complexity of stability and controllability of elementary hybrid systems in this paper we consider simple classes of nonlinear systems and prove that basic questions related to their stability and controllability are either undecidable or computationally intractable np hard as a special case we consider a class of hybrid systems in which the state space is partitioned into two halfspaces and the dynamics in each halfspace correspond to a different linear system

the logarithmic sobolev inequality for discrete spin systems on a lattice for finite range lattice gases with a finite spin space it is shown that the dobrushin shlosman mixing condition is equivalent to the existence of a logarithmic sobolev inequality for the associated unique gibbs state in addition implications of these considerations for the ergodic properties of the corresponding glauber dynamics are examined

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

classical dirichlet forms on topological vector spaces the construction of the associated diffusion process given a minimal classical dirichlet form onl 2 e we construct the associated diffusion process heree is a locally convex topological vector space and is a not necessarily quasi invariant probability measure one the construction is carried out under certain assumptions one and which can be easily verified in many examples in particular we explicitly apply our results to time zero and space time quantum fields with or with out cut off

classical dirichlet forms on topological vector spaces closability and a cameron martin formula abstract we prove a sufficient condition for the closability of classical dirichlet forms on l 2 e which is also necessary if all components of the dirichlet form are closable here e is a locally convex topological vector space and a not necessarily quasi invariant probability measure on e the same condition is shown to imply the existence of a closed extension whose domain can be described explicitly in the special case where is quasi invariant with respect to certain vectors in e our result generalises previous theorems on closability in addition we prove a cameron martin type formula for a large class of measures if e is finite dimensional our characterisation of closability is the analogue of the corresponding one dimensional result applications to quantum fields and the connection with the well studied case of abstract wiener spaces are discussed

brief equivalence of hybrid dynamical models this paper establishes equivalences among five classes of hybrid systems mixed logical dynamical mld systems linear complementarity lc systems extended linear complementarity elc systems piecewise affine pwa systems and max min plus scaling mmps systems some of the equivalences are established under rather mild additional assumptions these results are of paramount importance for transferring theoretical properties and tools from one class to another with the consequence that for the study of a particular hybrid system that belongs to any of these classes one can choose the most convenient hybrid modeling framework

fuzzy model based adaptive control for a class of nonlinear systems a fuzzy model based adaptive control algorithm for a class of continuous time nonlinear dynamic systems is presented the fuzzy model consisting of a set of linear fuzzy local models that are combined using a fuzzy inference mechanism is used to model a class of nonlinear systems each fuzzy local model represents a linearized model corresponding to the operating point of the controlled nonlinear system the proposed control algorithm employs the fuzzy controller that is designed by considering the linear state feedback controller corresponding to the fuzzy local model with the maximum weight and the switching spl sigma modification adaptive controller to adaptively compensate for the plant nonlinearities stability robustness of the closed loop system is analyzed in lyapunov sense it is shown that the proposed control algorithm guarantees global stability of the system with the output of the system approaching the origin if there are no disturbances and uncertainties converging to the neighborhood of the origin for all realizations of uncertainties and disturbances the simulation examples for controlling inverted pendulum system are given to illustrate the effectiveness of the proposed method

lie algebraic approach to the coupled mode oscillator the coupling of electromagnetic fields for the construction of light amplifiers is described by a certain hamiltonian which can be expressed as the sum of three differential operators following the method of steinberg 1977 and dattoli et al 1990 the solution of schrodinger s equation for the hamiltonian of the system is constructed from the solutions of the corresponding equations for the components of the hamiltonian

a clustering technique for the identification of piecewise affine systems we propose a new technique for the identification of discrete time hybrid systems in the piecewise affine pwa form this problem can be formulated as the reconstruction of a possibly discontinuous pwa map with a multi dimensional domain in order to achieve our goal we provide an algorithm that exploits the combined use of clustering linear identification and pattern recognition techniques this allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures moreover the clustering step used for classifying the datapoints is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure

adaptive control of mimo time varying systems with indicator function based parametrization abstract this paper studies a new solution framework for adaptive control of a class of mimo time varying systems with indicator function based parametrization motivated by a general discrete time mimo takagi sugeno t s fuzzy system model in an input output form with unknown parameters an indicator membership function based parametrization has some favorable capacity to deal with certain large parameter variations a new discrete time mimo system prediction model is derived for approximating a nonlinear dynamic system and its system properties are clarified an adaptive control scheme is developed with desired controller parametrization and stable parameter estimation for control of such uncertain mimo time varying systems a control singularity problem is addressed and the closed loop stability and output tracking properties are analyzed this work provides a new method for multivariable t s fuzzy system modeling and adaptive control an illustrative example and simulation results are presented to demonstrate the proposed novel concepts and to verify the desired adaptive control system performance

fuzzy model based control stability robustness and performance issues a nonlinear controller based on a fuzzy model of mimo dynamical systems is described and analyzed the fuzzy model is based on a set of arx models that are combined using a fuzzy inference mechanism the controller is a discrete time nonlinear decoupler which is analyzed both for the adaptive and the fixed parameter cases a detailed stability analysis is carried out and the main result is that the closed loop is globally stable and robust with respect to unstructured uncertainty which may include modeling error and disturbances in addition bounds on the asymptotic and transient performance are given the main assumptions on the system and model are that they must not have strong nonminimum phase effects except time delay and the unstructured uncertainty must not be too large a simulation example illustrates some of the properties of the modeling method and model based control structure

moving horizon estimation for hybrid systems we propose a state smoothing algorithm for hybrid systems based on moving horizon estimation mhe by exploiting the equivalence between hybrid systems modeled in the mixed logic dynamical form and piecewise affine systems we provide sufficient conditions on the time horizon and the penalties on the state at the beginning of the estimation horizon to guarantee asymptotic convergence of the mhe scheme moreover we propose two practical algorithms for the computation of penalties that allow us to implement mhe by solving a mixed integer quadratic program

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

control of discrete time nonlinear systems with a time varying structure in this paper we present a control methodology for a class of discrete time nonlinear systems that depend on a possibly exogenous scheduling variable this class of systems consists of an interpolation of nonlinear dynamic equations in strict feedback form and it may represent systems with a time varying nonlinear structure moreover this class of systems is able to represent some cases of gain scheduling control takagi sugeno fuzzy systems as well as input output realizations of nonlinear systems which are approximated via localized linearizations we present two control theorems one using what we call a global approach akin to traditional backstepping and a local approach our main result where backstepping is again used but the control law is an interpolation of local control terms an aircraft wing rock regulation problem with varying angle of attack is used to illustrate and compare the two approaches

stabilizing controller design for uncertain nonlinear systems using fuzzy models a lyapunov based stabilizing control design method for uncertain nonlinear dynamical systems using fuzzy models is proposed the controller is constructed using a design model of the dynamical process to be controlled the design model is obtained from the truth model using a fuzzy modeling approach the truth model represents a detailed description of the process dynamics the truth model is used in a simulation experiment to evaluate the performance of the controller design a method for generating local models that constitute the design model is proposed sufficient conditions for stability and stabilizability of fuzzy models using fuzzy state feedback controllers are given the results obtained are illustrated with a numerical example involving a four dimensional nonlinear model of a stick balancer

dirichlet operators on loop spaces essential self adjointness and log sobolev inequality for each 0 1 and potential function v rd r we consider the dirichlet form e and the associated dirichlet operator h for the gibbs measure on the loop space e c 0 1 rd 0 1 the gibbs measure is related to the gibbs state of the quantum anharmonic oscillator with the potential v via the feynman kac formula we formulate dirichlet forms in the framework of rigged hilbert spaces which are related to the loop space e we then give an approximate criterion for the essential self adjointness of dirichlet operators associated with dirichlet forms given by probability measures on hilbert spaces under appropriate conditions on the potential we apply the approximate criterion to show that the dirichlet operator h is essentially self adjoint on the domain of smooth cylinder functions in addition if the potential satisfies a uniform convexity condition we prove that the dirichlet operator h has a gap at the lower end of spectrum we also show that the gibbs measure satisfie

observability and controllability of piecewise affine and hybrid systems we prove in a constructive way the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics automata and propositional logic by focusing our investigation on the former class we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems instead we propose practical numerical tests based on mixed integer linear programming

brief paper squaring the circle an algorithm for generating polyhedral invariant sets from ellipsoidal ones this paper presents a new geometrical approach to the computation of polyhedral robustly positively invariant pi sets for general possibly discontinuous nonlinear discrete time systems possibly affected by disturbances given a b contractive ellipsoidal set e the key idea is to construct a polyhedral set that lies between the ellipsoidal sets be and e a proof that the resulting polyhedral set is contractive and thus pi is given and a new algorithm is developed to construct the desired polyhedral set the problem of computing polyhedral invariant sets is formulated as a number of quadratic programming qp problems the number of qp problems is guaranteed to be finite and therefore the algorithm has finite termination an important application of the proposed algorithm is the computation of polyhedral terminal constraint sets for model predictive control based on quadratic costs

on representations of lie algebras for quantized hamiltonians abstract we prove that the lie algebra ls k k sk0 k0 k k where s is a real number k0 is a hermitian diagonal operator and k k has nontrivial matrix representations if and only if s 0

stable adaptive tracking of uncertain systems using nonlinearly parametrized on line approximators the design of stable adaptive neural controllers for uncertain nonlinear dynamical systems with unknown nonlinearities is considered the lyapunov synthesis approach is used to develop state feedback adaptive control schemes based on a general class of nonlinearly parametrized on line approximation models the key assumptions are that the system uncertainty satisfies a strict feedback condition and that the network reconstruction error and higher order terms of the on line approximator with respect to the network weights satisfy certain bounding conditions an adaptive bounding design is used to show that the overall neural control system guarantees semi global uniform ultimate boundedness within a neighbourhood of zero tracking error the theoretical results are illustrated through a simulation example

technical communique improved robust backstepping adaptive control for nonlinear discrete time systems without overparameterization this paper reports a robust backstepping adaptive controller for output tracking of nonlinear discrete time systems the result improves the previous one in zhang wen and soh 2001 robust adaptive control for nonlinear discrete time systems without overparameterization automatica 37 551 558 by removing the lower bound constraints on the system nonlinearities

uniqueness of generalized schrodinger operators and applications abstract we prove necessary and sufficient conditions on r d r 0 a e so that the operator s 2 1 w1 n has exactly one self adjoint extension on w1 p which generates a sub markovian semigroup on w1 n these conditions are shown to be always fulfilled if d 1 and are verified for a large class of functions if d 1 we also prove an infinite dimensional analogue of this result where r d is replaced by some topological vector space e and the lebesgue measure dx by a gaussian measure the role of is taken by some ornstein uhlenbeck operator with general linear drift and dom s bounded smooth cylinder functions both results are derived as special cases from a general perturbation result we also give the corresponding probabilistic version i e we prove uniqueness for the associated martingale problem we present in some detail applications to the case where is a ground state of a hamiltonian in quantum field theory settling a problem which has been open for some time furthermore we apply our results to prove uniqueness in distribution of the diffusion first constructed by g jona lasinio and p k mitter for the stochastic quantization of f 2 field theory

stability analysis of a class of pwm systems this note considers stability analysis of a class of pulsewidth modulated pwm systems that incorporates several different switched mode dc dc converters the systems of the class typically have periodic solutions a sampled data model is developed and used to prove stability of these solutions conditions for global and local exponential stability are derived using quadratic and piecewise quadratic lyapunov functions the state space is partitioned and the stability conditions are verified by checking a set of coupled linear matrix inequalities lmis

brief robust adaptive control of uncertain discrete time systems in this paper a robust adaptive controller for a class of nonlinear uncertain discrete time systems is developed by combining the backstepping procedures with a simple parameter estimator subject to parameter projection it is shown that the proposed controller can ensure boundedness of all signals in the overall adaptive systems in the presence of unmodelled dynamics and disturbances it can also guarantee that the tracking error is bounded by a function of the size of the unmodelled dynamics in the ideal case when there are no unmodelled dynamics and disturbances perfect tracking is ensured

ultra fast stabilizing model predictive control via canonical piecewise affine approximations this paper investigates the use of canonical piecewise affine pwa functions for approximation and fast implementation of linear mpc controllers the control law is approximated in an optimal way over a regular simplicial partition of a given set of states of interest the stability properties of the resulting closed loop system are analyzed by constructing a suitable pwa lyapunov function the main advantage of the proposed approach to the implementation of mpc controllers is that the resulting stabilizing approximate mpc controller can be implemented on chip with sampling times in the order of tens of nanoseconds

adaptive control for a class of nonlinear systems with a time varying structure we present a direct adaptive control method for a class of uncertain nonlinear systems with a time varying structure we view the nonlinear systems as composed of a finite number of pieces which are interpolated by functions that depend on a possibly exogenous scheduling variable we assume that each piece is in strict feedback form and show that the method yields stability of all signals in the closed loop as well as convergence of the state vector to a residual set around the equilibrium whose size can be set by the choice of several design parameters the class of systems considered is a generalization of the class of strict feedback systems traditionally considered in the backstepping literature we also provide design guidelines based on l sub 2 bounds on the transient

the logarithmic sobolev inequality for continuous spin systems on a lattice abstract in this article we give cf theorem 1 6 a sufficient condition on a local specification for the associated gibbs state to satisfy a logarithmic sobolev inequality in the final section cf theorem 3 10 we relate our condition to the type of mixing condition introduced by dobrushin and shlosman in connection with their work on complete analyticity

uniqueness of generalized schrodinger operators part ii abstract we prove that for h 1 2 loc r d dx 0 dx a e the generalized schrodinger operator s 2 1 dom s c 0 r d has exactly one self adjoint extension on l 2 r d 2 dx which generates a sub markovian semigroup on l 2 r d 2 dx this is based on our previous work where a necessary and sufficient condition on for this to hold was proved but which was only verified to always hold if d 1 we also prove a corresponding result where r d is replaced by an infinite dimensional space and the lebesgue measure by some gaussian measure whose covariance operator has a discrete spectrum

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

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

stability analysis and design of fuzzy control systems abstract the stability analysis and the design technique of fuzzy control systems using fuzzy block diagrams are discussed first we show the concept of fuzzy blocks and consider the connection problems of fuzzy blocks diagrams we derive some theorems and corollaries with respect to two basic types of connections of fuzzy blocks in order to preserve some properties in a connection of fuzzy blocks continuous piecewise polynomial membership functions are defined secondly a sufficient condition which guarantees the stability of fuzzy systems is obtained in terms of lyapunov s direct method we give an important fact based on this condition thirdly we propose a new design technique of a fuzzy controller the fuzzy block diagrams and the stability analysis are applied to the design problems of a model based fuzzy controller

lie algebraic methods and solutions of linear partial differential equations in this paper an algebraic method to obtain the solution of linear partial differential equations of the evolution type is discussed the proposed method exploits the lie differential operators and their matrix realization to reduce the equation to an easily solvable generalized matrix form some applications to problems of specific interest are also discussed

piecewise linear quadratic optimal control the use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control lower bounds on the optimal control cost are obtained by semidefinite programming based on the bellman inequality this also gives an approximation to the optimal control law an upper bound to the optimal cost is obtained by another convex optimization problem using the given control law a compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy

the equivalence of the logarithmic sobolev inequality and the dobrushin shlosman mixing condition given a finite range lattice gas with a compact continuous spin space it is shown cf theorem 1 2 that a uniform logarithmic sobolev inequality cf 1 4 holds if and only if the dobrushin shlosman mixing condition cf 1 5 holds as a consequence of our considerations we also show cf theorems 3 2 and 3 6 that these conditions are equivalent to a statement about the uniform rate at which the associated glauber dynamics tends to equilibrium in this same direction we show cf theorem 3 19 that these ideas lead to a surprisingly strong large deviation principle for the occupation time distribution of the glauber dynamics

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

uniqueness of gibbs states for quantum lattice systems we prove uniqueness of euclidean gibbs states for certain quantum lattice systems with unbounded spins we use dobrushin s uniqueness criterion the necessary estimates for the vasershtein distance between the corresponding one point conditional distributions with boundary conditions differing only at one side are obtained by proving a log sobolev inequality on the infinite dimensional single spin loop spaces some important classes of concrete examples to which all this applies are discussed

stability and invariance analysis of uncertain discrete time piecewise affine systems this note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non invariant set x of states the approach relies on introducing fake dynamics outside x and on synthesizing a piecewise affine and possibly discontinuous lyapunov function via linear programming the existence of such a function proves stability properties of the original system and allows the determination of a region of attraction contained in x the procedure is particularly useful in practical applications for analyzing the stability of piecewise affine control systems that are only defined over a bounded subset x of the state space and to determine whether for a given set of initial conditions the trajectories of the state vector remain within the domain x

some remarks on the stability of mamdani fuzzy control systems this paper presents a passivity approach to the stability analysis of mamdani fuzzy control systems the main idea of the paper is that the fuzzy controller can be considered from an input output viewpoint as a nonlinear dissipative operator an input output approach is provided by considering a dynamical dependency of inputs of the fuzzy controller then the passivity theory is applied in order to obtain conditions for absolute stability of the closed loop control system

computation of lyapunov functions for smooth nonlinear systems using convex optimization linearly parameterized non quadratic lyapunov functions for smooth nonlinear systems are computed numerically using large scale linear or quadratic programming

mamdani type fuzzy controllers are universal fuzzy controllers abstract this paper addresses the issues of universal fuzzy controllers and shows that the mamdani type fuzzy controllers are universal fuzzy controllers furthermore a constructive procedure is also presented to obtain the universal fuzzy controller if the reference fuzzy model is given

input to state stability and interconnections of discontinuous dynamical systems in this paper we will extend the input to state stability iss framework to continuous time discontinuous dynamical systems dds adopting piecewise smooth iss lyapunov functions the main motivation for investigating piecewise smooth iss lyapunov functions is the success of piecewise smooth lyapunov functions in the stability analysis of hybrid systems this paper proposes an extension of the well known filippov s solution concept that is appropriate for open systems so as to allow interconnections of dds it is proven that the existence of a piecewise smooth iss lyapunov function for a dds implies iss in addition a small gain iss interconnection theorem is derived for two dds that both admit a piecewise smooth iss lyapunov function this result is constructive in the sense that an explicit iss lyapunov function for the interconnected system is given it is shown how these results can be applied to construct piecewise quadratic iss lyapunov functions for piecewise linear systems including sliding motions via linear matrix inequalities

stability of an analog optimization circuit for quadratic programming abstract we study the stability of an analog optimization circuit that solves quadratic programming qp problems the circuit dynamics are modeled as a switched affine system a piece wise quadratic lyapunov function and the kyp lemma are used to derive the stability criterion the stability criterion characterizes the range of critical circuit parameters for which the qp circuit is globally exponentially stable

dirichlet forms and dirichlet operators for gibbs measures of quantum unbounded spin systems essential self adjointness and log sobolev inequality for each 0 1 we consider the dirichlet form mu gamma and the associated dirichlet operator h mu gamma for the gibbs measure of quantum unbounded spin systems interacting via superstable and regular potential the gibbs measure is related to the gibbs state of the system via a functional euclidean integral procedure the configuration space for the spin systems is given by omega e mathbb z v e left omega in c left left 0 1 right mathbb r d right omega left 0 right omega left 1 right right we formulate dirichlet forms in the framework of rigged hilbert spaces which are related to the space under appropriate conditions on the potential we show that the dirichlet operator h mu left gamma right is essentially self adjoint on the domain of smooth cylinder functions we give sufficient conditions on the potential so that the corresponding gibbs measure is uniformly log concave ulc this property gives the spectral gap of the dirichlet operator h mu left gamma right at the lower end of the spectrum furthermore we prove that under the conditions of ulc the unique gibbs measure satisfies the log sobolev inequality ls we use an approximate argument used in the study of the same subjects for loop spaces which in turn is a modification of the method originally developed by s albeverio yu g kondratiev and m rockner

on the classification of the lie algebras lrs linear algebraic methods are used to classify the lie algebras lrs presented by generators and relations they were introduced as an algebraic model for quantized hamiltonians

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

convex relaxations for l 2 gain analysis of piecewise affine polynomial systems this paper proposes some sufficient conditions based on the computation of polynomial and piecewise polynomial storage functions for gain analysis of discrete time piecewise affine or piecewise polynomial systems the computation of such storage functions is performed by means of convex optimisation techniques via the sum of squares decomposition of multivariate polynomials

ergodicity for the stochastic dynamics of quasi invariant measures with applications to gibbs states the convex set maof quasi invariant measures on a locally convex spaceewith given shift radon nikodym derivatives i e cocycles a atk k k0 t ris analyzed the extreme points of maare characterized and proved to be non empty a specification of lattice type is constructed so that macoincides with the set of the corresponding gibbs states as a consequence via a well known method due to dynkin and follmer a unique representation of an arbitrary element in main terms of extreme ones is derived furthermore the corresponding classical dirichlet forms e d e and their associated semigroups t t t 0onl2 e are discussed under a mild positivity condition it is shown that mais extreme if and only if e d e is irreducible or equivalently t t t 0is ergodic this implies time ergodicity of associated diffusions applications to gibbs states of classical and quantum lattice models as well as those occuring in euclidean quantum field theory are presented in particular it is proved that the stochastic quantization of a guerra rosen simon gibbs state on d r2 ininfinite volumewith polynomial interaction is ergodic if the gibbs state is extreme i e is a pure phase which solves a long standing open problem

design of a multilevel fuzzy controller for nonlinear systems and stability analysis in this paper a multilevel fuzzy control mlfc system is developed and implemented to deal with the real world nonlinear plants with intrinsic uncertainties and time varying parameters the proposed fuzzy control strategy has a hierarchical structure with an adaptation mechanism embedded in the lower level to tune the output membership functions mfs of the first layer fuzzy controller and can be used to control a system with an input output monotonic relationship or a piecewise monotonic relationship the stability of the closed loop system under the proposed mlfc is theoretically proven simulations are carried out by applying the proposed multilevel fuzzy control mlfc to a uncertain nonlinear plants and it is shown that much better system performances are achieved compared with conventional fuzzy logic controllers flc even in presence of disturbance and noise

brief analysis of discrete time piecewise affine and hybrid systems in this paper we present various algorithms both for stability and performance analysis of discrete time piece wise affine pwa systems for stability different classes of lyapunov functions are considered and it is shown how to compute them through linear matrix inequalities that take into account the switching structure of the systems we also show that the continuity of the lyapunov function is not required in discrete time moreover the tradeoff between the degree of conservativeness and computational requirements is discussed finally by using arguments from the dissipativity theory for nonlinear systems we generalize our approach to analyze the l 2 gain of pwa systems

the essential self adjointness of generalized schrodinger operators a necessary and sufficient condition is given for the generalized schrodinger operator a 12 i 1n di di to be essentially self adjoint in l2 dx under general assumptions on and for arbitrary domains in rn in particular if is strictly positive and locally lipschitz continuous on rn then a is essentially self adjoint examples of non essential self adjointness and a complete discussion of the one dimensional case are also given these results have applications to the problem of the essential self adjointness of quantum hamiltonians and to the uniqueness problem of markov processes

dirichlet operators via stochastic analysis abstract we give sufficient conditions for essential self adjointness of symmetric differential operators dirichlet operators associated with classical dirichlet forms given by probability measures on hilbert spaces under an additional assumption of log concavity for the measures we prove the existence of a gap at the lower end of spectrum of the dirichlet operator and the ergodicity of the corresponding semi group we consider also applications to the study of stochastic dynamics in some classical lattice systems