on the antimaximum principle for the p laplacian with indefinite weight this paper is concerned with the antimaximum principle for the quasilinear prob 1 mathrm e mathrm m delta p u lambda m x u p 2 u h x delta p is the laplacian and m x is aweight function which may change sign we will in particular investigate the question of the uniformity of this principle and provide avariational characterization for the interval of uniformity an identity of picone s type for the mathrm p laplacian plays an important role in our approach

differential flatness of two one forms in arbitrary number of variables given a differentially flat system of odes flat outputs that depend only on original variables but not on their derivatives are called zero flat outputs and systems possessing such outputs are called zero flat in this paper we present a theory of zero flatness for a system of two one forms in arbitrary number of variables t x1 xn our approach splits the task of finding zero flat outputs into two parts first part involves solving for distributions that satisfy a set of algebraic conditions the second part involves finding an integrable distribution from the solution set of the first part typically this part involves solving pdes our results are also applicable in determining if a control affine system in n states and n 2 controls has flat outputs that depend only on states we illustrate our method by examples

smooth output feedback stabilization of planar systems without controllable observable linearization this note considers the problem of global stabilization by output feedback for a family of planar systems whose jacobian linearization is neither controllable nor observable the problem cannot be dealt with by existing output feedback design methods most of them are based on the separation principle under appropriate growth conditions we propose an output feedback control scheme that does not rely on the separation principle and achieves global asymptotic stabilization the novelty of our control scheme lies in the explicit design of a dynamic output compensator which combines a nonlinear gain observer design and the technique of adding a power integrator as a consequence an interesting global stabilization result by output feedback can be obtained for feedback linearizable systems in a triangular form which turns out to be new even in the two dimensional case

generalized controller canonical form for linear and nonlinear dynamics a generalized controller canonical form for linear and nonlinear dynamics is proposed it is obtained using the theorem of the primitive element from differential algebra the derivation of the controller form does not apply to multivariable constant linear systems with the transformations all nonlinear dynamics can be exactly linearized by dynamic feedback the main departure from standard theory is that transformations may depend on input derivatives once differential algebraic tools are introduced the proofs of the results are easy

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 bound on the number of integrators needed to linearize a control system this paper considers the problem of dynamic feedback linearization for nonlinear control systems for a restricted class of dynamic compensators that correspond to adding chains of integrators to the inputs we give an upper bound on the order of the compensator that needs to be considered in the case of 2 input systems we show that this bound is sharp

any controllable driftless system with 3 inputs and 5 states is flat abstract a very simple classification of pfaffian systems of dimension 2 in 5 variables is given it is used to show that any controllable driftless system with 3 inputs and 5 states is 0 flat and can be put into multi input chained form by dynamic feedback and coordinate change

feedback linearization and stabilization of second order non holonomic chained systems this paper presents a theoretical framework for non regular feedback linearization and stabilization of second order non holonomic chained systems by giving a new criterion for the problem of non smooth non regular feedback linearization it is proved that second order chained systems are non regular static state feedback linearizable a discontinuous control law is obtained based on linear system theory and the inversion technique the design mechanism is generalized to higher order non holonomic chained systems simulation studies are carried out to show the effectiveness of the approach

on feedback equivalence of nonlinear systems conditions are derived under which a given system can be modified by means of feedback to obtain a new system whose output is influenced only by a linear and controllable dynamics

a necessary condition for dynamic equivalence if two control systems on manifolds of the same dimension are dynamic equivalent we prove that either they are static equivalent i e equivalent via a classical diffeomorphism or they are both ruled for systems of different dimensions the one of higher dimension must be ruled a ruled system is one whose equations define at each point in the state manifold a ruled submanifold of the tangent space dynamic equivalence is also known as equivalence by endogenous dynamic feedback or by a lie backlund transformation when control systems are viewed as underdetermined systems of ordinary differential equations it is very close to absolute equivalence for pfaffian systems it was already known that a differentially flat system must be ruled this was a particular case of the present result in which one of the systems was assumed to be trivial or linear controllable

a linear algebraic framework for dynamic feedback linearization to any accessible nonlinear system we associate a so called infinitesimal brunovsky form this gives an algebraic criterion for strong accessibility as well as a generalization of kronecker controllability indices an output function which defines a right invertible system without zero dynamics is shown to exist if and only if the basis of the brunovsky form can be transformed into a system of exact differential forms this is equivalent to the system being differentially flat and hence constitutes a necessary and sufficient condition for dynamic feedback linearizability

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

on sufficient conditions to keep differential flatness under the addition of new inputs it is well known that a controllable nonlinear system will retain its controllabality when new actuator inputs are added to it in this article we ask the question if a system linearisable by static or dynamic feedback will retain this property when new actuator inputs are added to it alternatively a system may be linearisable after removing one or more inputs from it this question is important in the design of robotic systems from the perspective of trajectory planning and control specially if they are under actuated the goals of this article are as follows i using counter examples we first show that feedback linearisability may not be preserved when new inputs are added to a robotic system ii sufficient conditions are determined when a system will retain this property under the addition of new inputs the theory is illustrated through some examples from the robotics field

global output feedback stabilization of nonlinear systems with nonlinearity of unmeasured states this technical note deals with global stabilization of class of nonlinear dynamic systems using output feedback the systems considered have nonlinear functions of unmeasured state variables in addition to nonlinear functions of the system outputs a nonlinear reduced order observer is proposed to estimate the unknown system states estimated state variables are used for control design together with the system output certain conditions are identified for the proposed observer and control design under these conditions the proposed control design ensures the global asymptotic stability of the closed loop control system

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

cascaded feedback linearization and its application to stabilization of nonholonomic systems in this paper a new cascaded feedback linearization problem is formulated and a set of conditions on the cascaded feedback linearizability are established for a class of two input affine nonlinear systems the proposed cascaded feedback linearization method enlarges the classes of nonlinear systems which can be dealt with using the feedback linearization technique in particular the proposed design can be applied to address the feedback stabilization problem for a few classes of nonlinear systems which have uncontrollable linearization and do not satisfy the standard feedback linearization conditions as an illustrative application the proposed cascade feedback linearization concept is used to solve the feedback stabilization problem of nonholonomic systems within the framework of continuously differentiable state feedback control simulation results are provided to illustrate the proposed method

bifurcation problems for the laplacian in ⁿ in this paper we consider the bifurcation problem div ivulp 2vu ag x julp 2u f a x u in rn with p 1 we show that a continuum of positive solutions bifurcates out from the principal eigenvalue a1 of the problem div ivuip 2vu ag x ulp 2u here both functions f and g may change sign

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

dynamic output feedback linearization and global stabilization abstract we present a class of single input single output nonlinear systems which are globally transformable by a dynamic output feedback control and a time varying state space transformation into a linear observable and minimum phase system we then show how those systems can be globally stabilized by a dynamic output feedback nonlinear control and how global output tracking can be achieved as well

a counter example for the conjecture in an algorithm for interpolation with units in h abstract it is conjectured by dorato et al automatica 25 427 430 1989 that the algorithm given by them for interpolation with units in h gives the lowest possible degree unit a counter example presented in this technical communication shows that this is not the case for real as well as complex interpolation data

observers are unnecessary for output feedback control of lagrangian systems we address and solve some long standing yet well documented open problems on output feedback tracking control of euler lagrange systems with arbitrarily high relative degree this includes underactuated systems our main contribution is to establish a theoretical foundation for the use of so called dirty derivatives a common ad hoc replacement of unavailable state measurements such as generalized velocities whence obviating the the use of observers for the purpose of position feedback tracking control reminiscent of passivity based control for robot manipulators our control law is globally lipschitz and the controller dynamics is linear for relative degree two fully actuated lagrangian systems without dissipative forces friction and with bounded inertia matrix we establish uniform global asymptotic stability in closed loop furthermore we show that our control approach applies to lagrangian systems augmented by a chain of integrators relative degree m 2 systems the design method which is based on a recursive procedure in the spirit of backstepping control is intuitive as it exploits structural properties such as passivity and inherent input output stability as a corollary we solve an output feedback global tracking control problem for flexible joint robots but also for systems coupled with output feedback linearizable actuator dynamics in addition we discuss remaining open problems of fairly general interest in the realm of analysis and design of robust nonlinear systems

disturbance decoupling by measurement feedback for siso nonlinear systems the measurement feedback disturbance decoupling problem of nonlinear systems with single input single output and single measurement is considered in this paper necessary and sufficient conditions are given for disturbance decoupling by static measurement feedback new necessary conditions and sufficient conditions are presented for disturbance decoupling by dynamic measurement feedback

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

a remark on nonlinear accessibility conditions and infinite prolongations the lie rank condition for strong nonlinear accessibility is interpreted via the differential geometry of jets and prolongations of infinite order it yields to a new lie algebraic criterion and to the consideration of first integrals which apply to nonlinear systems in quite general form the latter characterization in particular is valid without distinguishing between the system variables and is independent of time scalings weak accessibility is also considered

observer design for a class of uncertain nonlinear systems with sampled outputs application to the estimation of kinetic rates in bioreactors a continuous discrete time observer is proposed for a class of uncertain nonlinear systems where the output is available only at non uniformly spaced sampling instants the underlying correction term depends on the output observation error and is updated in a mixed continuous discrete fashion the proposed observer is first introduced under a set of differential equations with instantaneous state impulses corresponding to the measured samples and their estimates two features of the proposed observer are worth to be pointed out the first one consists in the simplicity of its calibration while the second one lies in its comprehensive convergence analysis more specifically it is shown that in the case of noise free sampled outputs the observation error lies in a ball centered at the origin and its radius is proportional to the bounds of the uncertainties and the sampling partition diameter moreover in the free uncertainties case the exponential convergence to zero of the observation error is established under a well defined condition on the maximum value of the sampling partition diameter the ability of the proposed observer to perform a suitable estimation of the reactions rates in biochemical reactors is highlighted through a simulation study dealing with an ethanolic fermentation

brief paper some examples and remarks on quasi static feedback of generalized states three simple nonlinear examples with physical background are considered they illustrate how generalized state representations which depend on time derivatives of the input occur it is shown with these examples how quasi static feedback of such generalized states may be used for input output decoupling disturbance rejection and linearization and thus for trajectory tracking

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

new algebraic geometric conditions for the linearization by input output injection the goal of this paper is twofold it unifies and generalizes existing results on input output injection linearization of nonlinear systems the problem is solved as a realization problem since it is based on the analysis of the structure of the input output differential equation the necessary and sufficient conditions are derived from a simplified and constructive procedure for clarity the paper is limited to the case of single output systems exterior differential systems are extensively used throughout the paper giving constructive conditions

brief paper explicit construction of h control law for a class of nonminimum phase nonlinear systems this paper addresses a nonlinear h control problem for a class of nonminimum phase nonlinear systems the given system is first transformed into a special coordinate basis in which the system zero dynamics is divided into a stable part and an unstable part a sufficient solvability condition is then established for solving the nonlinear h control problem moreover based on the sufficient solvability condition an upper bound of the best achievable l 2 gain from the system disturbance to the system controlled output is estimated for the nonlinear h control problem the proofs of our results yield explicit algorithms for constructing required control laws for solving the nonlinear h control problem in particular the solution to the nonlinear h control problem does not require solving any hamilton jacobi equations finally the obtained results are utilized to solve a benchmark problem on a rotational translational actuator rtac system

differential flatness and absolute equivalence of nonlinear control systems this paper presents a formulation of differential flatness a concept originally introduced by fliess levine martin and rouchon in terms of absolute equivalence between exterior differential systems systems that are differentially flat have several useful properties that can be exploited to generate effective control strategies for nonlinear systems the original definition of flatness was given in the context of differential algebra and required that all mappings be meromorphic functions the formulation of flatness presented here does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems in particular it is shown that under regularity assumptions and in the case of single input control systems i e codimension 2 pfaffian systems a system is differentially flat if and only if it is feedback linearizable via static state feedback in higher codimensions our approach does not allow one to prove that feedback linearizability about an equilibrium point and flatness are equivalent one must be careful with the role of time as well as the use of prolongations that may not be realizable as dynamic feedback in a control setting applications of differential flatness to nonlinear control systems and open questions are also discussed

controlled invariance for nonlinear systems necessary and sufficient conditions are derived for a b invariance called here controlled invariance for nonlinear systems dot x f x u the obtained results generalize and elucidate already known results about systems dot x a x sum min i 1 max m u i b i x a new and direct differential geometric interpretation of the concept of controlled invariance and the derived conditions is given

antimaximum principle in rn local versus global we study the antimaximum principle for the p laplacian defined on the whole set rn with an indefinite weight function we show that a local version of this principle holds but that the global version does not hold

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

the matching of nonlinear models via dynamic state feedback it is well known that for linear systems the model matching problem is equivalent to a disturbance decoupling problem with disturbance measurement the solution of both problems can be expressed in terms of properties of invariant subspaces of the system and of the model in this paper it is shown that for nonlinear systems under appropriate hypotheses analogous results can be obtained the solvability of a model matching problem can be expressed in terms of properties of suitable invariant distributions it is also shown that as for linear systems those properties are related to the so called structures at infinity of the system and of the model

technical communique some remarks on static feedback linearization for time varying systems this work summarizes some results about static state feedback linearization for time varying systems three different necessary and sufficient conditions are stated in this paper the first condition is the one by sluis w m 1993 a necessary condition for dynamic feedback linearization systems control letters 21 277 283 the second and the third are the generalizations of known results due respectively to aranda bricaire e moog c h pomet j b 1995 a linear algebraic framework for dynamic feedback linearization ieee transactions on automatic control 40 127 132 and to jakubczyk b respondek w 1980 on linearization of control systems bulletin del academie polonaise des sciences serie des sciences mathematiques 28 517 522 the proofs of the second and third conditions are established by showing the equivalence between these three conditions the results are re stated in the infinite dimensional geometric approach of fliess m levine j martin p rouchon p 1999 a lie backlund approach to equivalence and flatness of nonlinear systems ieee transactions on automatic control 44 5 922 937

on least degree unit interpolation in rh examples are presented that give insight and suggest why it is difficult to develop a unit interpolation algorithm that will yield an interpolating unit in rh of least degree

output feedback disturbance decoupling in nonlinear systems the problem of disturbance decoupling by means of output feedback is addressed the notion of conditioned invariance is reconsidered in a linear algebraic framework using this geometric notion a necessary and sufficient condition respectively necessary condition is obtained for solving the disturbance decoupling problem by quasi static output feedback respectively the disturbance decoupling problem by dynamic output feedback dddpo the necessary conditions for dddpo which are derived are weaker than the existing ones a sufficient condition for the disturbance decoupling problem by static output feedback is given as well

on dynamic feedback linearization abstract we address the problem of transforming a nonlinear multi input system into a linear controllable one via nonsingular dynamic feedback and extended state space diffeomorphism we show that in the single input case if a system is dynamic feedback linearizable it is also static feedback linearizable we then give sufficient conditions for a class of multi input systems to be dynamic feedback linearizable all three dimensional systems with two controls and a controllable linear approximation about the origin are shown to belong to such a class

dynamic input output decoupling of nonlinear control systems the problem of dynamic input output decoupling of nonlinear control systems is studied based on an analytic algorithm the authors obtain necessary and sufficient conditions for the solvability of this problem the solution of the problem is constructed by applying a series of simple precompensations and linking maps some interesting connections with other approaches in nonlinear control theory are discussed the authors also give a few simple examples to illustrate the methods used

input linearization of nonlinear systems via pulse width control in this note it is shown that a general nonlinear system can be transformed to an affine nonlinear system by virtue of the use of pulsewidth control therefore the combined system from the pulse width control input to the nonlinear system output behaves as an affine linear in control system by this way a cumbersome nonlinear system model can be transformed to a simpler linear in control form without increasing the system dimension this in turn enables simpler control design furthermore using this methodology some control design methods developed only for affine systems can be adapted to general nonlinear systems

sufficient conditions for dynamic state feedback linearization sufficient conditions are given for the existence of a dynamic state feedback compensator for a multi input nonlinear system such that the closed loop system is transformable into a linear controllable one by an extended state space change of coordinates an example shows that the conditions are not necessary necessary conditions are also given which are shown to be sufficient when the number of states minus the number of controls is equal to one several examples illustrate how the sufficient conditions obtained lead to the design of the dynamic compensator

antimaximum principle in exterior domains abstract we consider the antimaximum principle for the p laplacian in the exterior domain p u k x u p 2 u h x in b 1 c u 0 on b 1 where p is the p laplace operator with p 1 is the spectral parameter and b 1 c is the exterior of the closed unit ball in r n with n 1 the function h is assumed to be nonnegative and nonzero however the weight function k is allowed to change its sign for k in a certain weighted lebesgue space we prove that the antimaximum principle holds locally a global antimaximum principle is obtained for h with compact support for a compactly supported k with n 1 and p 2 we provide a necessary and sufficient condition on h for the global antimaximum principle in the course of proving our results we also establish the boundary regularity of solutions of certain boundary value problems

linearization by generalized input output injection abstract the problem under interest is the linearization of nonlinear mimo systems by generalized input output injection in order to design observers with linear error dynamics the method is based on the study of the structure of the input output differential equations thus the problem is solved as a realization problem in this note one considers the linearization under two kinds of inout output injection in the first case the transformation depends on the output and time derivatives of the input whereas in the second case derivatives of both the input and the output are considered necessary and sufficient conditions are obtained which generalize the ones on standard input output injection linearization

a state space approach to parameterization of stabilizing controllers for nonlinear systems a state space approach to the youla parameterization of stabilizing controllers for linear and nonlinear systems is suggested the stabilizing controllers or a class of stabilizing controllers for nonlinear systems are characterized as fractional transformations of stable parameters the main idea behind this approach is to decompose the output feedback stabilization problem into state feedback and state estimation problems the parameterized output feedback controllers have separation structures this machinery allows the parameterization of stabilizing controllers to be conducted directly in state space without using coprime factorization

flatness based control of a single qubit gate this work considers the open loop control problem of steering a two level quantum system from any initial to any final condition the model of this system evolves on the state space having two inputs that correspond to the complex amplitude of a resonant laser field a symmetry preserving flat output is constructed using a fully geometric construction and quaternion computations simulation results of this flatness based open loop control are provided

a necessary condition for dynamic feedback linearization abstract a necessary condition for dynamic feedback linearizability of control systems x dot f x u in which the controls enter nonlinearly is derived for each x the image of the function f x needs to allow a ruling i e a foliation by straight lines

output feedback control of a class of nonlinear systems a nonseparation principle paradigm considers the problem of global stabilization by output feedback for a family of nonlinear systems that are dominated by a triangular system satisfying a linear growth condition the problem has remained unsolved due to the violation of the commonly assumed conditions in the literature using a feedback domination design method which is not based on the separation principle we explicitly construct a linear output compensator making the closed loop system globally exponentially stable

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

flatness and defect of non linear systems introductory theory and examples we introduce flat systems which are equivalent to linear ones via a special type of feedback called endogenous their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of kalman s controllability the distance to flatness is measured by a non negative integer the defect we utilize differential algebra where flatness and defect are best defined without distinguishing between input state output and other variables many realistic classes of examples are flat we treat two popular ones the crane and the car with n trailers the motion planning of which is obtained via elementary properties of plane curves the three non flat examples the simple double and variable length pendulums are borrowed from non linear physics a high frequency control strategy is proposed such that the averaged systems become flat

nonregular feedback linearization a nonsmooth approach in this note we address the problem of exact linearization via nonsmooth nonregular feedback a criterion of nonregular static state feedback linearizability is presented for a class of nonlinear affine systems with two control inputs and its application to nonholonomic systems is briefly discussed

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

robustness analysis with respect to exogenous perturbations for flatness based exact feedforward linearization a methodology to analyze robustness with respect to exogenous perturbations for exact feedforward linearization based on differential flatness is presented the analysis takes into consideration the tracking error equation and makes thereafter use of a stability result by kelemen coupled with results issued from interval analysis this turns exact feedforward linearization based on differential flatness into a general control methodology for flat systems

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

approximate linearization of nonlinear control systems abstract the paper address the problem of approximate linearization of a nonlinear control system by state feedback or dynamic feedback the main result proved is that if the fast k d relative degrees are equal to each other then the input output response of a nonlinear control system can be linearized to degree k any system having linear d relative degree can be linearized to any degree by dynamic feedbacks one example of signal tracking using dynamic feedback linearization method to improve the performance is also given

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

internal dynamics of flat nonlinear siso systems with respect to a non flat output in this article the internal dynamics of flat nonlinear siso systems with respect to a real non flat output is investigated in the coordinates of the flat output and its derivatives the main result constitutes that the parameterization of the real output by the flat output and its derivatives up to a certain order forms a differential equation which is diffeomorphic to the aforementioned internal dynamics

analysis and stabilization for networked linear hyperbolic systems of rationally dependent conservation laws in this paper for a networked linear hyperbolic partial differential equations pdes system of conservation laws the propagation periods of which are rationally dependent with coupled boundary conditions we propose a novel approach to analyze its controllability and observability in addition we propose a design method of a stabilizing controller where a boundary input with boundary valued feedback is considered first we characterize the control properties such as controllability of such a pde system in terms of the corresponding ones of a finite dimensional discrete time system defined on the boundaries of the pde system which is derived by fully exploiting the method of characteristics since the obtained discrete time system is low dimensional its analysis is relatively easier next we propose a design method of a stabilizing controller based on this discrete time system finally numerical simulations are presented to show that the proposed method is effective

on nonregular feedback linearization abstract this paper investigates the use of nonregular not necessarily regular static dynamic state feedbacks to achieve feedback linearization of affine nonlinear systems first we provide an example that is nonregular static feedback linearizable but is not regular dynamic feedback linearizable then we present some preliminary necessary conditions as well as sufficient conditions for nonregular feedback linearization the sufficient conditions are checkable and if they are verified a linearizing feedback could be calculated following a recursive procedure provided that the integrations of a set of completely integrable systems are available 1997 elsevier science ltd

linearization of discrete time systems by exogenous dynamic feedback it is shown that a discrete time system may be linearizable by exogenous dynamic feedback even if it cannot be linearized by endogenous feedback this property is completely unexpected and constitutes a fundamental difference with respect to the continuous time case the notion of exogenous linearizing output is introduced it is shown that existence of an exogenous linearizing output is a sufficient condition for dynamic linearizability necessary and sufficient conditions for the existence of an exogenous linearizing output are provided the results of the paper are obtained using transformal operator matrices the properties of such operators are studied the theory is applied to the exact discrete time model of a mobile robot showing that the above mentioned property concerns not only academic examples but also physical systems

a dynamical variable structure control strategy in asymptotic output tracking problems a dynamical discontinuous feedback strategy of the sliding mode type is presented for asymptotic output tracking problems in nonlinear dynamical systems n fliess 1989 1990 generalized observability canonical form gocf is used in the derivation of the dynamical variable structure feedback controller for a large class of nonlinear systems a truly effective smoothing of the sliding mode controlled responses is possible while substantially reducing the chattering for the control output for this reason the technique is especially suitable for the control of some mechanical and electromechanical systems an example including simulations is provided

an extension of maximum and anti maximum principles to a schrodinger equation in r2 abstract strong maximum and anti maximum principles are extended to weak l2 r 2 solutions u of the schrodinger equation u q x u u f x in l2 r 2 in the following form let 1 denote the positive eigenfunction associated with the principal eigenvalue 1 of the schrodinger operator a q x in l2 r 2 assume that q x q x f is a sufficiently smooth perturbation of a radially symmetric function f 0 and 0 f 1 c const a e in r 2 then there exists a positive number depending upon f such that for every 1 with 1 the inequality 1 u c 1 holds a e in r 2 where c is a positive constant depending upon f and it is shown that such an inequality is valid if and only if the potential q x which is assumed to be strictly positive and locally bounded has a superquadratic growth as x this result is applied to linear and nonlinear elliptic boundary value problems in strongly ordered banach spaces whose positive cone is generated by the eigenfunction 1 in particular problems of existence and uniqueness are addressed

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

an algorithm for interpolation with units in h with applications to feedback stabilization abstract the problem of finding a unit in h i e an h function the inverse of which is also h which interpolates to given points in the right half plane has important applications in a number of feedback stabilization problems i e strong stabilization and simultaneous stabilization an algorithm for computing such interpolating units is presented which requires a lower degree unit than other available algorithms

a note on direct interpolation algorithm for a strictly positive real function a procedure is developed in this technical correspondence to construct a strictly positive real function of degree 2l 1 which interpolates 2l complex conjugate points

quasi uniformity for the abstract neumann antimaximum principle and applications with a priori estimates abstract in this paper we prove a general result giving the maximum and the antimaximum principles in a unitary way for linear operators of the form l i provided that 0 is an eigenvalue of l with associated constant eigenfunctions to this purpose we introduce a new notion of quasi uniform maximum principle named k uniform maximum principle it holds for belonging to certain neighborhoods of 0 depending on the fixed positive multiplier k 0 which selects the good class of right hand sides our approach is based on a l l p estimate for some related problems as an application we prove some generalization and new results for elliptic problems and for time periodic parabolic problems under neumann boundary conditions

a triangular canonical form for a class of 0 flat nonlinear systems this article proposes a triangular canonical form for a class of 0 flat nonlinear systems necessary and sufficient geometrical conditions are given in order to guarantee the existence of a local diffeomorphism to transform the studied nonlinear systems into the proposed 0 flat canonical form which enables us to compute the flat output as well

an algorithm for interpolation with positive rational functions on the imaginary axis a procedure is shown to construct a rational transfer function that is real valued and positive on the imaginary axis the degree of the solution is lowered with respect to solutions based on existing algorithms the results can be applied to problems such as the robust strictly positive real problem

absolute equivalence and dynamic feedback linearization abstract elie cartan s results on absolute equivalence of differential systems are shown to imply a generalization of a recent result on dynamic feedback linearization of scalar control systems

stabilization via dynamic output feedback for systems with output nonlinearities abstract the problem of asmptotically stabilizing a class of systems by means of continuous output feedback is considered these systems are characterized by nonlinear terms depending only on the ouputs it is shown that for these systems stabilization via continuous state feedback plus stabilization via output injection imply stabilization via continuous dynamic output feedback this generalizes a well knwon result for linear systems

brief robustness analysis of exact feedforward linearization based on differential flatness a methodology to analyze robustness with respect to parametric uncertainty for exact feedforward linearization based on differential flatness is presented the analysis takes into consideration the tracking error equation and thereafter makes use of a stability result by kelemen coupled with results issued from interval analysis theory

a lie backlund approach to equivalence and flatness of nonlinear systems a new system equivalence relation using the framework of differential geometry of jets and prolongations of infinite order is studied in this setting two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives this is a lie backlund isomorphism the authors prove that although the state dimension is not preserved the number of input channels is kept fixed they also prove that a lie backlund isomorphism can be realized by an endogenous feedback the differentially flat nonlinear systems introduced by the authors 1992 via differential algebraic techniques are generalized and the new notion of orbitally flat systems is defined they correspond to systems which are equivalent to a trivial one with time preservation or not the endogenous linearizing feedback is explicitly computed in the case of the vtol aircraft to track given reference trajectories with stability

high gain observers with limited gain power for systems with observability canonical form we consider the problem of state observation for systems having a well defined observability canonical form gauthier and kupka 2004 by means of high gain observers the main goal is to show that for this class of systems observers can be designed with the high gain parameter powered just up to the order 2 regardless the dimension of the state system in this way we substantially overtake the main limitations of standard design procedures in which the high gain parameter is powered up to the order of the system the observer structure which generalizes the ideas presented in astolfi and marconi 2015 can be used in all those contexts where fast state observation is required such as in the design of output feedback stabilizers by means of the nonlinear separation principle that is also specifically addressed in the paper

a modification of the classical nevanlinna pick interpolation algorithm with applications to robust stabilization a modification is presented of the classical nevanlinna pick interpolation algorithm for bounded analytic functions which permits interpolation with bounded real functions this is an essential modification when the nevanlinna pick theory is applied to problems such as robust stabilization 2 since otherwise compensator transfer functions will in general have complex coefficients when complex interpolation points are present the theory underlying the modification presented is based on the theory developed by youla and saito 4 on interpolation with positive real functions the results are applied to a numerical problem in robust stabilization

relative flatness and flatness of implicit systems in this work we define the concept of relative flatness of a system with respect to a subsystem the subsystem associated to a set of outputs of a system is constructed and called here output subsystem it is shown that the relative flatness of a system with respect to the output subsystem implies the flatness of the corresponding implicit system obtained by setting these outputs to zero a sufficient condition of relative flatness based on a relative derived flag is presented based on these results a sufficient condition for the flatness of a class of nonlinear implicit systems is obtained