brief freedom in coordinate transformation for exact linearization and its application to transient behavior improvement this paper deals with the use of extra freedom in the exact linearization technique firstly the freedom in choosing the coordinate transformation and nonlinear state feedback for the exact linearization is clarified secondly a controller design strategy for the transient behavior improvement in the presence of impulsive disturbances is shown finally numerical and experimental examples exhibit the effectiveness of this method

statistical densities cumulatives quantiles and power obtained by s system differential equations abstract a comprehensive approach for the analysis of statistical univariate distributions is advanced the method is based on recasting a distribution in a canonical set of first order nonlinear differential equations called an s system in which the derivative of each variable equals a difference of products of power law functions the recasting techniques are illustrated with some examples from central and noncentral probability distributions the density and the cumulative because of their close relationship can be simultaneously evaluated within one s system a simple inversion procedure permits the calculation of quantiles when in addition a noncentral distribution and its central counterpart are represented in one s system the power function and the inverse power function are obtainable given a set of initial conditions any differential equation solver can generate the desired solution particularly convenient and efficient is the program essyns designed specifically to solve and analyze s

the zero dynamics form for nonlinear differential algebraic systems we show that any nonlinear differential algebraic system can be locally transformed into zero dynamics form which is a normal form with respect to the input output behavior only mild assumptions on the maximal output zeroing submanifold are required and thus the zero dynamics form even generalizes the byrnes isidori form for nonlinear systems with existing vector relative degree left and right invertibility of the system can be studied in terms of the solution properties of a subsystem in the zero dynamics form this is the basis for the investigation of various classical control problems such as output regulation and trajectory tracking

feedback stabilization of planar nonlinear systems abstract the stabilization of second order control systems by smooth state feedback is addressed a reduction procedure proposed in 8 is applied in order to reduce the problem to the stabilization of a first order control system by a c 2 feedback function generic sufficient conditions are given for the solution of the last problem and by the reduction procedure of the first problem as well counter examples show that the conditions are not necessary and which kind of pathologies may arise

output tracking control of nonlinear systems with mismatched uncertainties abstract this paper addresses the output tracking problem of a class of nonlinear systems given input output linearizability of the class of nonlinear systems a robust output tracking controller derived via a lyapunov based approach is proposed here the model uncertainties do not need to satisfy the conventional matching condition but states and tracking error remain bounded furthermore the magnitude of the tracking error will bear dominant dependence on the magnitude of the mismatched uncertainties

periodic orbits from spl delta modulation of stable linear systems the spl delta modulated control of a single input discrete time linear stable system is investigated the modulation direction is given by c sup t x where c spl isin r sup n spl bsol 0 is a given otherwise arbitrary vector we obtain necessary and sufficient conditions for the existence of periodic points of a finite order some concrete results about the existence of a certain order of periodic points are also derived we also study the relationship between certain polyhedra and the periodicity of the spl delta modulated orbit

passivity and absolute stabilization of a class of discrete time nonlinear systems abstract by using the theory of discrete time passive systems and the concept of feedback equivalence we present an approach toward deriving sufficient conditions for the global stabilization of discrete time nonlinear systems in the form x k 1 tf x k g x k u k the central feature of the approach is that a unifying set of stability criteria can be obtained and the stability results recover the previous stabilization schemes proposed in the literature

the walsh basis in the lp spaces of hyperfinite iiiλ factors 0 λ 1 abstract we introduce a non commutative walsh system and prove that it forms a schauder basis in the l p spaces 1 p associated with the hyperfinite iii factors 0 1

controlled invariance for nonlinear differential algebraic systems we study the concept of locally controlled invariant submanifolds for nonlinear differential algebraic descriptor systems in contrast to classical approaches we define controlled invariance as the property of solution trajectories to evolve in a given submanifold whenever they start in it it is then proved that this concept is equivalent to the existence of a feedback which renders the closed loop vector field invariant in the descriptor sense this result is exploited to show that the outcome of the differential algebraic version of the zero dynamics algorithm yields a maximal output zeroing submanifold the latter is then used to characterize the zero dynamics of the system in order to guarantee that the zero dynamics are locally autonomous i e locally resemble the behavior of an autonomous dynamical system sufficient conditions involving the locally maximal output zeroing submanifold are derived

output feedback stabilization the stabilization of control systems using output feedback is addressed necessary and sufficient lyapunov conditions are established generalizing the artstein s stabilization theorem for linear control systems a necessary and sufficient lyapunov condition is provided for stabilization by means of a linear output feedback law

colp spaces the local structure of non commutative lp spaces abstract developing the theory of col p spaces a variation of the non commutative analogue of l p spaces we provide new tools to investigate the local structure of non commutative l p spaces under mild assumptions on the underlying von neumann algebras non commutative l p spaces with grothendieck s approximation property behave locally like the space of matrices equipped with the p norm of the sequences of their singular values as applications we obtain a basis for non commutative l p spaces associated with hyperfinite von neumann algebras with separable predual von neumann algebras generated by free groups and obtain a basis for separable nuclear c algebras

nonlinear control via approximate input output linearization the ball and beam example approximate input output linearization of nonlinear systems which fail to have a well defined relative degree is studied for such systems a method for constructing approximate systems that are input output linearizable is provided the analysis presented is motivated through its application to a common undergraduate control laboratory experiment the ball and beam where it is shown to be more effective for trajectory tracking than the standard jacobian linearization

bounded input bounded output stabilization of nonlinear systems using state detectors abstract this paper is devoted to the study of relations between lyapunov stabilization and bounded input bounded output bibo stabilization of nonlinear systems when the state is not available for measurement and various state detectors are employed for implementing feedback control it is found that with some constraints imposed on the detectors lyapunov stabilization implies bibo stabilization a feedback control scheme for achieving bibo stability is presented

on normal forms of nonlinear systems affine in control the nonlinear equivalences of both finite and infinite zero structures of linear systems have been well understood for single input single output systems and have found many applications in nonlinear control theory the extensions of these notions to multiple input multiple output systems have proven to be highly sophisticated in this paper we propose constructive algorithms for decomposing a nonlinear system that is affine in control these algorithms require modest assumptions on the system and apply to general multiple input multiple output systems that do not necessarily have the same number of inputs and outputs they lead to various normal form representations and reveal the structure at infinity the zero dynamics and the invertibility properties all of which represent nonlinear equivalences of relevant linear system structural properties

δ modulated feedback in discretization of sliding mode control modulated feedback control introduces periodicity the global attracting property of the periodic points is established for a simple scalar discrete time system under d modulated feedback attracting regions of the periodic points are also characterized when the discretization effects of the equivalent control based sliding mode control systems are studied we show that the zero order hold discretization gives rise to d modulation in the sliding mode direction the global attracting property of d modulated feedback offers a vivid illustration of the way sliding is achieved interestingly we find that a zoh discretization scheme of the equivalent control based sliding mode control system with relative degree one results in only 2 periodic orbits

output feedback stabilization of uncertain plants a variable structure systems approach the problem of output stabilization for uncertain s1so systems is considered using structural transformations uncertain systems can change to the form convenient for output feedback design synthesis of observer based variable structure control for asymptotical stabilization or uniform ultimate boundedness of the closed loop system is provided examples are considered and simulation results are given

euler s discretization of single input sliding mode control systems in this note the dynamical behaviors of euler s discretization of the equivalent control based sliding mode control smc systems are studied we show that if the discretized smc system is asymptotically stable then every trajectory converges to a period 2 cycle bounds for the steady states are derived which allow one to estimate the maximum chattering amplitude for a given value of the time step the analysis and results are verified with several computer simulations

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

regulation of relaxed static stability aircraft the authors formulate and solve a regulator problem for nonlinear parameter dependent dynamics it is shown that the problem is solvable except at parameter values associated with bifurcation of the equilibrium equations and that such bifurcations are inherently linked to the system zero dynamics these results are applied to the study of the regulation of the longitudinal dynamics of aircraft it is shown how bifurcation points arise in these problems and why they affect solvability of the regulator problem the relationships between bifurcation system zeros and dynamic and static stability are illustrated

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

control and stabilization of nonholonomic dynamic systems a class of inherently nonlinear control problems has been identified the nonlinear features arising directly from physical assumptions about constraints on the motion of a mechanical system models are presented for mechanical systems with nonholonomic constraints represented both by differential algebraic equations and by reduced state equations control issues for this class of systems are studied and a number of fundamental results are derived although a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback a general procedure for constructing a piecewise analytic state feedback which achieves the desired result is suggested

variable structure regulation of partially linearizable dynamics it is shown how the theory of decoupling and partial linearization of nonlinear affine systems can enhance the design of variable structure control systems and expand their range of applicability refined insights into the design of nonlinear switching surfaces and a new regular form are obtained application to an adjustable speed induction motor drive illustrates how this method allows stabilization of a periodic attractor

zero dynamics of sampled nonlinear systems abstract the behaviour of the zero dynamics of a discrete time system obtained when sampling a continuous time nonlinear system is studied we give a result which generalizes the known behaviour of the zeros of a sampled linear system for small time intervals

discretization behaviors of equivalent control based sliding mode control systems in this note discretization behaviors of the equivalent control based sliding mode control smc systems are studied some inherent dynamical properties of the discretized second order systems are first explored upper bounds for the system steady states are established the system s steady state behaviors are discussed the analysis for the second order systems is then extended to higher order systems simulations are presented to verify the theoretical results

optimal controllers and output feedback stabilization abstract in this paper the output feedback stabilizability problem is explored in terms of control lyapunov functions sufficient conditions for stabilization are provided for a certain class of systems by means of output feedback stabilizers that can be obtained from an optimization problem our main results extends those developed in 31 and generalize a theorem due to sontag 23

nonlinear control via uniform system approximation abstract we introduce the notion of uniform system approximation and use it to solve the following problem given a single input nonlinear system f g x f x g x u that is linearly controllable on a manifold e of equilibrium points find vector fields f g such that f g and f g agree to first order on e and f g is input to state linearizable on a neighborhood of e the solution proceeds by constructing a linearizable uniform system approximation and yields as a by product a feedback control law that can be used to guarantee stable operation of the given system in a neighborhood of e this includes for example smooth transitions between operating points that are not necessarily close to each other a simple example is given to illustrate the approach

semi global stabilization of partially linear composite systems via feedback of the state of the linear part abstract we consider the problem of semi global stabilization of a class of partially linear composite systems we show by explicit construction of the control laws that a cascade of linear stabilizable and nonlinear asymptotically stable subsystems is semi globally stabilizable by a dynamic feedback of the state of the linear subsystem if a the linear subsystem is right invertible and has all its invariant zeros in the closed left half s plane and b the only linear variables entering the nonlinear subsystem are the output of the linear subsystem our work generalizes previous results by c i byrnes and a isidori 1991 h j sussmann and p v kokotovic 1991 and a r teel 1992

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

single boundary control of the two phase stefan system abstract this paper presents the control design of the two phase stefan problem the two phase stefan problem is a representative model of liquid solid phase transition by describing the time evolutions of the temperature profile which is divided by subdomains of liquid and solid phases as the liquid solid moving interface position the mathematical formulation is given by two diffusion partial differential equations pdes defined on a time varying spatial domain described by an ordinary differential equation ode driven by the neumann boundary values of both pde states resulting in a nonlinear coupled pde ode pde system we design a state feedback control law by means of energy shaping to stabilize the interface position to a desired setpoint by using single boundary heat input we prove that the closed loop system under the control law ensures some conditions for model validity and the global exponential stability estimate is shown in the spatial l 2 norm furthermore the robustness of the closed loop stability with respect to the uncertainties of the physical parameters is shown numerical simulation is provided to illustrate the desired performance of the proposed control law in comparison to the control design for the one phase stefan problem

decoupling with dynamic compensation for strong invertible affine non linear systems abstract in this paper we tackle for affine non linear systems the morgan problem i e the scalar input scalar output decoupling problem for square systems with dynamic compensation the result provided here theorem 3 1 generalizes that one previously given by wang 1970 for linear systems

feedback stabilization of control systems described by a class of nonlinear differential algebraic equations a theoretical framework for the stabilization of con trol systems defined by a class of nonlinear differential alge braic equations is established assumptions are stated which guarantee that the nonlinear differential algebraic equations can be described by a nonlinear control system defined on a smooth manifold a procedure for obtaining a local state realization is developed conditions for local stabilization of a single equilibrium solution including one set of conditions which can easily be checked using standard computations are indicated

stabilizability of nonholonomic control systems abstract we consider here the problem of stabilization of nonlinear hamiltonian control systems with nonholonomic constraints such systems are of interest in various applications including the control of robotic systems we discuss the formulation of hamiltonian systems with nonholonomic constraints in particular considering the differences between the dirac theory of constraints the classical theory of nonholonomic constraints and weber s theory of generalized nonholonomic constraints stabilization of systems with these constraints is discussed using the theory of hamiltonian control systems and a reduced stabilization criterion is given

normal form for linear systems with respect to its vector relative degree for multi input multi output mimo linear systems with existing vector relative degree a normal form is constructed this normal form is not only structural simple but allows to characterize the system s zero dynamics for the design of feedback controllers a characterization of the zero dynamics in terms of the normal form is given

output input stability implies feedback stabilization abstract we study the recently introduced notion of output input stability which is a robust variant of the minimum phase property for general smooth nonlinear control systems this paper develops the theory of output input stability in the multi input multi output setting we show that output input stability is a combination of two system properties one related to detectability and the other to left invertibility for systems affine in controls we derive a necessary and sufficient condition for output input stability which relies on a global version of the nonlinear structure algorithm this condition leads naturally to a globally asymptotically stabilizing state feedback strategy for affine output input stable systems

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

les espaces lp d une algebre de von neumann definies par la derivee spatiale abstract this work answers a question raised by a connes on the spatial theory of von neumann algebras preprint inst hautes etudes sci france and generalizes for a general von neumann algebra the theory of non commutative integration of j dixmier bull soc math france 81 1953 and i segal ann of math 57 1973

an alternative derivation of the modified gain function of song and speyer a simpler derivation of the modified gain function for the bearings only measurement problem as defined by t l song et al see ibid vol ac 30 no 30 1985 is presented the form which results show the relationship between the modified gain and the standard gain the relationship between the modified gain and the standard gain of an extended kalman filter is shown it is confirmed that the modified gain extended kalman filter performs better than the standard extended kalman filter

applications of the complex interpolation method to a von neumann algebra non commutative lp spaces non commutative lp spaces 1 p associated with a von neumann algebra are considered the paper consists of two parts in part i by making use of the complex interpolation method non commutative lp spaces are defined as interpolation spaces between the von neumann algebra in question and its predual also all expected properties such as duality and uniform convexity are proved in the frame of interpolaton theory and relative modular theory in part ii these lp spaces are compared with haagerup s lp spaces based on this comparison a non commutative analogue of the classical stein weiss interpolation theorem is obtained

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

local stabilization of minimum phase nonlinear systems abstract in this note we briefly review the notion of a nonlinear minimum phase system i e a system which when constrained in such a way as to produce zero output evolves with an asymptotically stable dynamics the main purpose of the paper is to show that any minimum phase nonlinear system can always be locally stabilized by smooth state feedback

s system modelling of endemic infections abstract infectious diseases often exhibit complex dynamics that can only be understood when analyzed with mathematical models these models are typically nonlinear which makes it difficult to compare their mutual merits it is shown how models for infectious diseases can be objectively compared upon representing them as special cases of a canonical form for nonlinear functions and differential equations called an s system besides comparison and classification this form allows natural generalizations of existing models and the objective evaluation of model extensions a variety of methods facilitate the analysis of infectious disease models in s system form

on tracking control for affine nonlinear systems by sliding mode abstract the stability problem of output tracking of a bounded time varying reference by decouplable affine nonlinear systems using sliding mode control is investigated it is shown that when the error dynamics on the sliding surface is chosen to be linear time invariant closed loop stability of systems under the presented sliding mode control can be guaranteed only if the systems are minimum phase

inner outer factorization for nonlinear noninvertible systems this paper considers inner outer factorization of asymptotically stable nonlinear state space systems in continuous time that are noninvertible our approach will be via a nonlinear analogue of spectral factorization which concentrates on first finding the outer factor instead of the inner factor an application of the main result to control of nonminimum phase nonlinear systems is indicated

robust output tracking control of nonlinear mimo systems via sliding mode technique abstract the robust output tracking control problem of general nonlinear multi input multi output mimo systems is discussed the robustness against parameter uncertainties and unknown disturbances is considered a second order sliding mode control smc technique is used to establish the desired tracking input output i o linearization relative degree minimum phase and matching condition concepts are reviewed some earlier smc strategies which are restricted to the systems in canonical form are extended to a much broader class of nonlinear dynamics it is also shown that for unperturbed dynamics the sliding phase of the smc applications have a direct correspondence to the i o linearization operations interesting parametric flexibilities emanate within the formation of the second order smc designating the s dynamics and the error dynamics segments as frequency domain filters however a critical impasse is posed in the off line selections of the design parameters a set of example cases is presented for a spacecraft attitude control problem these examples manifest that the proposed control strategy is tunable to a desired response despite the disturbances and uncertainties

global stabilization of a certain class of nonlinear systems abstract systems are considered which can be reduced to a regular form and possess an invariant manifold such that the restriction of the system to the manifold is globally asymptotically stable gas we construct a feedback which renders the manifold globally attracting it was proved that in this situation boundedness of all orbits is necessary and sufficient for the control system to be gas a lyapunov type condition for the latter property adapted to the situation in question is given results of andreini bacciotti and stefani are shown to be a special case of our result

on the inversion of a class of nonlinear systems this paper deals with the inversion problem of affine square multi input multi output mimo nonlinear systems it presents a new algorithm unifying the construction of the inverse of a dynamical system with a regular or a singular characteristic matrix this algorithm is based on the determination of a projector on the fibre bundle of the state space and incorporates a regularization of the singular case it has the advantage of avoiding the input derivatives numerical examples are given to illustrate the proposed approach

on p normal forms of nonlinear systems using the differential geometric control theory we present in this note a necessary and sufficient condition under which an affine system is locally feedback equivalent to via a change of coordinates and restricted smooth state feedback a generalized normal form called p normal form which includes brunovsky canonical form and feedback linearizable systems in a lower triangular form as its special cases we also give an algorithm for computing the appropriate coordinate transformations and feedback control laws

2d universality of period doubling bifurcations in 3d conservative reversible mappings abstract infinite sequences of period doubling bifurcations are known to occur generically i e with codimension 1 not only in dissipative 1d systems but also in 2d conservative systems described by area preserving mappings in this paper we study a 3d volume preserving reversible mapping and show that it does possess period 2 m m 1 2 orbits with stability intervals whose length decreases rapidly with increasing m varying one parameter of the system we find that these orbits always bifurcate out of one another with the usual stability exchange and universal properties of period doubling sequences of 2d conservative maps this raises the interesting question whether these 3d reversible maps possess an analytic integral which would render them essentially 2 dimensional

non linear predictive control by inversion discontinuities for critical behaviour the predictive control by inversion pci technique is presented in this paper this technique permits extending in a simple way the predictive control principles to non linear models without any linearizing transformation singularities and non minimum phase phenomena which can arise from inversion are treated by introducing control discontinuities either directly on the control or some of its derivatives or indirectly through reference trajectory discontinuities performance and robustness properties of the technique are illustrated by several simulation results

efficient solution of nonlinear ordinary differential equations expressed in s system canonical form ordinary differential equations can be recast into a nonlinear canonical form called an s system evidence for the generality of this class comes from extensive empirical examples that have been recast and from the discovery that sets of differential equations and functions recognized as among the most general are special cases of s systems identification of this nonlinear canonical form suggests a radically different approach to numerical solution of ordinary differential equations by capitalizing on the regular structure of s systems efficient formulas for a variable order variable step taylor series method are developed the minimum improvement in efficiency over conventional runge kutta methods is shown to be more than 20 to 60 percent for equations expressed in s system form tests with implemented methods demonstrate that 10 to 100 fold reductions in time are actually realized for solution of s systems to examine the potential benefit of recasting ordinary differential equations and then sol

global stabilization of nonlinear cascade systems abstract we present sufficient conditions for the global stabilizability of two cascade connected nonlinear systems these are based on general results concerning global asymptotic stability of triangular systems which are proved in the last section for polynomial systems in particular the stabilizing feedback is given explicitly

interval propagation method for finding trajectories of chaotic maps the algorithm for calculation of trajectories of chaotic maps based on the interval analysis is proposed each of the image points is constrained by enclosing it in a corresponding interval improvement of one of the constraints results in the chain of adjustments of other interval bounds propagating along the trajectory eventually causing the constraints to converge no knowledge of well defined symbolic dynamics is necessary since the pruning rules and non uniqueness of the symbolic path are automatically resolved for cycles and fixed end orbits the algorithm provides linear uniform convergence the algorithm is demonstrated for the hamiltonian system where existence of both positive and negative lyapunov exponents allows introduction of a simple interval contracting procedure

a reduction method for noncommutative l_p spaces and applications we consider the reduction of problems on general noncommutative l p spaces to the corresponding ones on those associated with finite von neumann algebras the main tool is an unpublished result of the first named author which approximates any noncommutative l p space by tracial ones we show that under some natural conditions a map between two von neumann algebras extends to their crossed products by a locally compact abelian group or to their noncommutative l p spaces we present applications of these results to the theory of noncommutative martingale inequalities by reducing most recent general noncommutative martingale ergodic inequalities to those in the tracial case

a necessary condition for local asymptotic stability of nonlinear systems with exogenous disturbance local asymptotic stability of nonlinear systems with real parametric uncertainty or disturbance is one of the important problems in control systems literature in this paper we investigate this problem for nonlinear systems with time varying disturbance we assume that the disturbance vector is generated by an exosystem which is neutrally stable thus the disturbances that we consider include both constant and periodic signals for this class of nonlinear systems with time varying disturbance we derive a necessary condition for local asymptotic stability of equilibria as corollaries of our general result we deduce the necessary condition obtained by byrnes and sundarapandian 1 for nonlinear systems with constant real parametric uncertainty and the necessary condition obtained by brockett 2 for nonlinear autonomous systems we illustrate our result with several examples

asymptotic stabilization of minimum phase nonlinear systems how a class of multivariable nonlinear systems can be stabilized about an equilibrium via smooth state feedback is shown more precisely conditions under which for every compact set of initial states it is possible to design a feedback law which drives to the equilibrium all initial states in this compact set are described the theory includes the development of globally defined transformations of the system equations to their global normal form

output input stability and minimum phase nonlinear systems this paper introduces and studies the notion of output input stability which represents a variant of the minimum phase property for general smooth nonlinear control systems the definition of output input stability does not rely on a particular choice of coordinates in which the system takes a normal form or on the computation of zero dynamics in the spirit of the input to state stability philosophy it requires the state and input of the system to be bounded by a suitable function of the output and derivatives of the output modulo a decaying term depending on initial conditions the class of output input stable systems thus defined includes all affine systems in global normal form whose internal dynamics are input to state stable and also all left invertible linear systems whose transmission zeros have negative real parts as an application we explain how the new concept enables one to develop a natural extension to nonlinear systems of a basic result from linear adaptive control

a neural approach for control of nonlinear systems with feedback linearization several schemes for feedback linearization using neural networks have been investigated and compared then an approach to design a neurocontroller in the sense of feedback linearization is introduced the contents include 1 full input output linearization when a system has relative degree n 2 partial input output linearization when a system has relative degree r r n and 3 approximate linearization when the involutivity condition does not hold corresponding programs and examples are given to illustrate the proposed methodology

on static output feedback stabilization of systems with stable generalized zero dynamics in this note we define generalized zero dynamics introduce a generalized zero dynamics algorithm and give a sufficient condition which ensures stabilizability of linear systems with asymptotically stable generalized zero dynamics by static output feedback

stabilization of discrete time nonlinear systems by smooth state feedback abstract for a class of nonlinear discrete time systems of the form x k 1 x k g x k u k we investigate conditions under which a nonlinear system can be rendered globally asymptotically stable via smooth state feedback our main result is that any nonlinear system with lyapunov stable unforced dynamics can always be globally stabilized by smooth state feedback if suitable controllability like rank conditions are satisfied several examples are presented to demonstrate the applications of the stability results developed in this paper

high gain feedback in non linear control systems abstract high gain state and output feedback are investigated for non linear control systems with a single additive input by using singular perturbation techniques classical approximation results tihonov like theorems in singular perturbation theory are extended to non linear control systems by defining a composite additive control strategy a control dependent fast equilibrium manifold and non linear change of coordinates those tools and an appropriate change of coordinates show that high gain state feedback and variable structure control systems can be equivalently used for approximate non linearity compensation in feedback linearizable systems next the effect of high gain output feedback is shown to be related to the strong invertibility property and the relative order of invertibility for strongly invertible systems the slow reduced subsystem coincides with the dynamics of the inverse system when zero input is applied and with the unobservable dynamics when a certain input output feedback linear

asymptotic feedback stabilization a sufficient condition for the existence of control lyapunov functions abstract in this paper we study the feedback stabilization problem for a wide class of nonlinear systems that are affine in the control we offer sufficient conditions for the existence of control lyapunov functions that according to 3 23 and 28 30 guarantee stabilization at a specified equilibrium by means of a feedback law which is smooth except possibly at the equilibrium we note that the results of the paper present a local nature

nonlinear strong model matching the problem of matching a given input output behavior for systems described by general nonlinear differential equations is considered it is shown that by appropriately modifying the zero dynamics algorithm it is possible to obtain a simple necessary and sufficient condition for the solvability of the model matching problem which requires that the initial state be on an appropriate submanifold of the state space another condition necessary and sufficient for the solvability of the strong model matching problem is proposed this last condition is then related to an equality of a list of integers which under some regularity assumptions coincide with the algebraic structures at infinity of the process and of a composition of the process and the model the relation between these conditions and the equality of the algebraic structures at infinity of the process and the model is established

a necessary condition for local asymptotic stability of discrete time nonlinear systems with exogenous disturbance local asymptotic stability of nonlinear systems with real parametric uncertainty or disturbance is one of the important problems in the control systems literature in this paper we investigate the problem of asymptotic stability for discrete time nonlinear systems with time varying disturbance we assume that the disturbance vector is generated by an exosystem which is neutrally stable thus the disturbances that we consider include both constant and periodic signals for this class of nonlinear systems with time varying disturbance we derive a necessary condition for local asymptotic stability of equilibria as corollaries of our general result we deduce the necessary condition obtained by sundarapandian 1 for discrete time nonlinear systems with constant real parametric uncertainty and the necessary condition obtained by lin and byrnes 2 for discrete time nonlinear autonomous systems we illustrate our result with several examples

inversion of nonlinear time varying systems a procedure for inverting nonlinear systems that presents some computational advantages when applied to flexible robot arms or more generally to mechanical structures is given the procedure is presented in a general setting for nonlinear time varying systems an iterative algorithm that computes a smooth controlled invariant time varying manifold the mathematical properties of which are illustrated and exploited is also proposed an application to a flexible two link manipulator illustrates the algorithm and its computational advantages

on weak relative degree and the mcgehee transformation points where jumps in relative degree occur are presented as singularities in the vector field of the internal dynamics of systems that are candidates for input output linearization via nonlinear feedback for a certain class of vector fields it is shown that the point at which the relative degree is weak can be transformed to a saddle equilibrium point at the origin

brief paper zoh discretization effect on single input sliding mode control systems with matched uncertainties in this paper discretization behaviors of equivalent control based sliding mode control systems with matched uncertainties are studied upper bounds for system steady states are established some inherent dynamical periodic properties of the systems subject to matched constant and periodic uncertainties are explored simulations are presented to verify the theoretical results

an efficient method for locating and computing periodic orbits of nonlinear mappings abstract the accurate computation of periodic orbits of nonlinear mappings and the precise knowledge of their properties are very important for studying the behavior of many dynamical systems of physical interest in this paper we present an efficient numerical method for locating and computing to any desired accuracy periodic orbits stable unstable and complex of any period the method described here is based on the topological degree of the mapping and is particularly useful since the only computable information required is the algebraic signs of the components of the mapping this method always converges rapidly to a periodic orbit independently of the initial guess and is particularly useful when the mapping has many periodic orbits stable and unstable close to each other all of which are desired for the application we illustrate this method first on a two dimensional quadratic mapping used in the study of beam dynamics in particle accelerators to compute rapidly and accurately its periodic orbits of periods p 1 5 16 144 1296 10368 and then obtain periodic orbits of its four dimensional complex version for periods which also reach up to the thousands

dynamical behaviors of an euler discretized sliding mode control systems the dynamical behaviors of an euler discretized sliding mode control smc systems based on equivalent control strategy are studied a periodic 2 orbit in steady state is found for the switching function of the euler discretized smc systems the time steps for the switching function to converge toward the periodic 2 orbit are obtained when the discretized smc system is stable it further shows that the system states of the smc systems will also enter into some periodic 2 orbits and these periodic 2 orbits are characterized by explicit analytic expressions finally simulation examples are given to illustrate the theoretical results

noncommutative burkholder rosenthal inequalities we investigate martingale inequalities in noncommutative lp spaces associated with a von neumann algebra equipped with a faithful normal state we prove the noncommutative analogue of the classical burkholder inequality on the conditioned or little square function and extend the noncommutative burkholder gundy inequalities from comm math phys 189 1997 667 698 to this nontracial setting we include several related results

on sampled data models for nonlinear systems models for deterministic continuous time nonlinear systems typically take the form of ordinary differential equations to utilize these models in practice invariably requires discretization in this paper we show how an approximate sampled data model can be obtained for deterministic nonlinear systems such that the local truncation error between the output of this model and the true system is of order spl delta sup r 1 where spl delta is the sampling period and r is the system relative degree the resulting model includes extra zero dynamics which have no counterpart in the underlying continuous time system the ideas presented here generalize well known results for the linear case we also explore the implications of these results in nonlinear system identification

passivity and global stabilization of cascaded nonlinear systems an alternative stability analysis is presented for recent results on global stabilization of a nonlinear system in cascade with a linear system the analysis is carried out using passivity arguments the relationship between passivity and an important class of lyapunov function is also presented

generalized normal form and stabilization of non linear systems this paper considers the normal form of non linear control systems first we propose a generalized relative degree relative degree vector for non linear single respectively multiple input control system which is called the point relative degree respectively point relative degree vector for the systems without output the concepts of essential relative degree respectively essential relative degree vector and the essential point relative degree respectively essential point relative degree vector are defined unlike the classical definition which requires regularity the point relative degree vector is always well defined using these new concepts the generalized normal form is obtained its relationship with the jacobian linearization is investigated using it a straightforward computation algorithm is provided to achieve the generalized normal form based on the generalized normal form we prove that with an additional condition if the zero dynamics is stable the overall system is stabil

stabilization of minimum phase nonlinear systems by dynamic output feedback in this paper the stabilization problem of minimum phase nonlinear systems by dynamic output feedback is investigated it is shown that if the zero dynamics of an affine nonlinear system is asymptotically stable according to the kth approximation then the system is stabilizable by dynamic output feedback the proof is constructive which provides a method to design the stabilizer the result is applied to investigating the stabilization problem of the rotating stall in axial flow compressors

modular smoothing of action the central quantity in the theory of transport for hamiltonian systems and in particular the area preserving twist maps is the action of rotational periodic orbits usually this is a complicated discontinuous function of two arguments some perturbation parameter k and a rational rotation number denoted by we applied the idea of modular smoothing to this complicated fractal our main result is that all the information contained in the fractal can be retrieved from a set of continuous or smooth functions of one variable

mapping based algorithm for large scale computation of quasi polynomial zeros a method for computing all zeros of a retarded quasi polynomial that are located in a large region of the complex plane is presented the method is based on mapping the quasi polynomial and on utilizing asymptotic properties of the chains of zeros first the asymptotic exponentials of the chains are determined based on the distribution diagram of the quasi polynomial secondly large regions free of zeros are defined finally the zeros are located as the intersection points of the zero level curves of the real and imaginary parts of the quasi polynomial which are evaluated over the areas of the region outside those free of zeros

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

output tracking design of affine nonlinear plant via variable structure system an output tracking design for affine nonlinear systems via a variable structure system is proposed the structure algorithm is used to determine if the considered system is left invertible it is shown that if such a condition is satisfied then a sliding mode controller can be designed to achieve output tracking the decouplability condition in conventional approaches is now replaced by the weaker left invertibility condition stable tracking is guaranteed if the internal mode is bounded input bounded state stable simulation results are included to demonstrate the design procedure