on vanishing stability regions in nonlinear systems with high gain feedback when local stabilization of nonlinear systems is achieved by linear feedback the resulting stability region may vanish as the feedback gains increase this is demonstrated by examples in which neglected nonlinearities create an unstable limit cycle around an asymptotically stable equilibrium as the feedback gains tend to infinity the unstable limit cycle shrinks to the equilibrium if a feedback linearization design is applied the same instability mechanism may occur when the nonlinearities are not precisely known

on the inequivalence of generalized preparata codes if m is odd and sigma in aut gf 2 m is such that x rightarrow x sigma 2 1 is 1 1 there is a 2 m 1 1 2 m l 2m 2 nonlinear binary code p sigma having minimum distance 5 all the codes p sigma have the same distance and weight enumerators as the usual preparata codes which rise as p sigma when x sigma x 2 it is shown that p sigma and p tau are equivalent if and only if tau sigma pm 1 and aut p sigma is determined

bifurcation and exact traveling wave solutions for dual power zakharov kuznetsov burgers equation with fractional temporal evolution abstract in this article we introduce the dual power zakharov kuznetsov burgers equation with fractional temporal evolution in the sense of modified riemann liouville derivative we investigate the dynamical behavior bifurcations and phase portrait analysis of the exact traveling wave solutions of the system with and without damping effect we apply the g g expansion method in context of fractional complex transformation and seek a variety of exact traveling wave solutions including solitary wave kink type wave breaking wave and periodic wave solutions of the equation furthermore the remarkable features of the traveling wave solutions and phase portraits of dynamical system are demonstrated through interesting figures

high gain feedback in non linear control systems abstract high gain state and output feedback are investigated for non linear control systems with a single additive input by using singular perturbation techniques classical approximation results tihonov like theorems in singular perturbation theory are extended to non linear control systems by defining a composite additive control strategy a control dependent fast equilibrium manifold and non linear change of coordinates those tools and an appropriate change of coordinates show that high gain state feedback and variable structure control systems can be equivalently used for approximate non linearity compensation in feedback linearizable systems next the effect of high gain output feedback is shown to be related to the strong invertibility property and the relative order of invertibility for strongly invertible systems the slow reduced subsystem coincides with the dynamics of the inverse system when zero input is applied and with the unobservable dynamics when a certain input output feedback linear

slow peaking and low gain designs for global stabilization of nonlinear systems this paper presents an analysis of the slow peaking phenomenon a pitfall of low gain designs that imposes basic limitations to large regions of attraction in nonlinear control systems the phenomenon is best understood on a chain of integrators perturbed by a vector field up x u that satisfies p x 0 0 peaking may cause a loss of global controllability unless severe growth restrictions are imposed on p x u these growth restrictions are expressed as a higher order condition with respect to a particular weighted dilation related to the peaking exponents of the nominal system when this higher order condition is satisfied an explicit control law is derived that achieves global asymptotic stability of x 0 this stabilization result is extended to more general cascade nonlinear systems in which the perturbation p x spl upsi spl upsi spl upsi spl xi u sup t contains the state spl xi and the control u of a stabilizable subsystem spl xi spl dot a spl xi u as an illustration a control law is derived that achieves global stabilization of the frictionless ball and beam model

duality for modules over finite rings and applications to coding theory this paper sets a foundation for the study of linear codes over finite rings the finite frobenius rings are singled out as the most appropriate for coding theoretic purposes because two classical theorems of mac williams the extension theorem and the mac williams identities generalize from finite fields to finite frobenius rings it is over frobenius rings that certain key identifications can be made between the ring and its complex characters

variational approach and exact solutions for a generalized coupled zakharov kuznetsov system abstract in the present paper we obtain a variational principle for a generalized coupled zakharov kuznetsov system which does not admit any lagrangian formulation in its present form the eminent noether s theorem will then be employed to compensate for this approach in addition exact solutions will be constructed for the generalized coupled zakharov kuznetsov system using the kudryashov method and the jacobi elliptic function method

cocyclic hadamard matrices from forms over finite frobenius rings abstract we give a construction of cocyclic butson hadamard matrices from bilinear forms over finite frobenius rings which generalizes previous constructions we then prove a classification result showing that the resulting matrices depend only on the additive group of the underlying module of the form

lie point symmetries of the lane emden systems abstract it is shown that a lie point symmetry of the lane emden system is a noether symmetry if and only if its parameters belong to the critical hyperbola

correspondence comments on robust stabilization of mimo nonlinear time varying mismatched uncertain systems the main false conclusion wang soh chai automatica 33 1997 2197 was pointed out by a simple counterexample

generators and relations for the unitary group of a skew hermitian form over a local ring abstract let s be an involutive local ring and let u 2 m s be the unitary group associated to a nondegenerate skew hermitian form defined on a free s module of rank 2m a presentation of u 2 m s is given in terms of bruhat generators and their relations this presentation is used to construct an explicit weil representation of the symplectic group s p 2 m r when s r is commutative and is the identity when s is commutative but is arbitrary with fixed ring r an elementary proof that the special unitary group s u 2 m s is generated by unitary transvections is given this is used to prove that the reduction homomorphisms s u 2 m s s u 2 m s and u 2 m s u 2 m s are surjective for any factor ring s of s the corresponding results for the symplectic group s p 2 m r are obtained as corollaries when is the identity

on the algebraic identification of the frequencies amplitudes and phases of two sinusoidal signals from their noisy sum an algebraic identification approach is used for the fast and reliable on line determination of the defining parameters of two sinusoidal signals of different unknown amplitudes phases and frequencies from their noise perturbed measured sum the proposed method is based on the algebraic derivative approach defined in the frequency domain yielding exact calculation formulae for the unknown parameters when interpreted in a noise free time domain environment the proposed computation formulae are synthesized in terms of time varying linear unstable filters in combination with classical low pass filters the proposed algorithms are insensitive to initial conditions require no special design parameter tuning and the fast convergence is of non asymptotic nature the on line computations are performed in a time interval which is only a fraction of the first full cycle of one of the integrating components of the measured signal several simulations are shown to verify the algorithm proposed finally expe

on stabilization of nonlinear systems with enlarged domain of attraction this paper presents a systematic procedure to design a control law that guarantees asymptotic stability of an equilibrium with an enlarged domain of attraction for a class of nonlinear systems to this end we use a natural extension of well known linear time invariant transformation methods to write the system in controller canonical form with a forcing term the control law is implemented in two steps first we calculate a nonlinear state feedback that cancels the nonlinear terms of the unforced system so that for the resulting system a suitable lyapunov function candidate is available then we add a linear state feedback that stabilizes the equilibrium and maximizes its domain of attraction interestingly enough the latter maximization problem reduces to a classical linear time invariant h minimization problem an example is given to illustrate the procedure

complete joint weight enumerators and self dual codes we define the complete joint weight enumerator in genus g for codes over spl zopf sub 2k and use it to study self dual codes and their shadows these weight enumerators are related to the theta series of the associated lattices and siegel and jacobi forms are formed from these series

a basic exact sequence for the lee and euclidean weights of linear codes over zl abstract recently many papers have been published dealing with codes over finite rings in this paper we introduce some singleton type bounds of lee and euclidean weights for codes over the ring z l and give a proof of the macwilliams identities for the lee and euclidean weight enumerators

a survey of adaptive fuzzy controllers nonlinearities and classifications adaptive fuzzy controllers afcs i e fuzzy controllers using heuristic expert knowledge and equipped with adaption ability are widely used in the industry in the present days as they are capable of dealing with ill formulated nonlinear systems where exact mathematical formulas are not known or partially described nonlinear systems afcs have been widely deployed to control many nonlinear systems with different types of critical nonlinearities over the last two decades many different approaches toward adaptive fuzzy control have been reported in this paper we recapitulate the latest research works related to afcs and provide an up to date survey on the latest development made in adaptive fuzzy control theory and applications based on different types of fuzzy systems considered and nonlinearities associated with the nonlinear system to be controlled we categorize the different approaches based on different types of nonlinearities and consider basic nonlinear systems nonlinear systems with external disturbances nonlinear systems with some special type of nonlinearities nonaffine nonlinear systems and strict feedback nonlinear systems it turns out that many existing methods are subject to various limitations and none of them is capable of controlling a general nonlinear systems hence it is still an open problem to design and develop a universal afc for a general class of nonlinear systems

bounds on the minimum homogeneous distance of the p r ary image of linear block codes over the galois ring hbox gr p r m in this correspondence bounds are derived on the minimum homogeneous distance of the image of a linear block code over the galois ring gr pr m with respect to any basis of gr pr m these bounds depend on the parameters of gr pr m the minimum hamming distance of the block code and the average value of the homogeneous weight applied on the base ring zopf p r examples are given of galois ring codes that meet these bounds

a note on self dual group codes we classify group algebras over galois rings containing self dual ideals i e ideals c which satisfy c c sup spl perp with respect to the natural nondegenerate bilinear form given on group algebras

soft decoding techniques for codes and lattices including the golay code and the leech lattice two kinds of algorithms are considered 1 if is a binary code of length n a soft decision decoding algorithm for changes an arbitrary point of r n into a nearest codeword nearest in euclidean distance 2 similarly a decoding algorithm for a lattice lambda in r n changes an arbitrary point of r n into a closest lattice point some general methods are given for constructing such algorithms ami are used to obtain new and faster decoding algorithms for the gosset lattice e 8 the golay code the leech lattice

a fast on line frequency estimator of lightly damped vibrations in flexible structures a significant research effort has been conducted in the past to achieve a reliable on line vibration mode estimator frequently pure sinusoidal models of the underlying mechanical system have been used to accomplish the estimation task in this paper an algebraic approach is proposed for the fast and reliable on line identification of the natural frequency of a flexible link manipulator the proposed method uses the pure sinusoidal model in combination with the algebraic derivative method for parameter identification the method leads in the time domain to an exact computation formulae for the unknown frequency parameter this formula is synthesized in terms of time varying linear unstable filters in combination with classical low pass filters of the butterworth type the computations are performed in a quite small time interval which is only a small fraction of the first full cycle of the measured sinusoidal signal the proposed method is verified to be robust with respect to un modeled small attenuations present in the flexible structure and to measurement noise an experimental setup has been developed as a benchmark to test and compare the proposed method with other recently developed parameter estimation techniques

frequency domain analysis and tuning of the algebraic differentiators abstractthe algebraic differentiators introduced by mboup join and fliessare studied in the frequency domain the study complements the time domain developments of the previous reference where a least squares interpretation has allowed to explain the main properties of the method and also to devise efficient differentiators the frequency domain analysis gives answers to the central question of the choice of the algebraic differentiator parameters also an interpretation of the algebraic differentiators in terms of wavelet decomposition is given

stabilization in probability of nonlinear stochastic systems with guaranteed region of attraction and target set we deal with nonlinear dynamical systems consisting of a linear nominal part perturbed by model uncertainties nonlinearities and both additive and multiplicative random noise modeled as a wiener process in particular we study the problem of finding suitable measurement feedback control laws such that the resulting closed loop system is stable in some probabilistic sense to this aim we introduce a new notion of stabilization in probability which is the natural counterpart of the classical concept of regional stabilization for deterministic nonlinear dynamical systems and stands as an intermediate notion between local and global stabilization in probability this notion requires that given a target set a trajectory starting from some compact region of the state space containing the target remains forever inside some larger compact set eventually enters any given neighborhood of the target in finite time and remains thereinafter all these events being guaranteed with some probability we give a lyapunov based sufficient condition for achieving stability in probability and a separation result which splits the control design into a state feedback problem and a filtering problem finally we point out constructive procedures for solving the state feedback and filtering problem with arbitrarily large region of attraction and arbitrarily small target for a wide class of nonlinear systems which at least include feedback linearizable systems the generality of the result is promising for applications to other classes of stochastic nonlinear systems in the deterministic case our results recover classical stabilization results for nonlinear systems

symmetry analysis of the bidimensional lane emden systems abstract we carry out a complete group classification of the nonlinear lane emden systems in dimension two the noether symmetries are found and their corresponding conservation laws are established

almost disturbance decoupling for single input single output nonlinear systems the almost disturbance decoupling problem for nonlinear single input single output systems is addressed by using singular perturbation methods and high gain feedback sufficient conditions and the explicit high gain nonlinear state feedback in solvable cases are given they generalize both previous almost results for linear systems and exact ones for nonlinear systems the necessity of the conditions is discussed in particular an example is given where the main structural condition is not satisfied and the high gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system

a unifying framework for the semiglobal stabilization of nonlinear uncertain systems via measurement feedback we study the problem of semiglobally stabilizing an uncertain nonlinear system consisting of a linear nominal system perturbed by either nonlinearities or model uncertainties our approach relies on well known h sub spl infin linear control tools and allows one to recover and improve in the unifying framework of a semiglobal separation result existing results on the semiglobal stabilization via output feedback in particular we discuss the case of uncorrupted outputs input and output nonlinearities or model uncertainties which may include for example practical situations such as backlash hysteresis and saturations the key feature of our design procedure is given by the choice of two continuous functions the first one is instrumental in constructing a stabilizing controller the second one arises in the candidate lyapunov function for the closed loop system relying on our main theorem we give general tools for achieving large regions of attraction via bounded measurement feedback for a wide class of nonlinear uncertain interconnected systems

trajectory tracking for the magnetic ball levitation system via exact feedforward linearisation and gpi control the output feedback control of the popular magnetic ball levitation system is addressed from a suitable combination of several complementary viewpoints we use first recent developments on exact feedforward linearisation controllers for nonlinear flat systems to substantially reduce the linear feedback controller efforts through pre compensation second an on line ball velocity estimation strategy is proposed by using a model based integral reconstructor which is a linear combination of iterated integrals of the input and the output of the system thus avoiding the use of traditional observers or noisy derivative estimations finally we use a generalised proportional integral gpi controller which compensates the errors in the integral reconstructor and further bestows the enhanced robustness on the closed loop system via output tracking error iterated integration feedback this methodology only requires the measurements of the position of the levitated ball and of the control input voltage the pro

binary sequences with gold like correlation but larger linear span a new construction of optimal binary sequences identical to the well known family of gold sequences in terms of maximum nontrivial correlation magnitude and family size but having larger linear span is presented the distribution of correlation values is determined for every odd integer spl tau spl ges 3 the construction provides a family that contains 2 sup spl tau 1 cyclically distinct sequences each of period 2 sup spl tau 1 the maximum nontrivial correlation magnitude equals 2 spl tau 1 sup 2 1 with one exception each of the sequences in the family has linear span at least spl tau sup 2 spl tau 2 compared to 2 spl tau for gold sequences the sequences are easily implemented using a quaternary shift register followed by a simple feedforward nonlinearity

p adic valuation of weights in abelian codes over spl zopf p sup d counting polynomial techniques introduced by wilson are used to provide analogs of a theorem of mceliece mceliece s original theorem relates the greatest power of p dividing the hamming weights of words in cyclic codes over gf p to the length of the smallest unity product sequence of nonzeroes of the code calderbank li and poonen presented analogs for cyclic codes over zopf 2d using various weight functions hamming lee and euclidean weight as well as count of occurrences of a particular symbol some of these results were strengthened by wilson who also considered the alphabet zopf pd for p an arbitrary prime these previous results new strengthened versions and generalizations are proved here in a unified and comprehensive fashion for the larger class of abelian codes over zopf pd with p any prime for abelian codes over zopf 4 combinatorial methods for use with counting polynomials are developed these show that the analogs of mceliece s theorem obtained by wilson for hamming weight lee weight and symbol counts and the analog obtained here for euclidean weight are sharp in the sense that they give the maximum power of 2 that divides the weights of all the codewords whose fourier transforms have a specified support

achieving nonvanishing stability regions with high gain cheap control using h techniques the second order case abstract this paper demonstrates how to use an asymptotically h optimal controller to stabilize a second order system subject to unknown disturbances such that the stability region does not vanish as the feedback gains increase the high gain feedback arises when one attempts to achieve the lowest achievable limit of the disturbance attenuation under the h design this type of gain increase can cause the stability region to vanish if the disturbance contains nonlinear terms the analysis using lyapunov techniques derives a sufficient condition on the design parameters to prevent the stability region from vanishing in addition to describing exact solutions for six different cases the paper provides simulations to illustrate the results

type iv self dual codes over rings we study type iv self dual codes over the commutative rings of order 4 gleason type theorems of type iv codes and their shadow codes are investigated a mass formula of type iv codes over these rings are given we give a classification of type tv codes over z sub 4 and f2 uf sub 2 for reasonable lengths we also construct a number of optimal type tv codes

macwilliams type identities on the lee and euclidean weights for linear codes over zl abstract motivated by the works of shiromoto 3 and shi et al 4 we study the existence of the macwilliams type identities with respect to the lee and euclidean weight enumerators for linear codes over the ring z l necessary and sufficient conditions for the existence of the macwilliams type identities with respect to the lee and euclidean weight enumerators for linear codes over z l are given some examples about such macwilliams type identities are also presented

the z sub 4 linearity of kerdock preparata goethals and related codes certain notorious nonlinear binary codes contain more codewords than any known linear code these include the codes constructed by nordstrom robinson 1967 kerdock 1972 preparata 1968 goethals 1974 and delsarte goethals 1975 it is shown here that all these codes can be very simply constructed as binary images under the gray map of linear codes over z sub 4 the integers mod 4 although this requires a slight modification of the preparata and goethals codes the construction implies that all these binary codes are distance invariant duality in the z sub 4 domain implies that the binary images have dual weight distributions the kerdock and preparata codes are duals over z sub 4 and the nordstrom robinson code is self dual which explains why their weight distributions are dual to each other the kerdock and preparata codes are z sub 4 analogues of first order reed muller and extended hamming codes respectively all these codes are extended cyclic codes over z sub 4 which greatly simplifies encoding and decoding an algebraic hard decision decoding algorithm is given for the preparata code and a hadamard transform soft decision decoding algorithm for the i kerdock code binary first and second order reed muller codes are also linear over z sub 4 but extended hamming codes of length n spl ges 32 and the golay code are not using z sub 4 linearity a new family of distance regular graphs are constructed on the cosets of the preparata code

generalized solitary and periodic wave solutions to a 2 1 dimensional zakharov kuznetsov equation abstract in this paper the exp function method is employed to the zakharov kuznetsov equation as a 2 1 dimensional model for nonlinear rossby waves the observation of solitary wave solutions and periodic wave solutions constructed from the exponential function solutions reveal that our approach is very effective and convenient the obtained results may be useful for better understanding the properties of two dimensional coherent structures such as atmospheric blocking events

on dualizing trellis based app decoding algorithms the trellis of a finite abelian group code is locally i e trellis section by trellis section related to the trellis of the corresponding dual group code which allows one to express the basic operations of the a posteriori probability app decoding algorithm defined on a single trellis section of the primal trellis in terms of the corresponding dual trellis section using this local approach any algorithm employing the same type of operations as the app algorithm can thus be dualized even if the global dual code does not exist e g nongroup codes represented by a group trellis given this the complexity advantage of the dual approach for high rate codes can be generalized to a broader class of app decoding algorithms including suboptimum algorithms approximating the true app which may be more attractive in practical applications due to their reduced complexity moreover the local approach opens the way for mixed approaches where the operations of the app algorithm are not exclusively performed on the primal or dual trellis this is inevitable if the code does not possess a trellis consisting solely of group trellis sections as e g for certain terminated group or ring codes the complexity reduction offered by applying dualization is evaluated as examples we give a dual implementation of a suboptimum app decoding algorithm for tailbiting convolutional codes as well as dual implementations of app algorithms of the sliding window type moreover we evaluate their performance for decoding usual tailbiting codes or convolutional codes respectively as well as their performance as component decoders in iteratively decoded parallel concatenated schemes

4 phase sequences with near optimum correlation properties two families of four phase sequences are constructed using irreducible polynomials over z sub 4 family a has period l 2 sup r 1 size l 2 and maximum nontrivial correlation magnitude c sub max

cubic self dual binary codes we study binary self dual codes with a fixed point free automorphism of order three all binary codes of that type can be obtained by a cubic construction that generalizes turyn s we regard such cubic codes of length 3 spl lscr as codes of length spl lscr over the ring f sub 2 spl times f sub 4 classical notions of type ii codes shadow codes and weight enumerators are adapted to that ring two infinite families of cubic codes are introduced new extremal binary codes in lengths spl les 66 are constructed by a randomized algorithm necessary conditions for the existence of a cubic 72 36 16 type ii code are derived

continuous time linear predictive control and flatness a module theoretic setting with examples a general flatness based framework for linear continuous time predictive control is presented the mathematical setting which is valid for multivariable systems is provided by the algebraic theory of modules where a controllable system corresponds to a finitely generated free module over a principal ideal ring any basis of this free module is a flat output which yields an easy calculation of the predicted trajectory this formalism permits one to handle non minimum phase systems system constraints and to deal with additive perturbations three concrete case studies namely a dc motor a flexible system and a cement mill are analysed and simulations are given these examples are written in such a way that any reader who is not familiar with module theory may nevertheless grasp the proposed control strategy

representations of mclain groups abstract basic modules of mclain groups m m r are defined and investigated these are possibly infinite dimensional analogues of andre s supercharacters of u n q the ring r needs not be finite or commutative and the field underlying our representations is essentially arbitrary we deal with all characteristics prime or zero on an equal basis the set totally ordered by is allowed to be infinite we show that distinct basic modules are disjoint determine the dimension of the endomorphism algebra of a basic module find when a basic module is irreducible and exhibit a full decomposition of a basic module as direct sum of irreducible submodules including their multiplicities several examples of this decomposition are presented and a criterion for a basic module to be multiplicity free is given in general not every irreducible module of a mclain group is a constituent of a basic module

orbit and coset analysis of the golay and related codes let b be a code of length n over a field f with automorphism group g b sub w denotes the subset of codewords of weight w the goal is to classify the vectors of f sup n into orbits under g and to determine their distances from the various subcodes b sub w this is done for the first order reed muller nordstrom robinson and hamming codes of length 16 the golay and shortened golay codes of lengths 22 23 24 and the ternary golay code of length 12

uniform semiglobal practical asymptotic stability for non autonomous cascaded systems and applications it is due to the modularity they provide that results for cascaded systems have proved their utility in numerous control applications as well as in the development of general control techniques based on adding integrators nevertheless the standing assumptions in most of the present literature on cascaded systems is that when decoupled the subsystems constituting the cascade are uniformly globally asymptotically stable ugas hence existing results fail in the more general case when the subsystems are uniformly semiglobally practically asymptotically stable uspas this situation is often encountered in control practice e g in control of physical systems with external perturbations measurement noise unmodelled dynamics etc after giving a rigorous framework for the analysis of such stability properties this paper generalizes previous results for cascades by establishing that under a uniform boundedness condition on its solutions the cascade of two uspas systems remains uspas an analogous result is derived for uniformly semiglobally asymptotically stable usas systems in cascade furthermore we show the utility of our results in the pid control of mechanical systems affected by unknown non dissipative forces and considering the dynamics of the dc motors

linear feedback stabilization of nonlinear systems with an uncontrollable critical mode abstract linear feedback stabilization of nonlinear systems is studied for systems whose linearization at an equilibrium point possesses a simple critical mode that is uncontrollable the results complement previous work on the synthesis of nonlinear stabilizing control laws the present work addresses continuous time systems for which the linearization has either a simple zero eigenvalue or a pair of simple pure imaginary eigenvalues both the stability analysis and stabilizing control design employ results on stability of bifurcations of parameterized systems

a note on a basic exact sequence for the lee and euclidean weights of linear codes over zl abstract this paper is devoted to presenting two counterexamples to shiromoto s 1999 results 2 on macwilliams type identities with respect to lee weight enumerators and euclidean weight enumerators over z l

on the assignability of infinite root loci in almost disturbance decoupling in this paper we investigate in detail the almost disturbance decoupling problem with state feedback an alternative proof of the sufficiency part of the original result by willoms 1981 on this problem requiring the construction of a sequence of feedback matrices is given it is shown that one can achieve almost disturbance decoupling by letting some of the closed loop eigenvalues run to infinity according to a spatial arrangement determined by the infinite zero structure the proofs of our results use the fact that almost controllability subspaces can be approximated by controlled invariant subspaces our results on the closed loop eigenstructure are stated in terms of such approximating sequences we also prove a generalization of a theorem by wonham 1979 used in the context of minimal order observer design

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

linearization and input output decoupling for general nonlinear systems necessary and sufficient conditions are obtained for the linearization and input decoupling by state feedback of general nonlinear systems it is shown how these conditions can be derived from the already known conditions for affine nonlinear systems thereby also elucidating the existing theory for affine systems

global steady state controllability of one dimensional semilinear heat equations we investigate the problem of exact boundary controllability of semilinear one dimensional heat equations we prove that it is possible to move from any steady state to any other by means of a boundary control provided that both are in the same connected component of the set of steady states the proof is based on an effective feedback stabilization procedure which is implemented

non standard analysis and representation of reality the aim of this paper is to show that the representation with the help of non standard analysis of a real phenomenon presenting different observation scales allows an important simplification of language indeed it is convenient to have available the concept of infinitely small and infinitely large quantities in dealing with the macroscopic effects of microscopic phenomena this is illustrated on two examples the representation of two time scales systems and the representation of noise

invariant analysis and conservation laws of 2 1 dimensional time fractional zk bbm equation in gravity water waves abstract this paper intends to make an in depth study on the symmetry properties and conservation laws of the 2 1 dimensional time fractional zakharov kuznetsov benjamin bona mahony zk bbm equation with riemann liouville fractional derivative symmetry properties have been investigated here via lie symmetry analysis method in view of erdelyi kober fractional differential operator the reduction of 2 1 dimensional time fractional zk bbm equation has been done into fractional ordinary differential equation to analyse the conservation laws new theorem of conservation law has been proposed here for constructing the new conserved vectors for 2 1 dimensional time fractional zk bbm equation with the help of formal lagrangian

model free control model free control and the corresponding intelligent pid controllers ipids which already had many successful concrete applications are presented here for the first time in an unified manner where the new advances are taken into account the basics of model free control is now employing some old functional analysis and some elementary differential algebra the estimation techniques become quite straightforward via a recent online parameter identification approach the importance of ipis and especially of ips is deduced from the presence of friction the strange industrial ubiquity of classic pid s and the great difficulty for tuning them in complex situations is deduced via an elementary sampling from their connections with ipids several numerical simulations are presented which include some infinite dimensional systems they demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them

controller synthesis free of analytical models three term controllers the main focus of this paper is on direct data driven synthesis and design of controllers we show that the complete set of stabilizing proportional integral derivative pid and first order controllers for a finite dimensional linear time invariant plant possibly cascaded with a delay can be calculated directly from the frequency response nyquist bode data p jomega for omega epsi 0 infin without the need of producing an identified analytical model it is also shown that complete sets achieving guaranteed levels of performance measures such as gain margin phase margin and hinfin norms can likewise be calculated directly from only nyquist bode data the solutions have important new features for example it is not necessary to know the order of the plant or even the number of left half plane or right half plane poles or zeros the solution also identifies in the case of pid controllers an exact low frequency band over which the plant data must be known with accuracy and beyond which the plant information may be rough or approximate these constitute important new guidelines for identification when the latter is to be used for control design the model free approach to control synthesis and design developed here is an attractive complement to modern and post modern model based design methods which require complete information on the plant and generally produce a single optimal controller a discussion is included with illustrative example of the sharp differences between model free and model based approaches when computing sets of stabilizing controllers for example it is shown that the identified model of a high order system can be non pid stabilizable whereas the original data indicates it is pid stabilizable the results given here are also a significant improvement over classical control loop shaping approaches since we obtain complete sets of controllers achieving the design specifications it can enhance fuzzy and neural approaches which are model free but cannot guarantee stability and performance finally these results open the door to adaptive model free fixed order designs of real world systems

on the macwilliams identity for convolutional codes the adjacency matrix associated with a convolutional code collects in a detailed manner information about the weight distribution of the code a macwilliams identity conjecture stating that the adjacency matrix of a code fully determines the adjacency matrix of the dual code will be formulated and an explicit formula for the transformation will be stated the formula involves the macwilliams matrix known from complete weight enumerators of block codes the conjecture will be proven for the class of convolutional codes where either the code itself or its dual does not have forney indices bigger than one for the general case the conjecture is backed up by many examples and a weaker version will be established

on the linear equivalents of nonlinear systems this paper studies feedback equivalence of nonlinear systems an equivalence relation is established for the systems x f x u a complete characterization of the class of nonlinear systems which are equivalent to controllable linear systems is obtained

new code equivalence based on relative generalized hamming weights code equivalence is a basic concept in coding theory the well known theorem by macwilliams gives a sufficient condition for code equivalence recently the macwilliams theorem has been generalized by fan liu and puig making use of the generalized hamming weights ghws in this paper we will present a further generalization of the macwilliams theorem our result extends both the macwilliams theorem and the result by fan liu and puig we will first define relative subcodes of a linear code based on the relative generalized hamming weights rghws which is a generalization of the ghws and then establish a method based on finite projective geometry to characterize relative subcodes using this method we will prove our main result

averaging on slow and fast cycles of a three time scale system abstract pontryagin rodygin s theorem for slow and fast systems describes the slow drift during the rolling up of the trajectories around the cycles of the fast dynamics this drift is approximated by the averaging on the cycles the calculation of this average is generally a difficult task since it requires the knowledge of the closed orbits and their periods we present two paradigms of three time scale systems where we can overcome this limitation it is the case of systems the fast dynamics of which have cycles with relaxation presenting or not a canard phenomenon we can not apply pontryagin rodygin s theorem to these systems because their fast equation is itself singularly perturbed we also investigate the extension of the results to unbounded time intervals the results are stated classically and proved within the framework of nonstandard analysis

an optimal stochastic multivariable pid controller a direct output tracking approach abstractthis paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise we consider multi input multi output linear time invariant systems and a proportional integral derivative pid controller the system under consideration needs not be stable a recursive algorithm providing optimal time varying pid gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs the development of the proposed algorithm aims for per time sample minimisation of the mean square output error in the presence of erroneous initial conditions measurement noise and process noise necessary and sufficient conditions are provided for the convergence of the output error covariance in addition convergence results are presented for discretised continuous time plants simulation results are included to illustrate the performance capabilities of the proposed algorithm performan

second order weight distributions a fundamental property of codes the second order weight distribution is proposed to solve the problems such as computing second moments of weight distributions of linear code ensembles a series of results parallel to those for weight distributions is established for second order weight distributions in particular an analogue of macwilliams identities is proved the second order weight distributions of regular ldpc code ensembles are then computed as easy consequences the second moments of weight distributions of regular ldpc code ensembles are obtained furthermore the application of second order weight distributions in random coding approach is discussed the second order weight distributions of the ensembles generated by a so called 2 good random generator or parity check matrix are computed where a 2 good random matrix is a kind of generalization of the uniformly distributed random matrix over a finite filed and is very useful for solving problems that involve pairwise or triple wise properties of sequences it is shown that the 2 good property is reflected in the second order weight distribution which thus plays a fundamental role in some well known problems in coding theory and combinatorics an example of linear intersecting codes is finally provided to illustrate this fact

covering radius survey and recent results all known results on covering radius are presented as well as some new results there are a number of upper and lower bounds including asymptotic results a few exact determinations of covering radius some extensive relations with other aspects of coding theory through the reed muller codes and new results on the least covering radius of any linear n k code there is also a recent result on the complexity of computing the covering radius

latroids and their representation by codes over modules it has been known for some time that there is a connection between linear codes over fields and matroids represented over fields in fact a generator matrix for a linear code over a field is also a representation of a matroid over that field there are intimately related operations of deletion contraction minors and duality on both the code and the matroid the weight enumerator of the code is an evaluation of the tutte polynomial of the matroid and a standard identity relating the tutte polynomials of dual matroids gives rise to a macwilliams identity relating the weight enumerators of dual codes more recently codes over rings and modules have been considered and macwilliams type identities have been found in certain cases in this paper we consider codes over rings and modules with code duality based on a morita duality of categories of modules to these we associate latroids defined here we generalize notions of deletion contraction minors and duality on both codes and latroids and examine all natural relations among these we define generating functions associated with codes and latroids and prove identities relating them generalizing above mentioned generating functions and identities

semi global robust output regulation of minimum phase nonlinear systems based on high gain nonlinear internal model we consider the assumption of existence of the general nonlinear internal model that is introduced in the design of robust output regulators for a class of minimum phase nonlinear systems with rth degree r 2 the robust output regulation problem can be converted into a robust stabilisation problem of an augmented system consisting of the given plant and a high gain nonlinear internal model perfectly reproducing the bounded including not only periodic but also nonperiodic exogenous signal from a nonlinear system which satisfies some general immersion assumption the state feedback controller is designed to guarantee the asymptotic convergence of system errors to zero manifold furthermore the proposed scheme makes use of output feedback dynamic controller that only processes information from the regulated output error by using high gain observer to robustly estimate the derivatives of the regulated output error the stabilisation analysis of the resulting closed loop systems leads to regional as wel

a linear construction for certain kerdock and preparata codes the nordstrom robinson kerdock and slightly modified preparata codes are shown to be linear over z4 the integers mod 4 the kerdock and preparata codes are duals over z4 and the nordstrom robinson code is self dual all these codes are just extended cyclic codes over z4 this provides a simple definition for these codes and explains why their hamming weight distributions are dual to each other firstand second order reed muller codes are also linear codes over z4 but hamming codes in general are not nor is the golay code

the structure of linear codes of constant weight in this paper we determine completely the structure of linear codes over z nz of constant weight namely we determine exactly which modules underlie linear codes of constant weight and we describe the coordinate functionals involved the weight functions considered are hamming weight lee weight two forms of euclidean weight and pre homogeneous weights we prove a general uniqueness theorem for virtual linear codes of constant weight existence is settled on a case by case basis

characterization of stability region for general autonomous nonlinear dynamical systems the existing characterization of stability regions was developed under the assumption that limit sets on the stability boundary are exclusively composed of hyperbolic equilibrium points and closed orbits the characterizations derived in this technical note are a generalization of existing results in the theory of stability regions a characterization of the stability boundary of general autonomous nonlinear dynamical systems is developed under the assumption that limit sets on the stability boundary are composed of a countable number of disjoint and indecomposable components which can be equilibrium points closed orbits quasi periodic solutions and even chaotic invariant sets

an exponential number of generalized kerdock codes if n 1 is an odd composite integer then there are at least 2 1 2 n pairwise inequivalent binary error correcting codes of length 2 n size 2 2 n and minimum distance 2 n 1 2 1 2 n 1

fast ml decoding algorithm for the nordstrom robinson code corresp the extended nordstrom robinson code is an optimum nonlinear double error correcting code of length 16 with considerable practical importance this code is also useful as a rate 1 2 vector quantizer for random waveforms such as speech linear predictive coding lpc residual a fast decoding algorithm is described for maximum likelihood decoding or nearest neighbor search in the squared error sense with 304 additions and 128 comparisons

maximum distance codes over rings of order 4 in this correspondence we study bounds on the euclidean hamming lee and bachoc weights of codes over rings of order 4 similar to the singleton bound and investigate the relationship between these bounds moreover we give some characterizations of the codes meeting these bounds

guaranteed roll off in a class of high gain feedback design problems a number of synthesis problems associated with almost disturbance decoupling by state or measurement feedback is considered starting from a mathematical definition of the notion of high frequency roll off known results on the solvability of these problems are generalized to the situation in which we require their solvability together with a certain guaranteed roll off between disturbance and control the conditions are formulated in terms of the solvability and approximate solvability of certain matrix equations in rational functions

mixed mode oscillations with multiple time scales mixed mode oscillations mmos are trajectories of a dynamical system in which there is an alternation between oscillations of distinct large and small amplitudes mmos have been observed and studied for over thirty years in chemical physical and biological systems few attempts have been made thus far to classify different patterns of mmos in contrast to the classification of the related phenomena of bursting oscillations this paper gives a survey of different types of mmos concentrating its analysis on mmos whose small amplitude oscillations are produced by a local multiple time scale mechanism recent work gives substantially improved insight into the mathematical properties of these mechanisms in this survey we unify diverse observations about mmos and establish a systematic framework for studying their properties numerical methods for computing different types of invariant manifolds and their intersections are an important aspect of the analysis described in this paper

on generalized reed solomon codes over commutative and noncommutative rings in this paper we study generalized reed solomon codes grs codes over commutative and noncommutative rings we show that the classical welch berlekamp and guruswami sudan decoding algorithms still hold in this context and we investigate their complexities under some hypothesis the study of noncommutative grs codes over finite rings leads to the fact that grs codes over commutative rings have better parameters than their noncommutative counterparts also grs codes over finite fields have better parameters than their commutative rings counterparts but we also show that given a unique decoding algorithm for a grs code over a finite field there exists a unique decoding algorithm for a grs code over a truncated power series ring with a better asymptotic complexity moreover we generalize a lifting decoding scheme to obtain new unique and list decoding algorithms designed to work when the base ring is for example a galois ring or a truncated power series ring or the ring of square matrices over the latter ring

robust output feedback control of nonlinear stochastic systems using neural networks we present an adaptive output feedback controller for a class of uncertain stochastic nonlinear systems the plant dynamics is represented as a nominal linear system plus nonlinearities in turn these nonlinearities are decomposed into a part obtained as the best approximation given by neural networks plus a remaining part which is treated as uncertainties modeling approximation errors and neglected dynamics the weights of the neural network are tuned adaptively by a lyapunov design the proposed controller is obtained through robust optimal design and combines together parameter projection control saturation and high gain observers high performances are obtained in terms of large errors tolerance as shown through simulations

proportional integral controllers for minimum phase nonaffine in control systems we show that stabilizing tracking proportional integral pi controllers can be constructed for minimum phase nonaffine in control systems the constructed pi controller is an equivalent realization of an approximate dynamic inversion controller this equivalence holds only for the time response when applied to the unperturbed system even when restricted to unperturbed minimum phase linear time invariant systems their closed loop robustness properties differ this shows that in general properties that do not define the equivalence relation for systems controllers are not preserved under such equivalence transformations

further results on the semilinear equivalence of linear codes based on relative subcodes we address an equivalent condition for a one to one semilinear mapping between two linear codes to be in fact a semimonomial transformation that is the underlying two codes are semilinearly equivalent the result in the present paper substantially improves the equivalent condition in recent literatures moreover it also generalizes the well known macwilliams theorem of code equivalence

model free control of nonlinear stochastic systems with discrete time measurements consider the problem of developing a controller for general nonlinear and stochastic systems where the equations governing the system are unknown using discrete time measurement this paper presents an approach for estimating a controller without building or assuming a model for the system such an approach has potential advantages in accommodating complex systems with possibly time varying dynamics the controller is constructed through use of a function approximator such as a neural network or polynomial this paper considers the use of the simultaneous perturbation stochastic approximation algorithm which requires only system measurements a convergence result for stochastic approximation algorithms with time varying objective functions and feedback is established it is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite difference gradient approximations