explicit characterization of decentralized coprime factors this paper is concerned with parametrization of all decentralized stabilizing controllers the auxiliary diagonal system which is defined by the diagonal elements of bezout factors plays an important role in the parametrization of decentralized controllers this paper gives an explicit characterization of the auxiliary system

time delay estimation from low rate samples a union of subspaces approach time delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel previous methods for time delay recovery either operate on the analog received signal or require sampling at the nyquist rate of the transmitted pulse in this paper we develop a unified approach to time delay estimation from low rate samples this problem can be formulated in the broader context of sampling over an infinite union of subspaces although sampling over unions of subspaces has been receiving growing interest previous results either focus on unions of finite dimensional subspaces or finite unions the framework we develop here leads to perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate even in the presence of overlapping transmitted pulses and allows for a variety of different sampling methods the sampling rate depends only on the number of multipath components and the transmission rate but not on the bandwidth of the probing signal this result can be viewed as a sampling theorem over an infinite union of infinite dimensional subspaces by properly manipulating the low rate samples we show that the time delays can be recovered using the well known esprit algorithm combining results from sampling theory with those obtained in the context of direction of arrival estimation we develop sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate

on embeddings of logarithmic bessel potential spaces we present embedding theorems for certain logarithmic bessel potential spaces modelled upon generalized lorentz zygmund spaces and clarify the role of the logarithmic terms involved in the norms of the space mentioned in particular we get refinements of the sobolev embedding theorems trudinger s limiting embedding as well as embeddings of sobolev spaces into space of holder continuous functions including the result of brezis and wainger

nonuniform sampling and reconstruction in shift invariant spaces this article discusses modern techniques for nonuniform sampling and reconstruction of functions in shift invariant spaces it is a survey as well as a research paper and provides a unified framework for uniform and nonuniform sampling and reconstruction in shift invariant subspaces by bringing together wavelet theory frame theory reproducing kernel hilbert spaces approximation theory amalgam spaces and sampling inspired by applications taken from communication astronomy and medicine the following aspects will be emphasized a the sampling problem is well defined within the setting of shift invariant spaces b the general theory works in arbitrary dimension and for a broad class of generators c the reconstruction of a function from any sufficiently dense nonuniform sampling set is obtained by efficient iterative algorithms these algorithms converge geometrically and are robust in the presence of noise d to model the natural decay conditions of real signals and images the sampling theory is developed in weighted l p spaces

brief paper unification of independent and sequential procedures for decentralized controller design this paper is concerned with decentralized control problems there are two typical procedures to design decentralized controllers independent and sequential design procedures as the concepts and the techniques in these two approaches are too different from each other there have been no attempts to unify these approaches this paper proposes an iterative independent design procedure for decentralized control systems which is a unified approach to these conventional approaches

design of nonlinear interconnections guaranteeing the absence of periodic solutions abstract in this paper a novel methodology for scheming interconnection structure for a class of nonlinearly interconnected systems is proposed to guarantee the absence of a specific kind of periodic solutions those types of systems can be viewed as an interconnection of single input single output isolated subsystems with the interconnection structure specified by a square matrix frequency domain inequalities conditions as well as linear matrix inequalities lmis conditions for nonexistence of limit cycles of the second kind in the entire interconnected system are established the main results also define the frequency range on which cycles of the second kind of the system cannot exist based on this lmi approach an estimate of the largest bound of the frequency of cycles of the second kind can be explicitly computed by solving a generalized eigenvalue minimization problem numerical results show the effect of the nonlinear interaction on system behavior and the applicability and validity of the proposed method

sharp embeddings of besov type spaces we prove sharp embeddings of besov spaces involving both the classical smoothness and a slowly varying smoothness b into lorentz karamata spaces our methods are quite elementary we use neither the interpolation theory nor the atomic decomposition of spaces in question we cover both sub limiting and limiting cases and we determine growth envelopes of spaces

a parametrization approach to optimal h 2 and h decentralized control problems the paper proposes a two stage design approach to optimal h2 and h decentralized control problems in the first stage an optimal centralized controller is computed then in the second stage based on the optimization results for centralized controllers the parameter that decentralizes the controller is optimized the design approach is applied to an observer based decentralized controller optimality conditions are derived and examples are given to illustrate the design

brief decentralized h controller design a matrix inequality approach using a homotopy method this paper considers a decentralized h control problem for multi channel linear time invariant systems our interest is focused on dynamic output feedback the control problem is reduced to a feasibility problem of a bilinear matrix inequality bmi the objective of this paper is to propose an algorithm for solving the bmi by using the idea of the homotopy method where the controller s coefficient matrices are deformed from full matrices defined by a centralized h controller to block diagonal matrices of specified dimensions which describe a decentralized h controller when a feasible decentralized h control problem is considered it can be expected that there always exists a centralized h controller for which the algorithm converges and presents a desired solution to find such a suitable centralized h controller random search in a parametrized set of h controllers with a proper dimension is suggested the efficiency of the proposed algorithm is demonstrated by an example

special decentralized control problems in discrete time interconnected systems composed of two subsystems in this paper some special decentralized control problems are addressed for discrete time interconnected systems first it is pointed out that some subsystems must be unstable to ensure stability of the overall system in some special cases then a special kind of decentralized control problem is studied this kind of problem can be viewed as harmonic control among independent subsystems research results show that two unstable systems can generate a stable system through some effective cooperations in addition a decentralized controller design method based on linear matrix inequality is also given by using parameter dependent lyapunov function method developed for the study of robust stability a special linear star coupled dynamical network is also considered the central subsystem must be unstable to stabilize the whole network under a special coupling several examples are given to illustrate the results

reduce and boost recovering arbitrary sets of jointly sparse vectors the rapid developing area of compressed sensing suggests that a sparse vector lying in a high dimensional space can be accurately and efficiently recovered from only a small set of nonadaptive linear measurements under appropriate conditions on the measurement matrix the vector model has been extended both theoretically and practically to a finite set of sparse vectors sharing a common sparsity pattern in this paper we treat a broader framework in which the goal is to recover a possibly infinite set of jointly sparse vectors extending existing algorithms to this model is difficult due to the infinite structure of the sparse vector set instead we prove that the entire infinite set of sparse vectors can be recovered by solving a single reduced size finite dimensional problem corresponding to recovery of a finite set of sparse vectors we then show that the problem can be further reduced to the basic model of a single sparse vector by randomly combining the measurements our approach is exact for both countable and uncountable sets as it does not rely on discretization or heuristic techniques to efficiently find the single sparse vector produced by the last reduction step we suggest an empirical boosting strategy that improves the recovery ability of any given suboptimal method for recovering a sparse vector numerical experiments on random data demonstrate that when applied to infinite sets our strategy outperforms discretization techniques in terms of both run time and empirical recovery rate in the finite model our boosting algorithm has fast run time and much higher recovery rate than known popular methods

gradient regularity for solutions to quasilinear elliptic equations in the plane we investigate the dirichlet problem diva x v fin v 0on for a quasilinear elliptic equation in a planar domain when f belongs to the zygmund space l logl 12 loglogl 0 1 we prove that the gradient of the variational solution v w01 2 belongs to the space l2 loglogl 2 r2 a main tool is a result on the regularity of the gradient of the solution to the dirichlet problem diva x div in w01 1 where l2 loglogl r2 0 namely if the mapping a r2 r2 satisfies the leray lions type conditions then we prove the estimates l2 loglogl r2 c l2 loglogl r2 by applying a method recently suggested by l greco et al which is based on the uniform estimates l2 r2 c l2 r2 available for 0 provided that l2 r2

generalized n laplacian quasilinear nonhomogenous problem with critical growth abstract applying the generalized moser trudinger inequality the mountain pass theorem and the ekeland variational principle we study the existence of non trivial weak solutions to the problem div u u u v x u u u f x u h x x r n u w 1 l r n where is a young function such that the space w 1 l r n is embedded into exponential or multiple exponential orlicz space the nonlinearity f x t has the corresponding critical growth v x is a continuous potential h l r n is a nontrivial continuous function and 0 is a small parameter

static output feedback stabilisation with h performance for a class of plants in this paper the problem of static output feedback control of a linear system is considered the existence of a static output feedback control law is given in terms of the solvability of two coupled lyapunov inequalities which result in a non linear optimisation problem however using state coordinate and congruence transformations and by imposing a block diagonal structure on the lyapunov matrix we will see that the determination of a static output feedback gain reduces for a specific class of plants to finding the solution of a system of linear matrix inequalities the class of plants considered is those which are minimum phase with a full row rank markov parameter the method is extended to incorporate h performance objectives this results in a sub optimal static h control law found by non iterative means the simplicity of the method is demonstrated by a numerical example

recovering signals from lowpass data the problem of recovering a signal from its low frequency components occurs often in practical applications due to the lowpass behavior of many physical systems here we study in detail conditions under which a signal can be determined from its low frequency content we focus on signals in shift invariant spaces generated by multiple generators for these signals we derive necessary conditions on the cutoff frequency of the lowpass filter as well as necessary and sufficient conditions on the generators such that signal recovery is possible when the lowpass content is not sufficient to determine the signal we propose appropriate pre processing that can improve the reconstruction ability in particular we show that modulating the signal with one or more mixing functions prior to lowpass filtering can ensure the recovery of the signal in many cases and reduces the necessary bandwidth of the filter

higher order sampling and recovering of lowpass signals a higher order sampling function applied to lowpass signals is described to recover the original signal from its periodic nonuniform samples a formulation of the sampling function is introduced based on the occurrence of local gaps in the sampled signal spectrum as a result the interpolant is greatly simplified

a j spectral factorization approach to control necessary and sufficient conditions for the existence of suboptimal solutions to the standard model matching problem associated with mathcal h infty control j control are derived using j spectral factorization theory the existence of solutions to the model matching problem is shown to be equivalent to the existence of solutions to two coupled j spectral factorization problems with the second factor providing a parametrization of all solutions to the model matching problem the existence of the j spectral factors is then shown to be equivalent to the existence of nonnegative definite stabilizing solutions to two indefinite algebraic riccati equations allowing a state space formula for a linear fractional representation of all controllers to be given a virtue of the approach is that a very general class of problems may be tackled within a conceptually simple framework and no additional auxiliary riccati equations are required

sharpness of embeddings in logarithmic bessel potential spaces this paper is a continuation of 4 where embeddings of certain logarithmic bessel potential spaces modelled upon generalised lorentz zygmund spaces in appropriate orlicz spaces with young functions of single and double exponential type were derived the aim of this paper is to show that these embedding results are sharp in the sense of 8

the structure of finitely generated shift invariant spaces in l2 rd a simple characterization is given of finitely generated subspaces of l2 rd which are invariant under translation by any multi integer and is used to give conditions under which such a space has a particularly nice generating set namely a basis and more than that a basis with desirable properties such as stability orthogonality or linear independence the last property makes sense only for local spaces i e shift invariant spaces generated by finitely many compactly supported functions and special attention is paid to such spaces as an application we prove that the approximation order provided by a given local space is already provided by the shift invariant space generated by just one function with this function constructible as a finite linear combination of the finite generating set for the whole space hence compactly supported this settles a question of some 20 years standing

the graph metric for unstable plants and robustness estimates for feedback stability in this paper a graph metric is defined that provides a measure of the distance between unstable multivariable plants the graph metric induces a graph topology on unstable plants which is the weakest possible topology in which feedback stability is robust using the graph metric it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of rhp poles if the perturbed and unperturbed systems have the same rhp poles then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations as an application of these results the design of stabilizing controllers for unstable singularly perturbed systems is studied finally the relationship of the graph metric to the gap metric introduced by zames and el sakkary is studied in detail in particular it is shown that the robustness results of zames and el sakkary do not enable one to conclude the causality of the perturbed system whereas the present results do

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

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

brief decentralized h controller design in this paper a decentralized h controller design problem for two channel systems is considered a parametrization of all decentralized stable factors is proposed with the parametrization of all decentralized stable factors the class of decentralized compensators is parametrized the decentralized h controller design procedure is built upon the j spectral factorization approach to h control a class of decentralized suboptimal controllers satisfying the h norm bound is parametrized a design procedure for decentralized suboptimal h controllers is suggested

explicit controller formulas for lmi based h synthesis the set of h controllers with closed loop performance c can be implicitly parametrized by the solutions r s of a system of linear matrix inequalities lmi the matrices r and s play a role analogous to that of the riccati solutions x and y in classical riccati based h control useful applications include lmi based h synthesis mixed h 2h design and h design with a pole placement constraint this paper is concerned with the reliable computation of h controllers given a solution r s of the characteristic system of lmis explicit formulas are derived for both the regular and singular cases remarkably these formulas are extensions of the usual central controller formulas where the lmi solutions r and s replace the riccati solutions x and y simple and numerically appealing new formulas for discrete time h controllers are also derived

a new decentralised controller design method for a class of strongly interconnected systems abstractin this paper two interconnected structures are first discussed under which some closed loop subsystems must be unstable to make the whole interconnected system stable which can be viewed as a kind of strongly interconnected systems then comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown a new approach for the design of decentralised controllers is presented by determining the lyapunov function structure previously which allows the existence of unstable subsystems by fully utilising the orthogonal space information of input matrix some new understandings are presented for the construction of lyapunov matrix this new method can deal with decentralised state feedback static output feedback and dynamic output feedback controllers in a unified framework furthermore in order to reduce the design conservativeness and deal with robustness a new robust decentralised controller design method is given by combining with the parameter depend

a sharp form of an embedding into exponential and double exponential spaces abstract let be a bounded domain in r n n 2 in the well known paper indiana univ math j 20 1971 1077 moser found the smallest value of k such that sup exp f x k n n 1 f w 1 n 0 f l n 1 we extend this result to the situation in which the underlying space ln is replaced by the zygmund space l n log l the corresponding space of exponential growth then being given by a young function which behaves like exp t n n 1 1 for large t the case when n 1 which gives rise to a space of double exponential growth is also discussed

optimal embeddings and compact embeddings of bessel potential type spaces first we establish necessary and sufficient conditions for embeddings of bessel potential spaces h sigma x mathbb r n with order of smoothness less than one modelled upon rearrangement invariant banach function spaces x mathbb r n into generalized holder spaces to this end we derive a sharp estimate of modulus of smoothness of the convolution of a function f in x mathbb r n with the bessel potential kernel g 0 1 such an estimate states that if g sigma belongs to the associate space of x then omega f g sigma t precsim int limits 0 t n s frac sigma n 1 f s ds quad rm for all quad t in 0 1 quad rm and every quad f in x mathbb r n second we characterize compact subsets of generalized holder spaces and then we derive necessary and sufficient conditions for compact embeddings of bessel potential spaces h sigma x mathbb r n into generalized holder spaces we apply our results to the case when x mathbb r n is the lorentz karamata space l p q b mathbb r n in particular we are able to characterize optimal embeddings of bessel potential spaces h sigma l p q b mathbb r n into generalized holder spaces and also compact embeddings of spaces in question applications cover both superlimiting and limiting cases

on the game riccati equations arising in h_ infty control problems in the state space approach to h infty optimal control feasible closed loop gains gamma are characterized via a pair of game riccati equations depending on gamma this paper is concerned with the properties of these equations as gamma varies the most general problem is considered d 11 neq 0 and the variations of the riccati solutions are thoroughly analyzed insight is gained into the behavior near the optimum and into the dependence on gamma of the suboptimality conditions in addition concavity is established for a criterion that synthesizes the three conditions x geq 0 y geq 0 and rho xy gamma 2 this suggests a numerically reliable newton scheme for the computation of the optimal gamma most results presented here are extensions of earlier contributions the main concern is to provide a complete and synthetic overview as well as results and formulas tailored to the development of numerically sound algorithms

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

decentralized control of symmetric systems abstract this paper is concerned with the stabilizability problem of symmetric systems by means of decentralized controllers it is shown that the set of decentralized fixed modes of a symmetric system is equal to the set of uncontrollable and unobservable modes of the system and implies that the stabilizability of a state space symmetric system by means of a decentralized controller is equivalent to the stabilizability for the system by means of a centralized controller

stabilization and h control of symmetric systems an explicit solution abstract in this paper we address the h control analysis the output feedback stabilization and the output feedback h control synthesis problems for state space symmetric systems using a particular solution of the bounded real lemma for an open loop symmetric system we obtain an explicit expression to compute the h norm of the system for the output feedback stabilization problem we obtain an explicit parametrization of all asymptotically stabilizing control gains of state space symmetric systems for the h control synthesis problem we derive an explicit expression for the optimally achievable closed loop h norm and the optimal control gains extension to robust and positive real control of such systems are also examined these results are obtained from the linear matrix inequality formulations of the stabilization and the h control synthesis problems using simple matrix algebraic tools

some applications of small gain theorem to interconnected systems based on small gain theorem decentralized control of interconnected systems is studied linear matrix inequality conditions are given for stabilizability of interconnected systems interconnections can be used to improve system robustness in the sense of small gain theorem an example is given to illustrate the results finally interconnected systems composed of symmetric subsystems are studied

characterization of embeddings of sobolev type spaces into generalized holder spaces defined by lp modulus of smoothness abstract we prove a sharp estimate for the k modulus of smoothness modelled upon a l p lebesgue space of a function f in w k l p n n k p p where is a domain with minimally smooth boundary and finite lebesgue measure k n n k n and n n k p this sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of sobolev type spaces into generalized holder spaces defined by means of the k modulus of smoothness general results are illustrated with examples in particular we obtain a generalization of the classical jawerth embeddings