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

the matching of a prescribed linear input output behavior in a nonlinear system in this paper we deal with the problem of finding a feedback under which the input output behavior of a nonlinear system becomes exactly the same as that of a specified linear model the solvability of this problem is shown to depend on a formal infinite zero structure associated with the system

exact linearizations of input output systems the problem of transforming non linear systems to linear systems is receiving much attention in the literature in this paper we present necessary and sufficient conditions such that a non linear control system with output can be equivalent to a linear control system with linear output that is controllable and observable the conditions depend on certain lie derivatives of the output and can be verified in a finite number of steps for simplicity we consider only the single input single output case

on manipulator control by exact linearization comments on the application to rigid link manipulators of geometric control theory resolved acceleration control operational space control and nonlinear decoupling theory are given and the essential unity of these techniques for externally linearizing and decoupling end effector dynamics is discussed exploiting the fact that the mass matrix of a rigid link manipulator is positive definite and the fact that there is an independent input for each degree of freedom it is shown that a necessary and sufficient condition for a locally externally linearizing and output decoupling feedback law to exist is that the end effector jacobian matrix be nonsingular

web spline based mesh free finite element analysis for the approximation of the stationary navier stokes problem he objective in this paper is to discuss the existence and the uniqueness of a weighted extended b spline web spline based discrete solution for the stationary incompressible navier stokes equations the web spline discretization is newly developed methodology which satisfies the inf sup condition or ladyshenskaya babus ka brezzi lbb condition the main advantage of these new elements over standard finite elements is that they use regular grids instead of irregular partitions of the domain thus eliminating the difficult and time consuming pre processing step an error estimate for this web spline based discrete solution is also obtained

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

strictness totality and non standard type inference in this paper we present two non standard type inference systems for conjunctive strictness and totality analyses of higher order typed functional programs and prove completeness results for both the strictness and the totality type entailment relations we also study the interactions between strictness and totality analyses showing that the information obtainable by a system that combines the two analyses even though more refined than the information given by the two separate systems cannot be effectively used a main feature of our approach is that all the results are proved by relying directly on the operational semantics of the programming language considered this leads to a rather direct presentation which involves relatively little mathematical overhead copyright 2002 elsevier science b v

trajectory tracking problem causal solutions for non linear time delay systems the trajectory tracking problem is considered for a general class of non linear time delay systems the existence of causal static state feedback solutions is investigated within an algebraic approach two classes of causal static compensators are considered that either involve delayed dynamics or not sufficient conditions are derived which are weaker than the ones existing in the current literature these results are innovative for both linear and non linear time delay systems the most advanced results do not imply a maximal loss of observability in opposition to more standard solutions

global stabilization of a class of invertible mimo nonlinear systems in this paper we consider the class of input affine mimo nonlinear systems which are assumed to be invertible and input output linearizable this class includes as a trivial special case the class of mimo systems possessing a well defined vector relative degree it is shown that if a system in this class is strongly minimum phase in a sense specified in the paper it is globally stabilizable via partial state feedback or semiglobally stabilizable via dynamic output feedback the result substantially broadens the class of nonlinear mimo systems for which global semiglobal stabilization via limited state information is known to be possible

input output feedback linearization of time delay systems in this note the input output linearization problem iolp for a class of single input single output nonlinear systems with multiple delays in the input the output and the state is studied the problem is solved by means of various static or dynamic compensators including state and output feedback the mathematical setting is based on some noncommutative algebraic tools and the introduction of a nonlinear version of the so called roesser models for this class of systems these are claimed to be the cornerstones for studying nonlinear time delay systems necessary and sufficient conditions are given for the existence of a static or pure shift output feedback which solves the iolp sufficient conditions for the existence of a dynamic state feedback solution are included as well

an input output characterization for linearization by feedback for a stationary initially relaxed single input single output bilinear realizable system that is described by a sequence of regular transfer functions the relative degrees of the individual transfer functions are defined in a manner similar to the linear case these relative degrees are used to characterize the region where linear input output behavior can be obtained by state feedback in a bilinear realization of the system

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

weighted extended b spline approximation of dirichlet problems we describe a new finite element method which uses weighted extended b splines on a regular grid as basis functions for solving dirichlet problems on bounded domains in arbitrary dimensions this web method does not require any grid generation and can be implemented very efficiently it yields smooth high order accurate approximations with relatively low dimensional subspaces

filter models for conjunctive disjunctive l calculi abstract the distinction between the conjunctive nature of non determinism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work calculus is extended with both a non deterministic choice and a parallel operator a notion of reduction is introduced extending reduction of the classical calculus we study type assignment systems for this calculus together with a denotational semantics which is initially defined constructing a set semimodel via simple types we enrich the type system with intersection and union types dually reflecting the disjunctive and conjunctive behaviour of the operators and we build a filter model the theory of this model is compared both with a morris style operational semantics and with a semantics based on a notion of capabilities

linearization of discrete time systems abstract we characterize the equivalence of single input single output discrete time nonlinear systems to linear ones via a state coordinate change and with or without feedback four cases are distinguished by allowing or disallowing feedback as well as by including the output map or not the interdependence of these problems is analyzed an important feature that distinguishes these discrete time problems from the corresponding problem in continuous time is that the state coordinate transformation is here directly computable as a higher composition of the system and output maps finally certain connections are made with the continuous time case

a finiteness criterion for nonlinear input output differential systems we solve the following problem which has been dealt with in several publications when does a system have the same input output behaviour as a system depending linearly on the state variables precise definitions of this question are supplied in the text a particular case of the problem is the equivalence of a system with a bilinear one at the end we illustrate our methods and the scope of our results by a brief study of several examples

type theories normal forms and d lambda models abstract a non standard inverse limit model d is constructed which has a non hilbert post complete theory moreover in d a simple semantic characterization of normalizable terms is given these results are proved using the properties of a generalized type assignment system which yields a filter model barendregt coppo and dezani ciancaglini 1983 j symbolic logic 48 931 940 coppo dezani ciancaglini honsell and longo 1983 pp 241 262 logic colloquium 82 north holland amsterdam isomorphic to d the type assignment system is also proved complete with respect to an interpretation of types in the term model of equality based only on normalization properties as an application a class of maximal monoids of normalizable terms is characterized

immersion of discrete time nonlinear system by regular dynamic state feedback into a linear system necessary and sufficient conditions for local solvability of the title problem around a given trajectory are obtained the proposed conditions are less restrictive than those obtained by lee and marcus for the problem of immersion a nonlinear system into a linear system via static state feedback instrumental in the problem solution is the inversion structure algorithm for a discrete time nonlinear system the solvability conditions are expressed in terms of the inversion algorithm moreover the construction of both the dynamic state feedback and the immersion map relies on this algorithm finally it is shown that for locally right invertible systems the considered problem unlike the problem of immersion via static state feedback is always solvable

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

on input output linearization of discrete time nonlinear systems abstract we consider a nonlinear discrete time system of the form x t 1 f x t u t y t h x t where x r n u r m y r q and f and h are analytic necessary and sufficient conditions for local input output linearizability are given we show that these conditions are also sufficient for a formal solution to the global input output linearization problem finally we show that zeros at infinity of can be obtained by the structure algorithm for locally input output linearizable systems

dynamical realizations of finite volterra series in this paper realizations of finite volterra series are viewed as nonlinear analytic input output systems with state space described by an analytic manifold for a minimal realization guaranteed by h j sussmann the state space which is unique up to diffeomorphism is shown to have the homogeneous space structure of a nilmanifold the quotient of two nilpotent lie groups the structure of nilmanifolds as described by a malcev is used to show that for these systems the state space has a vector space structure as a consequence of this result it is shown that a minimal realization of a finite volterra series can be described as a cascade of linear subsystems with polynomial link maps in which the dimension o f each linear subsystem is independent of the realization considered

what is a model of the lambda calculus an elementary purely algebraic definition of model for the untyped lambda calculus is given this definition is shown to be equivalent to the natural semantic definition based on environments these definitions of model are consistent with and yield a completeness theorem for the standard axioms for lambda convertibility a simple construction of models for lambda calculus is reviewed the algebraic formulation clarifies the relation between combinators and lambda terms

on dynamic input output linearization of discrete time nonlinear systems this paper studies the problem of linearizing the input output map of an analytic discrete time nonlinear system locally around a given trajectory necessary and sufficient conditions are given for the existence of a regular dynamic state feedback control law under which the input dependent part of the response of a nonlinear system becomes linear in the input and independent of the initial state the proposed conditions are less restrictive than those obtained by lee and marcus for linearizing the input output map via a static state feedback instrumental in the problem solution is the inversion structure algorithm for a discrete time nonlinear system firstly the solvability conditions are expressed in terms of the inversion algorithm secondly the proof of the existence and construction of the dynamic state feedback compensator relies on this algorithm

a characterization of f complete type assignments the aim of this paper is to investigate the soundness and completeness of the intersection type discipline for terms of the untyped calculus with respect to the f semantics f soundness and f completeness as pointed out by scott if d is the domain of a model there is a subset f of d whose elements are the canonical representatives of functions the f semantics of types takes into account that theintuitive meaning of is the type of functions with domain and range and interprets as a subset of f the type theories which induce f complete type assignments are characterized it follows that a type assignment is f complete iff equal terms get equal types and whenever m has a type n where is a type variable and is the universal type the term z1 zn mz1 zn has type here we assume that z1 z n do not occur free in m

principal type scheme and unification for intersection type discipline abstract the intersection type discipline for the calculus itd is an extension of the classical functionality theory of curry in the itd a term satisfying a given property has a principal type scheme in an extended meaning i e there is a type scheme deducible for it from which all and only the type schemes deducible for it are reachable by means of suitable operations the problem of finding the principal type scheme for a term if it exists is semidecidable in the paper a procedure is shown building the principal type scheme of a term through the construction of the most general unifier for intersection type schemes

computability in higher types pω and the completeness of type assignment p the powerset of the natural numbers may be turned into an applicative structure by myhill and shepherdson then for a b p set a b d p a a da b any effectively given domain in the sense of scott 1982 can be embedded into p by a continuous and computable retraction notation x c ax for some ax p which is also an effectively given domain we first prove that if x c ax and y c ay then also ax ay is an effectively given domain and cont x y c ax ay i e the continuous functions can be embedded into ax ay let now p p be the collection of single valued sets i e p is isomorphic to the effectively given domain of the partial functions on and let t be the function type symbols with 1 t then for p1 p p p p extends the classical recursive operators at higher types by ershov s model of the kleene kreisel countable functionals can effectively be embedded by some g s into the type structure p t in p thus the recursive functionals correspond to the r e sets in the due types for example f has type iff g f is an r e set in p p p t clearly yields a model for formal type assingnment to terms of calculus i e for any assignment b of types to variables and any t one has b m m b p where b var p according to b we prove that also the reverse implication holds for typable terms thus a completeness theorem for type checking is established over a model defined by an independent recursion theoretical motivation

completeness of type assignment in continuous lambda models abstract the completeness of curry s rules for assigning type schemes to terms of the pure lambda calculus has been proved by hindley 1983 and barendregt et al 1983 using models of syntactic nature a first result of this paper is a completeness proof with respect to the model p as asked by scott 1976 moreover an extension of curry s system in which type schemes can be assigned to the fixed point combinator is introduced together with a notion of type semantics for which it is proved sound and complete answering a question of scott 1980 also in this case completeness is proved with respect to the model p all results also hold for the alternative notions of type semantics proposed by hindley 1983 and scott 1976 1980

curry s type rules are complete with respect to the f semantics too abstract a formal system for assigning type schemes to untyped terms due in essence to h b curry was given in hindley the completeness theorem for typing terms theoret comput sci 22 1983 1 17 this issue the system was proved complete with respect to two different semantics and conjectured to be complete with respect to a third the f semantics this paper proves that conjecture the type schemes have exponentiation as their only connective

on the solution calculation of nonlinear ordinary differential equations via exact quadratization abstract we show a general method allowing the solution calculation in the form of a power series for a very large class of nonlinear ordinary differential equations odes namely the real analytic odes and more in general the real analytic reducible odes in many indeterminates characterized by an ode function given by generalized polynomials of the indeterminates and their derivatives i e functions formally polynomial with exponents though the exponent can be any real number and whose coefficients are analytic time functions the solution method consists in reducing the ode to a certain canonical homogeneous quadratic ode named driver type riccati equation with a larger number of indeterminates whose solutions include as sub solutions the original solutions and for which a recursive formula is shown giving all coefficients of the solution power series directly from the ode parameters the reduction method is named exact quadratization and was formerly introduced in another our article where we considered explicit odes only in the present paper which is self contained to a large extent we review and complete the theory of exact quadratization by solving issues such as for instance the existence of a piecewise quadratization that had remained open and also extend it to the more general case of an implicitly defined ode finally we argue that the result can be seen as a partial solution of a differential version of the 22nd hilbert s problem

some realizations of algorithms for nonlinear input output systems this paper develops an algorithm which given an input output differential equation produces under appropriate circumstances a parametrization of the observation space of the underlying state space system the paper extends previous results by the authors to a more general setting so that state space systems in which the controls enter nonlinearly can be accommodated and most importantly the paper deals with implicitly defined systems at both the input output and state space level fliess and hasler have demonstrated the importance of implicit input output models which yield only local state space descriptions various realizations are obtained depending on the properties of the derived candidate observation space examples of the algorithm are described with the aid of an implementation using the computer algebra system axiom

type inference with recursive types syntax and semantics abstract in this paper we study type inference systems for calculus with a recursion operator over types the main syntactical properties notably the existence of principal type schemes are proved to hold when recursive types are viewed as finite notations for infinite regular type expressions representing their infinite unfoldings exploiting the approximation structure of a model for the untyped language of terms types are interpreted as limits of sequences of their approximations we show that the interpretation is essentially unique and that two types have equal interpretation if and only if their infinite unfoldings are identical finally a completeness theorem is proved to hold w r t the specific model we consider for a natural infinitary extension of the type inference system

multigrid methods with web splines we describe and analyze a multigrid algorithm for finite element approximations of second order elliptic boundary value problems with weightedextended b splines web splines this new technique provides high accuracy with relatively low dimensional subspaces does not require any grid generation and is ideally suited for hierarchical solution techniques in particular we show that the standard w cycle yields uniform convergence i e the required number of iterations is bounded independent of the grid width

linear dynamics hidden by input output linearization abstract the input output linearization method has been quite useful in determining the linear input output responses of non linear systems however research has shown that this technique can often hide part of the non linear system which is linearizable we prove sufficient conditions that a non linear system contain a k dimensional linear system after the input output linearization control is applied here p k n where p is the relative degree of the system and n is the dimension of the non linear system the results for k n are known from the literature

survey approximate linearization via feedback an overview fostered by a growing interest in nonlinear control theory and catalyzed by the discovery in the early 1980s of the exact conditions under which a nonlinear plant can be linearized by static state feedback and coordinate transformation in the last decades there has been a rapid increase of interest in the search for approximate solutions to the problem of linearizing nonlinear systems by state or output feedback main reason for that is the limited applicability of the rigorous methods and the complexity sensitivity and design difficulties of the exact linearizing compensators if any in the present paper the literature on the subject is reviewed and organized in what is believed to be a new and consistent perspective recent works especially in the area of data based techniques are in fact described and related whenever possible to fundamental results previously obtained by model based differential geometric methods this is expected to bring modern system linearization methods closer to the needs of practicing control engineers and to stimulate further research eventually able to fill visible gaps in this direction

polymorphic type inference and containment abstract type expressions may be used to describe the functional behavior of untyped lambda terms we present a general semantics of polymorphic type expressions over models of untyped lambda calculus and give complete rules for inferring types for terms some simplified typing theories are studied in more detail and containments between types are investigated

lambda calculi for strict parallel functions we introduce two calculi and show that they are expressive for two canonical domains of parallel functions the first calculus is an enrichment of the lazy call by name calculus with call by value abstractions and parallel composition while in the second the usual call by name abstractions are disallowed the corresponding domains are respectively abramsky s domain d d d a lifted function space and d d d a lifted domain of strict functions these domains are lattices and we show that the parallelism is adequately represented by the join operator while call by value abstractions correspond to strict functions the proofs of the results rely on a completeness theorem for the logical presentation of the semantics

stabilization by output feedback of multivariable invertible nonlinear systems in this paper the problem of global stabilization of a rather general class of mimo nonlinear systems is addressed the systems considered in the paper are invertible have a trivial zero dynamics and possess a normal form in which certain multipliers are functions of the state vector of a special kind while special structural dependence of such multipliers on the components state vector has been exploited before in the context of achieving stabilization via full state feedback though the novelty in the approach of this paper is that a peculiar structure is identified which happens to be intimately related to the property of uniform complete observability thus making the design of observers possible and to the property of uniform invertibility relations never established before in the literature as a result for this class of mimo nonlinear systems a dynamic output feedback law can be designed yielding semiglobal and even global under appropriate assumptions asymptotic stability

on the largest input output linearizable subsystem feedback input output linearization is considered in this paper the main result provides the necessary and sufficient conditions to determine the largest dimension of a linear subsystem achievable by a suitable coordinate change after an input output linearization feedback has been applied a systematic method to find the desired coordinate change is also given in this paper

principal types and unification for simple intersection type systems in this paper we introduce a decidable restriction of the intersection type discipline the restriction is based on a uniform principle rather than on a notion of rank for this system we give a type checking algorithm that we prove to be sound and complete an extended language of types with labelled intersections and intersection schemes is needed to describe the principal type of terms which turns out to be unique module a set of equations between labels the unification algorithm far labelled types that extends first order unification could be used as a basis to define inference algorithms for other more powerful systems with intersection

on the synthesis of linear input output responses for nonlinear systems necessary and sufficient conditions are given for the existence of a feedback control law under which the input dependent part of the response of a given nonlinear system becomes linear in the input and independent of the initial state

necessary conditions for asymptotic tracking in nonlinear systems in the literature it has been shown that if a single input single output analytic nonlinear plant 1 has a well defined relative degree and 2 is minimum phase it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in c sup n 0 spl infin the space of n times continuously differentiable functions taking values in r when either of these sufficient conditions is not met various authors have investigated approximate analytic solutions discontinuous solutions and solutions for restricted sets of trajectories in this paper it is shown that conditions 1 and 2 are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories analogous results are established for multi input multi output systems

a general approach to input output pseudolinearization for nonlinear systems a nonlinear system is said to be input output pseudolinearized if its family of linearizations about constant operating points has input output behavior that is independent of the particular operating point the problem of constructing static state feedback laws that achieve input output pseudolinearization for a general class of nonlinear systems is considered a generalization of the well known structure algorithm to the case of parameterized families of linear systems plays an important role

immersion and immersion by nonsingular feedback of a discrete time nonlinear system into a linear system an analytic discrete time nonlinear system is considered necessary and sufficient conditions for immersion of the system into a linear system are given local immersion is defined by nonsingular feedback into a linear system and given necessary and sufficient conditions for this problem it is shown that a similar approach can also be applied to continuous time affine nonlinear systems

intersection and union types type assignment systems with intersection and union types are introduced although the subject reduction property with respect to s reduction does not hold for a natural deduction like system we manage to overcome this problem in two different ways the first is to adopt a notion of parallel reduction which is a refinement of gross knuth reduction the second is to introduce type theories to refine the system among which is the theory called that induces an assignment system preserving s reduction this type assignment system further clarifies the relation with the intersection discipline through the decomposition first of a disjunctive type into a set of conjunctive types and second of a derivation in the new type assignment system into a set of derivations in the intersection type assignment system for this system we propose three semantics and prove soundness and completeness theorems

the completeness theorem for typing λ terms abstract rules for assigning type schemes to untyped terms are given three different semantics are described and the rules are proved complete with respect to two of these semantics the type schemes are built up from type variables not constants by the semantics are defined in arbitrary models of the untyped calculus such models do not come with a type structures as part of their definition the fact that two distinct semantics are completely captured by one set of rules says that the usual type language with as its only connective is not expressive enough to describe the differences between them i conjecture that the rules are also complete with respect to the third semantics

type inference abstract interpretation and strictness analysis abstract filter domains coppo et al 1984 can be seen as abstract domains for the interpretation of functional type free programming languages what is remarkable is the fact that in filter domains the interpretation of a term is given by the set of its types in the intersection type discipline with inclusion thus reducing the computation of an abstract interpretation to typechecking as a main example an abstract filter domain for strictness analysis of type free functional languages is presented the inclusion relation between types representing strictness properties has a complete recursive axiomatization type inference rules cannot be complete strictness being a 0 1 property but a complete extension of the type inference system is presented

application of inverse system for linearization and decoupling abstract we show that for a special class of nonlinear systems the linearization and or decoupling of nonlinear dynamics by immersion under feedback is in fact an application of the right inverse system

generalized filter models abstract in this paper starting from filters which are a natural generalization of intersection filters barendregt et al j symbolic logic 48 1983 931 940 the existence of filter models and filter semimodels for the calculus is investigated the construction of filters is based on a z semilattice of types in which the subsets having infimum are given by a collection z called subset system the set of representable functions is characterized in the obtained domain in the case where the properties of the subset system z guarantee the existence of a filter model the proof of soundness and completeness of the associated natural z type assignment system is routine

weighted extended b spline method for the approximation of the stationary stokes problem a new stabilized mesh free method for the approximation of the stokes problem using weighted extended b splines web splines as shape functions has been proposed the web spline based bilinear velocity constant pressure element satisfies the so called inf sup condition or ladyshenskaya babus ka brezzi lbb condition the main advantage of this method over standard finite element methods is that it uses regular grids instead of irregular partitions of domain thus eliminating the difficult and time consuming pre processing step convergence and condition number estimates are derived numerical experiments in two space dimensions confirm the theoretical predictions

nonlinear control of a shunt dc motor the problem of controlling a shunt dc motor is considered recent methods for nonlinear control are compared including feedback linearization generalized controller canonical forms and input output linearization connections between the approaches as well as their respective advantages are discussed in detail

f semantics for type assignment systems abstract yokouchi h f semantics for type assignment systems theoretical computer science 129 1994 39 77 this paper develops f semantics for type systems that assign types to untyped terms curry s system is complete for f semantics but a polymorphic type assignment system is not so we introduce two additional rules fi and fe and show that a polymorphic type assignment system becomes complete for f semantics if we add these two rules furthermore we apply the same method to a polymorphic type assignment system without the equality rule and obtain a similar completeness result we also show that an intersection type assignment system is complete for f models if we add two rules defined on the basis of fi and fe

accessibility of nonlinear time delay systems a full characterization of accessibility is provided for nonlinear time delay systems it generalizes the rank condition which is known for weak controllability of linear time delay systems as well as the celebrated geometric approach for delay free nonlinear systems and the characterization of their accessibility besides fundamental results are derived on integrability and basis completion which are of major importance for a number of general control problems for nonlinear time delay systems they are shown to impact preconceived ideas about canonical forms for nonlinear time delay systems