efficient scalar quantization of exponential and laplacian random variables this paper presents solutions to the entropy constrained scalar quantizer ecsq design problem for two sources commonly encountered in image and speech compression applications sources having the exponential and laplacian probability density functions we use the memoryless property of the exponential distribution to develop a new noniterative algorithm for obtaining the optimal quantizer design we show how to obtain the optimal ecsq either with or without an additional constraint on the number of levels in the quantizer in contrast to prior methods which require a multidimensional iterative solution of a large number of nonlinear equations the new method needs only a single sequence of solutions to one dimensional nonlinear equations in some laplacian cases one additional two dimensional solution is needed as a result the new method is orders of magnitude faster than prior ones we show that as the constraint on the number of levels in the quantizer is relaxed the optimal ecsq becomes a uniform threshold quantizer utq for exponential but not for laplacian sources we then further examine the performance of the utq and optimal ecsq and also investigate some interesting alternatives to the utq including a uniform reconstruction quantizer urq and a constant dead zone ratio quantizer cdzrq

semiprime graded algebras of dimension two semiprime noetherian connected graded k algebras r of quadratic growth are described in terms of geometric data a typical example of such a ring is obtained as follows let y be a projective variety of dimension at most one over the base field k and let e be an oy order in a finite dimensional semisimple algebra a over k k y then for any automorphism of a that restricts to an automorphism of y and any ample invertible e bimodule b van den bergh constructs a noetherian twisted homogeneous coordinate ring b h0 y b b n 1 we show that r is noetherian if and only if some veronese ring r m of r has the form k i where i is a left ideal of such a ring b and where i b at each point p y at which has finite order this allows one to give detailed information about the structure of r and its modules

a progressive transmission capable diagnostically lossless compression scheme for 3d medical image sets this paper presents a novel and efficient diagnostically lossless compression for 3d medical image sets this compression scheme provides the 3d medical image sets with a progressive transmission capability an automated filter and threshold based preprocessing technique is used to remove noise outside the diagnostic region then a wavelet decomposition feature vector based approach is applied to determine the reference image for the entire 3d medical image set the selected reference image contains the most discernible anatomical structures within a relative large diagnostic region it is progressively encoded by a lossless embedded zerotree wavelet method so the validity of an entire set can be determined early this preprocessing technique is followed by an optimal predictor plus a 1st level integer wavelet transform to de correlate the 3d medical image set run length and arithmetic coding are used to further remove coding redundancy this diagnostically lossless compression method achieves an average compression of 2 1038 2 4292 and 1 6826 bits per pixel for three types of 3d magnetic resonance image sets the integrated progressive transmission capability degrades the compression performance by an average of 7 25 6 60 and 4 49 for the above three types moreover our compression without and with progressive transmission achieves better compression than the state of the art

toward optimality in scalable predictive coding a method is proposed for efficient scalability in predictive coding which overcomes known fundamental shortcomings of the prediction loop at enhancement layers the compression efficiency of an enhancement layer is substantially improved by casting the design of its prediction module within an estimation theoretic framework and thereby exploiting all information available at that layer for the prediction of the signal and encoding of the prediction error while the most immediately important application is in video compression the method is derived in a general setting and is applicable to any scalable predictive coder thus the estimation theoretic approach is first developed for basic dpcm compression and demonstrates the power of the technique in a simple setting that only involves straightforward prediction scalar quantization and entropy coding results for the scalable compression of first order gauss markov and laplace markov signals illustrate the performance a specific estimation algorithm is then developed for standard scalable dct based video coding simulation results show consistent and substantial performance gains due to optimal estimation at the enhancement layers

brief paper anti windup and bumpless transfer schemes this paper considers the problem of windup which occurs when a controller with unstable integrator modes is subjected to input saturation or multi mode operation an optimal strategy for the so called model based approach is proposed based on an h optimisation framework this has been found to give good results on numerical examples taken from the literature

graded modules of gelfand kirillov dimension one over three dimensional artin schelter regular algebras abstract let a be a three dimensional artin schelter regular algebra we give a description of the category of finitely generated a modules of gelfand kirillov dimension one modulo those of finite dimension over the ground field the proof is based upon a result by gabriel which says that locally finite categories can be described by module categories over topological rings

the geometry of arithmetic noncommutative projective lines abstract let k be a perfect field and let k k be a finite extension of fields an arithmetic noncommutative projective line is a noncommutative space of the form proj s k v where v be a k central two sided vector space over k of rank two and s k v is the noncommutative symmetric algebra generated by v over k defined by m van den bergh 26 we study the geometry of these spaces more precisely we prove they are integral we classify vector bundles over them we classify them up to isomorphism and we classify isomorphisms between them using the classification of isomorphisms we compute the automorphism group of an arithmetic noncommutative projective line

the structure of as gorenstein algebras abstract in this paper we define a notion of as gorenstein algebra for n graded algebras and show that symmetric as regular algebras of gorenstein parameter 1 are exactly preprojective algebras of quasi fano algebras this result can be compared with the fact that symmetric graded frobenius algebras of gorenstein parameter 1 are exactly trivial extensions of finite dimensional algebras the results of this paper suggest that there is a strong interaction between classification problems in noncommutative algebraic geometry and those in representation theory of finite dimensional algebras

non commutative graded algebras and their hilbert series abstract this paper begins to develop a theory of non commutative graded algebras and their hilbert series which parallels the extensive already existing theory on commutative graded algebras we begin with a discussion of order ideals of monomials which give us vector space bases for these algebras we develop next the concept of weak summand which is a special relationship a subalgebra may have to an algebra and the concept of strongly free sets strongly free sets have many properties which are analogous to the properties of regular sequences in commutative algebras we discuss combinatorially free sets which are useful for constructing examples of many of the preceding ideas we conclude with an application of our results to algebraic topology by showing that there is a finite cw complex with only nine positive dimensional cells whose loop space has an irrational poincare series

bounded derived categories and repetitive algebras abstract by a theorem due to the first author the bounded derived category of a finite dimensional algebra over a field embeds fully faithfully into the stable category over its repetitive algebra this embedding is an equivalence if the algebra is of finite global dimension the purpose of this paper is to investigate the relationship between the derived category and the stable category over the repetitive algebra from various points of view for algebras of infinite global dimension the most satisfactory results are obtained for gorenstein algebras especially for selfinjective algebras

quotients of cluster categories higher cluster categories were recently introduced as a generalization of cluster categories this paper shows that in dynkin types a and d half of all higher cluster categories can be obtained as quotients of cluster categories the other half are quotients of 2 cluster categories the lowest type of higher cluster categories hence in dynkin types a and d all higher cluster phenomena are implicit in cluster categories and 2 cluster categories in contrast the same is not true in dynkin type e

noetherian hereditary abelian categories satisfying serre duality norwegian univ sci technol dept math sci n 7491 trondheim norway limburgs univ ctr dept wni b 3590 diepenbeek belgium reiten i norwegian univ sci technol dept math sci n 7491 trondheim norway

distributions of the two dimensional dct coefficients for images for a two dimensional discrete cosine transform dct image coding system there have been different assumptions concerning the distributions of the transform coefficients this paper presents results of distribution tests that indicate that for many images the statistics of the coefficients are best approximated by a gaussian distribution for the dc coefficient and a laplacian distribution for the other coefficients furthermore from a simulation of the dct coding system it is shown that the assumption that the coefficients are laplacian yields a higher actual output signal to noise ratio and a much better agreement between theory and simulation than the gaussian assumption

interpolation for gain scheduled control with guarantees here a methodology is presented which considers the interpolation of linear time invariant lti controllers designed for different operating points of a nonlinear system in order to produce a gain scheduled controller guarantees of closed loop quadratic stability and performance at intermediate interpolation points are presented in terms of a set of linear matrix inequalities lmis the proposed interpolation scheme can be applied in cases where the system must remain at the operating points most of the time and the transitions from one point to another rarely occur e g chemical processes satellites

multiple model adaptive mixing control the discrete time case most of the work in multiple model adaptive control with various forms of switching focused on continuous time systems the purpose of this technical note is to extend the results of one approach the adaptive mixing control amc to discrete time systems further the technical note solves the tracking problem which has not been addressed in most schemes of this class stability and robustness properties of the amc scheme for discrete time systems are analyzed it is shown that in the ideal case when no disturbances or unmodeled dynamics are present the tracking error converges to zero in the non ideal case the mean square tracking error is of the order of magnitude of the modeling error provided the unmodeled dynamics satisfy a norm bound condition while these robustness results are conceptually similar to those of traditional robust adaptive control the proposed scheme does not suffer from the drawback of stabilizability of the estimated plant and in addition performs much better in simulation studies furthermore it allows well developed results from robust control to be incorporated in the design

noncommutative projective schemes an analogue of the concept of projective scheme is defined for noncommutative n graded algebras using the quotient category c of graded right a modules modulo its full subcategory of torsion modules we define proj a c a s where a is the object corresponding to the module aa and s is the autoequivalence defined by the shift of degrees the triples equivalent to proj a for a right noetherian graded algebra a are characterized in terms of a condition on extensions

design of controllers for linear parameter varying systems by the gain scheduling technique abstract design of controllers for linear multi input multi output systems whose dynamics depend on a time varying parameter is studied design algorithms for the state feedback control law based on the gain scheduling technique are proposed state feedback control laws are designed so that one of the following goals is achieved i the poles of the closed loop system for all fixed parameter values are placed in a small neighborhood of a set of desired closed loop poles ii the stability of the closed loop system for all fixed parameter values guarantees that the of the system with the time varying parameter independent of the rate of change of the parameter rigorously justified and computationally appealing design algorithms are developed

gain scheduling via linear fractional transformations abstract a linear finite dimensional plant with rational state space parameter dependence is controlled using a parameter dependent controller the parameters are known to take on values in a unit ball and are known in real time the goal of control is to stabilize the parameter dependent closed loop system and provide disturbance error attenuation as measured in induced l 2 norms the approach taken uses the optimally scaled small gain theorem and solves the control synthesis problem by reformulating the existence conditions into a finite dimensional convex optimization

the l2 l2 bumpless transfer problem for linear plants its definition and solution a novel characterization of bumpless transfer among alternative controllers both in continuous and discrete time is introduced the bumpless transfer problem is to design a compensation scheme guaranteeing an l 2 respectively l 2 bound on the mismatch after the switching time between the actual plant output and a particular target ideal response minimization of the gain from initial plant state mismatch to l 2 respectively l 2 plant output mismatch provides improved transients a solution to the bumpless transfer problem is given both for plants without input saturation and for plants with input saturation the solution guarantees anti windup features in the latter case

higher nakayama algebras i construction we introduce higher dimensional analogues of the nakayama algebras from the viewpoint of iyama s higher auslander reiten theory more precisely for each nakayama algebra a and each positive intege

abstract representation theory of dynkin quivers of type a abstract we study the representation theory of dynkin quivers of type a in abstract stable homotopy theories including those associated to fields rings schemes differential graded algebras and ring spectra reflection functors partial coxeter functors and serre functors are defined in this generality and these equivalences are shown to be induced by universal tilting modules certain explicitly constructed spectral bimodules in fact these universal tilting modules are spectral refinements of classical tilting complexes as a consequence we obtain split epimorphisms from the spectral picard groupoid to derived picard groupoids over arbitrary fields these results are consequences of a more general calculus of spectral bimodules and admissible morphisms of stable derivators as further applications of this calculus we obtain examples of universal tilting modules which are new even in the context of representations over a field this includes yoneda bimodules on mesh categories which encode all the other universal tilting modules and which lead to a spectral serre duality result finally using abstract representation theory of linearly oriented a n quivers we construct canonical higher triangulations in stable derivators and hence a posteriori in stable model categories and stable categories

rigid objects triangulated subfactors and abelian localizations we show that the abelian category mathsf mod text mathcal x of coherent functors over a contravariantly finite rigid subcategory mathcal x in a triangulated category mathcal t is equivalent to the gabriel zisman localization at the class of regular maps of a certain factor category of mathcal t and moreover it can be calculated by left and right fractions thus we generalize recent results of buan and marsh we also extend recent results of iyama yoshino concerning subfactor triangulated categories arising from mutation pairs in mathcal t in fact we give a classification of thick triangulated subcategories of a natural pretriangulated factor category of mathcal t and a classification of functorially finite rigid subcategories of mathcal t if the latter has serre duality in addition we characterize 2 cluster tilting subcategories along these lines finally we extend basic results of keller reiten concerning the gorenstein and the calabi yau property for categories arising from certain rigid not necessarily cluster tilting subcategories as well as several results of the literature concerning the connections between 2 cluster tilting subcategories of triangulated categories and tilting subcategories of the associated abelian category of coherent functors

generalized serre duality abstract we introduce a notion of generalized serre duality on a hom finite krull schmidt triangulated category t this duality induces the generalized serre functor on t which is a linear triangle equivalence between two thick triangulated subcategories of t moreover the domain of the generalized serre functor is the smallest additive subcategory of t containing all the indecomposable objects which appear as the third term of an auslander reiten triangle in t dually the range of the generalized serre functor is the smallest additive subcategory of t containing all the indecomposable objects which appear as the first term of an auslander reiten triangle in t we compute explicitly the generalized serre duality on the bounded derived categories of artin algebras and of certain noncommutative projective schemes in the sense of artin and zhang we obtain a characterization of gorenstein algebras an artin algebra a is gorenstein if and only if the bounded homotopy category of finitely generated projective a modules has serre duality in the sense of bondal and kapranov

skew group algebras in the representation theory of artin algebras then the corresponding crossed product algebra i g or i x g for short has an elements cgieg gi a li i addition is componentwise and multiplication is given by g a g and g g2 y g g2 m in this paper we assume that the values of y lie in the center z a of i hence the action of g on i is given by a group homomorphism g p aut i and 3 can be left out in the special case that y is the trivial map we write 1g instead of i g and the elements as c c li gi ag is then called a skew group ring there is a lot of literature on skew group algebras and crossed product algebras and on the relationship with the ring ac whose elements are those elements of a left fixed by g much work has been done on which properties of li are inherited by n g or ac some of the work on the relationship between these rings has its roots in trying to develop a galois theory for noncommutative rings we refer to 3 7 13 15 19 21 23 25 27 281 and their references in this paper we study these constructions when i is an artin algebra and g a finite group of order n such that n is invertible in 1 under these assumptions the construction preserves central properties of interest in the

gorenstein projective modules and symmetric recollements we introduce compatible bimodules if m is a compatible a b bimodule then the gorenstein projective modules over algebra am0b are explicitly described and if is gorenstein then this description implies that m is compatible as an application if m is compatible then there is a left recollement of the stable category gp and if is gorenstein and ma is projective then there is a symmetric recollement of the singularity category dsgb

rate distortion performance of dpcm schemes for autoregressive sources an analysis of the rate distortion performance of differential pulse code modulation dpcm schemes operating on discrete time auto regressive processes is presented the approach uses an iterative algorithm for the design of the predictive quantizer subject to an entropy constraint on the output sequence at each stage the iterative algorithm optimizes the quantizer structure given the probability distribution of the prediction error while simultaneously updating the distribution of the resulting prediction error different orthogonal expansions specifically matched to the source are used to express the prediction error density a complete description of the algorithm including convergence and uniqueness properties is given results are presented for rate distortion performance of the optimum dpcm scheme for first order gauss markov and laplace markov sources including comparisons with the corresponding rate distortion bounds furthermore asymptotic formulas indicating the high rate performance of these schemes are developed for both first order gaussian and laplacian autoregressive sources

switching lpv control designs using multiple parameter dependent lyapunov functions in this paper we study the switching control of linear parameter varying lpv systems using multiple parameter dependent lyapunov functions to improve performance and enhance control design flexibility a family of lpv controllers is designed each suitable for a specific parameter subregion they are switched so that the closed loop system remains stable and its performance is optimized two switching logics hysteresis switching and switching with average dwell time are examined the control synthesis conditions for both switching logics are formulated as matrix optimization problems which are generally non convex but can be convexified under some simplifying assumptions the hysteresis switching lpv control scheme is then applied to an active magnetic bearing problem

almost split sequences in dimension two a does not split b if h x r c is a morphism in c which is not a splittable epimorphism in c then there is a t x c such that gt h c if j ci y is a morphism in c which is not a splittable monomorphism in c then there is an s c y in c such that j sf almost split sequences were first introduced by us in the case a is the category of finitely generated modules over an artin algebra i and c a see 6 71 the reader is referred to the expository articles 11 121 for an account of the role almost split sequences have played in the theory of the representation theory of artin algebras that almost split sequences exist for various subcategories of module categories over a much wider class of rings than artin algebras was first shown in 2 31 where various existence theorems for almost split sequences were given these results seemed to indicate that there might be connections between the structure and existence of almost split sequences and algebraic geometry recent developments show that this is indeed the case in 4 it is shown that the structure of the almost split sequences in the category of reflexive modules of a complete rational double point over the complex numbers determines the desingularization graph of the singularity also it has been shown in s that a complete cohen macaulay local ring s is an isolated singularity if and only if the category of cohen macaulay

dynamic gain scheduled control and extended linearisation extensions explicit formulae and stability a controller designed for linearisations at various trim operating points of a nonlinear system using linear approaches is not necessarily performing well or stable once scheduled with a state under dynamic conditions the key idea of using this scheduled control law design is to retain states close to the current usually dynamically varying operating point dynamic gain scheduling dgs is a technique aimed to resolve this controller scheduling issue for rapidly changing dynamics and states it entails scheduling the control law gains with a fast varying state variable rather than with a slowly varying state it has been successfully applied to the aircraft system models allowing also for nested loops the aim of this paper is to extend dgs to a more general setting allowing for more complex multi input dynamics incorporating the more simple static scheduling within the same controller hence given a linear design suitable transformations are provided which allow fast scheduling of multi variable co

maximal rigid subcategories and cluster tilting subcategories in 2 cy categories abstract let c be a connected hom finite 2 cy triangulated category we prove that if t is a functorially finite maximal rigid subcategory of c without loops in its quiver then t is cluster tilting in particular this gives a positive answer to a conjecture proposed in 5

stabilization of nonlinear systems with moving equilibria this note provides a new method for the stabilization of nonlinear systems with parametric uncertainty unlike traditional techniques our approach does not assume that the equilibrium remains fixed for all parameter values the proposed method combines different optimization techniques to produce a robust control that accounts for uncertain parametric variations and the corresponding equilibrium shifts comparisons with analytical gain scheduling are provided

on delayed sequential coding of correlated sources motivated by video coding applications the problem of sequential coding of correlated sources with encoding and or decoding frame delays is studied the fundamental tradeoffs between individual frame rates individual frame distortions and encoding decoding frame delays are derived in terms of a single letter information theoretic characterization of the rate distortion region for general interframe source correlations and certain types of potentially frame specific and coupled single letter fidelity criteria the sum rate distortion region is characterized in terms of generalized directed information measures highlighting their role in delayed sequential source coding problems for video sources which are spatially stationary memoryless and temporally gauss markov mse frame distortions and a sum rate constraint our results expose the optimality of idealized differential predictive coding among all causal sequential coders when the encoder uses a positive rate to describe each frame somewhat surprisingly causal sequential encoding with one frame delayed noncausal sequential decoding can exactly match the sum rate mse performance of joint coding for all nontrivial mse tuples satisfying certain positive semidefiniteness conditions thus even a single frame delay holds potential for yielding significant performance improvements generalizations to higher order markov sources are also presented and discussed a rate distortion performance equivalence between causal sequential encoding with delayed noncausal sequential decoding and delayed noncausal sequential encoding with causal sequential decoding is also established

representations of super yang mills algebras we study in this article the representation theory of a family of super algebras called the super yang mills algebras by exploiting the kirillov orbit method a la dixmier for nilpotent super lie algebras these super algebras are an extension of the so called yang mills algebras introduced by a connes and m dubois violette in lett math phys 61 2 149 158 2002 and in fact they appear as a background independent formulation of supersymmetric gauge theory considered in physics in a similar way as yang mills algebras do the same for the usual gauge theory our main result states that under certain hypotheses all clifford weyl super algebras rm cliff q k otimes a p k for p 3 or p 2 and q 2 appear as a quotient of all super yang mills algebras for n 3 and s 1 this provides thus a family of representations of the super yang mills algebras

coherent algebras and noncommutative projective lines abstract a well known conjecture says that every one relator group is coherent we state and partly prove a similar statement for graded associative algebras in particular we show that every gorenstein algebra a of global dimension 2 is graded coherent this allows us to define a noncommutative analogue of the projective line p 1 as a noncommutative scheme based on the coherent noncommutative spectrum qgra of such an algebra a that is the category of coherent a modules modulo the torsion ones this category is always abelian ext finite hereditary with serre duality like the category of coherent sheaves on p 1 in this way we obtain a sequence p n 1 n 2 of pairwise non isomorphic noncommutative schemes which generalize the scheme p 1 p 2 1

brief stability preserving interpolation methods for the synthesis of gain scheduled controllers synthesis of gain scheduled controllers for nonlinear plants often requires that a parameter varying controller be generated from a finite set of linear time invariant controllers we propose interpolation methods for this task with the property that stability of the linearized closed loop system is preserved for all values of the scheduling parameter in addition slow variation arguments are presented that establish local stability of the nonlinear closed loop system with gain scheduled controller

an enhanced velocity based algorithm for safe implementations of gain scheduled controllers abstractthis paper presents an enhanced velocity based algorithm to implement gain scheduled controllers for nonlinear and parameter dependent systems a new scheme including pre and post filtering is proposed with the assumption that the time derivative of the controller inputs is not available for feedback control it is shown that the proposed control structure can preserve the input output properties of the linearised closed loop system in the neighbourhood of each equilibrium point avoiding the emergence of the so called hidden coupling terms moreover it is guaranteed that this implementation will not introduce unobservable or uncontrollable unstable modes and hence the internal stability will not be affected a case study dealing with the design of a pitch axis missile autopilot is carried out and the numerical simulation results confirm the validity of the proposed approach

smooth switching lpv controller design for lpv systems abstract this paper presents a method to design a smooth switching gain scheduled linear parameter varying lpv controller for lpv systems the moving region of the gain scheduling variables is divided into a specified number of local subregions as well as subregions for the smooth controller switching and one gain scheduled lpv controller is assigned to each of the local subregions for each switching subregion a function interpolating two local lpv controllers associated with its neighborhood subregions is designed to satisfy the constraint of smooth transition of controller system matrices the smooth switching controller design problem amounts to solving a feasibility problem which involves nonlinear matrix inequalities to find a solution to the feasibility problem an iterative descent algorithm which solves a series of convex optimization problems is proposed the usefulness of the proposed controller design method is demonstrated with a control example of a flexible ball screw drive system

a note on abelian quotient categories abstract let c be a triangulated category with a serre functor s and x a non zero contravariantly finite rigid subcategory of c then x is cluster tilting if and only if the quotient category c x is abelian and s x x 2 as an application this result generalizes the work by beligiannis

relations for the grothendieck groups of triangulated categories a class of triangulated categories with a finiteness condition is singled out these triangulated categories have auslander reiten triangles it is proved that the relations of the grothendieck group of a triangulated category in this class are generated by all auslander reiten triangles moreover the auslander reiten quivers of certain triangulated categories in this class are described in terms of dynkin diagrams 2002 elsevier science usa all rights reserved

the grothendieck group of non commutative non noetherian analogues of p1 and regular algebras of global dimension two abstract let v be a finite dimensional positively graded vector space let b v v be a homogeneous element whose rank is dim v let a t v b the quotient of the tensor algebra tv modulo the 2 sided ideal generated by b let gr a be the category of finitely presented graded left a modules and fdim a its full subcategory of finite dimensional modules let qgr a be the quotient category gr a fdim a we compute the grothendieck group k 0 qgr a in particular if the reciprocal of the hilbert series of a which is a polynomial is irreducible then k 0 qgr a z r as ordered abelian groups where is the smallest positive real root of that polynomial when dim k v 2 qgr a is equivalent to the category of coherent sheaves on the projective line p 1 or a stacky p 1 if v is not concentrated in degree 1 if dim k v 3 results of piontkovski and minamoto suggest that qgr a behaves as if it is the category of coherent sheaves on a non commutative non noetherian analogue of p 1

multiple model adaptive control with mixing despite the remarkable theoretical accomplishments and successful applications of adaptive control the field is not sufficiently mature to solve challenging control problems where strict performance and robustness guarantees are required critical to the design of practical control systems for these challenging applications and currently lacking in parameter estimation based adaptive control schemes is an approach that explicitly accounts for robust performance and stability specifications towards this goal this paper describes a robust adaptive control approach called adaptive mixing control that makes available the full suite of powerful design tools from lti theory e g mixed synthesis the stability and robustness properties of adaptive mixing control are analyzed it is shown that the mean square regulation error is of the order of the modeling error provided the unmodeled dynamics satisfy a norm bound condition and when the parameter estimate converges to its true value which is guaranteed if a persistence of excitation condition is satisfied the adaptive closed loop system converges exponentially fast to a closed loop system comprising the plant and some lti controller that satisfies the control objective a benchmark example is presented which is used to compare the adaptive mixing controller with other adaptive schemes

lq bumpless transfer between two tracking controllers in this article a linear quadratic lq scheme is proposed for bumpless transfer between two tracking controllers the controllers have integral actions which are used to eliminate the steady state tracking errors a compensator is designed using the lq technique to minimise the differences between two sets of signals the differences between two control signals as well as the differences between the two input signals which drive the two controllers under such circumstances complete information of the system is taken into account and utilised for achieving satisfactory control it is shown that the ideal bumpless transfer is achievable with the proposed control scheme moreover the results are extended to discrete time systems finally simulation results are given to demonstrate the effectiveness of the proposed control scheme

noncommutative graded domains with quadratic growth letk be an algebraically closed field and letr be a finitely generated connected gradedk algebra which is a domain of gelfand kirillov dimension two write the graded quotient ringq r ofr asd z z 1 for some automorphism of the division ringd we prove thatd is a finitely generated field extension ofk of transcendence degree one moreover we describer in terms of geometric data ifr is generated in degree one then up to a finite dimensional vector space r is isomorphic to the twisted homogeneous coordinate ring of an invertible sheaf over a projective curvey this implies in particular thatr is noetherian thatr is primitive when and thatr is a finite module over its centre when ifr is not generated in degree one thenr will still be noetherian and primitive if has infinite order butr need not be noetherian when has finite order

parameter dependent state observer design for affine lpv systems in this paper the design of a parameter dependent state observer that allows to estimate the state of an affine linear parameter varying lpv system is investigated the observer has the property of being parameter dependent since the corresponding state space matrices are scheduled using an interpolation method moreover the stability of the estimation error is based on the existence of an affine parameter dependent lyapunov function the main contribution of this paper is that the problem of the observer design and the existence of such a lyapunov function is interpreted as a flexible lmi feasibility condition some illustrative examples are presented at the end of this paper

continuous and discrete state estimation for switched lpv systems using parameter identification in this paper the problem of discrete and continuous state estimation for a class of uncertain switched lpv systems is addressed parameter identification techniques are applied to realize an approximate identification of the scheduled parameters of a switched lpv system with certain uncertainties and or disturbances a discrete state estimation is achieved using the parameter identification a luenberger like hybrid observer based on discrete state information and lmis approach is used for the continuous state estimation the simplicity of the proposed method is one of the main advantages of this paper the feasibility of the proposed method is illustrated by simulations

jacobian algebras with periodic module category and exponential growth abstract recently it was proven by geiss labardini fragoso and schroer in 1 that every jacobian algebra associated to a triangulation of a closed surface s with a collection of marked points m is tame and ladkani proved in 2 these algebras are weakly symmetric in this work we show that for these algebras the auslander reiten translation acts 2 periodically on objects moreover we show that excluding only the case of a sphere with 4 or less punctures these algebras are of exponential growth these results imply that the existing characterization of symmetric tame algebras whose non projective indecomposable modules are periodic has at least a missing class see 3 theorem 6 2 or 4 as a consequence of the 2 periodical actions of the auslander reiten translation on objects we have that the auslander reiten quiver of the generalized cluster category c s m consists only of stable tubes of rank 1 or 2

bumpless transfer between observer based gain scheduled controllers this paper deals with bumpless transfer between a number of observer based controllers in a gain scheduling architecture linear observer based controllers are designed for a number of linear approximations of a non linear system in a set of operating points and gain scheduling control can subsequently be achieved by interpolating between each controller the youla jabr bongiorno kucera yjbk parameterization is used to achieve a smooth scheduling between the controllers this approach produces a scheduled controller as a linear fractional transformation between a fixed controller and a scheduling parameter the approach is tested on a simple but highly non linear model of a fossil fuel power plant

interpolation of observer state feedback controllers for gain scheduling the authors propose a method of interpolating linear time invariant controllers with observer state feedback structure in order to generate a continuously varying family of controllers that stabilizes a family of linear plants gain scheduling is a motivation for this work and the interpolation method yields guidelines for the design of gain scheduled controllers the method is illustrated with the design of a missile autopilot using loop shaping h infinity controllers

on certain cohomological invariants of groups abstract let r be a left and right 0 noetherian ring we show that if all projective left and all projective right r modules have finite injective dimension then all injective left and all injective right r modules have finite projective dimension using this result we prove that the invariants silp z g and spli z g which were introduced by gedrich and gruenberg 1987 15 are equal for any group g as an application of the latter equality we show that a group g is finite if and only if cd g 0 where cd is the generalized cohomological dimension of groups introduced by ikenaga 1984 21

brief paper a velocity algorithm for the implementation of gain scheduled controllers a new method is proposed to implement gain scheduled controllers for nonlinear plants given a family of linear feedback controllers designed for linearizations of a nonlinear plant about constant operating points a nonlinear gain scheduled controller is derived that preserves the input output properties of the linear closed loop systems locally about each equilibrium point the key procedures in the proposed method are to provide integral action at the inputs to the plant and differentiate some of the measured outputs before they are fed back to the scheduled controller for a fairly general class of systems the nonlinear gain scheduled controllers are easy to obtain and their structure is similar to that of the original linear controllers

gain scheduling dynamic linear controllers for a nonlinear plant abstract for a general type of nonlinear tracking problem we consider gain scheduling based on a family of linear dynamic controllers designed for a family of plant linearizations about constant operating points a necessary and sufficient condition for the existence of gain scheduled controllers satisfying appropriate requirements is presented using this condition the impact of linear controller configuration on the existence of a gain scheduled controller can be assessed and ad hoc approaches to scheduling can be analyzed

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

on quantum groups associated to non noetherian regular algebras of dimension 2 we investigate homological and ring theoretic properties of universal quantum linear groups that coact on artin schelter regular algebras a n of global dimension 2 especially with central homological codeterminant or central quantum determinant as classified by zhang the algebras a n are connected mathbb n graded algebras that are finitely generated by n indeterminants of degree 1 subject to one quadratic relation in the case when the homological codeterminant of the coaction is trivial we show that the quantum group of interest defined independently by manin and by dubois violette and launer is artin schelter regular of global dimension 3 and also skew calabi yau homologically smooth of dimension 3 for central homological codeterminant we verify that the quantum groups are noetherian and have finite gelfand kirillov dimension precisely when the corresponding comodule algebra a n satisfies these properties that is if and only if n 2 we have similar results for arbitrary homological codeterminant if we require that the quantum groups are involutory we also establish conditions when hopf quotients of these quantum groups that also coact on a n are cocommutative

linear quadratic bumpless transfer a method for bumpless transfer using ideas from lq theory is presented and shown to reduce to the hanus conditioning scheme under certain conditions

tilting theory via stable homotopy theory we show that certain tilting results for quivers are formal consequences of stability and as such are part of a formal calculus available in any abstract stable homotopy theory thus these results are for example valid over arbitrary ground rings for quasi coherent modules on schemes in the differential graded context in stable homotopy theory and also in the equivariant motivic or parametrized variant thereof in further work we will continue developing this calculus and obtain additional abstract tilting results here we also deduce an additional characterization of stability based on goodwillie s strongly co cartesian n cubes as applications we construct abstract auslander reiten translations and abstract serre functors for the trivalent source and verify the relative fractionally calabi yau property this is used to offer a new perspective on may s axioms for monoidal triangulated categories