stokes first problem for sisko fluid over a porous wall we investigate the time dependent flow of an incompressible sisko fluid over a wall with suction or blowing the flow is caused by sudden motion of the wall in its own plane the magnetodynamic nature of the fluid is taken into account by applying a variable magnetic field the resulting nonlinear problem is solved by invoking a symmetry approach and numerical techniques the essential features of the embedded key parameters are described particularly the significance of the rheological effects is studied

controlled invariance for discrete time nonlinear systems with an application to the disturbance decoupling problems invariant distributions are defined for discrete time nonlinear control systems and necessary and sufficient conditions are given for their controlled invariance this extends to discrete time systems the basic tool which has been so important in solving the various synthesis problems for continuous time systems to indicate their utility in the discrete time setting they are used to locally solve the disturbance decoupling problem

peristaltic flow of blood under effect of a magnetic field in a non uniform channels the effect of a magnetic field on peristaltic transport of blood in a non uniform two dimensional channels has been investigated under zero reynolds number with long wavelength approximation blood is represented by a viscous incompressible and electrically conducting couple stress fluid a fluid which its particles size are taken into account a special case of a non newtonian fluid it is found that the pressure rise decreases as the couple stress fluid parameter c increases i e small size fluid particle and increases as the hartmann number m increases so the pressure rise for a couple stress fluid as a blood model is greater than that for a newtonian fluid and is smaller for a magnetohydrodynamic fluid than for a fluid without an effect of a magnetic field finally the maximum pressure rise q 0 increases as m increases and c decreases and the effect of the hartmann number m is more obvious for the same email protected l m a x as the couple stress parameter c increases newtonian fluid

linearization of time delay systems by input output injection and output transformation in the present paper necessary and sufficient geometric conditions for the equivalence of a single input single output nonlinear time delay system under bicausal change of coordinates and regular output transformation to a linear weakly observable time delay system up to input output injection are given the obtained results are then applied to the observer design problem

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

remarks on linearization of discrete time autonomous systems and nonlinear observer design abstract this paper presents necessary and sufficient conditions under which a discrete time autonomous system with outputs is locally state equivalent to an observable linear system or a system in the nonlinear observer form krener and isidori 1983 in particular an open problem raised in lee and nam 1991 namely the observer linearization problem is solved for a nonlinear system which may not be invertible i e the mapping f may not be a local diffeomorphism as a consequence the nonlinear observer design problem is solved by means of exact linearization techniques

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

linearization of discrete time nonlinear systems and a canonical structure linearizable nonlinear discrete time systems are described as a composition of diffeomorphisms linearizability of a general nonlinear system is obtained as an extension of linearizability of the system expressed in terms of the diffeomorphisms

normal forms and approximated feedback linearization in discrete time abstract the paper discusses approximated feedback linearization of nonlinear discrete time dynamics which are controllable in first approximation and introduces two types of normal forms the study is set in the context of differential difference representations of discrete time dynamics proposed in monaco normand cyrot in normand cyrot ed perspectives in control a tribute to ioan dore landau springer londres 1998 pp 191 205

integrability for nonlinear time delay systems in this note the notion of integrability is defined for 1 forms defined in the time delay context while in the delay free case a set of 1 forms defines a vector space it is shown that 1 forms computed for time delay systems have to be viewed as elements of a module over a certain non commutative polynomial ring two notions of integrability are defined strong and weak integrability which coincide in the delay free case necessary and sufficient conditions are given to check if a set of 1 forms is strongly or weakly integrable to show the importance of the topic integrability of 1 forms is used to characterize the accessibility property for nonlinear time delay systems the possibility of transforming a system into a certain normal form is also considered

a constructive condition for dynamic feedback linearization the paper deals with dynamic feedback linearization of continuous time affine systems a constructive procedure based on prolongations is proposed based on necessary geometric conditions the algorithm computes a set of prolongation indices

pulsatile flow of blood using a modified second grade fluid model we study the unsteady pulsatile flow of blood in an artery where the effects of body acceleration are included the blood is modeled as a modified second grade fluid where the viscosity and the normal stress coefficients depend on the shear rate it is assumed that the blood near the wall behaves as a newtonian fluid and in the core as a non newtonian fluid this phenomenon is also known as the fahraeus lindqvist effect the equations are made dimensionless and solved numerically

brief analysis of nonlinear time delay systems using modules over non commutative rings the theory of non commutative rings is introduced to provide a basis for the study of nonlinear control systems with time delays the left ore ring of non commutative polynomials defined over the field of meromorphic function is suggested as the framework for such a study this approach is then generalized to a broader class of nonlinear systems with delays that are called generalized roesser systems finally the theory is applied to analyze nonlinear time delay systems a weak observability is defined and characterized generalizing the well known linear result properties of closed submodules are then developed to obtain a result on the accessibility of such systems

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

classification of joinings for kleinian groups we classify all locally finite joinings of a horospherical subgroup action on g when g psl2 r or psl2 c and is a geometrically finite zariski dense subgroup of g this generalizes ratner s 1983 joining theorem for the case when is a lattice in g

unsteady unidirectional flow of second grade fluid between the parallel plates with different given volume flow rate conditions in this paper the velocity profile and pressure gradient of the unsteady state unidirectional flow of second grade fluids between the parallel plates are considered the flow motion in the plates is induced by a given but arbitrary inlet volume flow rate which varies with time based on the flow conditions described two basic flow situations are solved which are a sudden started and a constant acceleration flow respectively then we apply these two results to a practical case that is a trapezoidal piston motion which contains three phases of piston motion the constant acceleration from the rest to a fixed velocity then keeping at this velocity following with the constant deceleration to a stop in addition the oscillatory flow is also considered

invariant measures and arithmetic quantum unique ergodicity we classify measures on the locally homogeneous space i sl 2 r l which are invariant and have positive entropy under the diagonal subgroup of sl 2 r and recurrent under l this classification can be used to show arithmetic quantum unique ergodicity for compact arithmetic surfaces and a similar but slightly weaker result for the finite volume case other applications are also presented in the appendix joint with d rudolph we present a maximal ergodic theorem related to a theorem of hurewicz which is used in theproof of the main result

global state and feedback equivalence of nonlinear systems the problem of finding global state space transformations and global feedback of the form u t x t to transform a given nonlinear system xdot f x g x u to a controllable linear system on rn or on an open subset of rn is considered here we give a complete set of differential geometric conditions which are equivalent to the existence of a solution to the above problem

the metric entropy of diffeomorphisms part ii relations between entropy exponents and dimension on considere f m m m m un c 2 diffeomorphisme f d une variete de riemann compacte m preservant une mesure de probabilite de borel m soit hm f l entropie metrique de f et 1 x r x x les exposants de lyapunov distincts en x on etablit une formule qui relie h m f et les r x x

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 functional equations approach to nonlinear discrete time feedback stabilization through pole placement abstract the present work proposes a new approach to the nonlinear discrete time feedback stabilization problem with pole placement the problem s formulation is realized through a system of nonlinear functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using tools from functional equations theory one can prove that the solution to the above system of nonlinear functional equations is locally analytic and an easily programmable series solution method can be developed under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear discrete time state feedback control law that are both computed through the solution of the system of nonlinear functional equations the feedback stabilization with pole placement design objective can be attained under rather general conditions the key idea of the proposed single step design approach is to bypass the intermediate step of transforming the original system into a linear controllable one with an external reference input associated with the classical exact feedback linearization approach however since the proposed method does not involve an external reference input it cannot meet other control objectives such as trajectory tracking and model matching

pulsatile flow of blood through a stenosed porous medium under periodic body acceleration pulsatile flow of blood through a stenosed porous medium has been studied under the influence of body acceleration with the help of laplace and finite hankel transform analytical expressions for axial velocity fluid acceleration flow rate and shear stress have been obtained the effect of various parameters entering into the problem is discussed wiht the help of graphs

the immersion under feedback of a multidimensional discrete time non linear system into a linear system this paper deals with the problem of finding conditions which ensure the reproducibility of the input output behaviour of a linear analytic discrete time system by means of a linear discrete time system on this basis the problem of modifying the system by feedback in order for it to enjoy such a property is posed and solved

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

on measures invariant under tori on quotients of semisimple groups we classify invariant and ergodic probability measures on arithmetic homogeneous quotients of semisimple s algebraic groups invariant under a maximal split torus in at least one simple local factor and show that the algebraic support of such a measure splits into the product of four homogeneous spaces a torus a homogeneous space on which the measure is up to nite index the haar measure a product of homogeneous spaces on each of which the action degenerates to a rank one action and a homogeneous space in which every element of the action acts with zero entropy

exact peristaltic flow in tubes with an endoscope peristaltic flow of a jeffrey fluid through the gap between concentric uniform tubes has been investigated with particular reference to an endoscope effects the velocity components and axial pressure gradient are obtained analytically numerical integration is performed in order to analyze the pressure rise and frictional forces on the inner and outer tubes the obtained results are compared with the earlier studies existing in the literature

peristaltic flow of a micropolar fluid in an asymmetric channel in this paper we carry out a study of peristaltic motion of an incompressible micropolar fluid in an asymmetric channel the flow analysis has been developed for low reynolds number and long wavelength case exact analytic solutions have been established for the axial velocity microrotation component and stream function expression for the shear stresses are also obtained the effects of pertinent parameters on the pressure rise per wavelength are investigated by means of numerical integration the phenomena of trapping is further discussed the results for micropolar fluid are compared with those for newtonian fluid

on raghunathan s measure conjecture this paper represents the last in our three part series on raghunathan s measure conjecture see r1 r2 for parts i and ii more specifically let g be a real lie group all groups in this paper are assumed to be second countable with the lie algebra r a discrete subgroup of g and ir g r g the projection lwg rg the group g acts by right translations on r g x x g x e r g g e g let gt be a borel probability measure on r g define

nonstationary peristaltic transport of a heat conducting fluid abstract we study the peristaltic transport of a heat conducting fluid in a flexible lube with a prescribed pressure drop over a wavelength of the lube and newton s cooling law for the temperature and a prescribed velocity on the boundary using the oberbeck boussinesq equations as the governing equations and introducing a generalized solution we prove existence uniqueness and stability theorems for the nonstationary problem and develop and justify the stokes and long wave asymptotic expansions

invariant measures on g γ for split simple lie groups g we study the left action of a cartan subgroup on the space x g where is a lattice in a simple split connected lie group g of rank n 1 let be an invariant measure on x we give several conditions using entropy and conditional measures each of which characterizes the haar measure on x furthermore we show that the conditional measure on the foliation of unstable manifolds has the structure of a product measure the main new element compared to the previous work on this subject is the use of noncommutativity of root foliations to establish rigidity of invariant measures 2003 wiley periodicals inc

control systems in neural networks with local memory abstract based on a new paradigm of neural networks consisting of neurons with local memory nnlm we discuss the representation of a control system by neural networks using this representation the basic issues of complete controllability and observability for the system are addressed a separation principle of learning and control is presented for nnlm the result shows that the weights of the network will not affect its dynamics some results about local linearization via a regular static feedback and nonlinear transformation are also given

entropy geometry and disjointness for zero dimensional algebraic actions we show that many algebraic actions of higher rank abelian groups on zero dimensional compact abelian groups are mutually disjoint the proofs exploit differences in the entropy geometry arising from subdynamics and a form of abramov rokhlin formula for half space entropies

brief paper observer based control of a class of time delay nonlinear systems having triangular structure time delay systems constitute a special class of dynamical systems that are frequently present in many fields of engineering it has been shown in the literature that the existence of a stabilizing observer based controller is related to delay dependent conditions that are generally satisfied for a small time delay motivating works towards reducing the conservatism of the results are among the on going research topics especially when partial state measurements are imposed this paper investigates the problem of observer based stabilization of a class of time delay nonlinear systems written in triangular form first we show that a delay nonlinear observer is globally convergent under the global lipschitz condition of the system nonlinearity then it is shown that a parameterized linear feedback that uses the observer states can stabilize the system whatever the size of the delay an illustrative example is provided to approve the theoretical results

invariant measures and the set of exceptions to littlewood s conjecture we classify the measures on sl k r sl k z which are invariant and ergodic under the action of the group a of positive diagonal matrices with positive entropy we apply this to prove that the set of exceptions to littlewood s conjecture has hausdorff dimension zero

an efficient approach to study the pulsatile blood flow in femoral and coronary arteries by differential quadrature method abstract in this paper flow analysis for a non newtonian third grade blood in coronary and femoral arteries is simulated numerically blood is considered as the third grade non newtonian fluid under periodic body acceleration motion and pulsatile pressure gradient differential quadrature method dqm and crank nicholson method cnm are used to solve the partial differential equation pde governing equation by which a good agreement between them was observed in the results the influences of some physical parameters such as amplitude lead angle and body acceleration frequency on non dimensional velocity and profiles are considered for instance the results show that increasing the amplitude a g and reducing the lead angle of body acceleration make higher velocity profiles in the center line of both arteries

quadratic forms and approximate feed back linearization in discrete time quadratic feedback linearization is discussed for discrete time systems i e approximate feedback linearization up to the second order with respect to input and state variables after introducing in discrete time two equivalence classes invariant under quadratic static state feedback and diffeomorphism two canonical quadratic representations are proposed then it is shown that any nonlinear discrete time dynamics which are controllable in their first approximations can be linearized up to the second order under dynamic feedback the results stated here can be considered as the general discrete time analogues of the continuous time ones kang and krener 1992

effect of body acceleration on unsteady pulsatile flow of non newtonian fluid through a stenosed artery the laminar two dimensional pulsatile flow of blood under the influence of externally imposed periodic body acceleration through a stenosed artery is studied in the paper a mathematical model is developed by treating blood as a non newtonian fluid characterised by the generalised power law model incorporating both the shear thinning and shear thickening characteristics of the streaming blood the arterial wall has been treated as an elastic moving wall cylindrical tube having a stenosis in its lumen the unsteady flow mechanism in the stenosed artery subject to a pulsatile pressure gradient arising from the normal functioning of the heart has been accounted for the finite difference scheme helps estimating the effects of periodic body acceleration and the non newtonian rheology of the flowing blood on the flow velocity the rate of flow the wall shear stress and the fluid acceleration through their graphical representations quantitatively at the end of the paper in order to validate the applicability of the present improved mathematical model under consideration

delay adaptive feedback for linear feedforward systems abstract predictor techniques are an indispensable part of the control design toolbox for plants with input and state delays of significant size yet they suffer from sensitivity to the design values explicit feedback laws were recently introduced by jankovic for a class of feedforward linear systems with simultaneous state and input delays for the case where the delays are of unknown length using the certainty equivalence principle we design a lyapunov based adaptive controller which achieves global stability and regulation for arbitrary initial estimates for the delays we consider a two block sub class of linear feedforward systems a generalization to the n block case involves a recursive application of the same techniques

losslessness feedback equivalence and the global stabilization of discrete time nonlinear systems in this paper a necessary and sufficient condition for a nonlinear system of the form spl sigma given by x k 1 f x k g x k u k y k h x k j x k u k to be lossless is given and it is shown that a lossless system can be globally asymptotically stabilized by output feedback if and only if the system is zero state observable then we investigate conditions under which spl sigma can be rendered lossless via smooth state feedback in particular we show that this is possible if and only if the system in question has relative degree spl lcub 0 0 spl rcub and has lossless zero dynamics under suitable controllability like rank conditions we prove that nonlinear systems having relative degree spl lcub 0 0 spl rcub and lossless zero dynamics can be globally stabilized by smooth state feedback as a consequence we obtain sufficient conditions for a class of cascaded systems to be globally stabilizable the global stabilization problem of the nonlinear system spl sigma without output is also investigated in this paper by means of feedback equivalence some of the results are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

a mathematical description of peristaltic hydromagnetic flow in a tube abstract peristaltic motion of an incompressible non newtonian fluid in a deformable tube is studied under long wavelength and low reynolds number the effect of magnetic field on the motion of a johnson segalman fluid has been modelled analytical solutions are obtained for the stream function axial velocity and axial pressure gradient under the small weissenberg number the pressure rise and frictional force per wavelength have been computed through numerical integration the study shows that in addition to weissenberg number and the effect of magnetic field the occlusion and volume flux also affect the peristaltic flow these effects are noticeable in the stream function axial velocity axial pressure gradient the pressure rise and the frictional force graphs are plotted for axial pressure gradient pressure rise and frictional force and discussed in detail

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

feedback linearizing control of discrete time nonlinear systems with input constraints a feedback linearizing control strategy for discrete time nonlinear systems subject to input constraints is proposed the control system comprises i a feedback linearizing controller ii a constraint mapping algorithm that transforms the actual input constraints into constraints on the feedback linearized system and iii a linear model predictive controller that regulates the resulting constrained linear system closed loop stability analysis is a challenging problem because the transformed constraints are state dependent sufficient conditions for asymptotic stability are presented for fully and partially feedback linearizable systems as part of the analysis a new stability result for unconstrained discrete time nonlinear systems which parallels a well known continuous time result is derived

a finite spectrum assignment for retarded non linear systems and its solvability condition this paper considers a finite spectrum assignment problem for retarded non linear systems first using extensions of the lie derivative and the lie bracket for differential difference equations we propose a finite spectrum assignment procedure for a class of retarded non linear systems then we derive a necessary and sufficient condition for the solvability of a class of finite spectrum assignment problems for retarded non linear systems the obtained condition is an extension of the condition for the exact linearization of finite dimensional non linear systems and the finite spectrum assignment of retarded linear systems with controllability over polynomial rings

input output linearization of retarded non linear systems by using an extension of lie derivative this paper considers the input output linearization problem for retarded non linear systems which have time delays in the state by using an extension of the lie derivative for functional differential equations we derive a coordinates transformation and a static state feedback to obtain linear input output behaviour for a class of retarded non linear systems the obtained coordinates transformation is allowed to contain not only the current value of the state variables but also the past values of ones in addition we show that the coordinates transformation is invertible in a neighbourhood of the origin and examine the stability condition of the closed loop system with the static state feedback the effectiveness of the proposed technique is demonstrated through numerical simulations

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

controllability of driftless nonlinear time delay systems the controllability of a class of nonlinear driftless time delay systems is fully characterized for the first time this result is obtained within a newly introduced geometric approach moreover all those possible autonomous or non controllable elements which can depend on the delayed variables are also characterized when the system is not controllable and in consequence a canonical form of those systems is derived

measurable quotients of unipotent translations on homogeneous spaces let u be a nilpotent unipotent subgroup of a lie group g and let f be a closed subgroup of g marina ratner showed that every ergodic u invariant probability measure on the homogeneous space f g is of a simple algebraic form we use this fundamental new result to show that every measurable quotient of the u action on j g is of a simple algebraic form roughly speaking any quotient is a double coset space a g k

extended lie brackets for nonlinear time delay systems in this note the extended lie bracket operator is introduced for the analysis and control of nonlinear time delay systems nltds this tool is used to characterize the integrability conditions of a given submodule the obtained results have two fundamental outcomes first they define the necessary and sufficient conditions under which a given set of nonlinear one forms in the n dimensional delayed variables x t x t sd with d constant but unknown are integrable thus generalizing the well known fundamental frobenius theorem to delay systems secondly they set the basis for the extension to this context of the geometric approach used for delay free systems the effectiveness of the results is shown by solving the problem of the equivalence of a nltds to an accessible linear time delay system ltds by bicausal change of coordinates

some numerical aspects of approximate linearization of single input non linear systems we characterize approximate linearization to order m of a single input non linear system in terms of the existence of an integrating factor to order m 2 which is equivalent to the well known condition that a system of vector fields be order m 1 involutive we present a constructive method to obtain the required transformation for approximate linearization which results in substantial computational savings

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

identification of the delay parameter for nonlinear time delay systems with unknown inputs using the theory of non commutative rings this paper studies the delay identification of nonlinear time delay systems with unknown inputs a sufficient condition is given in order to deduce an output delay equation from the studied system then necessary and sufficient conditions are proposed to judge whether the deduced output delay equation can be used to identify delay involved in this equation two different cases are discussed for the dependent and independent outputs respectively the presented result is applied to identify delay in a biological system

joinings of higher rank diagonalizable actions on locally homogeneous spaces we classify joinings between a fairly general class of higher rank diagonalizable actions on locally homogeneous spaces in particular we classify joinings of the action of a maximal r split torus on g with g a simple lie group of r rank 2 and g a lattice we deduce from this a classification of measurable factors of such actions as well as certain equidistribution properties

feedback equivalence for a class of nonlinear singularly perturbed systems the feedback equivalence for a class of nonlinear singularly perturbed systems is studied this is accomplished by reducing the full order problem into a lower order exact problem using the slow manifold theory this facilitates development of an approximate and simpler linearizing control strategy achievable to an arbitrary degree of accuracy it is shown that in contradistinction to systems with unobservable parasitics where a state dependent transformation and a static feedback controller are required for systems with observable parasitics a state and control dependent transformation and a dynamic feedback controller should be used to transform the exact system into a linear system in controller and observer form

diagonal actions in positive characteristic we prove positive characteristic analogues of certain measure rigidity theorems in characteristic 0 more specifically we give a classification result for positive entropy measures on quotients of sld and a classification of joinings for higher rank actions on simply connected absolutely almost simple groups

stable inversion for nonlinear discrete time systems we solve the exact output tracking problem for square nonlinear discrete time systems through stable inversion this stable inversion problem involves finding a bounded solution of a dynamical system driven by a bounded signal such a solution is given by a difference representation formula whose existence under the proper assumptions can be proven using a picard process

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

linearisation via input output injection of time delay systems abstractthis paper deals with the problem of linearisation of systems with constant commensurable delays by input output injection using algebraic control tools based on the theory of non commutative rings solutions for the problem of linearisation free of delays and with delays of an observable nonlinear time delay systems are presented based on the analysis of the input output equation these results are achieved by means of constructive algorithms that use the nth derivative of the output expressed in terms of the state space variables instead of the explicit computation of the input output representation of the system necessary and sufficient conditions are established in both cases by means of an invertible change of coordinates

on the problem of feedback linearization the paper studies and solves in a geometric framework the problem of partial feedback linearization for discrete time dynamics an algorithm for computing the largest linearizable subsystem is proposed this approach can be considered as dual to the one already proposed in literature in an algebraic context

canonical forms of decouplable and controllable linear systems in this paper we present the canonical forms of decouplable and controllable linear systems some of the non zero elements in gilbert s canonically decoupled structure which remain undetermined are explicitly determined by a complete set of invariances our result constitutes the key step to characterization of the whole class of nonlinear systems that are feedback equivalent to decouplable and controllable linear systems

new insights on the analysis of nonlinear time delay systems application to the triangular equivalence in this paper we present recent advances towards an algebraic framework for the analysis and control of nonlinear systems with delays we show the usefulness of these results by applying them to obtain a constructive characterization of the equivalence of a given system to the so called triangular form

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