on the condition numbers of large semidefinite toeplitz matrices abstract this paper is devoted to asymptotic estimates for the spectral or euclidean condition numbers t n a t n a t 1 n a of large n n toeplitz matrices t n a in the case where the symbol a is an l function and re a 0 almost everywhere we describe several classes of symbols a for which t n a increases like log n x n x or even e xn

reduced order generalized h_ infty filtering for linear discrete time systems with application to channel equalization this paper investigates the problem of reduced order generalized h infty filtering for linear discrete time systems generalized h infty filtering covers standard h infty filtering as a special case and can make use of the frequency domain characteristics of practical signals moreover reduced order filters are more attractive than full order ones regarding implementability by virtue of the generalized bounded real lemma a new necessary and sufficient condition is proposed for analyzing the generalized h infty performance of the filtering error system to compute reduced order generalized h infty filters a necessary and sufficient condition is then derived in terms of matrix inequalities to solve which iterative linear matrix inequality algorithms are further developed in addition the proposed filter design method is applied to cope with the channel equalization problem examples are finally presented for illustrating the proposed method

h _ infty filtering for discrete time state delayed systems with finite frequency specifications this article researches the problem of finite frequency ff h filtering for linear discrete time state delayed systems the disturbance is assumed to reside in low middle high frequency ranges to reduce the conservatism of the results delay partitioning idea is used to derive a new ff bounded real lemma brl by applying the generalized kalman yakubovich popov lemma two equivalent approaches to the proof of the proposed ff brl are given respectively starting from transfer function and lyapunov krasovskii functional a new ff h filter design method is proposed in terms of solving a set of linear matrix inequalities finally a numerical example clearly demonstrates the merits and effectiveness of the proposed method

state constrained optimal control governed by non well posed parabolic differential equations this paper is concerned with a maximum principle of optimal control problems governed by some parabolic differential equations which could be non well posed both an integral type state constraint and a two point boundary time variable state constraint are considered

robust h sub 2 h sub spl infin filtering for linear systems with error variance constraints in this correspondence we consider the robust h sub 2 h sub spl infin filtering problem for linear perturbed systems with steady state error variance constraints the purpose of this multiobjective problem is to design a linear filter that does not depend on the parameter perturbations such that the following three performance requirements are simultaneously satisfied 1 the filtering process is asymptotically stable 2 the steady state variance of the estimation error of each state is not more than the individual prespecified value 3 the transfer function from exogenous noise inputs to error state outputs meets the prespecified h sub spl infin norm upper bound constraint we show that in both continuous and discrete time cases the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic riccati like equations inequalities we present both the existence conditions and the explicit expression of desired robust filters an illustrative numerical example is provided to demonstrate the flexibility of the proposed design approach

optimal distributed control for a new mechanochemical model in biological patterns abstract in this paper we consider a distributed optimal control problem for the new mechanochemical model in biological patterns which was proposed to describe the dynamics of basal lamina dermal and epidermal tissues the model consists of the time dependent ginzburg landau equation for the concentration difference of at least two pigments coupled with the swift hohenberg equation for the difference of dermal cellular densities of at least two types of cells first we prove the existence and uniqueness of a strong solution the existence of optimal controls is established then we prove the control to state operator s is frechet differentiable finally we derive the first order necessary optimality conditions for the optimal control problem

robust spl hscr sub spl infin filtering for uncertain discrete time state delayed systems this paper addresses the problem of robust spl hscr sub spl infin filtering for linear discrete time systems subject to parameter uncertainties in the system state space model and with multiple time delays in the state variables the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain a methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed spl hscr sub spl infin performance for the filtering error irrespective of the uncertainty and the time delays the proposed design is given in terms of linear matrix inequalities which has the advantage in that it can be implemented numerically very efficiently

optimal controls of 3 dimensional navier stokes equations with state constraints this work is concerned with the maximum principles for optimal control problems governed by 3 dimensional navier stokes equations some types of state constraints time variables are considered

on the extreme eigenvalues of hermitian block toeplitz matrices abstract we are concerned with the behavior of the minimum maximum eigenvalue 0 n n n of an n 1 n 1 hermitian toeplitz matrix tn where is an integrable real valued function kac murdoch and szego widom parter and r h chan obtained that 0 n min o 1 n2k in the case where c2k at least locally and inf has a zero of order 2k we obtain the same result under the second hypothesis alone moreover we develop a new tool in order to estimate the extreme eigenvalues of the mentioned matrices proving that the rate of convergence of 0 n to inf depends only on the order not necessarily even or integer or finite of the zero of inf with the help of this tool we derive an absolute lower bound for the minimal eigenvalues of toeplitz matrices generated by nonnegative l1 functions and also an upper bound for the associated euclidean condition numbers finally these results are extended to the case of hermitian block toeplitz matrices with toeplitz blocks generated by a bivariate integrable function

universal bounds on the convergence rate of extreme toeplitz eigenvalues abstract let t n denote the sequence of toeplitz matrices associated with f a non negative integrable function such that inf f 0 and sup f 0 it is well known that t n is ill conditioned since min t n the smallest eigenvalue of t n tends to zero as n if f satisfies some smoothness conditions then the convergence rate depends on the zeros of f here we prove that min t n mimics the zeros of f only up to exponential convergence i e min t n is always bounded from below by exp cn where c 0 depends on f under no smoothness assumption on f furthermore for multivariate f an even stronger bound is valid we also investigate toeplitz matrices generated by positive measures not necessarily absolutely continuous with respect to the lebesgue measure showing that in this case the convergence to zero of min t n can be arbitrarily fast

new approach to mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems this paper revisits the problem of mixed h sub 2 h sub spl infin filtering for polytopic discrete time systems differing from previous results in the quadratic framework the filter design makes full use of the parameter dependent stability idea not only is the filter dependent of the parameters which are assumed to reside in a polytope and be measurable online but in addition the lyapunov matrices are different for the entire polytope domain as well as for different channels with respect to the mixed performances these ideas are realized by introducing additional slack variables to the well established performance conditions and by employing new bounding techniques which results in a much less conservative filter design method a numerical example is presented to illustrate the effectiveness and advantage of the developed filter design method

pontryagin maximum principle of optimal control governed by fluid dynamic systems with two point boundary state constraint over all y u y mad 0 t u subject to the semilinear equation y t ay t by t du t f t a e t 0 t 1 1 with state constraint y 0 y t s 1 2 the following hypotheses will be e9ective throughout this paper h1 v and h are real hilbert spaces with norms and moreover v h v algebraically and topologically with compact injections where v denotes the dual of

brief paper robust finite frequency h filtering for uncertain 2 d roesser systems this paper investigates the problem of robust finite frequency ff h filtering for two dimensional 2 d roesser models with polytopic uncertainties our attention is focused on designing filters guaranteeing the robustly asymptotic stability and ff h disturbance attenuation level of the filtering error system by the parameter dependent idea and the generalized kalman yakubovich popov lemma for 2 d roesser models the existence conditions of robust ff h filters are obtained in terms of solving an optimization problem which is more general than the existing results an example is given to validate the proposed methods the contribution of the paper is twofold 1 systematic methods are proposed for designing ff h filters for roesser models 2 an improved strategy has been presented to deal with the robust h filter design for roesser models

fixed order robust h sub spl infin filter design for markovian jump systems with uncertain switching probabilities this paper discusses the fixed order robust h sub spl infin filtering problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertainties under consideration are assumed to be norm bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix respectively first a criterion based on linear matrix inequalities is provided for testing the h sub spl infin filtering level of a filter over all the admissible uncertainties then a sufficient condition for the existence of the fixed order robust h sub spl infin filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints to determine the filter a globally convergent algorithm involving convex optimization is suggested finally a numerical example is used to illustrate that the developed theory is more effective than the existing results

two level toeplitz preconditioning approximation results for matrices and functions large 2 level toeplitz systems arise in a variety of applications see e g r h chan and m ng siam rev 38 1996 pp 427 482 for which efficient numerical methods for their solution are required some successful numerical techniques need the explicit knowledge of the generating function f of the considered system t n f rm x b an assumption that usually is not fulfilled in real applications in this paper we analyze and complete the procedure proposed in d noutsas s serra capizzano and p vassalos numer linear algebra appl 12 2005 pp 231 239 for the 2 level case in such a way from the knowledge of the coefficients of t n f we determine optimal preconditioning strategies for the solution of our systems finally some numerical experiments are performed and discussed in connection with our theoretical analysis

analysis of a multistate control problem related to food technology this paper is concerned with an optimal control problem related to the determination of an optimal profile for the steam temperature into the autoclave along the processing of canned foods the problem studies a system coupling the evolution navier stokes equations with the heat transfer equation by natural convection the so called boussinesq equations and with the microorganisms removal equation the essential difficulties in the study of this multistate control problem arise from the lack of uniqueness for the solution of the state system here we obtain after a careful analysis of the problem mathematical formulation the uniqueness of part of the state and the existence of optimal solutions

paper sensitivity integrals for multivariable discrete time systems the purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete time systems we present extensions to both the classical poisson integral and bode s sensitivity integral formulae the main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete time systems due to such system characteristics as open loop unstable poles and nonminimum phase zeros and to such design requirements as stability and bandwidth constraints these formulae are similar to those for multivariable continuous time systems obtained elsewhere and they reveal that feedback design limitations depend on directionality properties of the sensitivity function and on those of unstable poles and nonminimum phase zeros in the open loop transfer function

design of delta sigma modulators via generalized kalman yakubovich popov lemma this paper is concerned with the design of delta sigma modulators via the generalized kalman yakubovich popov lemma the shaped noise transfer function ntf is assumed to have infinite impulse response and the optimization objective is minimizing the maximum magnitude of the ntf over the signal frequency band by virtue of the gkyp lemma the optimization of an ntf is converted into a minimization problem subject to quadratic matrix inequalities and then an iterative algorithm is proposed to solve this alternative minimization problem each iteration of the algorithm contains linear matrix inequality constraints only and can be effectively solved by the existing numerical software packages moreover specifications on the ntf zeros are also integrated in the design method a design example demonstrates that the proposed design method has an advantage over the benchmark one in improving the signal to noise ratio

robust h sub spl infin filtering for stochastic time delay systems with missing measurements in this paper the robust hinfin filtering problem is studied for stochastic uncertain discrete time delay systems with missing measurements the missing measurements are described by a binary switching sequence satisfying a conditional probability distribution we aim to design filters such that for all possible missing observations and all admissible parameter uncertainties the filtering error system is exponentially mean square stable and the prescribed hinfin performance constraint is met in terms of certain linear matrix inequalities lmis sufficient conditions for the solvability of the addressed problem are obtained when these lmis are feasible an explicit expression of a desired robust hinfin filter is also given an optimization problem is subsequently formulated by optimizing the hinfin filtering performances finally a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

stabilization of the boussinesq equation via internal feedback controls in this paper we show that the steady state solutions to boussinesq equations in three dimensional domain are stabilizable by internal controllers with the supports in subsets 1 under some conditions on and 1

optimal control of parabolic differential equations with two point boundary state constraints this paper deals with the necessary conditions of optimality for some optimal control problems governed by some parabolic differential equations involving monotone graphs the two point boundary time variable state constraints are discussed some analyses on the state equations are given

finite frequency h_ infty deconvolution with application to approximated bandlimited signal recovery this paper investigates a finite frequency h infty deconvolution problem for single input single output discrete time systems motivated by the fact that many practical signals are located in a finite frequency range this paper is focused on developing a design method for achieving better deconvolution performance over a finite frequency range first a finite frequency h infty deconvolution problem is formulated such that the deconvolution specification is characterized by a modified h mathbf infty index associated with the corresponding finite frequency range by an adapted generalized kalman yakubovich popov lemma and an auxiliary vector approach a matrix inequality condition is obtained for parameterizing a required deconvolution filter based on which a simple iterative algorithm is then constructed for optimizing the filter performance multiobjective deconvolution is further discussed in the same framework compared with the traditional frequency weighting strategy the proposed method can directly analyze and synthesize the deconvolution performance within finite frequency ranges the advantage of which is demonstrated in a bandlimited signal recovery example

necessary and sufficient conditions for optimal controls in viscous flow problems a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation characterising the feedback problem the maximum principle is established by two quite different methods

optimal control of the primitive equations of the ocean with state constraints abstract we investigate in this article pontryagin s maximum principle for a class of control problems associated with the primitive equations pes of the ocean these optimal problems involve a state constraint similar to that considered in wang 2002 7 for the three dimensional navier stokes ns equations the main difference between this work and wang 2002 7 is that the nonlinearity in the pes is stronger than in the three dimensional ns systems

local internal controllability of the boussinesq system in this paper we shall show that the h3 h3 steady state solutions to boussinesq equations in n dimensional bounded domain n 2 3 are locally controllable by internal controllers with the support in subsets

pontryagin s maximum principle for optimal control of the stationary primitive equations of the ocean abstract we study in this article pontryagin s maximum principle for a class of control problems associated with the stationary primitive equations pes of the ocean these optimal problems involve a state constraint similar to that considered in g wang pontryagin s maximum principle for optimal control of the stationary navier stokes equations nonlinear anal 52 2003 1853 1866 in the case of the three dimensional navier stokes ns equations the main difference between this work and the one cited above is that the nonlinearity in pes is stronger than that in the three dimensional ns equations

extended kalman filtering with stochastic nonlinearities and multiple missing measurements in this paper the extended kalman filtering problem is investigated for a class of nonlinear systems with multiple missing measurements over a finite horizon both deterministic and stochastic nonlinearities are included in the system model where the stochastic nonlinearities are described by statistical means that could reflect the multiplicative stochastic disturbances the phenomenon of measurement missing occurs in a random way and the missing probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over the interval 0 1 such a probability distribution is allowed to be any commonly used distribution over the interval 0 1 with known conditional probability the aim of the addressed filtering problem is to design a filter such that in the presence of both the stochastic nonlinearities and multiple missing measurements there exists an upper bound for the filtering error covariance subsequently such an upper bound is minimized by properly designing the filter gain at each sampling instant it is shown that the desired filter can be obtained in terms of the solutions to two riccati like difference equations that are of a form suitable for recursive computation in online applications an illustrative example is given to demonstrate the effectiveness of the proposed filter design scheme

extreme singular values and eigenvalues of non hermitian block toeplitz matrices abstract in this paper we are concerned with the analysis of the distribution and localization of the singular values of toeplitz matrices tn f generated by a p variate lebesgue integrable matrix valued function f q p c h k q we prove that the union of the essential ranges of the singular values of f is a proper weak cluster for the whole set of the singular values of tn f by showing that the number of outliers is strongly depending on the regularity features of the underlying function f in particular if f is continuous or from the krein algebra and p 1 then the cluster is proper other results concerning the extreme spectral behavior of tn f second order ergodic formulas and localization of eigenvalues of preconditioned matrices tn 1 g tn f are presented some examples of applications to the preconditioning of these results are also discussed

frequency domain min max optimization of noise shaping delta sigma modulators this paper proposes a min max design of noise shaping delta sigma modulators we first characterize the all stabilizing loop filters for a linearized modulator model by this characterization we formulate the design problem of lowpass bandpass and multi band modulators as minimization of the maximum magnitude of the noise transfer function ntf in fixed frequency band s we show that this optimization minimizes the worst case reconstruction error and hence improves the snr signal to noise ratio of the modulator the optimization is reduced to an optimization with a linear matrix inequality lmi via the generalized kyp kalman yakubovich popov lemma the obtained ntf is an fir finite impulse response filter which is favorable in view of implementation we also derive a stability condition for the nonlinear model of delta sigma modulators with general quantizers including uniform ones this condition is described as an norm condition which is reduced to an lmi via the kyp lemma design examples show advantages of our design

optimal controls of boussinesq equations with state constraints abstract this work is concerned with the maximum principle for an optimal control problem governed by boussinesq equations some integral type state constraints are considered

state constrained optimal control problems governed by coupled nonlinear wave equations with memory this work considers the optimal control problems governed by coupled nonlinear wave equations with memory where the state constraint is a type of integral first we investigate the existence of the optimal solution for the optimal control problem and then we deduce the maximum principle for the optimal solution with state constraint moreover we give a concrete example which is covered by the main result

fuzzy weighting dependent approach to h_ infty filter design for time delay fuzzy systems this correspondence is concerned with the hinfin filter design for takagi sugeno t s fuzzy systems with state delay a delay dependent design method is proposed in terms of linear matrix inequalities lmi the main contribution is the use of fuzzy weighting dependent lyapunov functionals which can reduce the conservatism arisen from the quadratic lyapunov functional approach an illustrative example is given to show the effectiveness of the present method

suboptimal reduced order filtering through an lmi based method this paper addresses the reduced order filtering design problem for continuous time linear systems the h2 and hinfin norms of the estimation error used as performance criteria are discussed and a new linear matrix inequalities lmi based method for reduced order filter design is proposed differently from the methods available in the literature to date the one presented here does not solve the associated nonconvex problem by means of an appropriate optimization procedure it is based on the a priori determination of a certain matrix that simultaneously rends convex the problem to be solved and reduces the suboptimality degree of the solution its efficiency is tested by means of two examples the first one borrowed from the literature allows the comparison of our method for the h2 norm case with three earlier techniques one of them being the well known balanced truncation the second one of higher order consists of the estimation of the displacement of a tapered bar using an hinfin norm criterion

h sub 2 h sub spl infin filter design for systems with polytope bounded uncertainty this correspondence presents a strategy for robust h2 h infin filtering design with regional pole placement applied to discrete or continuous time linear time invariant lti systems with polytope bounded uncertainty to overcome the conservatism of linear matrix inequality lmi based formulations the proposed design approach is based on a multiobjective optimization algorithm applied directly in the space of the filter parameters the h2 and hinfin norms computed in all polytope vertices and in possible worst case interior points are taken as the optimization objectives a combination of branch and bound algorithm and lmi guaranteed cost formulations is applied to compute the coordinates of the worst case norms and to validate the filter design to the whole polytope examples are presented to illustrate the effectiveness of the proposed strategy

mean squared error analysis of quantizers with error feedback quantization is a fundamental process in digital signal processing delta sigma modulators are often utilized for quantization which can be easily implemented with static uniform quantizers and error feedback filters in this paper we analyze the mean squared quantization error of the quantizer with error feedback including the delta sigma modulators first we study the quantizer with an ideal optimal error feedback filter that minimizes the mean squared error mse of quantization we show that the amplitude response of the optimal error feedback filter can be parameterized by one parameter this parameterization enables us to find the optimal error feedback filter numerically second the relationship between the number of bits used for the quantizer and the achievable mse is clarified by using the optimal error feedback filter this makes it possible to investigate the efficiency of the quantizer with the optimal error feedback filter in terms of mse then ideal optimal error feedback filters are approximated by practically implementable filters using the yule walker method and the linear matrix inequality based method numerical examples are provided for demonstrating our analysis and synthesis

necessary conditions for optimal control of distributed parameter systems the ekeland variational principle is used to prove a maximum principle for the optimal controls of a general semilinear evolutionary control system in a banach space with strictly convex dual the boundary constraint is of general type which includes the optimal periodic control problem as a special case

min max approximation of transfer functions with application to filter design this paper investigates the problem of frequency specific fs model approximation of transfer functions using a min max approach the objective is to find an approximation model for a transfer function such that the maximum error gain over a specific frequency range is minimized first a linear matrix inequality condition characterizing the fs gain of a transfer function is derived by using the generalized kalman yakubovich popov lemma and then a simple iterative approach is proposed to optimize the approximation model numerical experiments show that the proposed approach can produce better approximation models over a specific frequency range than some existing approaches moreover it is indicated how to apply the proposed approximation approach to the design problem of infinite impulsive response digital filters and design examples clearly illustrate that the proposed design flow can generate filters comparable with the latest design method

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

asymptotic behavior of the condition number of two level toeplitz matrix sequences in this note we give condition number estimates for two level toeplitz matrices generated by bivariate 2 periodic weakly sectorial symbols the largest class of symbols for which we can guarantee the invertibility of all the corresponding toeplitz matrices by using and extending tools previously developed in the one level context we show that the asymptotical ill conditioning is essentially related to the order of zeros of the symbol