on non equilibrium stochastic dynamics for interacting particle systems in continuum abstract we propose a general scheme for construction of markov stochastic dynamics on configuration spaces in continuum an application to the glauber type dynamics with competitions is considered

fast decay of solutions for linear wave equations with dissipation localized near infinity in an exterior domain abstract uniform energy and l 2 decay of solutions for linear wave equations with localized dissipation will be given in order to derive the l 2 decay property of the solution a useful device whose idea comes from ikehata matsuyama sci math japon 55 2002 33 is used in fact we shall show that the l 2 norm and the total energy of solutions respectively decay like o 1 t and o 1 t 2 as t for a kind of the weighted initial data

on the equivalence between dissipativity and optimality of discontinuous nonlinear regulators for filippov dynamical systems in this paper we derive guaranteed gain sector and disk margins for nonlinear optimal and inverse optimal discontinuous feedback regulators that minimize a nonlinear nonquadratic performance functional for filippov dynamical systems specifically we consider dynamical systems with lebesgue measurable and locally essentially bounded vector fields characterized by differential inclusions involving filippov set valued maps in addition we extend classical dissipativity theory to address the problem of dissipative discontinuous dynamical systems these results are then used to derive extended kalman yakubovich popov conditions for characterizing necessary and sufficient conditions for dissipativity of discontinuous systems using clarke gradients and locally lipschitz continuous storage functions furthermore using the newly developed dissipativity notions we develop a return difference inequality to provide connections between dissipativity and optimality of nonlinear discontinuous controllers for filippov dynamical systems specifically using the extended kalman yakubovich popov conditions we show that our discontinuous feedback control law satisfies a return difference inequality if and only if the controller is dissipative with respect to a quadratic supply rate

optimal disturbance rejection control for nonlinear impulsive dynamical systems in this paper we develop an optimality based framework for addressing the problem of nonlinear nonquadratic hybrid control for disturbance rejection of nonlinear impulsive dynamical systems with bounded exogenous disturbances specifically we transform a given nonlinear nonquadratic hybrid performance criterion to account for system disturbances as a consequence the disturbance rejection problem is translatedinto an optimal hybridcontrol problem furthermore the resulting optimal hybrid control law is shown to render the closed loop nonlinear input output map dissipative with respect to general supply rates in addition the lyapunov function guaranteeing closed loop stability is shown to be a solution to a stead y state hybridhamilton jacobi isaacs equation andthus guaranteeing optimality 2005 elsevier ltd all rights reserved

impulsive control in this paper the concept and principles of impulsive control are presented impulsive control can be applied to a class of systems whose state variables are changeable in a very short time period in particular the asymptotic stability of the impulsive control of a nonlinear system is given

stability with respect to part of the variables in systems with impulse effect abstract effective sufficient conditions are found for stability with respect to part of the variables in systems of ordinary differential equations with impulse effect the approach presented is based on the specially introduced piecewise continuous ljapunov functions

local existence of solutions for the initial boundary value problem of the nonlinear elastodynamic system outside a domain abstract in this paper we deal with the mixed initial boundary value problem of dirichlet type for the nonlinear elastodynamic system outside a domain the local existence of solutions to this problem is proved by iteration

energy decay rates of elastic waves in unbounded domain with potential type of damping abstract in this paper we first show that the total energy of solutions for a semilinear system of elastic waves in r n with a potential type of damping decays in an algebraic rate to zero we study the critical potential case and we assume that the initial data have a compact support an application for the euler poisson darboux type dissipation v t x is obtained and in this case the compactness of the support on the initial data is not necessary finally we shall discuss the energy concentration region for the linear system of elastic waves in an exterior domain

energy and entropy based stabilization for lossless dynamical systems via hybrid controllers a novel class of dynamic energy based hybrid controllers is proposed as a means for achieving enhanced energy dissipation in lossless dynamical systems these dynamic controllers combine a logical switching architecture with continuous dynamics to guarantee that the system plant energy is strictly decreasing across switchings the general framework leads to closed loop systems described by impulsive differential equations in addition we construct hybrid dynamic controllers that guarantee that the closed loop system is consistent with basic thermodynamic principles in particular the existence of an entropy function for the closed loop system is established that satisfies a hybrid clausius type inequality special cases of energy based and entropy based hybrid controllers involving state dependent switching are described

kyp lemma state feedback and dynamic output feedback in discrete time bilinear systems abstract this paper shows how a generalization of the kalman yacubovitch popov kyp lemma can be built for discrete time bilinear passive systems and how the concepts of passivity and feedback equivalence can be applied to solve the problem of global stabilization via smooth state feedback bounded state feedback and dynamic output feedback for a class of discrete time bilinear systems the results generalize some recent advances due to gauthier and kupka 1992 in continuous time bilinear systems to their discrete time counterparts

brief paper robust stability and h control of uncertain impulsive systems with time delay this paper investigates the problems of robust stability stabilization and h control for uncertain impulsive systems with time delay the parametric uncertainties are assumed to be time varying and norm bounded three classes of impulsive systems with time delay are considered the systems with stable stabilizable continuous dynamics and unstable unstabilizable discrete dynamics the systems with unstable unstabilizable continuous dynamics and stable stabilizable discrete dynamics and the systems where both the continuous time dynamics and the discrete time dynamics are stable stabilizable for each class of system by using the lyapunov function and razumikhin type techniques sufficient conditions for robust stability stabilization and h control are developed in terms of linear matrix inequalities numerical examples are given which illustrate the applicability of the theoretical results

compositional contraction analysis of resetting hybrid systems this note develops sufficient conditions for exponential convergence of resetting hybrid nonlinear dynamical systems using nonlinear contraction theory the analysis first develops a unified formulation of continuous time and discrete time nonlinear dynamics based on a differential transition matrix this yields enhanced dwell time based conditions for stability of such systems analogous to those existing for switched systems it turns out that such dwell time based conditions unlike their counterparts for switched systems include arbitrary stability conditions as a special case and are less conservative and much simpler to verify

analysis and geometry on configuration spaces the gibbsian case using a natural riemannian geometry like structure on the configuration space over rd we prove that for a large class of potentials the corresponding canonical gibbs measures on 1 can be completely characterized by an integration by parts formula that is if is the gradient of the riemannian structure on one can define a corresponding divergence div such that the canonical gibbs measures are exactly those measures for which and div are dual operators onl2 one consequence is that for such the corresponding dirichlet forms e are defined in addition each of them is shown to be associated with a conservative diffusion process on with invariant measure the corresponding generators are extensions of the operator div the diffusions can be characterized in terms of a martingale problem and they can be considered as a brownian motion on perturbed by a singular drift another main result of this paper is the following if is a canonical gibbs measure then it is extreme or a pure phase if and only if the corresponding weak sobolev spacew1 2 on is irreducible as a consequence we prove that for extreme canonical gibbs measures the above mentioned diffusions are time ergodic in particular this holds for tempered grand canonical gibbs measures ruelle measures provided that the activity constant is small enough we also include a complete discussion of the free case i e 0 where the underlying space rdis even replaced by a riemannian manifoldx

decay of solutions for a semilinear system of elastic waves in an exterior domain with damping near infinity abstract we show that the solutions of a semilinear system of elastic waves in an exterior domain with a localized damping near infinity decay in an algebraic rate to zero we impose an additional condition on the lame coefficients it seems that this restriction cannot be overcome by using the two finite speed propagation of the elastic model since we do not assume compact support on the initial data and because the dissipation does not have compact support the decay rates obtained for the total energy of the linear problem and the l 2 norm of the solution improve previous results for the semilinear problem the decay rates in this paper seem to be the first contribution mainly in the context of initial data without compact support and localized dissipation

passivity and stability of switched systems a multiple storage function method this paper presents a concept of passivity for switched systems using multiple storage functions this passivity property is invariant under compatible feedback interconnection branicky s stability theorem of multiple lyapunov functions is generalized by relaxing the non increasing condition on values of lyapunov like functions using this result we show that a passive switched system is stable in the sense of lyapunov moreover asymptotic stability is reached if all subsystems are asymptotically detectable

energy dissipating hybrid control for impulsive dynamical systems abstract a novel class of fixed order energy based hybrid controllers is proposed as a means for achieving enhanced energy dissipation in nonsmooth euler lagrange hybrid port controlled hamiltonian and lossless impulsive dynamical systems these dynamic controllers combine a logical switching architecture with hybrid dynamics to guarantee that the system plant energy is strictly decreasing across switchings the general framework leads to hybrid closed loop systems described by impulsive differential equations special cases of energy based hybrid controllers involving state dependent switching are described and an illustrative numerical example is given to demonstrate the efficacy of the proposed approach

dissipative structure and diffusion phenomena for doubly dissipative elastic waves in two space dimensions abstract in this paper we study the cauchy problem for doubly dissipative elastic waves in two space dimensions where two different damping terms consist of friction or structural damping we derive energy estimates and diffusion phenomena with different assumptions on initial data particularly we find a new threshold for the influence from different damping on diffusion phenomena additionally optimal decay estimates of solution from the above and the below in a weighted l 1 framework are obtained

semigroup approach to birth and death stochastic dynamics in continuum abstract we describe a general approach to the construction of a state evolution corresponding to the markov generator of a spatial birth and death dynamics in r d we present conditions on the birth and death intensities which are sufficient for the existence of an evolution as a strongly continuous semigroup in a proper banach space of correlation functions satisfying the ruelle bound the convergence of a vlasov type scaling for the corresponding stochastic dynamics is considered

the cauchy problem and integrability of a modified euler poisson equation we prove that the periodic initial value problem for a modified euler poisson equation is well posed for initial data in h s t m when s m 2 1 we also study the analytic regularity of this problem and prove a cauchy kowalevski type theorem after presenting a formal derivation of the equation on the semidirect product space diff c t as a hamiltonian equation we concentrate on one space dimension m 1 and show that the equation is bihamiltonian

linear evolution equations in scales of banach spaces abstract this work is devoted to the study of a class of linear time inhomogeneous evolution equations in a scale of banach spaces existence uniqueness and stability for classical solutions is provided we study also the associated dual cauchy problem for which we prove uniqueness in the dual scale of banach spaces the results are applied to an infinite system of ordinary differential equations but also to the fokker planck equation associated with the spatial logistic model in the continuum

on quasi stability for impulsive differential systems on developpe une theorie de la stabilite relativement a une solution donnee de systemes differentiels impulsifs une telle etude conduit a un mecanisme complique et les notions de stabilite doivent etre modifiees

stability analysis of systems with impulse effects the authors establish conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulse effects described by systems of nonlinear time varying ordinary differential equations under mild additional assumptions these sufficient conditions turn out to be necessary as well for the case of time invariant systems with impulse effects described by nonlinear ordinary differential equations the above results are used to establish conditions under which the uniform asymptotic stability of equilibria can be deduced from the linearizations of such systems

a new topological approach to the l uniqueness of operators and the l1 uniqueness of fokker planck equations abstract the usual semigroups of kernels on a polish space e are in general not strongly continuous on l e with respect to the norm topology we introduce a new topology on l e such that they become c 0 semigroups for which we can establish a simplified hille yosida theorem the new topology will allow us to introduce the uniqueness of pre generator on l e which turns out to be equivalent to the l 1 uniqueness of the associated fokker planck equation among many others and it is intimately related with the liouville properties for l 1 harmonic functions the uniqueness of several second order elliptic differential operators in l are studied 1 one dimensional diffusion operators a x f b x f 2 schrodinger operators 1 2 v 3 multi dimensional diffusion generator 1 2

dissipative switched linear differential systems the authors develop a dissipativity theory for switched systems whose dynamical modes are described by systems of higher order linear differential equations they give necessary and sufficient conditions for dissipativity based on systems of linear matrix inequalities lmis constructed from the coefficient matrices of the differential equations describing the modes the relationship between dissipativity and stability is also discussed and an application to the stabilization of power converters is provided

energy decay for the linear and semilinear wave equations in exterior domains with some localized dissipations we derive the total energy decay e t leq i 0 1 t 1 and l 2 boundedness u t 2 leq ci 0 for the solutions to the initial boundary value problem for the wave equation in an exterior domain omega u tt delta u a x u t 0 mbox in omega times 0 infty with u x 0 u 0 x u t x 0 u 1 x mbox and u partial omega 0 where i 0 u 0 h 1 u 1 2 and a x is a nonnegative function which is positive near some part of the boundary partial omega and near infinity we apply these estimates to prove the global existence of decaying solutions for semilinear wave equations with nonlinearity f u like u alpha u alpha 0 we note that no geometrical condition is imposed on the boundary partial omega

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

on hybrid impulsive and switching systems and application to nonlinear control in this note a new class of hybrid impulsive and switching models is introduced and their asymptotic stability properties are investigated using switched lyapunov functions some new general criteria for exponential stability and asymptotic stability with arbitrary and conditioned impulsive switching are established in addition a new hybrid impulsive and switching control strategy for nonlinear systems is developed a typical example the unified chaotic system is given to illustrate the theoretical results

on the stability of invariant sets of systems with impulse effect abstract a system of differential equations with impulse effect is considered it is assumed that this system has an invariant set m by means of the direct lyapunov method the necessary and sufficient conditions of its uniform asymptotic stability are obtained the conditions on the perturbations of right hand sides of differential equations and impulse effects under which the uniform asymptotic stability of the invariant set m of the nonperturbed system implies the uniform asymptotic stability of the invariant set of the perturbed system are obtained the stability properties of invariant sets of periodic systems are also studied

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

brief energy based control for hybrid port controlled hamiltonian systems in this paper we develop an energy based hybrid control framework for hybrid port controlled hamiltonian systems in particular we obtain constructive sufficient conditions for hybrid feedback stabilization that provide a shaped energy function for the closed loop system while preserving a hybrid hamiltonian structure at the closed loop level furthermore an inverse optimal hybrid feedback control framework is developed that characterizes a class of globally stabilizing energy based controllers that guarantee hybrid sector and gain margins to multiplicative input uncertainty of hybrid hamiltonian systems

on the control of finite dimensional mechanical systems with unilateral constraints this paper focuses on the problem of the control of a class of mechanical systems with a finite number of degrees of freedom subject to unilateral constraints on the position roughly speaking those systems are described by a set of ordinary differential equations that represent smooth dynamics together with an algebraic inequality condition f q spl ges 0 where q is the vector of generalized coordinates and an impact rule relating the interaction impulse and the velocity nonsmooth dynamics is at the core of the study of such systems this implies that one can suitably define solutions and stability concepts that fit with the considered model we then discuss the closed loop control problem and analyze various switching control strategies

extensions of mixed µ bounds to monotonic and odd monotonic nonlinearities using absolute stability theory in this paper we make explicit connections between classical absolute stability theory and modern mixed analysis and synthesis specifically using the parameter dependent lyapunov function framework of haddad and bernstein and the frequency dependent off axis circle interpretation of how and hall we extend previous work on absolute stability theory for monotonic and odd monotonic nonlinearities to provide tight approximations for constant real parameter uncertainty an immediate application of this framework is the generalization and reformulation of mixed analysis and synthesis in terms of lyapunov functions and riccati equations this observation is exploited to provide robust reduced order controller synthesis while avoiding the standard d n k iteration and curve fitting procedures

a unified framework for hybrid control model and optimal control theory we propose a very general framework that systematizes the notion of a hybrid system combining differential equations and automata governed by a hybrid controller that issues continuous variable commands and makes logical decisions we first identify the phenomena that arise in real world hybrid systems then we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems evolving on continuous variable state spaces and subject to continuous controls and discrete transitions the model captures the identified phenomena subsumes previous models yet retains enough structure to pose and solve meaningful control problems we develop a theory for synthesizing hybrid controllers for hybrid plants in all optimal control framework in particular we demonstrate the existence of optimal relaxed and near optimal precise controls and derive generalized quasi variational inequalities that the associated value function satisfies we summarize algorithms for solving these inequalities based on a generalized bellman equation impulse control and linear programming

variational problems related to self similar solutions of the heat equation on demontre la compacite de certains plongements de sobolev sous de bonnes conditions sur les poids k x exp x c 2 r n r on considere des methodes variationnelles pour la resolution d equations elliptiques

analysis and geometry on configuration spaces abstract in this paper foundations are presented to a new systematic approach to analysis and geometry for an important class of infinite dimensional manifolds namely configuration spaces more precisely a differential geometry is introduced on the configuration space x over a riemannian manifold x this geometry is non flat even if x r d it is obtained as a natural lifting of the riemannian structure on x in particular a corresponding gradient divergence div and laplace beltrami operator h div gamma are constructed the associated volume elements i e all measures on x w r t which and div gamma become dual operators on l 2 x are identified as exactly the mixed poisson measures with mean measure equal to a multiple of the volume element dx on x in particular all these measures obey an integration by parts formula w r t vector fields on x the corresponding dirichlet forms e on l 2 x are therefore defined each is shown to be associated with a diffusion process which is thus the brownian motion on x and which is sub sequently identified as the usual independent infinite particle process on x the associated heat semigroup t t t 0 is calculated explicitly it is also proved that the diffusion process when started with is time ergodic or equivalently e gamma is irreducible or equivalently t t t 0 is ergodic if and only if is poisson measure z dx with intensity z dx for some z 0 furthermore it is shown that the laplace beltrami operator h div gamma gamma on l 2 x z dx is unitary equivalent to the second quantization of the laplacian x on x on the corresponding fock space n 0 l 2 x z dx n as another direct consequence of our results we obtain a representation of the lie algebra of compactly supported vector fields on x on poisson space finally generalizations to the case where dx is replaced by an absolutely continuous measure and also to interacting particle systems on x are described in particular the case where the mixed poisson measures are replaced by gibbs measures of ruelle type on x

lp lq estimates of solutions to the damped wave equation in 3 dimensional space and their application it has been asserted that the damped wave equation has the diffusive structure as t in this paper we consider the cauchy problem in 3 dimensional space for the linear damped wave equation and the corresponding parabolic equation and obtain the lp lq estimates of the difference of each solution which represent the assertion precisely explicit formulas of the solutions are analyzed for the proof the second aim is to apply the lp lq estimates to the semilinear damped wave equation with power nonlinearity if the power is larger than the fujita exponent then the time global existence of small weak solution is proved and its optimal decay order is obtained

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

on optimal control problems of a class of impulsive switching systems with terminal states constraints abstract the global optimal control problem is proposed for a special class of hybrid dynamical systems i e impulsive switching systems then the necessary condition of the above problem the minimum principle is given ekeland s variational principle and the matrix cost functional structure expression are utilized in the process of the proof based on the main result a special linear hybrid impulsive and switching system hiss is illustrated and the optimal control algorithm is presented moreover the cases of pure impulsive systems and pure switched systems are included in this paper

dynamical widom rowlinson model and its mesoscopic limit we consider the non equilibrium dynamics for the widom rowlinson model without hard core in the continuum the lebowitz penrose type scaling of the dynamics is studied and the system of the corresponding kinetic equations is derived in the space homogeneous case the equilibrium points of this system are described their structure corresponds to the dynamical phase transition in the model the bifurcation of the system is shown

global existence of solutions for semilinear damped wave equations in rn with noncompactly supported initial data abstract we consider the n dimensional cauchy problem in r n for a semilinear damped wave equation with a power type nonlinearity u p for a noncompactly supported initial data which has a small energy we shall derive a global in time existence result in the case when the power of the nonlinear term satisfies 1 2 n p n n 2 this generalizes a previous result due to todorova yordanov j differential equations 174 2001 464 489 which dealt with a solution in the framework of compactly supported initial data

lyapunov stability of a class of discrete event systems discrete event systems des are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals logical des are a class of discrete time des with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences recently there has been much interest in studying the stability properties of logical des and several definitions for stability and methods for stability analysis have been proposed here the authors introduce a logical des model and define stability in the sense of lyapunov and asymptotic stability for logical des then the authors show that more conventional analysis of stability which employs appropriate lyapunov functions can be used for logical des the authors provide a general characterization of the stability properties of automata theoretic des models petri nets and finite state systems furthermore the lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of n different types of parts according to a priority scheme to prove properties related to the machine s ability to reorient itself to achieve safe operation and a load balancing problem in computer networks to study the ability of the system to achieve a balanced load to minimize underutilization

non linear impulsive dynamical systems part ii stability of feedback interconnections and optimality in a companion paper nonlinear impulsive dynamical systems part i stability and dissipativity lyapunov and invariant set stability theorems and dissipativity theory were developed for non linear impulsive dynamical systems in this paper we build on these results to develop general stability criteria for feedback interconnections of non linear impulsive systems in addition a unified framework for hybrid feedback optimal and inverse optimal control involving a hybrid non linear non quadratic performance functional is developed it is shown that the hybrid cost functional can be evaluated in closed form as long as the cost functional considered is related in a specific way to an underlying lyapunov function that guarantees asymptotic stability of the non linear closed loop impulsive system furthermore the lyapunov function is shown to be a solution of a steady state hybrid hamilton jacobi bellman equation

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