interconnection and damping assignment passivity based control of port controlled hamiltonian systems passivity based control pbc is a well established technique that has shown to be very powerful to design robust controllers for physical systems described by euler lagrange el equations of motion for regulation problems of mechanical systems which can be stabilized shaping only the potential energy pbc preserves the el structure and furthermore assigns a closed loop energy function equal to the difference between the energy of the system and the energy supplied by the controller thus we say that stabilization is achieved via energy balancing unfortunately these nice properties of el pbc are lost when used in other applications which require shaping of the total energy for instance in electrical or electromechanical systems or even some underactuated mechanical devices our main objective in this paper is to develop a new pbc theory which extends to a broader class of systems the aforementioned energy balancing stabilization mechanism and the structure invariance towards this end we depart from the el description of the systems and consider instead port controlled hamiltonian models which result from the network modelling of energy conserving lumped parameter physical systems with independent storage elements and strictly contain the class of el models

immersion and invariance stabilization of strict feedback dynamics under sampling abstract the paper deals with sampled data stabilization of continuous time dynamics in strict feedback form via immersion and invariance starting from the characterization of the sampled data target dynamics and its invariant manifold a multi rate control law is designed to achieve attractiveness and invariance of such a manifold simulations on an academic example and a practical case illustrate the performances

paper zeros of sampled systems the zeros of the discrete time system obtained when sampling a continuous time system are explored theorems for the limiting zeros for large and small sampling periods are given conditions which guarantee that the sampled system has stable zeros are also presented

integral versions of input to state stability for dual rate nonlinear sampled data systems abstract this paper presents versions of integral input to state stability and integral input to integral state stability for nonlinear sampled data systems under the low measurement rate constraint in particular we compensate the lack of measurements using an estimator approximately reconstructing the current state interestingly under certain checkable conditions we establish that a controller that semiglobally practically integral input to integral state stabilizes an approximate discrete time model of a single rate nonlinear sampled data system also stabilizes the exact discrete time model of the nonlinear sampled data system in the same sense implemented in a dual rate setting numerical simulations are given to illustrate the effectiveness of our results

brief paper continuous time controller redesign for digital implementation a trajectory based approach given a continuous time nonlinear closed loop system we investigate sampled data feedback laws for which the trajectories of the sampled data closed loop system converge to the continuous time trajectories with a prescribed rate of convergence as the length of the sampling interval tends to zero we derive necessary and sufficient conditions for the existence of such sampled data feedback laws and in case of existence provide explicit redesign formulas and algorithms for these controllers

impulsive vaccination and dispersal on dynamics of an sir epidemic model with restricting infected individuals boarding transports to understand the effect of impulsive vaccination and restricting infected individuals boarding transports on disease spread we establish an sir model with impulsive vaccination impulsive dispersal and restricting infected individuals boarding transports this sir epidemic model for two regions which are connected by transportation of non infected individuals portrays the evolvement of diseases we prove that all solutions of the investigated system are uniformly ultimately bounded we also prove that there exists globally asymptotically stable infection free boundary periodic solution the condition for permanence is discussed it is concluded that the approach of impulsive vaccination and restricting infected individuals boarding transports provides reliable tactic basis for preventing disease spread

technical communique robust backstepping for the euler approximate model of sampled data strict feedback systems stabilization of uncertain sampled data strict feedback systems is addressed the stability study is carried out on the euler approximation of the exact discretized model of the plant firstly a class of state feedback controllers is developed that guarantees an input to state stability property for the closed loop system additionally assuming some hypotheses on the uncertain terms hold a practical asymptotic stability property is ensured by designing an appropriate class of controllers

sampled data stabilization of nonlinear dynamics with input delays through immersion and invariance in this technical note we show that immersion and invariance is a natural framework for the design of sampled data stabilizing controllers for input delayed systems assuming the existence of a continuous time feedback in the delay free case immersion and invariance stabilizability of the equivalent sampled data dynamics is proven the proof is constructive for the stabilizing controller two simulated examples illustrate the performances

design of discrete time nonlinear control systems via smooth feedback using the center manifold theory for maps in a systematic way the authors present in this note a necessary condition and sufficient conditions for discrete time nonlinear systems to be stabilizable via smooth state feedback then the authors derive a necessary and sufficient condition characterizing the existence of exponential observers for lyapunov stable discrete time nonlinear systems this in turn leads to a separation principle for the asymptotic stabilization problem as an application the output regulation problem is solved via error feedback

multirate sampled data output feedback control with application to smart material actuated systems we consider multirate sampled data output feedback control of a class of nonlinear systems using high gain observers where the measurement sampling rate is made faster than the control update rate we show that in the presence of bounded disturbances given a sampled data state feedback controller that achieves stabilization with respect to a closed set the multirate output feedback controller recovers stabilization of the same set provided the measurement sampling rate is sufficiently fast as an application we consider the control of smart material actuated systems this scheme combines a discrete time high gain observer with a hysteresis inversion controller where the hysteresis is modeled using a preisach operator experimental results for the control of a shape memory alloy actuated rotary joint are provided

sufficient conditions for stabilization of sampled data nonlinear systems via discrete time approximations given a parameterized by sampling period t family of approximate discrete time models of a sampled nonlinear plant and given a family of controllers stabilizing the family of plant models for all t sufficiently small we present conditions which guarantee that the same family of controllers semi globally practically stabilizes the exact discrete time model of the plant for sufficiently small sampling periods when the family of controllers is locally bounded uniformly in the sampling period the inter sample behavior can also be uniformly bounded so that the time varying sampled data model of the plant is uniformly semi globally practically stabilized the result justifies controller design for sampled data nonlinear systems based on the approximate discrete time model of the system when sampling is sufficiently fast and the conditions we propose are satisfied our analysis is applicable to a wide range of time discretization schemes and general plant models

sampled data stabilization a pbc approach two sampled data design procedures ensuring stabilization of passive systems are described in the general framework of passivity based control pbc strategies the first one makes reference to some modified output with respect to which passivity under sampling can be preserved the second one can be interpreted as the sampled data equivalent to the celebrated continuous time stabilizing and damping lg v controller a simulated example illustrates the performances

a generalization of greenberg s l invariant using the theory of phi gamma modules we generalize greenberg s construction of the cal l invariant to p adic representations which are semistable at p this allows us to formulate a quite general conjecture about the behavior of p adic l functions at trivial zeros

from chronological calculus to exponential representations of continuous and discrete time dynamics a lie algebraic approach in this paper formal exponential representations of the solutions to nonautonomous nonlinear differential equations are derived it is shown that the chronological exponential admits an ordinary exponential representation the exponent being given by an explicitly computable lie series expansion the results are then used to describe controlled dynamics dynamics under sampling and forced discrete time dynamics the study emphasizes the role of lie algebra techniques in nonlinear control theory and specifies structural similarities between nonautonomous differential equations dynamics under sampling and forced discrete time dynamics up to hybrid ones

theorie d iwasawa des representations p adiques d un corps local let k be finite extension of qp we give a description of the iwasawa modules attached to p adic representations of the absolute galois group of k in terms of the theory of modules of fontaine when the representation is de rham this gives a natural construction of the exponential map of perrin riou which is used in the construction and the study of p adic l functions

stabilization of sampled data nonlinear systems via backstepping on their euler approximate model two integrator backstepping designs are presented for digitally controlled continuous time plants in special form the controller designs are based on the euler approximate discrete time model of the plant and the obtained control algorithms are novel the two control laws yield respectively semiglobal practical stabilization and global asymptotic stabilization of the euler model both designs achieve semiglobal practical stabilization in the sampling period that is regarded as a design parameter of the closed loop sampled data system a simulation example illustrates that the obtained controllers may sometimes be superior to backstepping controllers based on the continuous time plant model that are implemented digitally

backstepping control under multi rate sampling the paper deals with the design of sampled data controllers which preserve the stabilizing performance of a continuous time backstepping control strategy this is achieved through matching of the control lyapunov functions evolutions at the sampling instants the method is developed for systems in strict feedback form the results are discussed and compared with similar strategies through simulated examples

the role of sampling for stability and performance in unconstrained nonlinear model predictive control we investigate the impact of sampling on stability and performance estimates in nonlinear model predictive control without stabilizing terminal constraints or costs interpreting the sampling period as a discretization parameter the relation between continuous and discrete time estimates depending on this parameter is analyzed the technique presented in this paper allows us to determine the sampling rate required in order to approximate the continuous time suboptimality bound arbitrarily well and thus gives insight into the trade off between sampling time and guaranteed performance

global dynamics of a two patch sis model with infection during transport a two patch sis model is formulated and studied the standard incidence rate and mass action incidence rate are used within each patch and during transport respectively the basic reproduction number is calculated and the global dynamics is investigated the simulation results show the influence of travel rates the different dynamics by using standard incidence rate and mass action incidence rate the importance of border screening is also explored by numerical simulation

formulas relating kl stability estimates of discrete time and sampled data nonlinear systems abstract we provide an explicit kl stability or input to state stability iss estimate for a sampled data nonlinear system in terms of the kl estimate for the corresponding discrete time system and a k function describing inter sample growth it is quite obvious that a uniform inter sample growth condition plus an iss property for the exact discrete time model of a closed loop system implies uniform iss of the sampled data nonlinear system our results serve to quantify these facts by means of comparison functions our results can be used as an alternative to prove and extend results in 1 or extend some results in 4 to a class of nonlinear systems finally the formulas we establish can be used as a tool for some other problems which we indicate

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

on the stabilization of sampled data non linear systems by using backstepping on the higher order approximate models in this paper we study the stabilization of non linear sampled data feedback control systems our controller design is based on a backstepping procedure applied on the higher order approximations of the exact discretized associated systems

global dynamics of sis models with transport related infection to understand the effect of transport related infection on disease spread an epidemic model for several regions which are connected by transportation of individuals has been proposed by cui takeuchi and saito j cui y takeuchi y saito spreading disease with transport related infection j theoret biol 239 2006 376 390 transportation among regions is one of the main factors which affects the outbreak of diseases the purpose of this paper is the further study of the local asymptotic stability of the endemic equilibrium and the global dynamics of the system sufficient conditions are established for global asymptotic stability of the endemic equilibrium permanence is also discussed it is shown that the disease is endemic in the sense of permanence if and only if the endemic equilibrium exists this implies that transport related infection on disease can make the disease endemic even if all the isolated regions are disease free

backward bifurcation of an epidemic model with saturated treatment function an epidemic model with saturated incidence rate and saturated treatment function is studied here the treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the number of infected individuals is getting larger and the medical condition is limited the global dynamics of the model indicate that the basic reproduction number being the unity is a strict threshold for disease eradication when such effect is weak however it is shown that a backward bifurcation will take place when this delayed effect for treatment is strong therefore driving the basic reproduction number below the unity is not enough to eradicate the disease and a critical value at the turning point is deduced as a new threshold some sufficient conditions for the disease free equilibrium and the endemic equilibrium being globally asymptotically stable are also obtained mathematical results in this paper suggest that giving the patients timely treatment improving the cure efficiency and decreasing the infective coefficient are all valid methods for the control of disease

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