finite size scaling and universality in the spectrum of the quantum ising chain i periodic and antiperiodic boundary condition the spectrum of the quantum ising chain is studied in the finite size scaling limit for periodic and antiperiodic boundary conditions the finite size corrections are computed for all energy gaps the results of the model are used to test the privman fisher universality hypothesis and conformal theory at the critical point it is shown how to build the spectrum from the irreducible representations of the virasoro algebra in addition the author finds evidence for an unsuspected symmetry for systems both non critical and of finite size

robustness of stochastic discrete time switched linear systems with application to control with shared resources motivated by control applications relying on shared resources such as computation time or bandwidth we analyze the stability and robustness of discrete time switched linear systems with stochastic commutations we show that a wide class of shared resources control strategies can be modeled by a stochastic jump linear system involving two stochastic processes the class of systems we study encompasses markov chains and independent and identically distributed switching processes for these systems we recall existing definitions of stability and robustness by relying on the input to state stability iss property we show that for the class of systems under concern delta moment stability is equivalent to delta moment iss and that they both imply almost sure iss several sufficient conditions are provided to guarantee these properties anytime control design for a translational oscillator rotational actuator tora system is used to illustrate all these concepts

on the universality of crossing probabilities in two dimensional percolation six percolation models in two dimensions are studied percolation by sites and by bonds on square hexagonal and triangular lattices rectangles of widtha and heightb are superimposed on the lattices and four functions representing the probabilities of certain crossings from one interval to another on the sides are measured numerically as functions of the ratioa b in the limits set by the sample size and by the conventions and on the range of the ratioa b measured the four functions coincide for the six models we conclude that the values of the four functions can be used as coordinates of the renormalization group fixed point

the concept of exponential input to state stability for stochastic systems and applications to feedback stabilization abstract this paper presents a version of the well known sontag s input to state stability property for stochastic systems this concept is used to derive sufficient conditions for global stabilization for certain class of stochastic nonlinear systems by means of static and dynamic output feedback

further results on output feedback regulation of stochastic nonlinear systems with siiss inverse dynamics this article further discusses the problem of output feedback regulation for more general stochastic nonlinear systems with stochastic integral input to state stable inverse dynamics and focuses on solving the important and unsolved problem proposed in yu and xie yu x and xie x j 2010 output feedback regulation of stochastic nonlinear systems with stochastic iiss inverse dynamics ieee transactions on automatic control 55 304 320 how to weaken the conditions on nonlinearities in drift and diffusion vector fields under the weaker conditions how to make full use of the known information of stochastic nonlinear systems to design an adaptive output feedback controller such that all the closed loop signals are almost surely bounded and the output is driven to zero almost surely

finite size corrections to matrix elements in a conformal theory applications to the magnetisation of the three state potts model using conformal invariance the authors calculate the leading corrections in 1 n to the magnetisation of the three state potts quantum chain the results are in good agreement with the numerical finite size results

a theorem on global stabilization of nonlinear systems by linear feedback abstract in this paper we investigate the global stabilizability problem for a wide class of single input nonlinear systems whose the linearization at the equilirrium is controllable we show that under general assumptions there exists a linear feedback law which globally exponentially stabilizes the system at its equilibrium the proof of our main theorem is based on some ideas from a previous paper we use the theorem to recover a recent result of gauthier et al concerning the observer design problem

universal functions in finite size scaling a numerical study in the ising and potts q 3 universality class the universality of the correlation length order parameter and susceptibility amplitudes is studied in the vicinity of the critical point of two dimensional models on strips with periodic boundary conditions for the ising and potts q 3 universality class the results confirm privman fisher conjecture 1984

output feedback control using small gain conditions for stochastic nonlinear systems with siiss inverse dynamics this article further discusses output feedback control for stochastic nonlinear systems with stochastic integral input to state stability siiss inverse dynamics based on the stochastic lasalle theorem and small gain type conditions on siiss an output feedback controller using the backstepping method is constructively designed to guarantee that all the closed loop signals are bounded almost surely and the stochastic closed loop system is globally asymptotically stable in probability

output feedback stabilization of stochastic nonlinear systems driven by noise of unknown covariance abstract we address the class of stochastic output feedback nonlinear systems driven by noise whose covariance is time varying and bounded but the bound is not known a priori this problem is analogous to deterministic disturbance attenuation problems we first design a controller which guarantees that the solutions converge in probability to a residual set proportional to the unknown bound on the covariance then for the case of a vanishing noise vector field we design an adaptive controller which besides global stability in probability guarantees regulation of the state of the plant to zero with probability one

stochastic adaptive backstepping controller design by introducing dynamic signal and changing supply function a more general class of stochastic non linear systems with unmodelled dynamics and uncertain non linear functions are considered in this paper with the concept of isps being extended to stochastic case by combining changing supply function technique with backstepping design technique an adaptive output feedback controller is proposed it is shown that all the solutions of the closed loop system are uniformly bounded in probability and the output can be regulated to an arbitrarily small neighbourhood of the origin in probability a simulation example demonstrates the control scheme

lyapunov like techniques for stochastic stability the purpose of this paper is to study the stabilizability problem for control stochastic nonlinear systems driven by a wiener process sufficient conditions for the existence of stabilizing feedback laws that are smooth except possibly at the equilibrium point of the system are provided by means of stochastic lyapunov like techniques the notion of dynamic asymptotic stability in probability of control stochastic differential systems is introduced and the stabilization by means of dynamic controllers is studied

a contraction theory approach to stochastic incremental stability we investigate the incremental stability properties of ito stochastic dynamical systems specifically we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system this bound can be expressed as a function of the noise intensity and the contraction rate of the noise free system we illustrate these results in the contexts of nonlinear observers design and stochastic synchronization

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

on input to state stability of stochastic nonlinear systems with markovian jumping parameters in this article the input to state stability iss properties of stochastic nonlinear systems with markovian jump parameters are considered firstly the notions of stochastic iss e t weighted integral iss in mean and in the pth mean are introduced then by the lyapunov like function method some corresponding criteria are provided lastly a simulation example is provided to illustrate the effectiveness of our results

critical probability and scaling functions of bond percolation on two dimensional random lattices we locate the critical probability of bond percolation on two dimensional random lattices as because of the symmetry with respect to permutation of the two axes for random lattices we expect that for an aspect ratio of unity and sufficiently large lattices the probability of horizontal spanning equals the probability of vertical spanning this is confirmed by our monte carlo simulations we show that the ideas of universal scaling functions and non universal metric factors can be extended to random lattices by studying the existence probability and the percolation probability p on finite square planar triangular and random lattices with periodic boundary conditions using a histogram monte carlo method our results also indicate that the metric factors may be the same between random lattices and planar triangular lattices provided that the aspect ratios are 1 and

stochastic stabilization and destabilization it is shown in this paper that any nonlinear systems dot x t f x t t in rd can be stabilized by brownian motion provided f hook x t k x for some k 0 on the other hand this system can also be destabilized by brownian motion if the dimension d 2 similar results are also obtained for any given stochastic differential equation dx t f hook x t t g x t t dw t

the two dimensional tricritical ising model in an external magnetic field the two dimensional tricritical ising model with an order parameter perturbation is studied using two different lattice models the mass spectrum is found to be the same as in the 2d ising model with a magnetic field results for the scaling functions are in agreement with universality and for the lowest mass a relationship with the scaling function of the ising model is observed the numerical results do not support a recent proposal of dotsenko on the dynamical generation of extra terms in the perturbative calculation of scaling functions

multiple summing maps coordinatewise summability inclusion theorems and p sidon sets we discuss the multiple summability of a multilinear map t x1 xm y when we have informations on the summability of the maps it induces on each coordinate our methods have applications to inclusion theorems for multiple summing multilinear mappings and to the product of p sidon sets

stochastic nonlinear stabilization ii inverse optimality after considering the stabilization of a specific class of stochastic nonlinear systems in a companion paper in this second part we address the classical question of when is a stabilizing in probability controller optimal and show that for every system with a stochastic control lyapunov function it is possible to construct a controller which is optimal with respect to a meaningful cost functional then we return to the problem from part i and design an optimal backstepping controller whose cost functional includes penalty on control effort and which has an infinite gain margin

output to state stability and detectability of nonlinear systems the notion of input to state stability iss has proved to be useful in nonlinear systems analysis this paper discusses a dual notion output to state stability oss a characterization is provided in terms of a dissipation inequality involving storage lyapunov functions combining iss and oss there results the notion of input output to state stability ioss which is also studied and related to the notion of detectability the existence of observers and output injection

universality of the excess number of clusters and the crossing probability function in three dimensional percolation extensive monte carlo simulations were performed to evaluate the excess number of clusters and the crossing probability function for three dimensional percolation on the simple cubic s c face centred cubic f c c and body centred cubic b c c lattices systems l l l0 with l0 l were studied for both bond s c f c c b c c and site f c c percolation the excess number of clusters q b per unit length was confirmed to be a universal quantity with a value q b 0 412 likewise the critical crossing probability in the l0 direction with periodic boundary conditions in thell plane was found to follow a universal exponential decay as a function of r d l 0 l for large r simulations were also carried out to find new precise values of the critical thresholds for site percolation on the f c c and b c c lattices yielding pc f c c d 0 199 2365 0 000 0010 pc b c c d 0 245 9615 0 000 0010 we also report the value pc s c d 0 311 6080 0 000 0004 for site percolation

an interpolation approach to hardy littlewood inequalities for norms of operators on sequence spaces we revisit estimates of hardy and littlewood for norms of operators on sequence spaces and exploit recent advances in interpolation theory to provide relatively simple proofs

brief paper small gain control method for stochastic nonlinear systems with stochastic iiss inverse dynamics this paper investigates the small gain type conditions on stochastic iiss siiss systems and makes full use of these conditions in the design and analysis of the controller the contributions are as follows 1 a new proof of the stochastic lasalle theorem is provided 2 the small gain type conditions on siiss are developed and their relationship is discussed 3 based on the stochastic lasalle theorem and siiss small gain type conditions the adaptive controllers are designed to guarantee that all of the closed loop signals are bounded almost surely and the stochastic closed loop systems are globally asymptotically stable in probability

a converse lyapunov theorem for nonuniform in time global asymptotic stability and its application to feedback stabilization lyapunov like characterizations for the concepts of nonuniform in time robust global asymptotic stability and input to state stability for time varying systems are established the main result of our work enables us to derive 1 necessary and sufficient conditions for feedback stabilization for affine in the control systems and 2 sufficient conditions for the propagation of the input to state stability property through integrators

analytical and non analytical corrections to finite size scaling using conformal invariance the author calculates finite size corrections to the scaled spectra of one dimensional quantum chains at the critical point an explicit application to the ising and three state potts model gives good agreement with analytical and numerical results respectively

adding an integrator for the stabilization problem abstract we study the relationship between the following two properties p1 the system x f x y y v is locally asymptotically stabilizable and p2 the system x f x u is locally asymptotically stabilizable where x r n y r dayawansa martin and knowles have proved that these properties are equivalent if the dimension n 1 here using the so called control lyapunov function approach a we propose another more constructive and somewhat simpler proof of dayawansa martin and knowles s result b we show that in general p1 does not imply p2 for dimensions n larger than 1 c we prove that p2 implies p1 if some extra assumptions are added like homogeneity of the system by using the latter result recursively we obtain a sufficient condition for the local asymptotic stabilizability of systems in a triangular form

exponential stability of large scale stochastic differential equations abstract given a large scale stochastic system described by a number of subsystems we introduce the corresponding isolated subsystems it is shown that the exponential stability of the isolated systems implies the exponential stability of the large scale system under some hypotheses added on the interconnected terms we also study a slightly special case where the large scale system is described in a hierarchical form i e the system consists of several subsystems and each subsystem interacts only with lower subsystems but not with higher subsystems

stabilization of stochastic nonlinear systems driven by noise of unknown covariance this paper poses and solves a new problem of stochastic nonlinear disturbance attenuation where the task is to make the system solution bounded by a monotone function of the supremum of the covariance of the noise this is a natural stochastic counterpart of the problem of input to state stabilization in the sense of sontag 1989 our development starts with a set of new global stochastic lyapunov theorems for an exemplary class of stochastic strict feedback systems with vanishing nonlinearities where the equilibrium is preserved in the presence of noise we develop an adaptive stabilization scheme based on tuning functions that requires no a priori knowledge of a bound on the covariance next we introduce a control lyapunov function formula for stochastic disturbance attenuation finally we address optimality and solve a differential game problem with the control and the noise covariance as opposing players for strict feedback systems the resulting isaacs equation has a closed form solution

hardy littlewood inequalities for norms of positive operators on sequence spaces abstract we consider estimates of hardy and littlewood for norms of operators on sequence spaces and we apply a factorization result of maurey to obtain improved estimates and simplified proofs for the special case of a positive operator

event triggered consensus control for discrete time stochastic multi agent systems this paper is concerned with the event triggered consensus control problem for a class of discrete time stochastic multi agent systems with state dependent noises a novel definition of consensus in probability is proposed to better describe the dynamics of the consensus process of the addressed stochastic multi agent systems the measurement output available for the controller is not only from the individual agent but also from its neighboring ones according to the given topology an event triggered mechanism is adopted with hope to reduce the communication burden where the control input on each agent is updated only when a certain triggering condition is violated the purpose of the problem under consideration is to design both the output feedback controller and the threshold of the triggering condition such that the closed loop system achieves the desired consensus in probability first of all a theoretical framework is established for analyzing the so called input to state stability in probability issip for general discrete time nonlinear stochastic systems within such a theoretical framework some sufficient conditions on event triggered control protocol are derived under which the consensus in probability is reached furthermore both the controller parameter and the triggering threshold are obtained in terms of the solution to certain matrix inequalities involving the topology information and the desired consensus probability finally a simulation example is utilized to illustrate the usefulness of the proposed control protocol