on computing the distance to stability for matrices using linear dissipative hamiltonian systems abstract in this paper we consider the problem of computing the nearest stable matrix to an unstable one we propose new algorithms to solve this problem based on a reformulation using linear dissipative hamiltonian systems we show that a matrix a is stable if and only if it can be written as a j r q where j j t r 0 and q 0 that is r is positive semidefinite and q is positive definite this reformulation results in an equivalent optimization problem with a simple convex feasible set we propose three strategies to solve the problem in variables j r q i a block coordinate descent method ii a projected gradient descent method and iii a fast gradient method inspired from smooth convex optimization these methods require o n 3 operations per iteration where n is the size of a we show the effectiveness of the fast gradient method compared to the other approaches and to several state of the art algorithms

asymptotic properties of moment estimators for overdispersed counts and proportions summary consistency and asymptotic normality of moment estimates of regression parameters and an overdispersion parameter are shown for data with extra binomial and extrapoisson variation the asymptotic covariance of the regression parameters is found to be unaffected by estimation of the overdispersion parameter the moment estimates may be obtained using iterated weighted least squares

unified treatment of robust stability conditions for discrete time systems through an infinite matrix framework abstract this paper is motivated by the study on clarifying further relationship between the conventional lifting free causal linear time invariant lti scaling and lifting based noncausal linear periodically time varying lptv scaling approaches to robust stability analysis to facilitate such a study this paper gives the infinite matrix representation counterparts of the robust stability conditions in the separator type robust stability theorems for these approaches these counterparts lead to the idea of infinite dimensional separators and provide us with a unified framework for studying the mutual relationship between these two approaches this paper takes causal lti and noncausal lptv separators characterized by finite impulse response which are respectively defined in the lifting free and lifting based frameworks and compares them with respect to conservativeness of robust stability analysis by means of the unified framework through such a discussion it is demonstrated that the unified framework can lead to a very comprehensible and intuitive study on the mutual relationship between causal lti and noncausal lptv scaling approaches

lpv system analysis via quadratic separator for uncertain implicit systems this paper considers a class of linear systems containing time varying parameters whose behavior is not known exactly we assume that the parameters vary within known intervals and there are known bounds on their rates of variation our objective is to give a computationally verifiable condition that guarantees stability of the system for all possible parameter variations we first point out that the information on the rate bounds can be exploited by considering an augmented system described by an implicit model we then develop a tool called the quadratic separator for stability analysis of uncertain implicit systems using this tool a sufficient stability condition is obtained for the original linear parameter varying system moreover we show that the stability condition obtained is equivalent to the existence of a lyapunov function that depends on the parameters in a linear fractional manner finally the computational aspects of the proposed stability conditions are addressed

analytical and numerical stability of neutral delay integro differential equations and neutral delay partial differential equations this paper is concerned with the analytical and numerical stability of neutral delay integro differential equations ndides and neutral delay partial differential equations ndpdes we study the delay dependent stability of the real coefficient linear test equations for ndides furthermore we prove that the trapezium rule can preserve the delay dependent stability of the test equations considered we also discuss the delay dependent stability of the continuous problems the semi discrete problems and the fully discrete problems of linear ndpdes some numerical experiments are given to confirm the theoretical results

further results on the boundedness of multidimensional systems a sufficient condition is derived in this paper for the boundedness of a linear time invariant lti multidimensional md dynamic system over a special class of frequency domains these frequency domains are able to include many practically adopted frequency domains such as fans rectangles etc as a special situation as well as to give an approximation with a tolerable accuracy to many other physically significant frequency domains like ellipsoids and diamonds this condition becomes also necessary when the prescribed frequency domain is path connected moreover it is expressed in a linear matrix inequality lmi form and can be directly applied to the optimization of system output matrix and direct transmission matrix as well as the minimization of the frequency response bound in addition the dimension of the lmi is in the same order as that of the system matrices

stochastic climate dynamics random attractors and time dependent invariant measures a b s t r a c t this article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s the nonlinear deterministic and the linear stochastic one this unification via the theory of random dynamical systems rds allows one to consider the detailed geometric structure of the random attractors associated with nonlinear stochastically perturbed systems we report on high resolution numerical studies of two idealized models of fundamental interest for climate dynamics the first of the two is a stochastically forced version of the classical lorenz model the second one is a low dimensional nonlinear stochastic model of the el nino southern oscillation enso these studies provide a good approximation of the two models global random attractors as well as of the time dependent invariant measures supported by these attractors the latter are shown to have an intuitive physical interpretation as random versions of sinai ruelle bowen srb measures

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

diagnostics for a cumulative multinomial generalized linear model with applications to grouped toxicological mortality data abstract toxicologists frequently conduct toxicity experiments in which different treatment conditions are applied to groups of animals and the resulting mortality in each group is measured at a number of discrete time points over the course of the experiment in this article we develop and extend a number of diagnostic tools for the detection of mean misspecification or systematic departures of the mean link specification in cumulative multinomial generalized linear models fit to such data several real data sets are used to illustrate these diagnostics these tools help the analyst to differentiate between two sources of lack of fit in such models mean misspecification and extra multinomial variation or overdispersion

stable internally positive representations of continuous time systems an internally positive representation ipr of a non positive system is a positive system that under suitable input state and output transformations exactly replicates the behavior of the original system any construction method of an ipr necessarily introduces additional natural modes which in some cases are unstable in a previous paper the authors have presented a method that provides a stable ipr if and only if the eigenvalues of the original system lie in a specific sector of the open left half complex plane in this technical note a new technique is proposed that overcomes such a limitation and provides a stable ipr for any stable system although in some cases the dimension of the ipr must be large in order to guarantee its stability although for simplicity the method is only illustrated for single input single output systems with distinct eigenvalues it also applies to multi input multi output systems with multiple eigenvalues

on the smoothing property of linear delay partial differential equations abstract we consider linear partial differential equations with an additional delay term which under spatial discretization lead to ordinary differential equations with fixed delay of retarded type this means that the semi discrete solution gains smoothness over time for the concept of classical mild and weak solutions we analyse whether this effect also takes place in the original system we show that some systems behave in a neutral way only as a result the smoothness of the exact solution remains unchanged instead of gaining smoothness over time

robustness in the presence of mixed parametric uncertainty and unmodeled dynamics continuing the development of the structured singular value approach to robust control design the authors investigate the problem of computing mu in the case of mixed real parametric and complex uncertainty the problem is shown to be equivalent to a smooth constrained finite dimensional optimization problem in view of the fact that the functional to be maximized may have several local extrema an upper bound on mu whose computation is numerically tractable is established this leads to a sufficient condition of robust stability and performance a historical perspective on the development of the mu theory is included

low rank differential equations for hamiltonian matrix nearness problems for a hamiltonian matrix with purely imaginary eigenvalues we aim to determine the nearest hamiltonian matrix such that some or all eigenvalues leave the imaginary axis conversely for a hamiltonian matrix with all eigenvalues lying off the imaginary axis we look for a nearest hamiltonian matrix that has a pair of imaginary eigenvalues the hamiltonian matrices can be allowed to be complex or restricted to be real such hamiltonian matrix nearness problems are motivated by applications such as the analysis of passive control systems they are closely related to the problem of determining extremal points of hamiltonian pseudospectra we obtain a characterization of optimal perturbations which turn out to be of low rank and are attractive stationary points of low rank differential equations that we derive we use a two level approach where in the inner level we determine extremal points of the hamiltonian varepsilon pseudospectrum for a given varepsilon by following the low rank differential equations into a stationary point and on the outer level we optimize for varepsilon this permits us to give fast algorithms exhibiting quadratic convergence for solving the considered hamiltonian matrix nearness problems

tests of hypotheses in overdispersed poisson regression and other quasi likelihood models abstract test statistics for evaluating the significance of added variables in a regression equation are developed for mixed poisson models where the structural parameter that determines the mean variance relationship var 2 is estimated by the method of moments and the regression coefficients are estimated by quasi likelihood the formulas presented for test statistics and related estimating equations are applicable generally to quasi likelihood models specified by an arbitrary mean value function x together with a variance function v that contains one or more unknown parameters two versions of the wald and score tests are investigated one calculated from the usual model based covariance matrix whose validity depends on correct specification of the variance function and another using an empirical covariance matrix that has a more general asymptotic justification monte carlo simulations demonstrate that the quasi likelihood method of moments ql m procedures yield ap

parameter estimation for energy balance models with memory we study parameter estimation for one dimensional energy balance models with memory ebmms given localized and noisy temperature measurements our results apply to a wide range of nonlinear parab

a dual formulation of mixed spl mu and on the losslessness of d g scaling this paper studies the mixed structured singular value spl mu and the well known d g scaling upper bound spl nu a dual characterization of spl mu and spl nu is derived which intimately links the two values using the duals it is shown that spl nu is guaranteed to be lossless i e equal to spl mu if and only if 2 m sub r m sub e m sub c spl les 3 where m sub r m sub c and m sub c are the numbers of repeated real scalar blocks repeated complex scalar blocks and full complex blocks respectively the losslessness result further leads to a variation of the well known kalman yakubovich popov lemma and lyapunov inequalities

a class of linear partial neutral functional differential equations with nondense domain abstract we consider a system of linear partial neutral functional differential equations with nondense domain a natural generalized notion of solutions is provided by the integral solutions we derive a variation of constants formula which allows us to transform the integral solutions of the neutral equation to solutions of an abstract volterra integral equation the basic existence and uniqueness results are given and the solutions are shown to generate an integrated semigroup

the mechanism of stochastic resonance it is shown that a dynamical system subject to both periodic forcing and random perturbation may show a resonance peak in the power spectrum which is absent when either the forcing or the perturbation is absent

an energy balance climate model with hysteresis abstract energy balance climate models of budyko type lead to reaction diffusion equations with slow diffusion and memory on the 2 sphere the reaction part exhibits a jump discontinuity at the snow line here we introduce a babuska duhem hysteresis in order to account for a frequent repetition of sudden and fast warming followed by much slower cooling as observed from paleoclimate proxy data existence of global solutions and of a trajectory attractor will be established for the resulting system of a parabolic differential inclusion and an ode

a formula for computation of the real stability radius this paper presents a readily computable formula for the real stability radius with respect to an arbitrary stability region in the complex plane

perforated strict pseudospectra of demmel s matrices abstract regarding the pseudospectra of matrices it is easy to derive some conclusions from computer made graphics however those conclusions might be false without further analysis indeed it happened when discussing the presence of a local maximum at the origin for the least singular value of the characteristic matrix of the n n real toeplitz matrix whose first row and first column are 1 b b 2 b n 1 and 1 0 0 0 t respectively which was first taken into account by demmel in this paper we determine the value of a local maximum for the last singular value of the characteristic matrix of such toeplitz matrices in the cases n 3 and n 5 we also specify the point where this local maximum is attained at

transition to turbulence small disturbances and sensitivity analysis i a motivating problem abstract for over 100 years researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized navier stokes equations however for many simple flows this approach fails to match experimental results recently new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system these new mostly linear theories have increased our understanding of the transition process but the role of nonlinearity has not been explored in detail this paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence in this part we study a highly sensitive one dimensional burgers equation as a motivating problem sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance also sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem in the second part of this work this analysis will be extended to the three dimensional navier stokes equations to show that small disturbances have great potential to trigger transition to turbulence

on a class of retarded partial differential equations on developpe des resultats recents sur des equations d evolution abstraites afin de les appliquer a un type d equations dans des espaces de banach avec un retard discret et continu ces equations peuvent etre considerees comme la version abstraite d equations integrodifferentielles partielles a retard

some properties of an upper bound for spl mu a convex upper bound of the mixed structured singular value spl mu is analyzed the upper bound is based on a multiplier method it is simple it can exploit low rank properties and it is shown to be less conservative than the well known d g scaling a direct relationship with d g scaling is given the upper bound can be modified to one that is continuous with an explicit lipschitz constant

a counterexample for two conjectures about stability one measure of the stability of a matrix a is the distance to the nearest unstable matrix b recently van loan presented an algorithm to compute b which depended on a conjecture about the location of its eigenvalues we provide a counterexample to this conjecture which shows that the algorithm may overestimate the distance to b by an arbitrary amount the same counterexample invalidates another conjecture and algorithm of the author

pseudospectra of the orr sommerfeld operator this paper investigates the pseudospectra and the numerical range of the orr sommerfeld operator for plane poiseuille flow a number z in bf c is in the epsilon pseudospectrum of a matrix or operator a if zi a 1 geq epsilon 1 or equivalently if z is in the spectrum of a e for some perturbation e satisfying e leq epsilon the numerical range of a is the set of numbers of the form au u where cdot cdot is the inner product and u is a vector or function with huh u 1 the spectrum of the orr sommerfeld operator consists of three branches it is shown that the eigenvalues at the intersection of the branches are highly sensitive to perturbations and that the sensitivity increases dramatically with the reynolds number the associated eigenfunctions are nearly linearly dependent even though they form a complete set to understand the high sensitivity of the eigenvalues a model operator is considered related to the airy equation tha

modelling overdispersion in toxicological mortality data grouped over time toxicologists frequently conduct toxicity experiments in which different treatment conditions are applied to groups of animals and the resulting mortality in each group is measured at a number of discrete time points over the course of the experiment both survival analysis and generalized linear models have been proposed for analyzing this type of data whatever the approach taken the model should allow for the presence of extra multinomial variation arising from the use of groups of animals rather than individuals as the experimental units we consider a number of models for overdispersion that can be incorporated into the generalized linear model framework for multinomial data these models are extensions of ones proposed for binomial data by williams 1982 applied statistics 31 144 148 and moore 1986 biometrika 73 583 588 1987 applied statistics 36 8 14 in addition we examine robust asymptotic covariance matrix estimators for regression parameters similar to those given in liang and zeger 1986 biometrika 73 13 22 and zeger and liang 1986 biometrics 42 121 130 and compare them to the model based asymptotic estimators recommendations for analysis are given

input output finite time stability of linear systems necessary and sufficient conditions in the recent paper input output finite time stabilization of linear systems f amato a sufficient condition for input output finite time stability io fts when the inputs of the system are l2 signals has been provided such condition requires the existence of a feasible solution to an optimization problem involving a certain differential linear matrix inequality dlmi roughly speaking a system is said to be input output finite time stable if given a class of norm bounded input signals over a specified time interval of length t the outputs of the system do not exceed an assigned threshold during such time interval io fts constraints permit to specify quantitative bounds on the controlled variables to be fulfilled during the transient response in this context this paper presents several novel contributions first by using an approach based on the reachability gramian theory we show that the main theorem of f amato is actually also a necessary condition for io fts at the same time we provide an alternative still necessary and sufficient condition for io fts in this case based on the existence of a suitable solution to a differential lyapunov equality dle we show that the last condition is computationally more efficient however the formulation via dlmi allows to solve the problem of the io finite time stabilization via output feedback the effectiveness and computational issues of the two approaches for the analysis and the synthesis respectively are discussed in two examples in particular our methodology is used in the second example to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude

models for quantal response experiments over time response carter and hubert 1984 biometrics 40 699 706 propose and apply an approach based on multivariate growth curve theory to quantal bioassay over time their experimental data are reanalyzed using a fairly standard approach based on models for grouped response time data this alternate approach is considerably more direct and theoretically more satisfactory practical advantages include direct assessment of model adequacy and parsimonious modelling of extra multinomial variation

eigenvalues pseudospectrum and structured perturbations we investigate the behavior of eigenvalues under structured perturbations we show that for many common structures such as complex symmetric toeplitz symmetric toeplitz circulant and others the structured condition number is equal to the unstructured condition number for normwise perturbations and prove similar results for real perturbations an exception are complex skewsymmetric matrices we also investigate componentwise complex and real perturbations here hermitian and skew hermitian matrices are exceptional for real perturbations furthermore we characterize the structured complex and real pseudospectrum for a number of structures and show that often there is little or no significant difference to the usual unstructured pseudospectrum

data driven non markovian closure models abstract this paper has two interrelated foci i obtaining stable and efficient data driven closure models by using a multivariate time series of partial observations from a large dimensional system and ii comparing these closure models with the optimal closures predicted by the mori zwanzig mz formalism of statistical physics multilayer stochastic models msms are introduced as both a generalization and a time continuous limit of existing multilevel regression based approaches to closure in a data driven setting these approaches include empirical model reduction emr as well as more recent multi layer modeling it is shown that the multilayer structure of msms can provide a natural markov approximation to the generalized langevin equation gle of the mz formalism a simple correlation based stopping criterion for an emr msm model is derived to assess how well it approximates the gle solution sufficient conditions are derived on the structure of the nonlinear cross interactions between the constitutive layers of a given msm to guarantee the existence of a global random attractor this existence ensures that no blow up can occur for a broad class of msm applications a class that includes non polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants the emr msm methodology is first applied to a conceptual nonlinear stochastic climate model of coupled slow and fast variables in which only slow variables are observed it is shown that the resulting closure model with energy conserving nonlinearities efficiently captures the main statistical features of the slow variables even when there is no formal scale separation and the fast variables are quite energetic second an msm is shown to successfully reproduce the statistics of a partially observed generalized lotka volterra model of population dynamics in its chaotic regime the challenges here include the rarity of strange attractors in the model s parameter space and the existence of multiple attractor basins with fractal boundaries the positivity constraint on the solutions components replaces here the quadratic energy preserving constraint of fluid flow problems and it successfully prevents blow up

on the stability and robust stability of networked dynamic systems some necessary and sufficient conditions are derived for the stability of a networked system with linear time invariant dynamics connections among its subsystems are fixed but arbitrary and every subsystem can have different dynamics based on these results some necessary or sufficient conditions are further obtained for both its stability and robust stability which essentially depend only on parameter matrices of each individual subsystem and the subsystem connection matrix this characteristic makes them attractive in the analysis and synthesis of a large scale networked system

group velocity in finite difference schemes the relevance of group velocity to the behavior of finite difference models of time dependent partial differential equations is surveyed and illustrated applications involve the propagation of wave packets in one and two dimensions numerical dispersion the behavior of parasitic waves and the stability analysis of initial boundary value problems

correlated binary regression with covariates specific to each binary observation regression methods are considered for the analysis of correlated binary data when each binary observation may have its own covariates it is argued that binary response models that condition on some or all binary responses in a given block are useful for studying certain types of dependencies but not for the estimation of marginal response probabilities or pairwise correlations fully parametric approaches to these latter problems appear to be unduly complicated except in such special cases as the analysis of paired binary data hence a generalized estimating equation approach is advocated for inference on response probabilities and correlations illustrations involving both small and large block sizes are provided

the numerical solution of delay differential algebraic equations of retarded and neutral type in this paper we consider the numerical solution of initial value delay differential algebraic equations ddaes of retarded and neutral types with a structure corresponding to that of hessenberg daes we give conditions under which the ddae is well conditioned and show how the ddae is related to an underlying retarded or neutral delay ordinary differential equation dode we present convergence results for linear multistep and runge kutta methods applied to ddaes of index 1 and 2 and show how higher index hessenberg ddaes can be formulated in as stable a way as index 2 hessenberg ddaes we also comment on some practical aspects of the numerical solution of these problems

robust stability of linear systems described by higher order dynamic equations the stability radius of higher order differential and difference systems with respect to various classes of complex affine perturbations of the coefficient matrices is studied different perturbation norms are considered the aim is to derive robustness criteria that are expressed directly in terms of the original data previous results on robust stability of hurwitz and schur polynomials are extended to monic matrix polynomials for disturbances acting via a uniform input matrix computable formulas are obtained whereas for perturbations with multiple input matrices structured singular values are involved

on nonsingularity verification of uncertain matrices over a quadratically constrained set nonsingularity of a matrix is investigated in this technical note that depends affinely on several uncertainty matrices whose real and imaginary parts are constrained by some quadratic forms based on some equivalent descriptions for these uncertainty matrices a sufficient condition is derived this condition is given in a linear matrix inequality form and can in principle be efficiently validated the obtained result includes some well known results in systems and control theory as a special case such as the lyapunov equation based stability criterion for linear time invariant systems the d g scaling based upper bound for the mixed structured singular value a sufficient condition for the stability of spatially interconnected systems etc a computationally verifiable condition is also provided that indicates situations under which the aforementioned condition becomes necessary

robustness under bounded uncertainty with phase information the authors consider uncertain linear systems where the uncertainties in addition to being bounded also satisfy constraints on their phase in this context the authors define the phase sensitive structured singular value ps ssv of a matrix and show that sufficient and sometimes necessary conditions for stability of such uncertain linear systems can be rewritten as conditions involving ps ssv they then derive upper bounds for ps ssv computable via convex optimization they extend these results to the case where the uncertainties are structured diagonal or block diagonal for instance

global existence and asymptotic behavior for a quasilinear reaction diffusion system from climate modeling abstract this paper is concerned with a weakly coupled system of quasilinear autonomous strongly parabolic equations on a compact two dimensional manifold without boundary the system arises from an energy balance climate model we establish l hoelder and sobolev estimates and apply general results on quasilinear evolution equations in order to guarantee the existence of classical nonnegative solutions more precisely it is shown that the system generates a global solution semiflow in the positive cone of some fractional order sobolev space employing elements of the theory of infinite dimensional dissipative systems we prove the existence of a connected global attractor finally we present some results about stationary solutions and forced periodic oscillations the present paper extends earlier work of the authors on a semilinear problem

the rank one mixed m problem and kharitonov type analysis the general mixed problem has been shown to be np hard so that the exact solution of the general problem is computationally intractable except for small problems in this paper we consider not the general problem but a particular special case of this problem the rank one mixed problem we show that for this case the mixed problem is equivalent to its upper bound which is convex and it can in fact be computed easily and exactly this special case is shown to be equivalent to the so called affine parameter variation problem for a polynomial with perturbed coefficients which has been examined in detail in the literature and for which several celebrated kharitonov type results have been proven

a survey of the s lemma in this survey we review the many faces of the s lemma a result about the correctness of the s procedure the basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization convex geometry and linear algebra as well these were all active research areas but as there was little interaction between researchers in these different areas their results remained mainly isolated here we give a unified analysis of the theory by providing three different proofs for the s lemma and revealing hidden connections with various areas of mathematics we prove some new duality results and present applications from control theory error estimation and computational geometry

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

interconnected systems with uncertain couplings explicit formulae for mu values spectral value sets and stability radii in this paper we study the variation of the spectrum of block diagonal systems under perturbations of compatible block structure with fixed zero blocks at arbitrarily prescribed locations gershgorin type perturbations we derive explicit and computable formulae for the associated mu values the results are then applied to characterize spectral value sets and stability radii for such perturbed systems by specializing our results to the scalar diagonal case the classical eigenvalue inclusion theorems of gershgorin brauer and brualdi are obtained as corollaries moreover it follows that the inclusion regions of brauer and brualdi are optimal for the corresponding perturbation structures

computation of the structured singular value via moment lmi relaxations the structured singular value ssv provides a powerful tool to test robust stability and performance of feedback systems subject to structured uncertainties unfortunately computing the ssv is an np hard problem and the polynomial time algorithms available in the literature are only able to provide except for some special cases upper and lower bounds on the exact value of the ssv in this work we present a new algorithm to compute an upper bound on the ssv in case of mixed real complex uncertainties the underlying idea of the developed approach is to formulate the ssv computation as a nonconvex polynomial optimization problem which is relaxed into a sequence of convex optimization problems through moment based relaxation techniques two heuristics to compute a lower bound on the ssv are also discussed the analyzed numerical examples show that the developed approach provides tighter bounds than the ones computed by the algorithms implemented in the robust control toolbox in matlab and it provides in most of the cases coincident lower and upper bounds on the structured singular value

on the computation of structured singular values and pseudospectra structured singular values and pseudospectra play an important role in assessing the properties of a linear system under structured perturbations this paper discusses computational aspects of structured pseudospectra for structures that admit an eigenvalue minimization characterization including the classes of real skew symmetric hermitian and hamiltonian perturbations for all these structures we develop algorithms that require o n2 operations per grid point combining the schur decomposition with a lanczos method these algorithms form the basis of a graphical matlab interface for plotting structured pseudospectra 2009 elsevier b v all rights reserved

a note on structured pseudospectra in this note we study the notion of structured pseudospectra we prove that for toeplitz circulant hankel and symmetric structures the structured pseudospectrum equals the unstructured pseudospectrum we show that this is false for hermitian and skew hermitian structures we generalize the result to pseudospectra of matrix polynomials indeed we prove that the structured pseudospectrum equals the unstructured pseudospectrum for matrix polynomials with toeplitz circulant hankel and symmetric structures we conclude by giving a formula for structured pseudospectra of real matrix polynomials the particular type of perturbations used for these pseudospectra arise in control theory

internally positive representation of a class of continuous time systems the problem of realizing arbitrary transfer functions as combinations of positive filters or more in general of representing arbitrary systems by means of internally positive representations iprs has been widely investigated in the discrete time framework an ipr is a positive state space representation endowed with input state and output transformations that realizes arbitrary input state output dynamics this technical note investigates the problem of the ipr construction for continuous time systems and proposes a technique that provides stable iprs for a particular class of systems

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

on the stability of spatially distributed systems in this note a sufficient condition is derived for the stability of a spatially invariant distributed dynamical system based on the geometrical structure of the null space of a matrix polynomial this condition is less conservative than the available computationally feasible criteria moreover using the idea of parameter dependent linear matrix inequalities a necessary and sufficient condition is obtained both of these two conditions are expressed by lmis while the necessity of the latter is lost if the degree of the related matrix polynomials is small its conservativeness can be sequentially reduced

trigonometric polynomials positive on frequency domains and applications to 2 d fir filter design we propose a characterization of multivariate trigonometric polynomials that are positive on a given frequency domain the positive polynomials are parameterized as a linear function of sum of squares polynomials and so semidefinite programming sdp is applicable the frequency domain is expressed via the positivity of some trigonometric polynomials we also give a bounded real lemma brl in which a bounding condition on the magnitude of the frequency response of a multidimensional finite impulse response fir filter is expressed as a linear matrix inequality lmi this brl avoids the problem of a lack of spectral factorization in the multidimensional case all the proposed theoretical contributions can be implemented only as sufficient conditions due to degree limitations on the sum of square polynomials however the two dimensional 2 d fir filter designs we study numerically suggest that these limitations have negligible impact on the optimality

semigroups and linear partial differential equations with delay abstract we prove the equivalence of the well posedness of a partial differential equation with delay and an associated abstract cauchy problem this is used to derive sufficient conditions for well posedness exponential stability and norm continuity of the solutions applications to a reaction diffusion equation with delay are given

on the stability properties of polynomials with perturbed coefficients given a polynomial p c s s n t 1 s n 1 t n 0 which is hurwitz or p d z z n t 1 z n 1 t n 0 which has zeros only within or on the unit circle it is of interest to know how much the coefficients t j can be perturbed while preserving the stability properties in this note a method is presented for obtaining the largest hypersphere centered at t t t 1 t n containing only polynomials which are stable

systems of parabolic equations with continuous and discrete delays abstract in this paper we investigate the global existence and the dynamics of a coupled system of nonlinear parabolic equations where the nonlinear reaction function may depend on both continuous infinite or finite and discrete delays it is shown that if the reaction function is locally lipschitz continuous and the system possesses a pair of coupled upper and lower solutions then there exists a unique global solution to the system without any quasimonotone condition on the reaction function for systems with mixed quasimonotone reaction functions we use the monotone method to establish more dynamic property of the parabolic system in terms of the quasisolutions of the corresponding elliptic system this approach yields a global attractor of the parabolic system and under some additional conditions this attractor leads to the existence and asymptotic stability of a solution of the elliptic system application to three model problems in population dynamics and chemical reactions is given

nearest stable system using successive convex approximations stability is a crucial property in the study of dynamical systems we focus on the problem of enforcing the stability of a system a posteriori the system can be a matrix or a polynomial either in continuous time or in discrete time we present an algorithm that constructs a sequence of successive stable iterates that tend to a nearby stable approximation x of a given system a the stable iterates are obtained by projecting a onto the convex approximations of the set of stable systems some possible applications for this method are correcting the error arising from some noise in system identification and a possible solver for bilinear matrix inequalities based on convex approximations in the case of polynomials a fair complexity is achieved by finding a closed form solution to first order optimality conditions

navier stokes equations with delays some results on the existence and uniqueness of solutions to navier stokes equations when the external force contains some hereditary characteristics are proved

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

s shaped bifurcation branch in a quasilinear multivalued model arising in climatology abstract in this paper we show the existence of a continuous and unbounded connected s shaped set q u where q is the solar constant and u satisfies a quasilinear eventually multivalued stationary equation on a riemannian manifold without boundary arising as a stationary energy balance model for the earth surface temperature