tilting and refined donaldson thomas invariants abstract we study tilting for the heart a of the canonical t structure of the finite dimensional derived category of the ginzburg algebra for a quiver with potential q w we give conditions on that the stable objects for a central charge on a define a sequence of simple tilts from a to a 1 on that conditions the refined donaldson thomas invariant associated to q w is independent of the chosen central charge

robust stabilization of interval plants using lead or lag compensators abstract a lead or lag compensator robustly stabilizes a family of interval plants if and only if it simultaneously stabilizes the vertex plants

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

to stabilize an interval plant family it suffices to simultaneously stabilize sixty four polynomials it is shown that stability of three specific polynomial families can be deduced from the stability of a finite number of polynomials these polynomial families are the characteristic polynomials of unity feedback loops with the controller in the forward path and where the plant includes a specific form of parameter uncertainty for the first polynomial family the plant has parameter uncertainty in the even or odd terms of the numerator or denominator polynomial for the second polynomial family the plant has a numerator or denominator which is an interval polynomial for the third polynomial family the plant is interval because of the structure of these results it is shown that they lead to robust stabilization results two examples are included the approach employed here was developed for plants with affine uncertainty it is demonstrated that considerable simplification results if the plants under investigation are interval

robust controller synthesis using kharitonov s theorem the authors present a method based upon kharitonov s theorem for synthesizing robustly stabilizing feedback controllers the approach is based upon a multiple plant model formulation with a quadratic cost functional sufficient conditions are obtained for characterizing robustly stabilizing static output feedback proportional controllers for mimo multiple input multiple output plants with denominator polynomial uncertainty

simultaneous stabilization of single input single output discrete time systems the problem of finding one compensator which simultaneously stabilizes a family of single input single output siso discrete time plants is considered the family of plants is described by the transfer functions pz q q in q which are generated via a z transformation a number of assumptions describing the set of allowable plants are then given these assumptions include some regularity conditions on the plants and a minimum phase requirement the satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator c z for simultaneous stabilization an iterative computation method is provided for control design

painless nonorthogonal expansions in a hilbert space h discrete families of vectors hj with the property that f j hj f hj for every f in h are considered this expansion formula is obviously true if the family is an orthonormal basis of h but also can hold in situations where the hj are not mutually orthogonal and are overcomplete the two classes of examples studied here are i appropriate sets of weyl heisenberg coherent states based on certain non gaussian fiducial vectors and ii analogous families of affine coherent states it is believed that such quasiorthogonal expansions will be a useful tool in many areas of theoretical physics and applied mathematics

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

on the nyquist envelope of an interval plant family in this note we study the envelope of the nyquist plots generated by an interval plant family and show that this boundary is not always contained in the nyquist plots of the kharitonov plants with this motivation in mind we give a sufficient condition for an envelope point to be contained in the nyquist plot of a kharitonov plant and use it to generate large and critical portions of the nyquist envelope e g we show that the outer nyquist envelope of a stable interval plant is generated by the nyquist plots of the kharitonov plants another by product of this sufficient condition is a framework for developing new extreme point results for interval feedback systems this framework is useful in computing the phase margin and the maximal peaking in the sensitivity and complementary sensitivity functions and in stating a robust version of the circle criterion we also use this framework to easily explain existing extreme point results for the gain margin the h sub spl infin norm and the positive realness of interval plants one conclusion which emerges is this seemingly all important properties of an interval feedback system are deducible from the kharitonov plants

mas consensus and delay limits under delayed output feedback in this technical note we study the consensus problem for discrete time multi agent systems over an undirected fixed network communication graph focusing on the robustness of consensus with respect to communication delay we assume that the agents input is subject to a constant albeit possibly unknown time delay and is generated by a distributed dynamic output feedback control protocol drawing upon concepts and techniques from robust control notably those concerning gain margin optimization and analytic interpolation we derive explicit closed form conditions for general linear agents to achieve consensus our results display an explicit dependence of the consensus condition on the delay value as well as on the agent s unstable poles and non minimum phase zeros showing that delayed communication between agents will generally hinder consensus and impose restrictions on the network topology we also show that a lower bound on the maximal delay allowable for consensus can be computed by a simple line search method

simultaneous partial pole placement a new approach to multimode system design simultaneous partial pole placement of a family of single input single output plants is proposed as a generalization of the classical pole placement and stabilization problems this problem finds application in the design of a compensator for a family of linear dynamical systems in this note we show that the proposed problem is equivalent to a new class of transcendental problem using stable minimum phase rational functions with real coefficients a necessary condition for the solvability of the associated transcendental problem is obtained finally a counterexample to the following conjecture is obtained pairs of simultaneously stabilizable plants of bounded mcmillan degree have simultaneously stabilizing compensators of bounded mcmillan degree

theoretical comparison of fourier and wavelet encoding in magnetic resonance imaging a theoretical comparison of the wavelet and fourier encoding methods is made with respect to resolution sensitivity to artifact and signal to noise ratios snr s a general mathematical description is developed in which magnetic resonance mr image encoding is represented by a projection of the function representing the mr signal density onto an approximation subspace of the finite energy functions characteristics of the subspace are used to define a generalized point spread function for space variant systems using the formal model of mr image encoding it is shown that wavelet encoding approaches the resolution limit defined by fourier encoding artifact is treated according to whether or not the source of the variation in the measured data is stationary nonstationary imperfections perturb the projection operation and result in encoding method dependent effects which can be modeled by a distortion matrix suitable for treating shift variant systems a framework is developed in which to derive expressions for snr s applicable to a general class of mr encoding methods

stabilization of a linear plant via a stable compensator having no real unstable zeros abstract this paper studies the following problem under what conditions can a linear plant be stabilized by a stable compensator having no real zeros in the closed right half plane solving this problem is an important step towards to solving the problems of stabilization of linear systems via stable minimum phase compensation and simultaneous stabilization of n n 2 plants in the paper necessary and sufficient conditions are derived these conditions are completely general and therefore encompass unstable nonminimum phase plants as well it is shown that the stabilizability solely depends on the locations of real zeros and real poles of a given plant for a plant satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is also provided and illustrated via an example

principal component filter banks for optimal multiresolution analysis an important issue in multiresolution analysis is that of optimal basis selection an optimal p band perfect reconstruction filter bank prfb is derived in this paper which minimizes the approximation error in the mean square sense between the original signal and its low resolution version the resulting prfb decomposes the input signal into uncorrelated low resolution principal components with decreasing variance optimality issues are further analyzed in the special case of stationary and cyclostationary processes by exploiting the connection between discrete time filter banks and continuous wavelets an optimal multiresolution decomposition of l sub 2 r is obtained analogous results are also derived for deterministic signals some illustrative examples and simulations are presented

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

an interpolated controller for stabilization of a plant with variable operating conditions this paper considers stabilization of a linear time invariant single input single output plant with variable operating conditions it is assumed that the plant is described by a linear interpolation of proper stable coprime factorizations of the transfer functions of two representative models which are defined at two representative operating points a linear interpolation of stabilizing controllers for the representative models is applied to the interpolated plant the necessary and sufficient condition for the interpolated plant to be stabilizable by the interpolated controller is presented using the nevanlinna pick theory it is also shown that simultaneous stabilizability of the two representative models is necessary for such stabilization an example is given which illustrates that the class of stabilizable plants via interpolated controllers is larger than that of plants stabilizable by fixed controllers

on the order of simultaneously stabilizing compensators in this paper simultaneous strong stabilization problem is considered and it is shown that there is no upper bound for the minimal order of a simultaneously strongly stabilizing compensator in terms of the plant orders a similar problem was also considered by smith et al 1986 where it was shown that such a bound does not exist for the strong stabilization problem of a single plant but the examples given in the article were forcing an approximate unstable pole zero cancellation or forcing the distance between two distinct unstable zeros to go to zero in this paper it is shown that 1 if approximate unstable pole zero cancellation does not occur and the distances between distinct unstable zeros are bounded below by a positive constant then it is possible to find an upper bound for the minimal order of a strongly stabilizing compensator and 2 for the simultaneous strong stabilization problem even for the two plant case such a bound cannot be found

an approach to simultaneous system design part 11 nonswitching gain and dynamic feedback compensation by algebraic geometric methods this paper studies structured uncertainty problems in feedback system design considers a compact parameterization of the space of linear dynamical systems and introduces base points and critical points as two algebraic geometric objects that have significance in sensitivity and robustness studies respectively using the nevanlinna pick interpolation theory the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one parameter family of plants a recent result due to kharitonov on the simultaneous stability of a parameterized family of polynomials leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants furthermore the author considers simultaneous pole placement of an r tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system the concept of nondegenerate and twisted r tuples of plants is introduced as the pole placement problem is studie

non euclidian metrics and the robust stabilization of systems with parameter uncertainty this paper considers from a complex function theoretic point of view certain kinds of robust synthesis problems in particular we use a certain kind of metric on the disk the hyperbolic metric which allows us to reduce the problem of robust stabilization of systems with many types of real and complex parameter variations to an easily solvable problem in non euclidian geometry it is shown that several apparently different problems can be treated in a unified general framework a new result on the gain margin problem for multivariable plants is also given finally we apply our methods to systems with real zero or pole variations

comments on extreme point results for robust stabilization of interval plants with first order compensators the authors point out a simple alternative proof of the main result theorem 1 of the paper by barmish hollot kraus and tempo 1992 this proof follows immediately on applying the vertex result of hollot and yang 1990 to the generalization of kharitonov s theorem given by chapellat and bhattacharyya 1988 1989 the authors also point out that more general vertex results are known

robust strong stabilizability of interval plants it suffices to check two vertices it is shown that a proper interval plant is strongly stabilizable if and only if all members are free from unstable pole zero cancellations and two specially selected vertex plants are strongly stabilizable

an overview of extremal properties for robust control of interval plants abstract this paper provides an overview of recent results on the problem of robust stability and performance of feedback control systems in the presence of plant perturbations the widely studied class of interval plants is considered and an effort is made to cover different types of plant perturbations by incorporating in addition to the interval plant description unstructured norm bounded perturbations extremality results for these classes of uncertain systems are provided in a unifying framework robust performance of control systems is addressed in the paper and a number of extremal results are given for the computation of the structured singular value function for feedback systems with interval plants also classical frequency response analysis for interval plant controller families of open loop transfer functions is surveyed with the aim of providing extremal results for the computation of specification parameters such as phase or gain margins and sensitivity and complementary sensitivity peaks

bogomolny prasad sommerfeld state counting in local obstructed curves from quiver theory and seiberg duality in this paper we study the bogomolny prasad sommerfeld bps state counting in the geometry of local obstructed curve with normal bundle o o 2 we find that the bps states have a framed quiver description using this quiver description along with the seiberg duality and the localization techniques we can compute the bps state indices in different chambers dictated by stability parameter assignments this provides a well defined method to compute the generalized donaldson thomas invariants this method can be generalized to other affine ade quiver theories

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

modified nevanlinna pick interpolation and feedback stabilization of linear plants with uncertainty in the gain factor abstract this paper is a sequel to an earlier work in which we applied classical novnnlinna pick interpolation to the stabilization of a single input output plant with uncertainly in the gain factor by means of an asymptotically stable control and feedback sensor in this present work we show that for the proper design we need a modification of the classical interpolation procedure a point not clearly brought out in our previous paper

a necessary and sufficient condition for the stability of interval matrices consider the linear dynamical system described by the equation xdot t ax t where a is a constant real matrix with dimensions n n and the elements of matrix a are not known precisely we know only the upper and lower bounds of the intervals in which the elements of matrix a are confined in this paper there is proved a necessary and sufficient condition for the stability of solutions of eqn 1 with incomplete information about the elements of matrix a

robust stabilization some extensions of the gain margin maximization problem considers robust stabilization for siso systems with linear dependence on a real uncertain parameter which may occur either in the numerator or denominator of the plant transfer function the authors show necessary and sufficient conditions for the existence of robust controllers their structure and parameterization can be obtained from the corresponding nevanlinna pick interpolation problems this work extends the previously known case of an uncertain gain parameter

closed loop hyperstability of interval plants this note examines the conditions for robust bounded input bounded output closed loop stability of interval plants when there is a nonlinear element in the feedback path specifically the authors present the robust generalized circle criterion and popov s criterion

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

a doubly adaptive approach to dynamic mri sequence estimation dynamic magnetic resonance imaging mri refers to the acquisition of a sequence of mri images to monitor temporal changes in tissue structure we present a method for the estimation of dynamic mri sequences based on two complimentary strategies an adaptive framework for the estimation of the mri images themselves and an adaptive method to tailor the mri system excitations for each data acquisition we refer to this method as the doubly adaptive temporal update method datum for dynamic mri analysis of the adaptive image estimate framework shows that calculating the optimal system excitations for each new image requires complete knowledge of the next image in the sequence since this is not realizable we introduce a linear predictor to aid in determining appropriate excitations simulated examples using real mri data are included to illustrate that the doubly adaptive strategy can provide estimates with lower steady state error than previously proposed methods and also the ability to recover from dramatic changes in the image sequence

all constant gain stabilizing controllers for an interval delay system with uncertain parameters a computationally tractable design method is presented which explicitly yields the entire set of all constant gain controllers which robustly stabilize a family of systems with uncertainty a desired optimal controller may then be selected from the feasible set the method applies to the class of systems where a delay element e hs with interval finite or infinite uncertainty about h is followed by a plant characterized by a rational transfer function with independent interval coefficients illustrative numerical examples are provided

efficient design of orthonormal wavelet bases for signal representation the efficient representation of a signal as a linear combination of elementary atoms or building blocks is central to much signal processing theory and many applications wavelets provide a powerful flexible and efficiently implementable class of such atoms in this paper we develop an efficient method for selecting an orthonormal wavelet that is matched to a given signal in the sense that the squared error between the signal and some finite resolution wavelet representation of it is minimized since the squared error is not an explicit function of the design parameters some form of approximation of this objective is required if conventional optimization techniques are to be used previous approximations have resulted in nonconvex optimization problems which require delicate management of local minima in this paper we employ an approximation that results in a design problem that can be transformed into a convex optimization problem and efficiently solved constraints on the smoothness of the wavelet can be efficiently incorporated into the design we show that the error incurred in our approximation is bounded by a function that decays to zero as the number of vanishing moments of the wavelet grows in our examples we demonstrate that our method provides wavelet bases that yield substantially better performance than members of standard wavelet families and are competitive with those designed by more intricate nonconvex optimization methods

on minimal degree simultaneous pole assignment problems in this paper we show that a generic r tuple of m input p output linear systems is simultaneously pole assignable if r m p and the mcmillan degrees of the systems are not too different we also obtain upper bounds for the degrees of the compensators which simultaneously assign the characteristic polynomials of the r tuple of closed loop systems the upper bounds are obtained for each of the two cases r max m p and max m p r m p 2002 elsevier science inc all rights reserved

h optimal feedback controllers for linear multivariable systems this paper treats the problem of designing for a linear multivariable plant a feedback controller which minimizes the h infty norm of a weighted sensitivity matrix there exists a family of optimal improper feedbacks this family is determined by application of a theory of ball and helton a method for computing optimal feedbacks is described in detail and a numerical example is included it is shown that an optimal improper feedback can be approximated by a proper one under certain conditions on the weighting matrices

sufficient conditions for generic simultaneous pole assignment and stabilization of linear mimo dynamical systems it has been shown that a generic r tuple of m input p output dynamical systems is simultaneously stabilizable pole assignable if r m p and the mcmillian degrees of the systems are not too different this result improves the currently known upper bound r spl les max m p on the number of plants in the case r spl les max m p an upper bound on the degree of the simultaneous pole assigning compensator has also been derived which improves the bound obtained by ghosh and byrnes 1983

invariance of the strict hurwitz property for polynomials with perturbed coefficients given a strictly hurwitz polynomial f lambda lambda n a n 1 lambda n 1 a n 2 lambda n 2 a 1 lambda a 0 it is of interest to know how much the coefficients a i can be perturbed while simultaneously preserving the strict hurwitz property for systems with n leq 4 maximal intervals of the a i are given in a recent paper by guiver and bose 1 in this note a theorem of kharitonov is exploited to obtain a general result for polynomials of any degree

robust parametric classical control design this paper extends well known graphical design tools such as the nyquist plot bode plot and nichols charts to the domain of control systems containing parameter uncertainty we have specifically considered linear interval control systems namely those where the uncertain parameters appear linearly in the characteristic polynomial and vary in intervals because in these cases exact construction of frequency envelopes is possible using these developments we calculate various extremal stability margins for such systems and these are used with standard classical control design techniques to deal with robustness with respect to parametric uncertainty in addition we give an effective technique to iteratively select values of the design parameters within given ranges so that the closed loop system produces improved gain or phase margin

on h optimal sensitivity theory for siso feedback systems this paper deals with the design of feedback controllers which minimize the h infty norm of the sensitivity function suitably weighted this approach to the theory of feedback design was introduced by zames 1 and developed by zames and francis 2 in this paper the theory of sarason 3 is applied to the determination of the optimal weighted sensitivity function and an upper bound on its norm the problem of achieving small sensitivity over a specified frequency band is studied and the effect of nonminimum phase is elucidated finally a method is introduced for handling plant poles and zeros on the imaginary axis

a pole placement design approach for systems with multiple operating conditions the author proposes design procedures based on state space pole placement techniques for systems with multiple operating conditions this is the so called simultaneous pole placement problem first the full state feedback problem is studied in which a nonlinear local pole placement solution is proposed the design condition is formulated in terms of the rank condition of a multimode controllability matrix then the output feedback problem is approached using a multimodel controller design which is an extension of the observer design to multimode systems the design is decomposed into separated global pole placement subproblems and a local pole placement subproblem for a system with some operating conditions having modes on the j omega axis but no modes at the origin in the open right half of the complex plane stabilizability and detectability conditions for the design of an asymptotically stabilizing control are established without any restriction on the number of inputs or outputs relations of this approach to other simultaneous control design approaches are pointed out

multivariable feedback sensitivity and decentralized control in this paper the problem of sensitivity reduction by feedback is studied and related to a problem of decentralized control a plant will be represented by an n times n matrix of frequency responses which may be unstable or irrational the object will be to find conditions on p s under which a diagonal feedback f s can make the sensitivity parallel i p s f s 1 parallel arbitrarily small over some specified frequency interval j omega 0 j omega 0 without violating a global sensitivity bound parallel i p s f s 1 parallel leq m m geq some const 1 for re s geq 0 it will be shown that such a diagonal feedback of the high gain type can be constructed whenever p 1 s is analytic in re s geq 0 p s satisfies an attenuation condition near s infty and p s approaches diagonal dominance at high frequencies it will also be shown that these conditions on the plant can be interpreted as conditions for the existence of a decentralized wide band control scheme

a survey of extreme point results for robustness of control systems abstract this paper surveys a subset of the body of research which was sparked by kharitonov s theorem the focal point is extreme point results for robust stability and robust performance that is we give conditions under which satisfaction of a performance specification is ascertained for a family of systems by only checking a finite subset of the extreme members of this family the results which are surveyed apply mainly to systems with structured real parametric uncertainty in addition a number of counterexamples are given to illustrate cases for which an extreme point result does not hold for such cases a solution via the so called edge theorem is often possible

extreme point results for robust stability of interval plants beyond first order compensators motivated by robust stabilization of interval plants this paper concentrates on a fundamental problem involving a family of polynomials obtained via convex combination of extreme members the objective is to provide conditions under which stability of the extremes implies stability of the entire family although the existing literature contains rather strong extreme point results involving frequency domain analysis there is a paucity of more direct coefficient space criteria this paper deals exclusively with the coefficient space problem to this end we introduce the so called alternating hurwitz minor condition ahmc and show how it can be used to enlarge the class of polynomial families for which extreme point results can be obtained subsequently the ramifications on robust stability of interval plants are fully explained in contrast to existing literature for first order compensators the ahmc makes it possible to deal with classes of higher order compensators in an extreme point context

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

t structures on some local calabi yau varieties abstract let z be a smooth fano variety satisfying the condition that the rank of the grothendieck group of z is one more than the dimension of z let z denote the total space of the canonical line bundle of z considered as a non compact calabi yau variety we use the theory of exceptional collections to describe t structures on the derived category of coherent sheaves on z the combinatorics of these t structures is determined by a natural action of an affine braid group closely related to the well known action of the artin braid group on the set of exceptional collections on z

mutations vs seiberg duality abstract for a quiver with potential derksen weyman and zelevinsky defined in h derksen j weyman a zelevinsky quivers with potentials and their representations i mutations arxiv 0704 0649v2 math ra a combinatorial transformation mutations mukhopadhyay and ray on the other hand tell us how to compute seiberg dual quivers for some quivers with potentials through a tilting procedure thus obtaining derived equivalent algebras in this text we compare mutations with the concept of seiberg duality given by s mukhopadhyay k ray seiberg duality as derived equivalence for some quiver gauge theories arxiv hep th 0309191v2 concluding that for a certain class of potentials the good ones mutations coincide with seiberg duality therefore giving derived equivalences

an extreme point result of robust stability of a diamond of polynomials it is shown that a family of polynomials with real coefficients lying in a diamond is hurwitz if and only if eight distinguished extreme polynomials are hurwitz for the case of complex coefficients it is shown by a counterexample that no analogous extreme point result holds

structured singular values and stability analysis of uncertain polynomials part 2 a missing link abstract in part 1 of this paper a generalized notion of structured singular value is introduced and studied specifically in the case when a certain matrix is of rank one in part 2 of this series we demonstrate that the framework developed in part 1 is particularly suitable for a class of stability problems and its unifies several frequency based stability conditions obtained via alternative approaches generally these problems correspond to a class of uncertain polynomials whose coefficients are perturbed in an affine fashion several stability conditions are derived readily from solution of the structured singular value presented in part 1 which either extend or coincide with previously known results in particular for family of interval and diamond polynomials we further show that the stability conditions based on the structured singular value and the corresponding results in the spirit of kharitonov theorem lead to one another thus establishing a link between the two types of drastically different results and accomplishing one of our main goals in this series a related robust stabilization problem is also investigated in this framework

some new results on the simultaneous stabilizability of a family of single input single output systems abstract in this paper we obtain sufficiency conditions on the problem of simultaneous stabilization of a parameterized family of single input single output plants by a non switching compensator the sufficiency conditions include simultaneous stabilization and simultaneous pole assignment of a finite number of plants

a sufficient condition for simultaneous stabilization the condition under which it is possible to find a single controller that stabilizes k single input single output linear time invariant systems p sub i s i 1 k is investigated the concept of avoidance in the complex plane is introduced and used to derive a sufficient condition for k systems to be simultaneously stabilizable a method for constructing a simultaneous stabilizing controller is also provided and is illustrated by an example

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

consistency of open loop experimental frequency response data with coprime factor plant models the model data consistency problem for coprime factorization considered is given some possibly noisy frequency response data obtained by running open loop experiments on a system show that these data are consistent with a given family of perturbed coprime factor models and a time domain spl lscr sub spl infin noise model in the noise free open loop case the model data consistency problem boils down to the existence of an interpolating function in spl rscr spl hscr sub spl infin that evaluates to a finite number of complex matrices at a finite number of points on the imaginary axis a theorem on boundary interpolation in spl rscr spl hscr sub spl infin is a building block that allows one to devise computationally simple necessary and sufficient tests to check if the perturbed coprime factorization is consistent with the data for standard coprime factorizations the test involves the computation of minimum norm solutions to underdetermined complex matrix equations the schmidt mirsky theorem is used in the case of special factorizations of flexible systems for spl lscr sub spl infin noise corrupting the frequency response measurements a complete solution to the open loop noisy siso problem using the structured singular value spl mu is given

on the thirty two virtual polynomials to stabilize an interval plant this paper studies the conservatism of the 32 virtual polynomials to stabilize an interval plant it is shown that working with the 32 virtual vertices is generally less conservative than with the kharitonov polynomials of the smallest interval polynomial containing the characteristic polynomial polytope by means of the former it is possible to find all the controllers such that the value set of the polytope of characteristic polynomials is applied in two quadrants as a maximum for each spl omega while using the latter only some of them can be found the cases in which both methods coincide are also analyzed and the conditions on the numerator and denominator of the controller are developed thus this coincidence can be known a priori from the characteristics of the coefficients of the numerator and denominator of the controller it is shown that these conditions are satisfied by the first order controllers

block bialternate sum and associated stability formulae abstract a new block bialternate sum of a partitioned square matrix with itself is defined and some basic properties established it has similar properties to the bialternate sum but it preserves the block structure of the summand it is used in place of the block kronecker sum and the block lyapunov sum to solve maximal stability problems of stable systems under low gain integral control and of singularly perturbed systems it is also used to find the critical gains for a first order controller with a scalar plant from which all stabilizing first order controllers can be constructed in each stability problem the internal dimensions of the resulting closed formulae are lower than those currently available

comments on a necessary and sufficient condition for the stability of interval matrices in a recent paper by bialas a new proof of a known result concerning interval polynomials was given this result is summarized here and a much stronger result is mentioned bialas main theorem on the stability of interval matrices is shown to be false

a convex parameterization of robustly stabilizing controllers this paper treats synthesis of robust controllers for linear time invariant systems uncertain real parameters are assumed to appear linearly in the closed loop characteristic polynomial the main contribution is to give a convex parameterization of all controllers that simultaneously stabilize the system for all possible parameter combinations with the new parameterization certain robust performance problems can be stated in terms of quasi convex optimization

the solution of a transcendental problem and its applications in simultaneous stabilization problems a complete solution for a special transcendental problem in system theory is given one of the interpretations of this transcendental problem is the following simultaneous stabilization problem under what conditions can two linear plants be simultaneously stabilized by a single compensator having no real poles in the closed right half of the complex plane these conditions are completely general and therefore encompass unstable non minimum phase plants as well it is shown that the simultaneous stabilizability of two given plants via such a restricted compensator depends solely on the locations of the real zeros of the two plants and their difference plant in the closed right half of the complex plane for two plants satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is provided and illustrated a computationally checkable necessary condition for simultaneous stabilization of three plants is also given

controller synthesis via the 4 k polynomial approach abstract in some recent work it was shown that to stabilize systems with real parameter uncertainty it suffices to find a controller that simultaneously stabilizes a finite number of polynomials these polynomials include those generated from the vertex plants as well as some generated by some fictitious vertex plants that involve the controller this paper deals with the issues of existence of such a controller controller synthesis and conservativeness of the design it is shown how this approach can enhance the stability robustness of an h design

maximal modifications and auslander reiten duality for non isolated singularities we first generalize classical auslander reiten duality for isolated singularities to cover singularities with a one dimensional singular locus we then define the notion of ct modules for non isolated singularities and we show that these are intimately related to noncommutative crepant resolutions nccrs when r has isolated singularities ct modules recover the classical notion of cluster tilting modules but in general the two concepts differ then wanting to generalize the notion of nccrs to cover partial resolutions of operatorname spec r in the main body of this paper we introduce a theory of modifying and maximal modifying modules under mild assumptions all the corresponding endomorphism algebras of the maximal modifying modules for three dimensional gorenstein rings are shown to be derived equivalent we then develop a theory of mutation for modifying modules which is similar but different to mutations arising in cluster tilting theory our mutation works in arbitrary dimension and in dimension three the behavior of our mutation strongly depends on whether a certain factor algebra is artinian

two applications of wavelet transforms in magnetic resonance imaging the authors describe two different applications of wavelet transforms in magnetic resonance imaging mri in each case the use of wavelets offers tangible benefits over the traditional fourier transform based imaging these stem from the simultaneous time and frequency localization properties of the wavelets the first application utilizes the localization properties of wavelets to acquire single t sub 2 weighted images in times which are short relative to current methods an interesting combinatorial scheduling problem arises from the multiscale structure inherent in the formulation of this procedure its solution is sketched and applied to the imaging process the second example is a technique for potentially instant imaging image acquisition is modeled as an inverse wavelet transform of the spin density in the region in question signal acquisition takes place in as few as one or two echoes after the excitation by rf pulses designed to excite a moving band of spins in a slice these sweeping rf pulses excite strips of spins which rephase at different times during acquisition they replace phase encoding gradients no fast pulsed gradients are required

on informational completeness of covariant localization observables and wigner coefficients an orthogonality theorem is obtained for square integrable representations on homogeneous spaces of a locally compact group from this a series of lemmas is derived showing the informational completeness of natural covariant localization operators as well as of the generalized wigner distributions matrix elements of the group some of these results give explicit reconstruction formulas for the quantum state from its expectation values against these families of operators the results are applied to special phase space representations of the heisenberg affine and galilei groups

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

correction to optimal control of perturbed linear static systems this paper presents a typographical correction to the proof of theorem 4 in the above mentioned paper smith et al 1996

to stabilize a k real parameter affine family of plants it suffices to simultaneously stabilize 4 4 polynomials a controller stabilizes an entire family of plants with affine uncertainty if it simultaneously stabilizes a finite number of polynomials an upper bound for this number is 4k

a note on robust stabilization for systems with parameters we consider the problem of stabilizing a linear time invariant multivariable system whose transfer function admits a factorization which contains parametric type uncertainties the parameters are known to take values in some region a we first give a sufficient condition for robust stability when a proper feedback compensator is used here it is important to note that no assumption is made about the number of unstable plant poles following this we focus attention on how to compute an appropriate robustly stabilizing compensator this is done in a two step procedure initially the solutions of a diophantine equation generate a class of proper compensators each of which stabilizes the nominal closed loop system this is followed by a nyquist theorem inspired minimization which yields the final choice an illustrative physical example is given the compensator thus constructed guarantees stability over u a discussion about how to compute the size of the attainable robust stability region u is also included

feature preserving mri denoising a nonparametric empirical bayes approach this paper presents a novel method for bayesian denoising of magnetic resonance mr images that bootstraps itself by inferring the prior i e the uncorrupted image statistics from the corrupted input data and the knowledge of the rician noise model the proposed method relies on principles from empirical bayes eb estimation it models the prior in a nonparametric markov random field mrf framework and estimates this prior by optimizing an information theoretic metric using the expectation maximization algorithm the generality and power of nonparametric modeling coupled with the eb approach for prior estimation avoids imposing ill fitting prior models for denoising the results demonstrate that unlike typical denoising methods the proposed method preserves most of the important features in brain mr images furthermore this paper presents a novel bayesian inference algorithm on mrfs namely iterated conditional entropy reduction icer this paper also extends the application of the proposed method for denoising diffusion weighted mr images validation results and quantitative comparisons with the state of the art in mr image denoising clearly depict the advantages of the proposed method