstrap estimators unlike the observed fisher information these estimators are not optimal

frequency response estimation for normalized coprime factors this paper investigates estimating the frequency response of the normalized coprime factors of a possibly unstable transfer function from closed loop frequency domain experimental data a stochastic framework has been adopted the dual youla kucera parametrization approach in closed loop system identification has been developed to guarantee the normality of the estimated frequency response a parametrization of all the normalized coprime factors has been established for transfer functions internally stabilizable by a known controller based on this parametrization interpolation conditions have been derived for the measurement errors being consistent with the stabilizing controller and experimental data an analytic expression has been obtained for the maximum likelihood estimate of the frequency response the effectiveness of the suggested method is confirmed through numerical simulations

distributed tracking of correlated equilibria in regime switching noncooperative games we consider a class of regime switching noncooperative repeated games where agents exchange information over a graph the parameters of the game number of agents payoffs information exchange graph evolve randomly over time according to a markov chain we present a regret based stochastic approximation algorithm with constant step size that prescribes how individual agents update their randomized strategies over time we show that if the markov chain jump changes on the same timescale as the adaptation rate of the stochastic approximation algorithm and agents independently follow this algorithm their collective behavior is agile in tracking the time varying convex polytope of correlated equilibria the analysis is carried out using weak convergence methods and lyapunov stability of switched markovian differential inclusions

properties of the mixed spl mu problem and its bounds upper and lower bounds for the mixed spl mu problem have recently been developed and here we examine the relationship of these bounds to each other and to spl mu a number of interesting properties are developed and the implications of these properties for the robustness analysis of linear systems and the development of practical computation schemes are discussed in particular we find that current techniques can only guarantee easy computation for large problems when spl mu equals its upper bound and computational complexity results prohibit this possibility for general problems in this context we present some special cases where computation is easy and make some direct comparisons between mixed spl mu and kharitonov type analysis methods

loss functions for loss estimation on introduit une classe de fonctions de scores propres qui combinent l erreur dans un probleme de decision et la precision de la regle de decision