an axiomatization of the serial cost sharing method we offer an axiomatization of the serial cost sharing method of friedman and moulin 1999 the key property in our axiom system is group demand monotonicity asking that when a group of agents raise their demands not all of them should pay less

further results on global stabilization of discrete nonlinear systems in this paper we show how recent advances 11 12 in global stabilization of continuous time nonaffine nonlinear systems with stable free dynamics can be nontrivially generalized to their discrete time counterparts by means of passivity and bounded state feedback as a consequence global stabilization results of discrete time nonlinear systems with triangular structure are established

discrete time nonlinear h control with measurement feedback abstract this paper deals with the problem of h control via measurement feedback with internal stability for discrete time nonlinear systems using the theory of discrete time dissipative systems and differential game we first present a parameterization of a family of static state feedback h nonlinear controllers then we provide sufficient conditions for the existence of a dynamic output compensator which solves the problem of disturbance attenuation with internal stability for discrete time nonlinear systems the theory developed in this paper incorporates the well known results for discrete time linear systems and generalizes some recent advances in h control of continuous time nonlinear systems to their discrete time counterparts

on uniform asymptotic stability of time varying parameterized discrete time cascades recently a framework for controller design of sampled data nonlinear systems via their approximate discrete time models has been proposed in the literature in this paper we develop novel tools that can be used within this framework and that are useful for tracking problems in particular results for stability analysis of parameterized time varying discrete time cascaded systems are given this class of models arises naturally when one uses an approximate discrete time model to design a stabilizing or tracking controller for a sampled data plant while some of our results parallel their continuous time counterparts the stability properties that are considered the conditions that are imposed and the the proof techniques that are used are tailored for approximate discrete time systems and are technically different from those in the continuous time context a result on constructing strict lyapunov functions from nonstrict ones that is of independent interest is also presented we illustrate the utility of our results in the case study of the tracking control of a mobile robot this application is fairly illustrative of the technical differences and obstacles encountered in the analysis of discrete time parameterized systems

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

lagrange stability and performance analysis of discrete time piecewise affine systems with logic states in this paper we consider discrete time piecewise affine systems with boolean inputs outputs and states and show that they can be represented in a logic canonical form where the logic variables influence the switching between different submodels but not the continuous valued dynamics we exploit this representation for studying lagrange stability and developing performance analysis procedures based on linear matrix inequalities moreover by using arguments from dissipativity theory for non linear systems we generalize our approach to solve the h analysis problem

an lmi approach for h analysis and control of discrete time piecewise affine systems in this paper we investigate some analysis and control problems for discrete time hybrid systems in the piece wise affine form by using arguments from the dissipativity theory for non linear systems we show that h x analysis and synthesis problems can be formulated and solved via linear matrix inequalities by taking into account the switching structure of the considered system in this paper we address the generalized problem of controlling hybrid systems whose switching structure does not depend only on the state but also on the control input

nonlinear average passivity and stabilizing controllers in discrete time abstract a novel notion of average passivity is proposed on this basis passivity based controllers pbc such as the discrete time versions of the well known continuous time negative output feedback and l g v controllers are introduced and discussed

stability improvement of nonlinear systems by feedback this paper is concerned with the property of stabilizing a nonlinear system to a specified equilibrium point arbitrarily fast by appropriate smooth feedback two closely related forms of this property are explored one refers to the asymptotic transfer to the critical point with exponential decay and it is shown that the systems possessing the above property are precisely those whose corresponding linearization is controllable the second stabilizability form defined here amounts to driving the system back to an arbitrarily small neighborhood of the given point arbitrarily fast by smooth feedback a global stabilization result is also included finding application in hamiltonian systems special emphasis is given to the bilinear case

on passivity of a class of discrete time switched nonlinear systems this paper analyzes the passivity and feedback passivity of discrete time switched nonlinear systems with passive and nonpassive modes that are affine in the control input when a nonpassive mode is active the increase in storage function is not necessarily bounded by the energy supplied to the switched system at every time step therefore a switched system with at least one nonpassive mode is defined to be nonpassive in the classical passivity theory in this paper we propose a framework to analyze the passivity of such switched systems in a more general sense we consider switched nonlinear systems which are affine in the control input and may consist of passive feedback passive modes and modes which cannot be rendered passive using feedback in the proposed framework we prove that a switched nonlinear system is locally feedback passive if and only if its zero dynamics are locally passive a lower bound on the ratio of total activation time between feedback passive and nonfeedback passive modes is obtained to guarantee passive zero dynamics finally we prove that two important properties of classical passivity still hold for the proposed passivity definition that is 1 output feedback control can be used to stabilize the switched system and 2 parallel and negative feedback interconnections of two such passive systems are also passive

zero state observability and stability of discrete time nonlinear systems abstract this paper studies discrete time invariant autonomous systems x k 1 tf x k y k h x k we investigate the problem of when asymptotic stability of can be characterized by means of zero state observability of and square summability of the output function h x k the relationship among observability square summable series and stability of discrete time autonomous systems is exposed the main result developed in this paper unifies a series of stability theorems recently proposed in the literature and generalizes morse s lemma morse a s 1990 towards a unified theory of parameter adaptive control tunability ieee trans autom contr 35 1002 1012 in two directions from continuous time linear systems to their discrete counterparts and from linear systems to nonlinear systems

robust control of nonlinear feedback passive systems in this paper we consider a class of nonlinear systems with uncertain parameters which enter the system nonlinearly we assume that the uncertain nonlinear system is minimum phase and the uncertain parameters are from a bounded compact set the problem under consideration is the design of a nonlinear static state feedback controller such that the closed loop system is passive for all admissible uncertainties

equilibrium independent dissipativity with quadratic supply rates equilibrium independent dissipativity eid is a recently introduced system property that requires a system to be dissipative with respect to any forced equilibrium configuration this paper is a detailed examination of eid with quadratic supply rates for a common class of nonlinear control affine systems we provide an algebraic characterization of eid for such systems in the spirit of the hill moylan lemma where the usual stability condition is replaced by an incremental stability condition based on this characterization we state results concerning internal stability feedback stability and absolute stability of eid systems finally we study eid for discrete time systems providing the relevant definitions and an analogous hill moylan type characterization results for both continuous time and discrete time systems are illustrated through examples on physical systems and convex optimization algorithms

non linear impulsive dynamical systems part i stability and dissipativity in this paper we develop lyapunov and invariant set stability theorems for non linear impulsive dynamical systems furthermore we generalize dissipativity theory to non linear dynamical systems with impulsive effects specifically the classical concepts of system storage functions and supply rates are extended to impulsive dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy dissipated energy over the continuous time system dynamics and dissipated energy over the resetting instants furthermore extended kalman yakubovich popov conditions in terms of the impulsive system dynamics characterizing dissipativeness via system storage functions are derived finally the framework is specialized to passive and non expansive impulsive systems to provide a generalization of the classical notions of passivity and non expansivity for non linear impulsive systems these results are used in the second part of this paper to develop extensions of the small gain and p

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

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

h sub spl infin control of discrete time nonlinear systems this paper presents an explicit solution to the problem of disturbance attenuation with internal stability via full information feedback state feedback and dynamic output feedback respectively for discrete time nonlinear systems the h sub spl infin control theory is first developed for affine systems and then extended to general nonlinear systems based on the concepts of dissipation inequality differential game and lasalle s invariance principle in discrete time a substantial difficulty that v a x b x u e x w respectively v f x u w is no longer quadratic in sub w sup u arising in the case of discrete time nonlinear systems has been surmounted in the paper in the case of a linear system we show how the results reduce to the well known ones recently proposed in the literature

exact theory for the self similarity and decay of homogeneous turbulence it is shown that space time dilatation invariance x 1x t 2t with concomitant transformations for dependent variables and linearity of the equation engender an exact time explicit generic form for the solution applicable to freely decaying homogeneous incompressible fluid turbulence this solution features a summation over mutually independent dynamical modes labeled by the dilatation scaling index n 1 without the assumption of isotropy nor introduction of a closure approximation procedure the theory provides an explanation for the experimentally observed self similarity of the correlation tensors and the decay laws u x t 2 t n for the different types and decay stages of homogeneous turbulence

feedback stabilization of general nonlinear control systems a passive system approach abstract this paper develops sufficient conditions for a general nonlinear control system 1 x f x u to be locally resp globally asymptotically stabilizable via smooth state feedback in particular it is shown that as in the case of affine systems this is possible if the unforced dynamic system of 1 is lyapunov stable and appropriate controllability like rank conditions are satisfied our results incorporate a series of well known stabilization theorems proposed in the literature for affine control systems and extend them to nonaffine nonlinear control systems

geometrical quasi dissipativity and boundedness property for switched discrete time nonlinear systems this paper studies geometrical quasi dissipativity and boundedness properties for switched discrete time nonlinear systems first a new concept of geometrical quasi dissipativity for a switched di

global stabilization of partially linear composite systems a linear stabilizable nonlinear asymptotically stable cascade system is globally stabilizable by smooth dynamic state feedback if a the linear subsystem is right invertible and weakly minimum phase and b the only linear variables entering the nonlinear subsystem are the output and the zero dynamics corresponding to this output both of these conditions are coordinate free and there is freedom of choice for the linear output variable this result generalizes several earlier sufficient conditions for stabilizability moreover the weak minimum phase condition for the linear subsystem cannot be relaxed unless a growth restriction is imposed on the nonlinear subsystem

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

on feedback passivity of discrete time nonlinear networked control systems with packet drops we analyze the feedback passivity of a networked control system in which the control packets may be dropped by the communication channel specifically we consider a discrete time switched nonlinear system with relative degree zero that switches between two modes at the instants when the communication link transmits the packet successfully the system evolves in closed loop and the increase in storage function is bounded below the energy supplied by the control input at the instants when a packet drop occurs the system evolves in open loop according to the free dynamics of the closed loop mode and the increase in storage function is not necessarily bounded by the supplied energy the literature on passivity of switched systems seems to consider only the case when all the modes are passive which is not the case here we prove that if the ratio of time steps for which the system evolves in closed loop versus in open loop is lower bounded by a critical number the system is locally feedback passive in a suitably defined sense this generalized definition of feedback passivity is useful since it preserves two important properties of classical passivity that feedback passivity implies asymptotic stabilizability for zero state detectable systems and that feedback passivity is preserved in parallel and negative feedback interconnections

input saturation and global stabilization of nonlinear systems via state and output feedback for multi input multi output nonlinear systems whose free dynamics are lyapunov stable the author shows how the problem of global stabilization via dynamic output feedback can be solved by using the technique of input saturation the power of this technique is also illustrated by solving the problem of global stabilization via bounded state feedback for affine nonlinear systems with stable unforced dynamics analogous results are established for discrete time nonlinear systems

a variational integrators approach to second order modeling and identification of linear mechanical systems the theory of variational integration provides a systematic procedure to discretize the equations of motion of a mechanical system preserving key properties of the continuous time flow the discrete time model obtained by variational integration theory inherits structural conditions which in general are not guaranteed under general discretization procedures we discuss a simple class of variational integrators for linear second order mechanical systems and propose a constrained identification technique which employs simple linear transformation formulas to recover the continuous time parameters of the system from the discrete time identified model we test this approach on a simulated eight degrees of freedom system and show that the new procedure leads to an accurate identification of the continuous time parameters of second order mechanical systems starting from discrete measured data

on the dissipativity of nonlinear systems fuzzy control approach a controller with large dissipativity is designed and implemented the stability margin is increased in order to tolerate the uncertainties and the disturbance in the nonlinear system in this study the dissipativity of a nonlinear system is facilitated via fuzzy control method first the nonlinear system is represented by an takagi and sugeno fuzzy model if the state variables of the nonlinear system are available then a state feedback fuzzy control is developed to guarantee that the nonlinear control system is dissipative this design problem becomes a linear matrix inequality lmi problem the maximum dissipativity design is obtained by solving an eigenvalue problem evp if the state variables are not available a fuzzy observer based state feedback controller will be used to solve the dissipative problem of the nonlinear system simulation examples are given to illustrate the design procedures and performances of the proposed method

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