classification of irreducible weight modules over w algebra w 2 2 in this paper we show that the support of an irreducible weight module over the w algebra w 2 2 which has an infinite dimensional weight space coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional as a corollary we obtain that every irreducible weight module over the w algebra w 2 2 having a nontrivial finite dimensional weight space is a harish chandra module and hence is either an irreducible highest or a lowest weight module or an irreducible module of the intermediate series

model structure simplification of nonlinear systems via immersion this paper concerns the simplification of model structures of nonlinear systems while preserving their input output maps the basic technique is an immersion of a system which is a mapping of the initial state from the original system to another system of an identical input output map the necessary and sufficient conditions are presented for the immersibility of a given system into a state space representation of such particular structures as rational functions or polynomials with respect to the state the conditions are so mild that many types of nonlinear systems can be represented by rational or polynomial model structures moreover it is also shown that a polynomial state space representation can always be constructed to be at most quadratic with respect to the state

observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

exact finite dimensional filters via systems realization for a class of discrete time nonlinear systems abstract we obtain necessary and sufficient conditions for the existence of a finite dimensional filter for the discrete time nonlinear system x k 1 x k y k h x k x k k k 0 1 this system is distinguished by the absence of noise in the dynamic and by the correlation between the state and the intensity of noise in the observations the necessary and sufficient condition provides an explicit formula for the minimal filter and various system theoretic properties of and of the minimal filter

observer design using a generalized time scaled block triangular observer form this paper presents an observer design for uncontrolled nonlinear multi output continuous time systems based on a time scaled block triangular observer form tbtof the tbtof generalizes an established block triangular observer form btof by including generalized time scaling functions tsfs which have both state and output dependence introducing these stability preserving tsfs broadens the class of systems which admits a btof based observer design necessary conditions for the tsfs are provided when a tbtof exists an observer can be constructed subsystem at a time sufficient conditions are given to prove estimate error stability a physical example illustrates the tbtof construction and observer design

the drinfeld realization of the elliptic quantum group bq λ a2 2 we construct a realization of the l operator satisfying the rll relation of the face type elliptic quantum group bq a2 2 the construction is based on the elliptic analog of the drinfeld currents of uq a2 2 which forms the elliptic algebra uq p a2 2 we give a realization of the elliptic currents e z f z and k z as a tensor product of the drinfeld currents of uq a2 2 and a heisenberg algebra in the level one representation we also give a free field realization of the elliptic currents applying these results we derive a free field realization of the uq p a2 2 analog of the bq a2 2 intertwining operators the resultant operators coincide with those of the vertex operators in the dilute al model which is known to be a rsos restriction of the a2 2 face model

vertex operators of uq gl n n and highest weight representations of uq gl 2 2 we determine the exchange relations of the level one q vertex operators of the quantum affine superalgebra uq gl n n we study in detail the level one irreducible highest weight representations of uq gl 2 2 and compute the characters and supercharacters associated with these irreducible modules

restricted dynamic observer error linearizability following the general dynamic observer error linearization problem state equivalence to a triangular nonlinear observer canonical form with index d and the restricted dynamic observer error linearization problem are defined in this paper the necessary and sufficient conditions for the above two problems are given since our proofs are constructive a desired state transformation can also be found in the theorem

high gain observers in the state and estimation of robots having elastic joints the paper deals with the state and parameter estimation of robots having elastic joints the estimation of the unknown parameters of the robot is reduced to the estimation of its state variables by a state space immersion the luenberger observer is used in the state estimation of the extended robot model the use of high gains is studied in the cancellation of nonlinearities in order to simplify the observer design the high gain induces a time scale separation between the robot model and the observer and therefore the singular perturbation theory can be used in the stability analysis of the estimate error dynamics in particular it is shown that the error dynamics reaches the stable equilibrium in a very fast transient ensuring that the slow dynamics of the observer is just that of the given robot

commutativity of immersion and linearization a given nonlinear system can be represented via an immersion as rational or polynomial functions thus leading to a simplified model structure an immersion is a mapping of the initial state from the original state space to another state space while exactly preserving the input output map in this note we show that the linearization of the system after immersion has an identical input output map to the linearization of the original system before immersion in other words immersion and linearization commute this is potentially useful for applications such as linear control design and sensitivity analysis after nonlinear identification and has important implications for system approximation by linearization

an algorithm for system immersion into nonlinear observer form siso case the class of nonlinear systems that can be put into nonlinear observer form linear system with output injection can be broadened if we employ the system immersion we provide an immersion algorithm for siso nonlinear systems with relative degree r the proposed algorithm is an extension of the previous results and does not require the relative degree 1 assumption in addition it is seen that the immersion can always be computed via algebraic computations and simple integrations except in a very special case in which the relative degree equals the system dimension in this case only one first order differential equation appears in the algorithm

a level one representation of the quantum affine superalgebra uqmn a level one representation of the quantum affine superalgebra uqmn and vertex operators associated with the fundamental representations are constructed in terms of free bosonic fields character formulas of level one irreducible highest weight modules of uq are conjectured

vertex operators of quantum affine lie algebras u q d n 1 we give an explicit formula for the vertex operators related to the level 1 representations of the quantum affine lie algebrasuq dn 1 in terms of bosons as an application we derive an integral formula for the correlation functions of the vertex models withuq dn 1 symmetry

the elliptic algebra and the drinfeld realization of the elliptic quantum group by using the elliptic analogue of the drinfeld currents in the elliptic algebra we construct a l operator which satisfies the rll relations characterizing the face type elliptic quantum group for this purpose we introduce a set of new currents k j v 1 leq j leq n in as in the n 2 case we find a structure of as a certain tensor product of and a heisenberg algebra in the level one representation we give a free field realization of the currents in using the coalgebra structure of and the above tensor structure we derive a free field realization of the analogue of intertwining operators the resultant operators coincide with those of the vertex operators in the a n 1 1 type face model

vertex operators for twisted quantum affine algebras we construct explicitly the q vertex operators intertwining operators for the level one modules v i of the classical quantum affine algebras of twisted types using interacting bosons where i 0 1 for a 2 n 1 i 0 for d 3 i 0 n for d 2 1 and i n for a 2 n a perfect crystal graph for d 3 4 is constructed as a by product

discrete time observer error linearizability via restricted dynamic systems in this technical note we define the observer error linearization problem of a discrete time autonomous nonlinear system via a restricted dynamic system this is the dual to restricted dynamic feedback linearization in a loose sense necessary and sufficient conditions for this problem are obtained in terms of the index

dynamic observer error linearization in this paper a new framework of observer error linearization problem is proposed the main idea of our approach is twofold the one is to introduce an auxiliary dynamics whose input is the system output and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics it is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output it is also shown that whenever an n dimensional system is immersible into an n d dimensional linear system up to an output injection then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics moreover we show that the converse is not true by providing a counterexample which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method

commutation relations of vertex operators for uq sl m n we consider commutation relations and invertibility relations of vertex operators for the quantum affine superalgebra uq sl m n by using bosonization we show that vertex operators give a representation of the graded zamolodchikov faddeev algebra by direct computation invertibility relations of type ii vertex operators for n m are very similar to those of type i for m n we consider commutation relations and invertibility relations of vertex operators for the quantum affine superalgebra uq sl m n by using bosonization we show that vertex operators give a representation of the graded zamolodchikov faddeev algebra by direct computation invertibility relations of type ii vertex operators for n m are very similar to those of type i for m n

an immersion based observer design for rank observable nonlinear systems in this note an observer design for a wide class of nonlinear systems is proposed it is based on some high gain design for the particular case of state affine systems up to triangular nonlinearity on the one hand and immersion of nonlinear systems into such a form on the other hand conditions for the observer convergence are given in terms of appropriate excitation and a constructive procedure for the immersion is presented the methodology is illustrated by examples of application

left symmetric algebra structures on the w algebra w 2 2 we study the compatible left symmetric algebra structures on the w algebra w 2 2 with some natural grading conditions the results of earlier work on left symmetric algebra structures on the virasoro algebra play an essential role in determining these compatible structures as a corollary any such left symmetric algebra contains an infinite dimensional trivial subalgebra that is also a submodule of the regular module

an efficient method for observer design with approximately linear error dynamics exact error linearization is a well known full order observer design method which yields linear time invariant stable error dynamics in normal form coordinates the difficult procedure associated with exact error linearization has led to the simpler extended luenberger observer design however extended luenberger observers can only guarantee a first order approximation to the exact error linearization design this paper provides an explicit formula involving only derivative lie derivative and bracket and matrix inversion operations for computing an nth order approximation of the exact error linearization observer hence the proposed method is a computational simple tool for designing observers for systems admitting exact error linearization observers two examples demonstrate the application of the method

constructive algorithm for system immersion into non linear observer form there exists a class of non linear systems which cannot be transformed into a non linear observer form an observable linear system up to output injection via diffeomorphism but can be immersed into a higher dimensional non linear observer form this class of systems can be characterized by a differential equation called characteristic equation if the system is an n dimensional system and it is immersible into n m dimensional observer form the characteristic equation involves n m 1 unknowns where n m unknowns are for the state immersion and one for the output transformation in general one should solve these unknowns simultaneously which makes the characterization difficult after investigating the algebraic structure of the characteristic equation we present an algorithm to check the immersibility under a constant rank assumption using the algorithm one can check the immersibility iteratively since only one unknown is involved at each step of the algorithm

harish chandra modules over the twisted heisenberg virasoro algebra in this paper we classify all indecomposable harish chandra modules of the intermediate series over the twisted heisenberg virasoro algebra meanwhile some bosonic modules are also studied

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

on the immersion of a discrete time polynomial analytic system into a polynomial affine one abstract the concept of immersion just recently introduced by fliess and kupka is related to the capability of reproducing the input output maps of a given system by means of another one in this paper we give necessary and sufficient conditions under which a polynomial analytic system i e a system whose dynamics are polynomial with respect to the input and nonlinear analytic with respect to the state is immersed into a polynomial affine system i e a system whose dynamics are polynomial in the input and linear in the state an application to the problem of the reproducibility of a linear analytic state feedback acting on a given system by means of a preprocessor suitably initialized is also performed

new classes of finite dimensional nonlinear filters abstract we derive sufficient conditions for the estimation algebras of two special classes of nonlinear estimation systems to be finite dimensional by carrying out the brockett wei norman program new classes of finite dimensional filters are obtained these systems can be regarded respectively as extensions of the kalman bucy filters and the benes filters

nonlinear observer design by dynamic observer error linearization in this note we address the problem of transforming a nonlinear system into nonlinear observer canonical form in the extended state space with the aid of dynamic system extension and introduction of virtual outputs as an intermediate step for the general problem we consider a restricted structure of dynamic extension which is obtained roughly speaking by adding the chains of integrators to the outputs of original system we propose sufficient conditions which can be verified using the system dynamics expressed in their original coordinates an illustrative example is included that demonstrates the advantage of the proposed method over the conventional method

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

difference equations for the correlation functions of the eight vertex model the authors propose that the correlation functions of the inhomogeneous eight vertex model in the anti ferroelectric regime satisfy a system of difference equations with respect to the spectral parameters solving the simplest difference equation they obtain the expression for the spontaneous staggered polarization conjectured by baxter and kelland 1974 they also discuss a related construction of vertex operators on the lattice

on the structure of verma modules over the w algebra w 2 2 in this paper we describe the structure of verma modules over the w algebra w 2 2 we show that either a verma module over w 2 2 is irreducible or its maximal submodule is cyclic

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

a state observer for nonlinear dynamical systems the problem of state observation for nonlinear systems is of main importance in automatic control in recent years many contributions have been presented in literature that solve the design problem for classes of nonlinear systems most works can be roughly classi ed into two categories in one the geometrical properties of vector elds de ning the system are exploited and therefore mathematical tools of the di erential geometry are extensively employed in the other one the functional properties of the input state and state output maps which de ne the system are mainly used while the geometrical methods often provide a general solution of the problem for systems that belong to restricted classes characterized by geometrical properties 1 2 3 4 5 6 7 13 14 17 18 19 the second approach gives solutions for classes of nonlinear systems whose geometrical nature is not investigated and only macroscopic parameters norms gains lipschitz constants and so on are involved in the design procedure 8 9 11 12 21 one main problem in state observation for nonlinear systems is that the property of driftobservability does not imply observability for any input function as shown in 16 19 thus it is interesting to investigate when the drift observability property allows the solution of the state observation problem nding conditions that restricts the class of input functions due to the mathematical tools employed this work may be considered as belonging to both the categories above mentioned in this paper nonlinear systems of the form

bilinearization up to output injection abstract this paper deals with nonlinear systems that can be steered to bilinear systems by output injection and nonlinear change of coordinates we give an abstract non constructive theorem and an algorithm which allows us to recognize such systems

moduli spaces of curves and representation theory we establish a canonical isomorphism between the second cohomology of the lie algebra of regular differential operators on x of degree 1 and the second singular cohomology of the moduli space hat f g 1 of quintuples c p z l wherec is a smooth genusg riemann surface p a point onc z a local parameter atp l a degreeg 1 line bundle onc and a class of local trivializations ofl atp which differ by a non zero factor the construction uses an interplay between various infinite dimensional manifolds based on the topological spaceh of germs of holomorphic functions in a neighborhood of 0 in x and related topological spaces the basic tool is a canonical map from hat f g 1 to the infinite dimensional grassmannian of subspaces ofh which is the orbit of the subspaceh of holomorphic functions on x vanishing at under the group auth as an application we give a lie algebraic proof of the mumford formula n 6n2 6n 1 1 where n is the determinant line bundle of the vector bundle on the moduli space of curves of genusg whose fiber overc is the space of differentials of degreen onc

observer design based on triangular form generated by injective map a procedure is provided for constructing an injective map as a generalized coordinate change for triangular form transformation based on the triangular form a method is developed for designing nonlinear state observers

brief paper full order observer design for a class of port hamiltonian systems we consider a special class of port hamiltonian systems for which we propose a design methodology for constructing globally exponentially stable full order observers using a passivity based approach the essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state space on which the state estimation error is zero we first introduce the concept of passivity of a system with respect to a manifold by defining a new input and output on the extended state space and then perform a partial state feedback passivation which leads to the construction of the observer we then illustrate this observer design procedure on two physical examples the magnetic levitation system and the inverted pendulum on the cart system

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

immersion of non linear systems into linear systems up to output injection characteristic equation approach there exists a class of non linear systems which cannot be transformed into non linear observer form via diffeomorphism but can be immersed into higher dimensional non linear observer form this paper investigates when n dimensional non linear systems can be immersed into n m dimensional non linear systems in non linear observer form and provides a necessary and sufficient condition we also present an algorithm to check the immersibility in general at the first step of the algorithm one should solve a differential equation with m 1 unknowns rather than solving one with n m unknowns simultaneously when a solution to the differential equation can be obtained the immersibility can be checked by a recursive algorithm moreover when 2m n a straightforward algorithm is provided to check the immersibility

classification of harish chandra modules over some lie algebras related to the virasoro algebra abstract in this paper we provide a uniform method to thoroughly classify all harish chandra modules over some lie algebras related to the virasoro algebras we first classify such modules over the lie algebra w s for s 0 1 2 with this result and method we can also do such works for some lie algebras related to the virasoro algebra including the several kinds of schrodinger virasoro lie algebras which are open up to now

verifiable conditions for multioutput observer error linearizability the verifiable necessary and sufficient conditions for the multioutput observer error linearization problem have not been found over the last three decades in this technical note we give the unverifiable necessary and sufficient conditions which are more specific than the ones in the literature using these conditions a verifiable sufficient condition also necessary with additional restriction on the problem is derived since our proofs are constructive a desired state transformation can also be found in the theorem also our algorithmic conditions can be easily implemented by a matlab programming

adaptive observers for single output nonlinear systems an adaptive version of the nonlinear observer obtained by a j krener et al 1983 is presented this version involves the cancellation of nonlinear terms by output injection as an intermediate step necessary and sufficient conditions are given for transforming a nonlinear system by state space change of coordinates into the special adaptive observer form that was used by y bastin et al 1988 to design adaptive observers

nonlinear system immersion observers and finite dimensional filters abstract nonlinear deterministic and stochastic systems which can be immersed into linear observable ones are identified by necessary and sufficient conditions those systems are shown to admit observers in the deterministic case and exact finite dimensional filters in the stochastic case the sufficient conditions obtained generalize earlier results in both cases

design of state observers from a drift observability property in this paper the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed for such an observer the drift observability property of the system i e observability for zero input together with an assumption on the input amplitude or on the observation relative degree are sufficient conditions for exponential convergence of the observation error the existence of an exponential observer is correlated to the existence of a solution for an h sub spl infin riccati like inequality global and semiglobal convergence results are presented

brief paper linearization through state immersion of nonlinear systems admitting lie symmetries in this paper it is shown that if a nonlinear system admits a lie symmetry that can be transformed into its poincare dulac normal form by a state diffeomorphism then under some technical conditions such a nonlinear system can be immersed into a linear one this allows us to compute in closed form the flow all algebraic invariant curves through semi invariants of the nonlinear system and lyapunov functions to study stability properties

uq sl 2 1 vertex operators screen currents and correlation functions at an arbitrary level bosonized q vertex operators related to the four dimensional evaluation modules of the quantum affine superalgebra uq sl 2 1 are constructed for arbitrary level k where 0 1 is a complex parameter appearing in the four dimensional evaluation representations they are intertwiners among the level highest weight fock wakimoto modules screen currents which commute with the action of uq sl 2 1 up to total differences are presented integral formulas for n point functions of type i and type ii q vertex operators are proposed

classification of simple weight virasoro modules with a finite dimensional weight space we show that the support of a simple weight module over the virasoro algebra which has an infinite dimensional weight space coincides with the weight lattice and that all non trivial weight spaces of such module are infinite dimensional as a corollary we obtain that every simple weight module over the virasoro algebra having a non trivial finite dimensional weight space is a harish chandra module and hence is either a simple highest or lowest weight module or a simple module from the intermediate series this implies positive answers to two conjectures about simple pointed and simple mixed modules over the virasoro algebra

exploiting isochrony in self triggered control event triggered control and self triggered control have been recently proposed as new implementation paradigms that reduce resource usage for control systems in self triggered control the controller is augmented with the computation of the next time instant at which the feedback control law is to be recomputed since these execution instants are obtained as a function of the plant state we effectively close the loop only when it is required to maintain the desired performance thereby greatly reducing the resources required for control in this paper we present a new technique for the computation of the execution instants by exploiting the concept of isochronous manifolds also introduced in this paper while our previous results showed how homogeneity can be used to compute the execution instants along some directions in the state space the concept of isochrony allows us to compute the executions instants along every direction in the state space moreover we also show in this paper how to homogenize smooth control systems thus making our results applicable to any smooth control system the benefits of the proposed approach with respect to existing techniques are analyzed in two examples

weight modules with a finite dimensional weight space over truncated virasoro algebras truncated virasoro algebras can be viewed as quotient algebras of the loop virasoro algebra in this paper we prove that any weight module m with a finite dimensional weight space over any truncated virasoro algebra l f vir c t 1 fc t 1 has a harish chandra submodule where vir is the virasoro algebra and f is a nonzero and not invertible laurent polynomial in c t 1 more precisely if m has a nontrivial upper bounded vir submodule then it has a highest weight l f submodule if m has a nontrivial lower bounded vir submodule then it has a lowest weight l f submodule if m is nontrivial over l f and does not contain any nontrivial upper bounded nor any nontrivial lower bounded vir submodules then it has a nontrivial harish chandra l f submodule s such that dims 1 for all supp s 0 as a corollary any irreducible weight module with a finite dimensional weight space over l f is a harish chandra module

level one representations and vertex operators of quantum affine superalgebra uq gl n n level one representations of the quantum affine superalgebra uq gl n n associated with the appropriate nonstandard system of simple roots and q vertex operators intertwining operators associated with the level one modules are constructed explicitly in terms of free bosonic fields