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

entropy pattern entropy and related methods for the analysis of data on the time intervals between heartbeats from 24 h electrocardiograms sequences of the time intervals between heartbeats char22 medically termed rr intervals char22 extracted from 24 h electrocardiogram recordings are examined as three dimensional return map images the recordings were made in humans by means of the medically widely used portable electrocardiograph holter system a time window measured in the number of heartbeats is used and different types of behavior are classified bifurcations between the types of dynamics of the heart are noted and a form of intermittency is found an alternative quantitative measure char22 a form pattern entropy of the return map image char22 is defined that characterizes the dynamics of the rr interval sequence it is shown that this is a measure of the degree of ordering of the rr interval sequence and as such it is a good novel medical diagnostic tool for analyzing heart rate variability which distinguishes between illness and health where other diagnostics fail

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

on the stability of jump diffusions with markovian switching in this paper we consider the stability for a class of jump diffusions with markovian switching we first construct them successively and show that they can be associated with some appropriate generators and they are non explosive we then prove their feller continuity by the coupling methods furthermore we also prove their strong feller continuity by making use of the relation between the transition probabilities of jump diffusions and the corresponding diffusions finally we also investigate their exponential ergodicity

intensity approximation of random fluctuation in complex systems abstract the markov and non markov processes in complex systems are examined with the help of dynamical information shannon entropy method here we consider the essential role of two mutually independent channels of entropy involving creation of correlation and annihilation of correlation the developed method has been used to analyze the intensity fluctuation of the complex systems of various nature in psychology to analyze numerical and pattern short time human memory to study the effect of stress on the parameters of the dynamical taping test and in cardiology to analyze the random dynamics of rr intervals in human ecg s and to diagnose various diseases of human cardiovascular systems the received results show that the application of intensity approximation allows to improve essentially the diagnostics of parameters in the evolution of human dynamic states

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

generalized schrodinger equation using tsallis entropy abstract in a previous paper we developed an axiomatic approach to quantum mechanics that allowed us to derived the schrodinger equation from first principles using the concept of the boltzmann gibbs entropy in the present continuation paper we will generalize our derivation to the whole class of tsallis entropies whose particular case q 1 is just the boltzmann gibbs one we will thus arrive at a q generalized schrodinger equation presenting a great number of new features absent from the usual q 1 particular case

markov and non markov processes in complex systems by the dynamical information entropy abstract we consider the markov and non markov processes in complex systems by the dynamical information shannon entropy dise method the influence and important role of the two mutually dependent channels of entropy alternation creation or generation of correlation and anti correlation destroying or annihilation of correlation have been discussed the developed method has been used for the analysis of the complex systems of various natures slow neutron scattering in liquid cesium psychology short time numeral and pattern human memory and effect of stress on the dynamical taping test random dynamics of rr intervals in human ecg problem of diagnosis of various disease of the human cardio vascular systems chaotic dynamics of the parameters of financial markets and ecological systems

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

nonextensive foundation of levy distributions a deep connection between the ubiquity of l evy distributions in nature and the nonextensive thermal statistics introduced a decade ago has been established recently tsallis et al phys rev lett 75 3589 1995 by using unnormalized q expectation values it has just been argued on physical grounds that normalized q expectation values should be used instead we revisit within this more appropriate scheme the l evy problem and verify that the relevant analytic results become sensibly simplified whereas the basic physics remains unchanged

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

stochastic dynamics of time correlation in complex systems with discrete time in this paper we present the concept of description of random processes in complex systems with discrete time it involves the description of kinetics of discrete processes by means of the chain of finite difference non markov equations for time correlation functions tcfs we have introduced the dynamic time dependent information shannon entropy s i t where i 0 1 2 3 ellipsis as an information measure of stochastic dynamics of time correlation i 0 and time memory i 1 2 3 ellipsis the set of functions s i t constitute the quantitative measure of time correlation disorder i 0 and time memory disorder i 1 2 3 ellipsis in complex system the theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states we examine two stochastic processes involving the creation and annihilation of time correlation or time memory in details we carry out the analysis of vectors dynamics employing finite difference equations for random variables and the evolution operator describing their natural motion the existence of tcf results in the construction of the set of projection operators by the usage of scalar product operation harnessing the infinite set of orthogonal dynamic random variables on a basis of gram shmidt orthogonalization procedure tends to creation of infinite chain of finite difference non markov kinetic equations for discrete tcfs and memory functions mfs the solution of the equations above thereof brings to the recurrence relations between the tcf and mf of senior and junior orders this offers new opportunities for detecting the frequency spectra of power of entropy function s i t for time correlation i 0 and time memory i 1 2 3 ellipsis the results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems application of this technique on the analysis of stochastic dynamics of rr intervals from human ecg s shows convincing evidence for a non markovian phenomemena associated with a peculiarities in short and long range scaling this method may be of use in distinguishing healthy from pathologic data sets based in differences in these non markovian properties

central limit theorems for the wasserstein distance between the empirical and the true distributions if x is integrable f is its cdf and f n is the empirical cdf based on an i i d sample from f then the wasserstein distance between f n and f which coincides with the l 1 norm f n t f t dt of the centered empirical process tends to zero a s the object of this article is to obtain rates of convergence and distributional limit theorems for this law of large numbers or equivalently stochastic boundedness and distributional limit theorems for the l 1 norm of the empirical process some limit theorems for the ornstein uhlenbeck process are also derived as a by product

non markov stochastic dynamics of real epidemic process of respiratory infections abstract the study of social networks and especially of stochastic dynamics of diseases spread in human population has recently attracted considerable attention in statistical physics in this work we present a new statistical method of analyzing the spread of epidemic processes of grippe and acute respiratory track infections arti by means of the theory of discrete non markov stochastic processes we use the results of our last theory phys rev e 65 2002 046107 to study statistical memory effects long range correlation and discreteness in real data series describing the epidemic dynamics of human arti infections and grippe we have carried out the comparative analysis of the data of the two infections grippe and arti in one of the industrial districts of kazan one of the largest cities of russia the experimental data are analyzed by the power spectra of the initial time correlation function and the memory functions of junior orders the phase portraits of the four first dynamic variables the three first points of the statistical non markov parameter and the locally averaged kinetic and relaxation parameters the received results give an opportunity to provide a strict quantitative description of regular and stochastic components in epidemic dynamics of social networks taking into account their time discreteness and effects of statistical memory they also allow to reveal the degree of randomness and predictability of the real epidemic process in the specific social network

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

stochastic resonance in ion channels characterized by information theory we identify a unifying measure for stochastic resonance sr in voltage dependent ion channels which comprises periodic conventional aperiodic and nonstationary sr within a simplest setting the gating dynamics is governed by two state conductance fluctuations which switch at random time points between two values the corresponding continuous time point process is analyzed by virtue of information theory in pursuing this goal we evaluate for our dynamics the tau information the mutual information and the rate of information gain as a main result we find an analytical formula for the rate of information gain that solely involves the probability of the two channel states and their noise averaged rates for small voltage signals it simplifies to a handy expression our findings are applied to study sr in a potassium channel we find that sr occurs only when the closed state is predominantly dwelled upon upon increasing the probability for the open channel state the application of an extra dose of noise monotonically deteriorates the rate of information gain i e no sr behavior occurs

feedback stabilization of a class of nonsmooth systems in this paper we investigate global stabilization of nonsmooth systems the aim is to provide sufficient condition based on standard derivative for feedback stabilization of nonsmooth systems by means of a feedback of class cr r 1 the main result is a generalization of a result concerning smooth systems see for instance j control optimization 32 1994 358 to systems that are only continuous and locally lipschitz

stability in distribution for a class of singular diffusions a verifiable criterion is derived for the stability in distribution of singular diffusions that is for the weak convergence of the transition probability p t x dy as t rightarrow infty to a unique invariant probability for this we establish the following i tightness of p t x dy t geq 0 and ii asymptotic flatness of the stochastic flow when specialized to highly nonradial nonsingular diffusions the results here are often applicable where has minskii s well known criterion fails when applied to traps a sufficient condition for stochastic stability of nonlinear diffusions is derived which supplements has minskii s result for linear diffusions we also answer a question raised by l stettner originally posed to him by h j kushner is the diffusion stable in distribution if the drift is bx where b is a stable matrix and sigma cdot is lipschitzian sigma underline 0 neq 0 if not what additional conditions must be imposed

global asymptotic stabilization of periodic nonlinear systems with stable free dynamics abstract we consider a nonlinear control system with periodic coefficients we study the problem of asymptotic stabilization of the equilibrium x 0 of the closed loop system by state feedback we assume that the free dynamic system possesses a periodic lyapunov function ensuring lyapunov stability of the equilibrium x 0 we have developed a method for constructing a damping control for affine systems with periodic coefficients based on a generalization of weak jurdjevic quinn conditions using an extension of the notion of the commutator to non stationary vector fields using this approach we obtain sufficient conditions for uniform local and global asymptotic stabilization of general nonlinear systems in particular affine control systems with periodic coefficients stabilization results generalize known results for time invariant systems to time varying periodic systems

stability of a random diffusion with linear drift we consider a linear system with markovian switching which is perturbed by gaussian type noise if the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable we also show that under certain conditions the linear system with markovian switching can be stabilized by such noisy perturbation

possible generalization of boltzmann gibbs statistics with the use of a quantity normally scaled in multifractals a generalized form is postulated for entropy namelys q k 1 i 1 w p i q q 1 whereq characterizes the generalization andp i are the probabilities associated withw microscopic configurations w the main properties associated with this entropy are established particularly those corresponding to the microcanonical and canonical ensembles the boltzmann gibbs statistics is recovered as theq 1 limit

stability for a random evolution equation with gaussian perturbation in this paper we consider a random evolution equation which is perturbed by gaussian type noise and show how to construct its coupled solutions on the basis of the coupling results we discuss the asymptotic flatness and the stability in total variation norm for the solutions of the equation in addition we also prove the feller continuity and the existence and uniqueness of invariant measures of the solutions

dynamics of the information entropy in random processes abstract the problem of the description of temporal evolution of the random variables in terms of the information shannon entropy of correlation processes has been considered the influence and important role of the two mutually dependent channels of the entropy alternation correlation creation or the generation of correlations and anti correlation decay or the annihilation of correlation have been discussed the method developed is used for the analysis of chaotic dynamics of the long range fluctuation in the short time human memory

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

a non extensive approach to the entropy of symbolic sequences symbolic sequences with long range correlations are expected to result in a slow regression to a steady state of entropy increase however we prove that also in this case a fast transition to a constant rate of entropy increase can be obtained provided that the extensive entropy of tsallis with entropic index q is adopted thereby resulting in a new form of entropy that we shall refer to as kolmogorov sinai tsallis kst entropy we assume that the same symbols either 1 or 1 are repeated in strings of length l with the probability distribution p l 1 l the numerical evaluation of the kst entropy suggests that at the value 2 a sort of abrupt transition might occur for the values of in the range 1 3 it is argued that this phase transition like property signals the onset of the thermodynamical regime at 2

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

a passive system approach to feedback stabilization of nonlinear control stochastic systems the purpose of this paper is to provide sufficient conditions for asymptotic stabilization in probability of nonlinear control stochastic differential systems by means of smooth state feedback laws in particular we prove that as in the case of stochastic differential systems affine in the control one can compute stabilizing feedback laws provided the unforced stochastic differential system is lyapunov stable in probability and some rank conditions are fulfilled some well known stabilization results for stochastic differential systems affine in the control proved in the literature are extended to nonaffine nonlinear control stochastic differential systems

convergence in reaction diffusion systems an information theory approach abstract we have applied an information theory approach in order to study the problem of convergence to point like or extended attractors in reaction diffusion systems a distance between two states based on the kullback leibler relative information was defined different forms of the probability distribution some of them based on the knowledge of the nonequilibrium potential when accesible give the possibility to look for a faster and or more accurate convergence this approach offers the chance to estimate the attraction basins of the different attractors as well as detecting limit circles together with an easy evaluation of their periods

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

nonequilibrium statistical operator method in renyi statistics abstract the generalization of the zubarev nonequilibrium statistical operator nso method for the case of renyi statistics is proposed when the relevant statistical operator or distribution function is obtained based on the maximum entropy principle for the renyi entropy the nonequilibrium statistical operator and corresponding generalized transport equations for the reduced description parameters are obtained a consistent description of the kinetic and hydrodynamic processes in a system of interacting particles is considered as an example

dynamical shannon entropy and information tsallis entropy in complex systems abstract in this work we offer a new approach to the concept of the information entropy for the description of the dynamic behaviour of complex systems on the basis of the unification of the known information approach to the shannon entropy submitted in works of authors phys rev e 62 5 2000 6178 physica a 303 2002 427 and generalization of the boltzman gibbs entropy offered by tsallis braz j phys 29 1 1999 1 we have received a new representation of the dynamic information entropy here we present concrete applications of the received equations to the study of complex systems related to the electric signals of ecgs of healthy people and patients with myocardial infarction mi as an example various modifications of the non markovity parameter are also submitted they were received with the help of the new approach to the information entropy we have received detailed information about markov quasi markov and non markov characteristics of the rr interval fluctuations of the ecgs with the help of the chain of zwanzig mori s discrete kinetic equations and dynamical tsallis entropy

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

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

brief stabilization of invariant sets for nonlinear non affine systems the problem of the global and local stabilization of invariant sets for general nonlinear controlled systems is considered new state feedback stabilizing controllers and sufficient conditions of asymptotic stability of a goal set with the specified region of attraction are proposed the proofs of the obtained results are based on the detailed analysis of the w limit sets of the closed loop system with the speed gradient or jurdjevic quinn controllers for affinized controlled system two illustrating examples are given

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

adaptive control of a class of nonaffine systems using neural networks a neural control synthesis method is considered for a class of nonaffine uncertain single input single output siso systems the method eliminates a fixed point assumption and does not assume boundedness on the time derivative of a control effectiveness term one or the other of these assumptions exist in earlier papers on this subject using lyapunov s direct method it is shown that all the signals of the closed loop system are uniformly ultimately bounded and that the tracking error converges to an adjustable neighborhood of the origin simulation with a van der pol equation with nonaffine control terms illustrates the approach

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 relationships among passivity positive realness and dissipativity in linear systems the notions of passivity and positive realness are fundamental concepts in classical control theory but the use of the terms has varied for lti systems these two concepts capture the same essential property of dynamical systems that is a system with this property does not generate its own energy but only stores and dissipates energy supplied by the environment this paper summarizes the connection between these two concepts for continuous and discrete time lti systems beyond that relationships are provided between classes of strictly passive systems and classes of positive real systems the more general framework of dissipativity is introduced to connect passivity and positive realness and also to survey other energy based results the frameworks of passivity indices and conic systems are discussed to connect to passivity and dissipativity after surveying relevant existing results some clarifying results are presented these involve connections between classes of passive systems and finite gain l2l2 stability as well as asymptotic stability additional results are given to clarify some of the more subtle conditions between classes of these systems and stability results this paper surveys existing connections between classes of passive and positive real systems and provides results that clarify more subtle connections between these concepts

bounded smooth state feedback and a global separation principle for non affine nonlinear systems abstract in this paper we show that a single input nonlinear system z 0 x g 1 x u g l x u l is globally asymptotically stabilizable by arbitrarily small smooth state feedback if unforced dynamics of are lyapunov stable and satisfies appropriate controllability like rank conditions characterized by the lie bracket of vector fields f0 x and g1 x an explicit smooth state feedback control law is constructed this in turn leads to an analytic resp smooth state feedback control law which solves the problem of global stabilization for analytic resp smooth systems x f x u based on these results we then establish a global separation principle for the system with an output finally we briefly discuss how the results can be extended to a multi input system

global asymptotic stabilisation in probability of nonlinear stochastic systems via passivity abstractthe purpose of this paper is to develop a systematic method for global asymptotic stabilisation in probability of nonlinear control stochastic systems with stable in probability unforced dynamics the method is based on the theory of passivity for nonaffine stochastic differential systems combined with the technique of lyapunov asymptotic stability in probability for stochastic differential equations in particular we prove that a nonlinear stochastic differential system whose unforced dynamics are lyapunov stable in probability is globally asymptotically stabilisable in probability provided some rank conditions involving the affine part of the system coefficients are satisfied in this framework we show that a stabilising smooth state feedback law can be designed explicitly a dynamic output feedback compensator for a class of nonaffine stochastic systems is constructed as an application of our analysis

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

passivity and disturbance attenuation via output feedback for uncertain nonlinear systems the authors address the problem of disturbance attenuation with internal stability via output feedback for a class of passive systems with uncertainties the problem is approached by means of adaptive output feedback control which does not require any state observer the results obtained extend an earlier result of steinberg and corless 1985 sufficient conditions are proposed under which a nonlinear system can be made locally or globally passive via output feedback

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

time varying feedback control of nonaffine nonlinear systems without drift sufficient conditions are presented under which a general nonlinear system without drift is globally asymptotically stabilizable by time varying state feedback a novel approach is developed for the design of a time varying smooth state feedback controller the controller is explicitly constructed by using the bounded state feedback strategy lin 1995 1996 combined with lyapunov technique as well as lossless systems theory this work incorporates earlier global stabilization results coron 1992 pomet 1992 for controllable affine systems without drift which are known not to be smoothly stabilizable via any time invariant state feedback

direct passivity of a class of mimo non linear systems using adaptive feedback in this paper an adaptive controller with adaptive laws specially designed is proposed to solve the problem of making a multi input multi output mimo non linear system with explicit linear parametric uncertainty equivalent to a passive system these results are an extension of those obtained by the authors for the siso case some stability issues associated to the resultant closed loop passive system are also discussed the results obtained are applied to models of dynamical mimo systems to illustrate the controller design methodology

feedback passivation of discrete time systems under communication constraints passivity is a desirable property of a dynamical system because it implies stability and is invariant under negative feedback and parallel interconnections feedback passivation is the process of making a nonpassive system passive through feedback control in this technical note we study the problem of feedback passivation when the controller has limited information about the state of the plant nonlinear plants that are linear in the control inputs are considered the main result of the technical note is a certainty equivalence principle any state feedback controller that ensures closed loop input strict passivity with index mu using the exact state of the plant will also ensure closed loop stochastic quasi passivity using an estimate of the state provided that the infinity norm of the estimation error process is bounded by some function of mu a corollary is that for linear systems although passivity is more strict than stability feedback passivation does not place more constraints on the estimation error and hence does not demand more from the communication channel than mean square stabilization

deviations from uniform power law scaling in nonstationary time series a classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long range correlations here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat to beat fluctuations in the human heart rate we develop techniques based on the fano factor and allan factor functions as well as on detrended fluctuation analysis for quantifying deviations from uniform power law scaling in nonstationary time series by analyzing extremely long data sets of up to n 10 5 beats for 11 healthy subjects we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude by contrast we find that in data sets of comparable length for 14 subjects with heart disease the fluctuations grow erratically indicating a loss of scaling stability

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