robust control of cascaded and individually feedback linearizable nonlinear systems abstract feedback linearization technique is applied to design robust controllers for a class of nonlinear uncertain systems every system in the class is a series connection of finite number of nonlinear subsystems which are individually feedback linearizable and have significant but matched nonlinear functional uncertainties the key difference between this work and existing robust results is that the matching conditions and the existence of feedback linearization transformation are only required individually for each subsystem a constructive robust control design procedure is proposed for the unique control in the overall system the procedure is conceptually simple and contains three steps first perform input output feedback linearization for all individual subsystems second design fictitious robust controllers for inputs of each subsystem as if the subsystem had an independent control finally a mapping is developed which maps the individual fictitious controls recursively into the unique control of the overall system since neither the matching conditions nor feedback linearization are required for the overall system this becomes the broadest class of nonlinear uncertain or known systems for which a robust regular tracking control can be constructed using feedback linearization method global stability of the overall system is always guaranteed

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

group inverse for the block matrices with an invertible subblock let m abcd a is square be a square block matrix with an invertible subblock over a skew field k in this paper we give the necessary and sufficient conditions for the existence as well as the expressions of the group inverse for m under some conditions

on the linearization via a restricted class of dynamic feedback we deal with the problem of linearization of nonlinear systems using a restricted class of dynamic compensator which is composed of chains of integrators followed by static feedback in the vector field formulation we present an upper bound on the number of integrators to linearize nonlinear systems and show that the bound is sharp when n 2 spl ges m spl ges 2 this results in the checkable necessary and sufficient conditions

a model reference adaptive control scheme for pure feedback nonlinear systems a model reference adaptive control mrac scheme is presented for nonlinear systems in a pure feedback canonical form with unknown parameters the present of parameter uncertainty in the system causes imperfect linearization i e it introduces nonlinear additive terms in the transformed coordinates under some mild technical assumptions global convergence of the output error is established for all initial estimates of the parameter vector lying in an open neighborhood of the true parameters in the parameter space

fuzzy approximation adaptive fault tolerant control for nonlinear pure feedback systems with unknown control directions and sensor failures abstract in this paper the problem of adaptive fuzzy fault tolerant control ftc is investigated for a class of nonlinear pure feedback systems with unknown control directions and sensor failures by utilizing the mean value theorem the considered nonlinear pure feedback system is transformed into a strict feedback structure the unavailability of state variables caused by sensor faults is dealt with by using parameter separation and regrouping technique based on cancelation and decoupled backstepping technique an adaptive fuzzy fault tolerant control method is developed it is proved that the proposed adaptive ftc scheme can guarantee the exponential stabilization of the resulting closed loop system furthermore all the signals of the system remain semi global uniformly ultimately bound sguub the simulation results are provided to illustrate the effectiveness of the proposed control scheme

singular pdes and the single step formulation of feedback linearization with pole placement the present work proposes a new formulation and approach to the problem of feedback linearization with pole placement the problem under consideration is not treated within the context of geometric exact feedback linearization where restrictive conditions arise from a two step design method transformation of the original nonlinear system into a linear one in controllable canonical form with an external reference input and the subsequent employment of linear pole placement techniques in the present work the problem is formulated in a single step using tools from singular pde theory in particular the mathematical formulation of the problem is realized via a system of first order quasi linear singular pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the system of singular pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear state feedback law computed through the solution of the system of singular pdes both feedback linearization and pole placement design objectives may be accomplished in a single step effectively overcoming the restrictions of the other approaches by bypassing the intermediate step of transforming the original system into a linear controllable one with an external reference input

state feedback control of non linear systems a design method for state feedback controllers for single input non linear systems is proposed the method makes use of the transformations of the non linear system into controllable like canonical forms the resulting non linear state feedback is designed in such a way that the eigenvalues of the linearized closed loop model are invariant with respect to any constant operating point the method constitutes an alternative approach to the design methodology recently proposed by baumann and rugh also a review of different transformation methods for non linear systems is presented an example and simulation results of different control strategies are provided to illustrate the design technique

on the classification of regular holonomic d modules on skew symmetric matrices abstract we give a classification of regular holonomic d modules on 2 m 2 m skew symmetric matrices related to the action of the general linear group gl 2 m c actually we establish one more case of the conjecture by t levasseur levasseur 2009 12 p 508 conjecture 5 17

the capelli identity the double commutant theorem and multiplicity free actions 0 the capelli identity cal 3 w p 39 is one of the most celebrated and useful formulas of classical invariant theory w d cl z the double commutant theorem w p 91 is likewise a basic result in the general theory of associative algebras both play key roles in weyl s book the classical groups the main purpose of this paper is to demonstrate a close connection between the two in the context of multiplicity free actions ekj of groups on vector spaces the focus of our discussion will be the structure of the differential operators which commute with a multiplicity free action applications include a new derivation of some formulas of shimura shl and rubenthaler and schiffmann rs for b functions associated to hermitian symmetric spaces and a construction of interesting sets of generators for the center of the universal enveloping algebra of gin we also give a detailed discussion of certain aspects of multiplicity free representations here is an overview of the contents of the paper in sect 1 we review the classical capelli identities we observe how their existence is predicted by a double commutant result 1 6 and 1 8 and we show how they can be used to compute b functions we remark that capelli understood that his operators generate the center of the algebra generated by the polarization operators see b1 p 77 also capelli s motivation in introducing his operators was to explain a formula of cayley essentially the computation of a b function capelli s point of view was remarkably modern and structuralist in certain ways more modern even than that of weyl sections 2 through 9 provide a conceptual context for understanding the capelli identities as a feature of multiplicity free actions they contain a general discussion of the structure of g the algebra of polynomial coefficient differential operators which commute with a given group g of linear transformations the results of the discussion are summarized in theorem 9 1 which says in particular that the polynomial coefficient differential operators commuting with a

on a class of holonomic d modules on mn c related to the action of gln c gln c abstract we give an algebraic description of regular holonomic d modules whose characteristic variety is the union of conormal bundles to the orbits of the action of the general linear group on square matrices

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

observer based adaptive stabilization for a class of non linear systems abstract we determine via geometric conditions a class of single input single output non linear systems linear with respect to an unknown constant parameter vector which are globally stabilizable by an adaptive observer based control the only restriction on the non linearities is the dependence in suitable coordinates on the output only they are not restricted by sector or global lipschitz conditions when the parameter vector is known we obtain as a special case new sufficient conditions for global output feedback stabilization

direct adaptive control and robust analysis for unknown multivariable nonlinear systems with fuzzy logic systems in this paper we are dealing with the problem of controlling an unknown nonlinear dynamical system modeled by fuzzy logic systems in the ideal case of complete model matching convergence of the state to zero plus boundedness of all signals in the closed loop system is ensured moreover the robustness of the controller designed in the ideal case is given in the framework of singular perturbation theory

robust adaptive neural control for a class of perturbed strict feedback nonlinear systems this paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities the unknown nonlinearities comprise two types of nonlinear functions one naturally satisfies the triangularity condition and can be approximated by linearly parameterized neural networks while the other is assumed to be partially known and consists of parametric uncertainties and known bounding functions with the utilization of iterative lyapunov design and neural networks the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied the design method does not require a priori knowledge of the signs of the unknown virtual control coefficients leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural network approximation errors it is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed loop system signals the control performance can be guaranteed by an appropriate choice of the design parameters simulation studies are included to illustrate the effectiveness of the proposed approach

the 2 2 0 drazin inverse problem abstract we consider the additive drazin problem and we study the existence of the drazin inverse of a two by two matrix with zero 2 2 entry

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

nonlinear adaptive control of permanent magnet step motors abstract the problem of accurate positioning of permanent magnet step motors with sinusoidal flux distribution is considered on the basis of a nonlinear model containing six unknown parameters a nonlinear adaptive control is designed that guarantees asymptotic tracking of a desired angle reference signal feeding back the whole state measurements position speed and currents the algorithm may be used for preliminary on line identification of those parameters that do not vary during operation persistency of excitation conditions are given that guarantee identification with exponential convergence when the only unknown parameters are load torque and stator resistance which vary during operations persistency of excitation conditions are satisfied when stator currents are not zero in this case the adaptive control provides on line exponential parameter estimation and exponential tracking of desired position signals simulations show the performance of the adaptive algorithm and a comparison with pid control

a note on the representation for the drazin inverse of 2 2 block matrices abstract in this note we consider representations of the drazin inverse of 2 2 block matrices under conditions weaker than those used in recent papers on the subject in particular in d s djordjevic p s stanimirovic on the generalized drazin inverse and generalized resolvent czechoslovak math j 51 126 2001 617 634 r hartwig x li y wei representations for the drazin inverse of 2 2 block matrix siam j matrix anal appl 27 2006 757 771

neural networks based adaptive control for nonlinear time varying delays systems with unknown control direction this paper investigates a neural network nn state observer based adaptive control for a class of time varying delays nonlinear systems with unknown control direction an adaptive neural memoryless observer in which the knowledge of time delay is not used is designed to estimate the system states furthermore by applying the property of the function tanh2 e the function can be defined at 0 and introducing a novel type appropriate lyapunov krasovskii functional an adaptive output feedback controller is constructed via backstepping method which can efficiently avoid the problem of controller singularity and compensate for the time delay it is highly proven that the closed loop systems controller designed by the nn basis function property new kind parameter adaptive law and nussbaum function in detecting the control direction is able to guarantee the semi global uniform ultimate boundedness of all signals and the tracking error can converge to a small neighborhood of zero the characteristic of the proposed approach is that it relaxes any restrictive assumptions of lipschitz condition for the unknown nonlinear continuous functions and the proposed scheme is suitable for the systems with mismatching conditions and unmeasurable states finally two simulation examples are given to illustrate the effectiveness and applicability of the proposed approach

global robust stabilization of nonlinear cascaded systems this paper gives a sufficient condition for a class of nonlinear cascaded systems to be globally stabilizable via state feedback in the presence of uncertainty which does not necessarily satisfy the so called matching condition the authors result is an extension of the former stabilization results which treated systems without uncertainty in the sense that the uncertainty is taken into account

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 new method for linearizing non linear systems the pseudolinearization consider the single input non linear system x f x u it has been shown that under mild conditions there exist transformations z t x v s x u such that in the z space the linear tangent model is independent of the operating point a constructive procedure to obtain the above transformations is described this new method is computationally attractive and effective in many practical cases

on the extension of the korobov s class of linearizable triangular systems by nonlinear control systems of the class c1 abstract we give the complete description of nonlinear control systems of the class c 1 with one dimensional control which are feedback linearizable by means of a change of the control of the class c 1 and a change of variables of the class c 2 as well as the control systems which are linearizable by means of a change of variables only the both results are originated from the approach proposed by v i korobov in 1973 for the linearization of triangular control systems

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

an adaptive variable structure control for a class of nonlinear systems abstract motivated by the recent advance in adaptive output feedback control for a class of nonlinear systems which can be transformed into the so called output feedback form 7 10 11 an adaptive structure controller is proposed in this paper to solve the nonlinear model reference adaptive control problem it is shown that an asymptotic output tracking performance can be achieved for this class of nonlinear system even if some nonlinearity is not available or some unknown parameters are fast time varying

some additive results on drazin inverse some additive perturbation results for drazin inverses are given in particular a formula is given for the drazin inverse of a sum of two matrices when one of the products of these matrices vanishes some special applications of this are also considered

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 corrective feedback design for nonlinear systems with fast actuators recent two time scale results can be derived from a geometric framework which allows further extensions and computational improvements in this note the two time scale behavior of singularly perturbed systems is exploited to design slow and fast controls and to combine them into a composite control as an illustration we present a corrective design to compensate for fast actuator dynamics modeled as singular perturbations

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

d modules on representations of capelli type abstract let g v be an irreducible multiplicity free finite dimensional representation of a connected reductive complex group g as classified by v g kac 17 and g its derived subgroup denote by g the lie algebra of g and u g its universal enveloping algebra assume that there exists a polynomial f generating the algebra of g invariant polynomials on v c v g c f and such that f c v g such representations are said to be of capelli type if the algebra of g invariant differential operators is the image of the center of u g under the differential of the g action they fall into eight cases given by r howe and t umeda 14 five infinite families and three exceptional examples we prove that the category of regular holonomic d v modules invariant under the action of g is equivalent to the category of graded modules of finite type over a suitable algebra a except for few special cases indeed the levasseur s conjecture 28 conjecture 5 17 p 508 fails in these cases because of the disconnectedness of the stabilizers of some smaller orbits

higher order tracking properties of nonlinear adaptive control systems abstract while the asymptotic output tracking property has been proven for many nonlinear adaptive control systems their higher order output tracking property has not been reported in this paper the higher order derivative convergence of the output tracking error e t is studied for nonlinear adaptive control systems using the feedback linearization design it is proven that not only each error component e j t from e t e 1 t e 2 t e m t t converges to zero asymptotically but also its up to k th order time derivative e j k t converges to zero for k 1 2 j where j j 1 2 m are the control relative degrees of the nonlinear system with m inputs

exact and approximate feedback linearization without the linear controllability assumption the feedback linearization problem of nonlinear control systems has been solved in the literature under the assumption that the nonlinear system is linearly controllable in this paper the assumption of linear controllability is removed necessary and sufficient conditions are given through lie orbital symmetries thus giving a geometric characterization of the problem in the analytic case both the exact and the approximate linearization problems are considered in the analytic case

the representation and characterization of drazin inverses of operators on a hilbert space in this note the representation and characterization of drazin inverses of operators on a hilbert space are established

feedforward and feedback linearization of non linear systems with disturbances the problem of transforming non linear systems with input disturbances to their linear equivalents is investigated a characterization of the class of non linear systems with disturbances that are equivalent to controllable quasi linear systems with disturbances z az bv z d is given the necessary transformations state space coordinate changes and control input space coordinate changes by non linear feedforward and feedback are presented and their implications for control system synthesis are discussed finally a numerical example is given

global exact quadratization of continuous time nonlinear control systems we consider a class denoted by cal q of the nonlinear control systems which can be densely represented as a subsystem of a certain kind of quadratic system namely a quadratic target we say that a system in cal q undergoes a globally exact quadratization here globally adds up to a slight extension of the notion of c infty immersion of systems namely a dense immersion which amounts to saying that it is defined on the whole manifold of the system states except possibly a zero measure set it is proven that the class cal q includes all systems characterized by vector fields whose components are analytic integral closed form functions icffs the result is first proven for algebraic system functions by means of a constructive proof and next extended up to analytic icffs for nonanalytic icffs a weaker result is proven as well also the case of a partially observed system is considered as well as the internal structure of every quadratic representation which is proven to be alwa

robust switching adaptive control of multi input nonlinear systems during the last decade a considerable progress has been made in the design of stabilizing controllers for nonlinear systems with known and unknown constant parameters new design tools such as adaptive feedback linearization adaptive back stepping control lyapunov functions clfs and robust control lyapunov functions rclfs nonlinear damping and switching adaptive control have been introduced most of the results developed are applicable to single input feedback linearizable systems and parametric strict feedback systems these results however cannot be applied to multi input feedback linearizable systems parametric pure feedback systems and systems that admit a linear in the parameters clf in this paper we develop a general procedure for designing robust adaptive controllers for a large class of multi input nonlinear systems this class of nonlinear systems includes as a special case multi input feedback linearizable systems parametric pure feedback systems and systems that admit a linear in the parameters clf the proposed approach uses tools from the theory of rclf and the switching adaptive controllers proposed by the authors for overcoming the problem of computing the feedback control law when the estimation model becomes uncontrollable the proposed control approach has also been shown to be robust with respect to exogenous bounded input disturbances

feedback equivalence of control systems abstract cartan s method of equivalence is applied to the problem of equivalence of 2 state systems with scalar control under feedback the differential invariants produced by the method completely characterize equivalence classes the phenomenon of linearizability is associated with the presence of infinite lie pseudogroups the generic non linearizable case has a geometrically defined variational problem which yields a time optimal closed loop control

on categories of equivariant d modules abstract let x be a variety with an action by an algebraic group g in this paper we discuss various properties of g equivariant d modules on x such as the decompositions of their global sections as representations of g when g is reductive and descriptions of the categories that they form when g acts on x with finitely many orbits the category of equivariant d modules is equivalent to the category of finite dimensional representations of a finite quiver with relations we describe explicitly these categories for irreducible g modules x that are spherical varieties and show that in such cases the quivers are almost always representation finite i e with finitely many indecomposable representations

adaptive nn control for a class of discrete time non linear systems in this paper adaptive neural network nn control is investigated for a class of single input single output siso discrete time unknown non linear systems with general relative degree in the presence of bounded disturbances firstly the systems are transformed into a causal state space description adaptive state feedback nn control is presented based on lyapunov s stability theory then by converting the systems into a causal input output representation adaptive output feedback nn control is given finally adaptive nn observer design and observer based adaptive control are presented under the assumption of persistent excitation pe all the control schemes avoid the so called controller singularity problem in adaptive control by suitably choosing the design parameters the closed loop systems are proven to be semi globally uniformly ultimately bounded sguub simulation studies show the effectiveness of the newly proposed schemes

expression of the drazin and mp inverse of partitioned matrix and quotient identity of generalized schur complement in this paper we give representations of the drazin and mp inverse of a 2x2 block matrix and quotient identities for the generalized schur complement of a partitioned 3x3 matrix under conditions different than those used in recent papers on the subject we present numerical examples to illustrate our results

on time scaling for nonlinear systems application to linearization in this note we propose a method to analyze systems in a time scale which is varied depending on the state such as dt d tau s x where t and are the actual time scale and that of new one respectively and s x is the function which we call time scaling function analysis of the system in the new time scale enables us to investigate the intrinsic structure of the system a linearization problem in the new time scale is formulated as wide sense feedback equivalence and is solved it is also shown that the time scaling function which makes the system linear is derived as the solution of differential equations

global robust stabilization of minimum phase nonlinear systems with uncertainty the problem of global stabilization via state feedback is studied for a class of minimum phase nonlinear systems with unknown unmodelled time varying parameters or disturbances belonging to a given compact set sufficient conditions are presented for the existence of a robust stabilizing state feedback controller the controller is constructed explicitly by using a lyapunov based recursive design procedure the proposed feedback control law is a smooth function of the state and requires information of bounding functions on the size of uncertainties in the case where the disturbance signals represent only an unknown constant vector parameter and appear linearly in the system an adaptive controller is developed based on similar arguments achieving global stability with state regulation the main results of this paper incorporate and generalize a number of robust and adaptive control schemes for global stabilization of uncertain feedback linearizable systems without zero dynamics

on drazin inverse of operator matrices in this short paper we offer another formula for the drazin inverse of an operator matrix for which certain products of the entries vanish we also give formula for the drazin inverse of the sum of two operators under special conditions

some comments on global linearization of nonlinear systems it is shown that even in the case of a single input system on r 2 it will be rather difficult to find conditions sufficient to guarantee existence of a global linearization and that local conditions alone will definitely not be enough a class of examples which is fairly typical and it is hoped useful is discussed

solvability of certain quadratic operator equations and representations of drazin inverses abstract let e be a banach space b e be the set of bounded linear operators on e and i be the identity operator on e in this paper the solvability of the quadratic operator equations ax x 2 b and xa i xbx is studied where a b e is invertible and b b e is nilpotent it is proved that the first quadratic operator equation is solvable if furthermore ab ba or e c n for n 2 3 and b 2 0 a counterexample is given such that the second quadratic operator equation is unsolvable as an application in the general setting of bounded linear operators on banach spaces a new expression of the drazin inverse a b i 0 d is given under the condition that a b b e are drazin invertible and ab ba

a slow manifold approach to linear equivalents of nonlinear singularly perturbed systems abstract the problem of external feedback linearization of a nonlinear system into a linear controllable system has received considerable attention during the past few years in this paper the concept of slow manifold theory is applied to a class of nonlinear singularly perturbed systems to achieve external linearization for the full system via reduced order decompositions into exact slow and fast subsystems approximations to the exact state feedback and the control space transformation are obtained in particular by a specific choice of the manifold the same state space coordinate transformation can be utilized to approximate the exact solution the notion of weakly and strongly linearizable systems are introduced it is shown that if the system is weakly linearizable the state space coordinate transformation and the state feedback results in a high gain feedback control finally the notion of input output linearization and parasitic decoupling problem is introduced

robust semi global output tracking for nonlinear singularly perturbed systems in this work a robust controller design methodology for a broad class of singularly perturbed nonlinear systems with time varying uncertainties is developed when the fast subsystem is stabilizable and the slow subsystem is input output linearizable with input to state stable iss inverse dynamics the developed state feedback controller guarantees boundedness of the trajectories of the closed loop system and robust output tracking with arbitrary degree of asymptotic attenuation of the effect of uncertainty on the output for initial conditions and uncertainties in an arbitrarily large compact set so long as the singular perturbation parameter is sufficiently small the controller is a continuous function of the state of the system and its construction requires the knowledge of bounding functions on the size of uncertainty the developed method is applied to a non isothermal continuous stirred tank reactor with fast jacket dynamics

on the drazin inverse of an anti triangular block matrix in this paper we characterize the drazin invertibility of a two by two matrix with zero 2 2 entry under some suitable similarity transformation the results can be applied to obtain detailed drazin inverse formulae of various structured matrices and some special cases are analyzed

on the largest feedback linearizable subsystem abstract a feedback invariant set of integers is associated with any nonlinear multivariable system which is linear with respect to the inputs it is shown to be the set of controllability indices of the largest feedback linearizable subsystem i e the largest subsystem which can be made locally linear and controllable by means of nonsingular feedback transformations

state observers and state feedback controllers for a class of non linear systems a design methodology for observers and controllers for a class of single input single output non linear systems is developed a non linear observer form is defined and a corresponding observer using non linear observer gains is specified the resulting error dynamics which are non linear are asymptotically stable for a proper choice of those gains and bounded inputs and outputs a non linear controller form is defined and a corresponding controller which results in linear closed loop dynamics with arbitrary eigenvalue placement is devised transformations from the class of interest to the defined forms are derived in the observer case the transformation to the observer form and the non linear entries in the state matrix of that form can be determined separately leading to a system of linear partial differential equations a major simplification in the controller case a simple well known system of linear partial differential equations is obtained the efficacy of the developed methodology is sho

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

invariant hyperfunction solutions to invariant differential equations on the space of real symmetric matrices the real special linear group of degree n naturally acts on the vector space of n n real symmetric matrices how to determine invariant hyperfunction solutions of invariant linear differential equations with polynomial coefficients on the vector space of n n real symmetric matrices is discussed in this paper we prove that every invariant hyperfunction solution is expressed as a linear combination of laurent expansion coefficients of the complex power of the determinant function with respect to the parameter of the power then the problem is reduced to the determination of laurent expansion coefficients

the differential geometric structure of general mechanical systems from the lagrangian point of view several differential geometric points of view on analytical mechanics of systems with a finite number of degrees of freedom are developed in generality emphasizing cartan s calculus of differential forms and ehresmann s theory of jet spaces the classical theory of lagrange s equations with external forces and constraints holonomic or nonholonomic is put into an invariant and coordinate free form the relation between this lagrangian and the hamiltonian symplectic approach which is that most extensively used in the contemporary mathematical physics literature is also developed

fuzzy adaptive control of multivariable nonlinear systems abstract the robust fuzzy adaptive control scheme is developed for a class of unknown nonlinear mimo systems two types of uncertainties are considered i e the matched uncertainty and the unmatched uncertainties in the control procedure fuzzy logic systems are implemented to estimate the unknown functions and robust compensators are designed in h sense for attenuating the unmatched uncertainties it is shown that the proposed control is continuous guarantees global stability and the h performance index extensive simulations on the tracking control of a two link rigid robotics manipulator verify the effectiveness of the proposed algorithms

trigonometric rbf neural robust controller design for a class of nonlinear system with linear input unmodeled dynamics considered both the situation with unknown control function matrices and the situation with linear unmodeled input dynamics adaptive neural robust controller was designed by using adaptive backstepping method for a class of multi input to multi output nonlinear systems which could be turned to standard block control type it was proved by constructing lyapunov function step by step that all signals of the system are bounded and exponentially converge to the neighborhood of the origin globally and by adopting the trigonometric function as basis function the input need not be force to between 1 and 1 and there is no need to choose the centre of basis function which reduced the difficulty of doing simulation and made the neural net work more practical and the variable structure control is adopt to eliminate the error of approximation also the method of differential reconstruction of neural network is used to increase the damp of neural network and it makes the system more stable finally simulation study is given to demonstrate that the proposed method is effective and the known information of system was made use of as maximally as possible by introducing the pid control

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

global transformations of nonlinear systems recent results have established necessary and sufficient conditions for a nonlinear system of the form dot x t f x t u t g x t with f 0 0 to be locally equivalent in a neighborhood of the origin in rnto a controllable linear system we combine these results with several versions of the global inverse function theorem to prove sufficient conditions for the transformation of a nonlinear system to a linear system in doing so we introduce a technique for constructing a transformation under the assumptions that g ldot f dotg ad n 1 f ldotg span an n dimensional space and that g ldot f ldot g ad n 2 f ldotg is an involutive set

mathcal d modules on a representation of sp 2n mathbb c times gl 2 mathbb c we give an algebraic classification of holomorphic regular holonomic mathcal d modules on mathbb c 2n 2 related to the action of the group sp 2n mathbb c times gl 2 mathbb c product of the symplectic linear transformations group by the general linear group

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

an extended direct scheme for robust adaptive nonlinear control abstract the proposed adaptive scheme achieves regulation for a class of nonlinear systems with unknown constant parameters and unmodeled dynamics the scheme does not employ overparametrization and does not restrict the class of nonlinearities by any growth conditions instead the dependence on the unknown parameters is restricted by an extended matching condition which however is satisfied in many systems of practical importance such as most types of electric motors

adaptive fuzzy tracking control of nonlinear time delay systems with unknown virtual control coefficients in this paper a novel adaptive fuzzy control scheme is proposed for a class of uncertain single input and single output siso nonlinear time delay systems with the lower triangular form fuzzy logic systems are used to approximate unknown nonlinear functions then the adaptive fuzzy tracking controller is constructed by combining lyapunov krasovskii functionals and the backstepping approach the proposed controller guarantees uniform ultimate boundedness of all the signals in the closed loop system while the tracking error converges to a small neighborhood of the origin an advantage of the proposed control scheme lies in that the number of adaptive parameters is not more than the order of the systems under consideration finally simulation studies are given to demonstrate the effectiveness of the proposed design scheme

formulas for the drazin inverse of special block matrices properties of the drazin inverse of the matrix f iie0 with e square are investigated based on this approach it is obtained an explicit formula for the drazin inverse of matrices of the form a ip tquv t where u v p and q are nxk the representation for a d is given in terms of kxk matrices involving the individual blocks under some conditions some special cases are also analyzed

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

adaptive fuzzy tracking control for a class of perturbed strict feedback nonlinear time delay systems this paper is concerned with the problem of adaptive fuzzy output tracking for a class of perturbed strict feedback nonlinear systems with time delays and unknown virtual control coefficients fuzzy logic systems in mamdani type are used to approximate the unknown nonlinear functions then the adaptive fuzzy tracking controller is designed by using the backstepping technique and lyapunov krasovskii functionals the proposed adaptive fuzzy controller guarantees that all the signals in the closed loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal an advantage of the proposed control scheme lies in that the number of the online adaptive parameters is not more than the order of the original system finally two examples are used to demonstrate the effectiveness of our results proposed in this paper

adaptive dynamical feedback regulation strategies for linearizable uncertain systems abstract in this paper we address the design of adaptive dynamical feedback strategies of the continuou s and discontinuous types for the output stabilization of nonlinear systems the class of systems considered corresponds to nonlinear controlled systems exhibiting linear parametric uncertainty dynamical feedback controllers ideally achieving output stabilization via exact linearization are obtained by means of repeated output differentiation and either pole placement or sliding mode control techniques the adaptive versions of the dynamical stabilizing controllers are then obtainable through standard direct overparamemzed adaptive control strategies available for linearizable systems illustrative examples are provided which deal with the regulation of electro mechanical systems keywordk exact linearization adaptive control variable structure systemls electromechanical systems preferre d mailing address dr hebertt sira ramirez avenida la s ambricas edificio residencias el roble piso 6 apartamento d 6 mdrida 5101 venezuela this work was supported by the consejo de desarrollo cientifico humanistico y tecnol6gico of the universid ad de los andes mdrida venezulea under research grant 1 325 90 and by a grant from shin meiwa industries japan

asymptotic linearization on uncertain systems by variable structure control abstract a nonlinear control system with uncertain dynamics described by a single ordinary differential equation with scalar control and available state is given based on knowledge of upper and lower estimates of the unknown dynamics we show that the system can be transformed to an asymptotically equivalent linear model arbitrarily fixed described by a single linear ordinary differential equation of the same order by using an explicitly described discontinuous feedback control law of variable structure type the linear behaviour is obtained up to an arbitrarily fast exponentially decaying error term

some results on the 2 2 0 drazin inverse problem abstract in this paper we shall examine an additive problem of existence and presentation of a b d in terms of d invertible ring elements a and b and their drazin inverses and we shall study the existence of the drazin inverse of a two by two matrix with zero 2 2 entry we partly solved a problem posed by patricio and hartwig 2012 22

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

deterministic feedback linearization girsanov transformations and finite dimensional filters the problem of extending state feedback linearization methods of deterministic control theory to stochastic systems is addressed for stratonovitch stochastic differential equations with smooth vector fields necessary and geffucient geometric conditions for local and global linearization by diffeomorphism and absolutely continuous change of probability law are obtained using the interpretation of girsanov transformations as state feedback on brownian motions for stochastic systems with single with single input or onde dimensional brownian motion and single output or one dimensional observation process necessary and sufficient geometric conditions to transform the duncan mortensen zakai dmz equation of filtering into that of an affine prime system are obtained as well as interpretation of gauge transformation as girsanov change of probability law

delay estimation based adaptive fuzzy memory control for a class of uncertain nonlinear time delay systems abstract this paper is concerned with the problem of adaptive fuzzy memory control for a class of uncertain nonlinear systems with unknown time delays compared with the existing results the restrictions on the time delayed functions are overcome and the unknown delay parameters are estimated by establishing the piecewise adaptive laws based on the delay estimations and the backstepping technique a novel adaptive fuzzy memory output feedback controller is designed for the analysis of stability the cubic lyapunov functions with absolute value are constructed it is proved that the proposed control scheme can guarantee that all the signals in the closed loop system are bounded and the tracking error converges to a small neighborhood of the origin two practical simulation examples are given to demonstrate the effectiveness of the proposed control scheme

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

a simplified adaptive neural network prescribed performance controller for uncertain mimo feedback linearizable systems in this paper the problem of deriving a continuous state feedback controller for a class of multiinput multioutput feedback linearizable systems is considered with special emphasis on controller simplification and reduction of the overall design complexity with respect to the current state of the art the proposed scheme achieves prescribed bounds on the transient and steady state performance of the output tracking errors despite the uncertainty in system nonlinearities contrary to the current state of the art however only a single neural network is utilized to approximate a scalar function that partly incorporates the system nonlinearities furthermore the loss of model controllability problem typically introduced owing to approximation model singularities is avoided without attaching additional complexity to the control or adaptive law simulations are performed to verify and clarify the theoretical findings