canonical property of the miura maps between the mkp and kp hierarchies continuous and discrete apart from the case of the kp hierarchy all known miura maps between integrable hamiltonian systems had been proven to be canonical the remaining kp case is settled below as a corollary it is shown that the kp hierarchy is a factor hierarchy of the mkp one with the kernel consisting of a single scalar field a discrete mkp hierarchy and the associated miura map are constructed and the latter is shown to be canonical as well as in the continuous case this implies that one can extend the discrete kp hierarchy by a single new field into an extended discrete kp hierarchy in such a way that the extended discrete miura map mkp ekp is a canonical isomorphism

approximation based control of nonlinear mimo time delay systems approximation based control is presented for a class of multi input multi output mimo nonlinear systems in block triangular form with unknown state delays neural networks nns are utilized to approximate and compensate for unknown functions in the system dynamics including the unknown bounds of the functions of delayed states the use of a separation technique removes the need for any assumption on the function of delayed states and allows the handling of multiple delays in each function of delayed states by combining the use of lyapunov krasovskii functionals and adaptive nn backstepping the proposed control guarantees that all closed loop signals remain bounded while the outputs converge to a neighborhood of the desired trajectories simulation results demonstrate the effectiveness of the proposed scheme

generalized drinfel d sokolov hierarchies a general approach is adopted to the construction of integrable hierarchies of partial differential equations a series of hierarchies associated to untwisted kac moody algebras and conjugacy classes of the weyl group of the underlying finite lie algebra is obtained the generalized kdv hierarchies of v g drinfel d and v v sokolov are obtained as the special case for the coxeter element various examples of the general formalism are treated in some detail including the fractional kdv hierarchies

constrained kp hierarchy and bi hamiltonian structures the kakomtsev petviashvili kp hierarchy is considered together with the evolutions of eigenfunctions and adjoint eigenfunctions constraining the kp flows in terms of squared eigenfunctions one obtains 1 1 dimensional integrable equations with scattering problems given by pseudo differential lax operators the bi hamiltonian nature of these systems is shown by a systematic construction of two general poisson brackets on the algebra of associated lax operators gauge transformations provide miura links to modified equations these systems are constrained flows of the modified kp hierarchy for which again a general description of their bi hamiltonian nature is given the gauge transformations are shown to be poisson maps relating the bi hamiltonian structures of the constrained kp hierarchy and the modified kp hierarchy the simplest realization of this scheme yields the akns hierarchy and its miura link to the kaup broer hierarchy

n 2 kp and kdv hierarchies in extended superspace we give the formulation in extended superspace of an n 2 supersymmetric kp hierarchy using chirality preserving pseudo differential operators we obtain two quadratic hamiltonian structures which lead to different reductions of the kp hierarchy in particular we find two different hierarchies with the n 2 classical super algebra as a hamiltonian structure the relation with the formulation in n 1 superspace and the bosonic limit are carried out

nonlinear evolution equations and the euler flow abstract a new theorem on abstract nonlinear equations of evolution is proved as an application the existence uniqueness regularity and continuous dependence on the data are proved for the solution of the euler equation for incompressible fluids in a bounded domain in r m

classical r matrix theory for bi hamiltonian field systems this is a survey of the application of the classical r matrix formalism to the construction of infinite dimensional integrable hamiltonian field systems the main point is the study of bi hamiltonian structures appropriate constructions on poisson noncommutative and loop algebras as well as the central extension procedure are presented the theory is developed for 1 1 and 2 1 dimensional field and lattice soliton systems as well as hydrodynamic systems the formalism presented contains sufficiently many proofs and important details to make it self contained and complete the general theory is applied to several infinite dimensional lie algebras in order to construct both dispersionless and dispersive soliton integrable field systems

design of decentralised adaptive sliding mode controllers for large scale systems with mismatched perturbations based on the lyapunov stability theorem a methodology for designing a decentralised adaptive sliding mode control scheme is proposed in this paper this scheme is implemented for a class of large scale systems with both matched and mismatched perturbations the perturbations and the interconnection terms are assumed to be norm bounded under certain mild conditions the decentralised sliding surfaces with adaptive mechanisms embedded are specially designed for each subsystem so that when each subsystem enters the sliding mode the mismatched perturbations and the effects of interconnections can be effectively overcome and achieve asymptotic stability the decentralised controller with embedded adaptive mechanisms is capable of driving the controlled state trajectories into the designated sliding surface in finite time this is also achieved without the knowledge of upper bounds of the perturbations except those of the uncertainties in the input channels a numerical example is included to demonstrate the feasibility of the proposed control scheme

regular conjugacy classes in the weyl group and integrable hierarchies generalized kdv hierarchies associated by drinfeld sokolov reduction with grade 1 regular semisimple elements from non equivalent heisenberg subalgebras of a loop algebra g x c lambda lambda 1 are studied the graded heisenberg subalgebras containing such elements are labelled by the regular conjugacy classes in the weyl group w g of the simple lie algebra g a representative w epsilon w g of a regular conjugacy class can be lifted to an inner automorphism of g given by w exp 2i pi ad i0 m where i0 is the defining vector of an sl2 subalgebra of g the grading is then defined by the operator d m i0 m lambda d d lambda ad i0 and any grade 1 regular element lambda from the heisenberg subalgebra associated with w takes the form lambda c lambda c where i0 c m 1 c and c is included in an sl2 subalgebra containing i0 the largest eigenvalue of adi0 is m 1 except for some cases in f4 e6 7 8 we explain how these lie algebraic results follow from known results and apply them to construct integrable systems if the largest ad i0 eigenvalue is m 1 then using any grade 1 regular element from the heisenberg subalgebra associated with w we can construct a kdv system possessing the standard w algebra defined by i0 as its second poisson bracket algebra for g a classical lie algebra we derive pseudo differential lax operators for those non principal kdv systems that can be obtained as discrete reductions of kdv systems related to gln non abelian toda systems are also considered

abstract cauchy problem for weakly continuous operators abstract we discuss the solvability of the abstract cauchy problem u t a u t for t 0 and u 0 u 0 d where d is a weakly closed subset of a banach space y continuously embedded in the underlying banach space x and a is a nonlinear operator from d into x satisfying a local weak continuity condition described by a family of functionals we introduce a new type of weak compactness on the level sets of functionals and give a necessary and sufficient condition for the existence of a weakly continuously differentiable solution satisfying a growth condition we apply the abstract result obtained to the cauchy problem for a nonlinear schrodinger equation and a mixed problem for a logarithmic wave equation

extensions of the matrix gelfand dickey hierarchy from generalized drinfeld sokolov reduction thep p matrix version of ther kdv hierarchy has been recently treated as the reduced system arising in a drinfeld sokolov type hamiltonian symmetry reduction applied to a poisson submanifold in the dual of the lie algebra widehat gl pr 1 here a series of extensions of this matrix gelfand dickey system is derived by means of a generalized drinfeld sokolov reduction defined for the lie algebra widehat gl pr s 1 using the natural embeddinggl pr glpr s fors any positive integer the hierarchies obtained admit a description in terms of ap p matrix pseudo differential operator comprising anr kdv type positive part and a non trivial negative part this system has been investigated previously in thep 1 case as a constrained kp system in this paper the previous results are considerably extended and a systematic study is presented on the basis of the drinfeld sokolov approach that has the advantage that it leads to local poisson brackets and makes clear the conformal w algebra structures related to the kdv type hierarchies

adaptive statistic tracking control based on two step neural networks with time delays this paper presents a new type of control framework for dynamical stochastic systems called statistic tracking control stc the system considered is general and non gaussian and the tracking objective is the statistical information of a given target probability density function pdf rather than a deterministic signal the control aims at making the statistical information of the output pdfs to follow those of a target pdf for such a control framework a variable structure adaptive tracking control strategy is first established using two step neural network models following the b spline neural network approximation to the integrated performance function the concerned problem is transferred into the tracking of given weights the dynamic neural network dnn is employed to identify the unknown nonlinear dynamics between the control input and the weights related to the integrated function to achieve the required control objective an adaptive controller based on the proposed dnn is developed so as to track a reference trajectory stability analysis for both the identification and tracking errors is developed via the use of lyapunov stability criterion simulations are given to demonstrate the efficiency of the proposed approach

nonstandard drinfeld sokolov reduction subject to some conditions the input data for the drinfeld sokolov construction of kdv type hierarchies is a quadruplet where the are gradations of a loop algebra and is a semisimple element of the nonzero grade a new sufficient condition on the quadruplet under which the construction works is proposed and examples are presented the proposal relies on splitting the grade zero part of into a vector space direct sum of two subalgebras this permits one to interpret certain gelfand dickey type systems associated with a nonstandard splitting of the algebra of pseudodifferential operators in the drinfeld sokolov framework

a decentralized model reference adaptive variable structure controller for large scale time varying delay systems in this note the problem of decentralized model reference adaptive variable structure control for a class of perturbed large scale systems with varying time delay interconnections is investigated based on the lyapunov stability theorem an adaptive variable structure control strategy for solving the robust tracking problem without the knowledge of upper bound of perturbations is developed the use of adaptive technique is to adapt the unknown upper bound of perturbations so that the objective of globally asymptotical stability is achieved once the system enters the sliding manifold the dynamics of controlled systems are insensitive to matching perturbations finally an example is given to demonstrate the feasibility of the proposed control scheme

decentralized adaptive output feedback control for a class of nonlinear large scale systems with unknown time varying delayed interactions in this paper the authors investigate a decentralized adaptive output feedback controller design for large scale nonlinear systems with input saturations and time delayed interconnections unmatched in control inputs the interaction terms with unknown time varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems this point is a main contribution of this paper compared with previous output feedback control approaches which assume that the time delayed bounding functions only depend on measurable output variables the bounding functions are compensated by using appropriate lyapunov krasovskii functionals and the function approximation technique based on neural networks the observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem in addition we prove that all signals in the closed loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin finally an example is provided to illustrate the effectiveness of the proposed control system

generalized drinfel d sokolov hierarchies ii the hamiltonian structures in this paper we examine the bi hamiltonian structure of the generalized kdv hierarchies we verify that both hamiltonian structures take the form of kirillov brackets on the kac moody algebra and that they define a coordinated system classical extended conformal algebras are obtained from the second poisson bracket in particular we construct the w n l algebras first discussed for the case n 3 and l 2 by polyakov and bershadsky

a quantum group structure in integrable conformal field theories we discuss a quantization prescription of the conformal algebras of a class ofd 2 conformal field theories which are integrable we first give a geometrical construction of certain extensions of the classical virasoro algebra known as classicalw algebras in which these algebras arise as the lie algebra of the second hamiltonian structure of a generalized korteweg de vries hierarchy this fact implies that thew algebras obtained as a reduction with respect to the nilpotent subalgebras of the kac moody algebra describe the integrability of a toda field theory subsequently we determine the coadjoint operators of thew algebras and relate these to classical yang baxter matrices the quantization of these algebras can be carried out using the concept of a so called quantum group we derive the condition under which the representations of these quantum groups admit a hilbert space completion by exploring the relation with the braid group then we consider a modification of the miura transformation which we use to define a quantumw algebra this leads to an alternative interpretation of the coset construction for kac moody algebras in terms of nonlinear integrable hierarchies subsequently we use the connection between the induced braid group representations and the representations of the mapping class group of riemann surfaces to identify an action of thew algebras on the moduli space of stable curves and we give the invariants of this action this provides a generalization of the situation for the virasoro algebra where such as invariant is given by the so called mumford form which describes the partition function of the bosonic string

decentralized adaptive tracking control of nonaffine nonlinear large scale systems with time delays this paper addresses the problem of decentralized tracking control of large scale systems with uncertain nonaffine nonlinear isolated subsystems and nonlinear interconnections with time varying delays based on lyapunov krasovskii functional approach and implicit function theorem a delay independent decentralized tracking controller is proposed due to functional approximation capability of fuzzy logic systems fls neither strict structure restrictions on the isolated subsystems nor a priori knowledge of the strong interconnections with time varying delays is required in our control design furthermore transient performance of the resulting closed loop system is also addressed under an analytical framework finally two numerical examples are provided to show the effectiveness of the proposed controller

a unifying design of sliding mode and classical controllers a theory is given to unify output sliding mode control and classical control the idea is based on defining the sliding variable in such a way that once the system begins to slide the classical controller transfer function is realized this idea leads to the development of a hybrid sliding and classical controller which retains the merits of both types of controllers but eliminates their respective limitations the proposed method is robust and applies to non minimum phase single input single output siso systems no state measurement is required

memoryless state feedback controller design for time delay systems with matched uncertain nonlinearities the robust control problem for a class of uncertain time delay systems is investigated the systems include multiple time delays and uncertain nonlinear functions to our best knowledge no controller design method for the systems is reported in the literature except for sliding mode control smc however the sliding mode controller must use the delayed state of the system so that the precise time delays have to be known and also a large memory is needed for controller implementation to overcome the shortcomings we employ the backstepping method to design a memoryless state feedback controller by constructing a novel lyapunov krasovskii functional we show that the resulting closed loop system is asymptotically stable simulations are done to verify the effectiveness of the proposed method

traveling wave solutions u v to a generalized drinfel d sokolov system which satisfy u a1vm a0 abstract an analysis of the coupled generalized drinfel d sokolov equations u t 1 uu x 1 u xxx v x 0 and v t 2 uv x 2 v xxx 0 is performed in the case of traveling wave solutions u and v satisfying the condition u a 1 v m a 0 we are able to classify all such solutions in terms of the model parameters and we then discuss the planar dynamics of such solutions numerical solutions are obtained and discussed for a variety of parameter regimes such results are one possible generalization of those given by wu et al l wu s chen c pang traveling wave solutions for generalized drinfeld sokolov equations applied mathematical modeling 33 2009 4126 4130

large chiral diffeomorphisms on riemann surfaces and w algebras the diffeomorphism action lifted on truncated chiral taylor expansion of a complex scalar field over a riemann surface is presented in the paper under the name of large diffeomorphisms after an heuristic approach we show how a linear truncation in the taylor expansion can generate an algebra of symmetry characterized by some structure functions such a linear truncation is explicitly realized by introducing the notion of forsyth frame over the riemann surface with the help of a conformally covariant algebraic differential equation the large chiral diffeomorphism action is then implemented through a becchi rouet stora brs formulation for a given order of truncation leading to a more algebraic setup in this context the ghost fields behave as holomorphically covariant jets subsequently the link with the so called w algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones we give a general solution with the help of the structure functions pertaining to al

tracking with asymptotic sliding mode and adaptive input delay effect compensation of nonlinearly perturbed delayed systems applied to traffic feedback control abstractasymptotical sliding mode model reference adaptive control design for a class of systems with parametric uncertainty unknown nonlinear perturbation and external disturbance and with known input and state delays is proposed to overcome the difficulty to directly predict the plant state under uncertainties a control design is based on a developed decomposition procedure where a generalised error in conjunction with auxiliary linear dynamic blocks with adjustable gains is introduced and the sliding variable is formed on the basis of this error the effect of such a decomposition is to pull the input delay out of first step of the design procedure as a result similarly to the classical smith predictor the adaptive control architecture based only on the lumped delays i e without conventional in such cases difficult implemented distributed delay blocks two new adaptive control schemes are proposed a linearisation based control design is constructed for feedback control of an urban traffic

an application of semigroups of locally lipschitz operators to carrier equations with acoustic boundary conditions abstract a generation theorem of semigroups of locally lipschitz operators on a subset of a real banach space is given and applied to the problem of the well posedness of the carrier equation u t t u 2 u u t p 1 u t 0 in 0 with acoustic boundary condition where p 2 and is a bounded domain in an arbitrary dimensional space

mathematics of dispersive water waves a commuting hierarchy of dispersive water wave equations makes a three hamiltonian system which belongs to a general class of nonstandard integrable systems whose theory is developed the modified water wave hierarchy is a bi hamiltonian system its modification bifurcates the water wave hierarchy and the hierarchies of the korteweg de vries and the modified korteweg de vries equations as well as the classical miura map are given new representations through various specializations of nonstandard systems

simple method for model reference adaptive control abstract a simple method is presented for combined signal synthesis and parameter adaptation within the framework of model reference adaptive control theory the results are obtained using a simple derivation based on an improved lyapunov function

classical a n w geometry by analyzing theextrinsic geometry of two dimensional surfaces chirally embedded incp n thecp n w surface 1 we give exact treatments in various aspects of the classical w geometry in the conformal gauge first the basis of tangent and normal vectors are defined at regular points of the surface such that their infinitesimal displacements are given by connections which coincide with the vector potentials of the conformal a n toda lax pair since the latter is known to be intrinsically related with the w symmetries this gives the geometrical meaning of thea n w algebra second w surfaces are put in one to one correspondence with solutions of the conformally reduced wznw model which is such that the toda fields give the cartan part in the gauss decomposition of its solutions third the additional variables of the toda hierarchy are used as coordinates ofcp n this allows us to show that w transformations may be extended as particular diffeomorphisms of this target space higher dimensional generalizations of the wznw equations are derived and related with the zakharov shabat equations of the toda hierarchy fourth singular points are studied from a global viewpoint using our earlier observation 1 that w surfaces may be regarded as instantons the global indices of the w geometry which are written in terms of the toda fields are shown to be the instanton numbers for associated mappings of w surfaces into the grassmannians the relation with the singularities of w surface is derived by combining the toda equations with the gauss bonnet theorem

analytical solutions to a generalized drinfel d sokolov equation related to dssh and kdv6 abstract analytical solutions to the generalized drinfel d sokolov gds equations u t 1 uu x 1 u xxx v x 0 and v t 2 uv x 2 v xxx 0 are obtained for various values of the model parameters in particular we provide perturbation solutions to illustrate the strong influence of the parameters 1 and 2 on the behavior of the solutions we then consider a miura type transform which reduces the gds equations into a sixth order nonlinear differential equation under the assumption that 1 under such a transform the gds reduces to the sixth order drinfel d sokolov satsuma hirota dssh equation also known as kdv6 in the very special case 1 2 the method of homotopy analysis is applied in order to obtain analytical solutions to the resulting equation for arbitrary 1 and 2 an error analysis of the obtained approximate analytical solutions is provided

non local matrix generalizations of w algebras there is a standard way to define two symplectic hamiltonian structures the first and second gelfand dikii brackets on the space of ordinarymth order linear differential opeatorsl d m u1dm 1 u2dm 2 u m in this paper i consider in detail the case where theu k aren n matrix valued functions with particular emphasis on the more interesting second gelfand dikii bracket of particular interest is the reduction to the symplectic submanifoldu1 0 this reduction gives rise to matrix generalizations of the classical version of thenon linear w m algebras calledv n m algebras the non commutativity of the matrices leads tonon local terms in thesev n m algebra s i show that these algebras contain a conformal virasoro subalgebra and that combinationsw k of theu k can be formed that aren n matrices of conformally primary fields of spink in analogy with the scalar casen 1 in general however thev m n algebras have a much richer structure than thew m algebras as can be seen on the examples of thenon linear andnon local poisson brackets u2 ab u2 cd u2 ab w3 cd and w3 ab w3 cd which i work out explicitly for allm andn a matrix miura transformations is derived mapping these complicated second gelfand dikii brackets of theu k to a set of much simpler poisson brackets providing the analogoue of the free field representation of thew m algebras

on the completeness of the set of classical w algebras obtained from ds reductions we clarify the notion of the ds generalized drinfeld sokolov reduction approach to classical cal w algebras we first strengthen an earlier theorem which showed that an sl 2 embedding cal s subset cal g can be associated to every ds reduction we then use the fact that a cal w algebra must have a quasi primary basis to derive severe restrictions on the possible reductions corresponding to a given sl 2 embedding in the known ds reductions found to date for which the cal w algebras are denoted by cal w s g algebras and are called canonical the quasi primary basis corresponds to the highest weights of the sl 2 here we find some examples of noncanonical ds reductions leading to cal w algebras which are direct products of cal w s g algebras and lq lq free field algebras with conformal weights delta in 0 1 over 2 1 we also show that if the conformal weights of the generators of a cal w algebra obtained from ds reduction are nonnegative delta geq 0 which is the case for all ds reductions known to date then the delta geq 3 over 2 subsectors of the weights are necessarily the same as in the corresponding cal w s g algebra these results are consistent with an earlier result by bowcock and watts on the spectra of cal w algebras derived by different means we are led to the conjecture that up to free fields the set of cal w algebras with nonnegative spectra delta geq 0 that may be obtained from ds reduction is exhausted by the canonical ones

nonlinear poisson structures and r matrices we introduce quadratic poisson structures on lie groups associated with a class of solutions of the modified yang baxter equation and apply them to the hamiltonian description of lax systems the formal analog of these brackets on associative algebras provides second structures for certain integrable equations in particular the integrals of the toda flow on generic orbits are shown to satisfy recursion relations finally we exhibit a third order poisson bracket for which ther matrix approach is feasible

trigonometric and hyperbolic type solutions to a generalized drinfel d sokolov equation abstract a class of trigonometric and hyperbolic type solutions to the generalized drinfel d sokolov gds equations u t 1 uu x 1 u xxx v x 0 and v t 2 uv x 2 v xxx 0 is obtained for the case in which 2 0 for various values of the other model parameters the method of homotopy analysis is then applied to obtain local analytical solutions for nonzero values of the parameter 2 in effect extending the exact solutions we do not assume traveling wave solution forms for the analytical solutions that is we solve the generalized drinfel d sokolov equations as pdes without resorting to transforming the system to odes an error analysis of the obtained approximate local analytical solutions is provided then we outline a general framework by which one many construct solutions in either sine cosine or sinh cosh basis we provide the general perturbation expansion via homotopy analysis and we also discuss a method of selecting the convergence control parameter so as to minimize residual errors travelling solutions with time dependent amplitude are then discussed

sliding mode control in the presence of input delay a singular perturbation approach sliding mode control smc in the presence of small unavoidable input delay as may be present in controller implementation is studied linear systems with bounded matched disturbances and uncertain system matrices are considered where input delay in the smc will produce oscillations or potentially even unbounded solutions without a priori knowledge of the bounds on the state dependent terms as required by existing methods the design objective is to achieve ultimate boundedness of the closed loop system with a bound proportional to the delay and disturbance bounds this is a non trivial problem because the relay gain depends on the state bound whereas the latter bound depends on the relay gain a controller with linear gain proportional to the scalar email protected is proposed which for small enough m 0 produces a closed loop singularly perturbed system and yields the desired ultimate bound a constructive linear matrix inequality lmi based solution for evaluation of both the design parameters and the ultimate bound is derived the superiority of the proposed control over existing methodologies that ignore input delay within the design is demonstrated through an example

stabilization of uncertain dynamic systems including state delay the authors consider a class of time varying systems with time varying state delay and uncertain input and parameters they present sufficient conditions on the open loop to obtain an arbitrary degree closed loop stability they construct a min max controller from knowledge of the upper bound of the delay

classical w algebras we reconsider the relation between classicalw algebras and deformations of differential operators emphasizing the consistency with diffeomorphisms generators of thew algebra that arek differentials are constructed by a systematic procedure the method extends following drinfeld and sokolov tow algebras based on arbitrary simple lie algebras

constraints of the kadomtsev petviashvili hierarchy for the kadomtsev petviashvili kp hierarchy constructed in terms of the famous sato theory a k constraint is proposed that leads the hierarchy to the nonlinear system involving a finite number of dynamical coordinates the eigenvalue problem of the k constrained system is naturally obtained from the linear system of the kp hierarchy which takes the form of kth order polynomial coupled with a first order one thus we are able to derive the correspondent lax pair recursion operator bi hamiltonian structures and conserved quantities the constraints for the bkp hierarchy are also sketched

the constrained modified kp hierarchy and the generalized miura transformations in this letter we consider the second hamiltonian structure of the constrained modified kp hierarchy after mapping the lax operator to a pure differential operator the second structure becomes the sum of the second and the third gelfand dickey brackets defined by this differential operator we simplify this hamiltonian structure by factorizing the lax operator into linear terms

design of decentralised sliding surfaces for a class of large scale systems with mismatched perturbations a novel design methodology of a decentralised sliding surface is proposed in this article for a class of large scale systems with mismatched perturbations and interconnections the main idea of this method is that the sliding surface function is obtained through a specially designed state transformation matrix this transformation matrix which includes the sliding surface coefficient function contains adaptive mechanisms with the capability of adapting some unknown constants embedded in the least upper bounds of mismatched perturbations as well as interconnections so that the perturbations mismatched and matched can be effectively overcome and asymptotical stability is guaranteed for each subsystem in the sliding mode in addition each decentralised controller also contains adaptive mechanisms to assure that the sliding mode is generated in a finite time without requiring the knowledge of upper bounds of the perturbations and interconnections a practical example is also demonstrated by simulation f

classical extended conformal algebras associated with constrained kp hierarchy the conformal property of the second hamiltonian structure of constrained kp hierarchy derived by oevel and strampp is examined it is found that it naturally gives a family of nonlocal extended conformal algebras two examples of such algebras are given and it is found that they are similar to bilal s v algebra by taking a gauge transformation one can map the constrained kp hierarchy to kupershmidt s nonstandard lax hierarchy the second hamiltonian structure in this representation is considered it is shown that after mapping the lax operator to a pure differential operator the second structure becomes the sum of the second and the third gelfand dickey brackets defined by this differential operator the corresponding conformally covariant form of this differential operator is also given

classical n 2 w superalgebras from superpseudodifferential operators we study the supersymmetric gelfand dickey algebras associated with the superpseudodifferential operators of positive as well as negative leading order we show that upon the usual constraint these algebras contain the n 2 super virasoro algebra as a subalgebra when the leading order is odd the decompositions of the coefficient functions into n 1 primary fields are then obtained by covariantizing the superpseudodifferential operators we discuss the problem of identifying n 2 supermultiplets and work out a couple of supermultiplets by explicit computations

stability criteria for linear time invariant systems with point delays based on one dimensional routh hurwitz tests this brief deals with the asymptotic stability of a class of linear time invariant systems subject to point constant uncommensurate delays results are obtained dependent on and independent of the delays which may be tested be performing a finite set of 1 d routh hurwitz tests on a corresponding set of auxiliary delay free linear time invariant systems plus some supplementary conditions related to either commutation pairwise of the associate dynamics matrices or their norm closeness or some simple testable conditions if the matrices have particular forms and there is only one single delay the obtained results are applicable to the case when a finite set of matrices describing the dynamics of a set of delay free auxiliary dynamical systems are hurwitz and either commute pair wise or their norms are sufficiently close to each other some extensions are given to robust stability of point time delay time invariant systems with commensurate delays parametrized by an uncertain parameter vector whose components are in real intervals of known limits

a variable structure control with simple adaptation laws for upper bounds on the norm of the uncertainties in deterministic design of feedback controllers for uncertain dynamical systems upper bounds on the norm of the uncertainties are an important clue to guarantee the stability of the closed loop system sometimes however these upper bounds may not be easily obtained because of the complexity of structure of the uncertainties simple adaptation laws for upper bounds on the norm of the uncertainties are proposed and these adaptive upper bounds are used to design a variable structure control system that guarantees the asymptotic stability of uncertain dynamical systems

canonical miura maps between the modified kp and kp hierarchies we investigate the hamiltonian nature of two miura maps between the modified kp and kp hierarchies we show that they are canonical in the sense that the bi hamiltonian structure of the modified kp hierarchy is mapped to the bi hamiltonian structure of the kp hierarchy

w algebras for generalized toda theories the generalized toda theories obtained in a previous paper by the conformal reduction of wznw theories possess a new class of w algebras namely the algebras of gauge invariant polynomials of the reduced theories an algorithm for the construction of base elements for the w algebras of all such generalized toda theories is found and the w algebras for the maximal sl n r generalized toda theories are constructed explicitly the primary field basis being identified 1992 springer verlag