on stability of fuzzy systems expressed by fuzzy rules with singleton consequents addresses the issue of stability of a fuzzy system described by fuzzy rules with singleton consequents it first presents two canonical forms of a fuzzy system a parametric expression and a state space expression a fuzzy system with singleton consequents is found to be a piecewise polytopic affine system then the paper gives stability theorems for a discrete time system as well as for a continuous time system it also gives a brief survey on the stability issues of fuzzy control systems

diffusion in energy conserving coupled maps we consider a dynamical system consisting of subsystems indexed by a lattice each subsystem has one conserved degree of freedom energy the rest being uniformly hyperbolic the subsystems are weakly coupled together so that the sum of the subsystem energies remains conserved we prove that the subsystem energies satisfy the diffusion equation in a suitable scaling limit

renormalization of correlations in a quasiperiodically forced two level system quadratic irrationals generalizing from the case of golden mean frequency to a wider class of quadratic irrationals we extend our renormalization analysis of the self similarity of correlation functions in a quasiperiodically forced two level system we give a description of all piecewise constant periodic orbits of an additive functional recurrence generalizing that present in the golden mean case we establish a criterion for periodic orbits to be globally bounded and also calculate the asymptotic height of the main peaks in the correlation function

model construction rule reduction and robust compensation for generalized form of takagi sugeno fuzzy systems this paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction rule reduction and robust compensation for nonlinear systems the model construction part replaces the nonlinear dynamics of a system with a generalized form of takagi sugeno fuzzy systems which is newly developed by us the generalized form has a decomposed structure for each element of a sub i and b sub i matrices in consequent parts the key feature of this structure is that it is suitable for constructing if then rules and reducing the number of if then rules the rule reduction part provides a successive procedure to reduce the number of if then rules furthermore we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models the robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties finally two examples demonstrate the utility of the systematic procedure developed

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

invariant distributions and scaling limits for some diffusions in time varying random environments we consider a family of one dimensional diffusions in dynamical wiener mediums which are random perturbations of the ornstein uhlenbeck diffusion process we prove quenched and annealed convergences in distribution and under weigh ted total variation norms we find two kind of stationary probability measures which are either the standard normal distribution or a quasi invariant measure depending on the environment and which is naturally connected to a random dynamical system we apply these results to the study of a model of time inhomogeneous brox s diffusions which generalizes the diffusion studied by brox ann probab 14 4 1206 1218 1986 and those investigated by gradinaru and offret ann inst henri poincare probab stat 2011 we point out two distinct diffusive behaviours and we give the speed of convergences in the quenched situations

random walks in space time mixing environments we prove that random walks in random environments that are exponentially mixing in space and time are almost surely diffusive in the sense that their scaling limit is given by the wiener measure

uniqueness of the srb measure for piecewise expanding weakly coupled map lattices in any dimension we prove the existence of a unique srb measure for a wide range of multidimensional weakly coupled map lattices these include piecewise expanding maps with diffusive coupling

random walk in markovian environment we prove a quenched central limit theorem for random walks with bounded increments in a randomly evolving environment on z d we assume that the transition probabilities of the walk depend not too strongly on the environment and that the evolution of the environment is markovian with strong spatial and temporal mixing properties

central limit theorems for additive functionals of markov chains central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic markov chain say s n g x 1 g x n where e g x 1 0 and e g x 1 2 the conditions imposed restrict the moments of g and the growth of the conditional means e s n x 1 no other restrictions on the dependence structure of the chain are required when specialized to shift processes the conditions are implied by simple integral tests involving g

renormalization analysis of correlation properties in a quasiperiodically forced two level system we give a rigorous renormalization analysis of the self similarity of correlation functions in a quasiperiodically forced two level system more precisely the system considered is a quantum two level system in a time dependent field consisting of periodic kicks with amplitude given by a discontinuous modulation function driven in a quasiperiodic manner at golden mean frequency mathematically our analysis consists of a description of all piecewise constant periodic orbits of an additive functional recurrence we further establish a criterion for such orbits to be globally bounded functions in a particular example previously only treated numerically we further calculate explicitly the asymptotic height of the main peaks in the correlation function

limit theory for random walks in degenerate time dependent random environments abstract we study continuous time variable speed random walks in random environments on z d d 2 where at time t the walk at x jumps across edge x y at time dependent rate a t x y the rates which we assume stationary and ergodic with respect to space time shifts are symmetric and bounded but possibly degenerate in the sense that the total jump rate from a vertex may vanish over finite intervals of time we formulate conditions on the environment under which the law of diffusively scaled random walk path tends to brownian motion for almost every sample of the rates the proofs invoke moser iteration to prove sublinearity of the corrector in pointwise sense a key additional input is a conversion of certain weighted energy norms to ordinary ones our conclusions apply to random walks on dynamical bond percolation and interacting particle systems as well as to random walks arising from the helffer sjostrand representation of gradient models with certain non strictly convex potentials

renormalization for the harper equation for quadratic irrationals in this paper we use renormalization methods to study self similarity in the fluctuations i of the harper equation in the strong coupling limit for quadratic irrationals of the form a2 4 a 2 for a n using the decimation method we obtain a second order functional recurrence which we prove rigorously has an entire fixed point this fixed point governs the scaling of the fluctuations i in the strong coupling limit

fuzzy adaptive output feedback control of mimo nonlinear systems with partial tracking errors constrained in this paper a partial tracking error constrained fuzzy output feedback dynamic surface control dsc scheme is proposed for a class of uncertain multi input and multi output mimo nonlinear systems the considered mimo nonlinear systems contain unknown functions and without the requirement of their states being available for the controller design with the help of fuzzy logic systems identifying the mimo unknown nonlinear systems a fuzzy adaptive observer is established to estimate the unmeasured states by transforming the tracking errors into new virtual error variables and based on the dsc backstepping recursive design technique a new adaptive fuzzy output feedback control method is developed it is proved that the proposed control approach can guarantee that all the signals of the resulting closed loop system are bounded and the partial state tracking errors are confined all times within the prescribed bounds the simulation results and comparisons with the previous control approaches confirm the effectiveness and utility of the proposed scheme

random walks on dynamical percolation mixing times mean squared displacement and hitting times we study the behavior of random walk on dynamical percolation in this model the edges of a graph g are either open or closed and refresh their status at rate mu while at the same time a random walker moves on g at rate 1 but only along edges which are open on the d dimensional torus with side length n we prove that in the subcritical regime the mixing times for both the full system and the random walker are n 2 mu up to constants we also obtain results concerning mean squared displacement and hitting times finally we show that the usual recurrence transience dichotomy for the lattice mathbb z d holds for this model as well

renormalization of correlations and spectra of a strange non chaotic attractor we study a simple nonlinear mapping with a strange nonchaotic attractor characterized by a singular continuous power spectrum we show that the symbolic dynamics is exactly described by a language generated from a suitable inflation rule we derive renormalization transformations for both the power spectrum and the autocorrelation function thus obtaining a quantitative description of the scaling properties the multifractal nature of the spectrum is also discussed

piecewise quadratic stability of fuzzy systems presents an approach to stability analysis of fuzzy systems the analysis is based on lyapunov functions that are continuous and piecewise quadratic the approach exploits the gain scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities examples demonstrate the many improvements over analysis based on a single quadratic lyapunov function special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described

a garden of orchids a generalized harper equation at quadratic irrational frequencies we consider a generalized harper equation at quadratic irrational flux showing in the strong coupling limit the fluctuations of the exponentially decaying eigenfunctions are governed by the dynamics of a renormalization operator on a renormalization strange set this work generalizes previous analyses which have considered only the golden mean case projections of the renormalization strange sets are illustrated analogous to the orchid present in the golden mean case

on homogenization of time dependent random flows we study a diffusion with a random time dependent drift we prove the invariance principle when the spectral measure of the drift satisfies a certain integrability condition this result generalizes the results of 13 7

renormalization of correlations in a quasiperiodically forced two level system for a general class of modulation function we provide a renormalization analysis of correlations in a quasi periodically forced two level system in a time dependent field with periodic kicks whose amplitude is given by a general class of discontinuous modulation function for certain intensities of modulation we give a complete understanding of the autocorrelation function furthermore once the locations of the discontinuities of the modulation function are known aperiodic orbits lead to correlations on renormalization strange sets which are determined by two specified features of the modulation function of which there are only a finite number of variations

dimensions of structurally stable and critical strange non chaotic attractors we provide evidence that the box counting dimension of a structurally stable strange non chaotic attractor sna of pinched skew product type is equal to 2 by showing that it has non negligible area the argument presented is made more accurate in the study of a piecewise linear sna furthermore we provide evidence that the fractal dimension of a critical sna is not equal to 2 but in fact lies between 1 and 2 we numerically calculate the box counting dimension for several critical snas providing further evidence to support this conjecture

chaotic correlations in barrier billiards with arbitrary barriers we study autocorrelation functions in symmetric barrier billiards for golden mean trajectories with arbitrary barriers renormalization analysis reveals the presence of a chaotic invariant set and thus that for a typical barrier there are chaotic correlations the chaotic renormalization set is the analogue of the so called orchid that arises in a generalized harper equation

central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions we prove a functional central limit theorem for additive functionals of stationary reversible ergodic markov chains under virtually no assumptions other than the necessary ones we use these results to study the asymptotic behavior of a tagged particle in an infinite particle system performing simple excluded random walk

why triangular membership functions abstract in this note we look at a certain theoretically sound motivation behind the common use of triangular and trapezoidal membership functions the studies are completed within a conceptual framework of fuzzy modelling whose structure comprises of input and output interfaces linked with a single transformation module aimed at processing linguistic information it is shown that under some additional mild assumptions these triangular fuzzy sets comply with a request for a uniformly excited codebook in the case of the input interfaces and a satisfaction of a zero error reconstruction criterion being formulated for the output interface

a new fuzzy lyapunov function approach for a takagi sugeno fuzzy control system design in this paper a new fuzzy lyapunov function approach is presented for a class of continuous time takagi sugeno fuzzy control system the proposed fuzzy lyapunov function is formulated as a line integral of a fuzzy vector which is a function of the state and it can be regarded as the work done from the origin to the current state in the fuzzy vector field unlike the approaches using a fuzzy blending of multiple quadratic lyapunov functions the time derivatives of membership functions do not appear in the proposed approach the effectiveness of the proposed approach is shown through numerical examples

observer based adaptive fuzzy tracking control of mimo stochastic nonlinear systems with unknown control directions and unknown dead zones in this paper an adaptive fuzzy backstepping output feedback tracking control approach is proposed for a class of multi input and multi output mimo stochastic nonlinear systems the mimo stochastic nonlinear systems under study are assumed to possess unstructured uncertainties unknown dead zones and unknown control directions by using a linear state transformation the unknown control coefficients and the unknown slopes characteristic of the dead zones are lumped together and the original system is transformed to a new system on which the control design becomes feasible fuzzy logic systems are used to approximate the unstructured uncertainties and a fuzzy state observer is designed to estimate the unmeasured states by introducing a special nussbaum gain function into the backstepping control design a stable adaptive fuzzy output feedback tracking control scheme is developed the main features of the proposed adaptive control approach are that it can guarantee the stability of the closed loop system and the tracking errors converge to a small neighborhood of zero moreover it can solve the problems of unknown control direction unknown dead zone and unmeasured states simultaneously two simulation examples are provided to show the effectiveness of the proposed approach

a practical method for calculating largest lyapunov exponents from small data sets detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the largest lyapunov exponent lyapunov exponents quantify the exponential divergence of initially close state space trajectories and estimate the amount of chaos in a system we present a new method for calculating the largest lyapunov exponent from an experimental time series the method follows directly from the definition of the largest lyapunov exponent and is accurate because it takes advantage of all the available data we show that the algorithm is fast easy to implement and robust to changes in the following quantities embedding dimension size of data set reconstruction delay and noise level furthermore one may use the algorithm to calculate simultaneously the correlation dimension thus one sequence of computations will yield an estimate of both the level of chaos and the system complexity

continuity and anomalous fluctuations in random walks in dynamic random environments numerics phase diagrams and conjectures we perform simulations for one dimensional continuous time random walks in two dynamic random environments with fast independent spin flips and slow simple symmetric exclusion decay of space time correlations respectively we focus on the asymptotic speeds and the scaling limits of such random walks we observe different behaviors depending on the dynamics of the underlying random environment and the ratio between the jump rate of the random walk and the one of the environment we compare our data with well known results for static random environment we observe that the non diffusive regime known so far only for the static case can occur in the dynamical setup too such anomalous fluctuations give rise to a new phase diagram further we discuss possible consequences for more general static and dynamic random environments

correlations and spectra of strange non chaotic attractors we consider correlations and spectra of strange nonchaotic attractors in quasiperiodically driven nonlinear systems it is demonstrated that a self similar autocorrelation function and a singular continuous spectrum may be observed in such systems the properties of correlations and spectra depend very subtly on the rotation number of the quasiperiodic force and on the parameters of the system for some parameter values the usual discrete spectrum is restored

random walks in quenched i i d space time random environment are always a s diffusive we consider a general model of discrete time random walk x t on the lattice 1 in a random environment t x t x 1 with i i d components t x previous results on the a s validity of the central limit theorem for the quenched model required a small stochasticity condition in this paper we show that the result holds provided only that an obvious non degeneracy condition is met the proof is based on the analysis of a suitable generating function which allows to estimate l 2 norms by contour integrals

convection diffusion equation with space time ergodic random flow we prove the homogenization of convection diffusion in a time dependent ergodic incompressible random flow which has a bounded stream matrix and a constant mean drift we also prove two variational formulas for the effective diffusivity as a consequence we obtain both upper and lower bounds on the effective diffusivity

a systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems this paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for takagi sugeno ts systems this approach is based on the idea of multiple lyapunov functions together with simple techniques for introducing slack matrices unlike some previous approaches based on multiple lyapunov functions both the stability and the stabilization conditions are written as linear matrix inequality lmi problems the proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the lmi problems numeric examples illustrate the effectiveness of this method

a new computational approach to stability analysis and synthesis of linguistic fuzzy control system in this paper stability analysis and synthesis of the type ii singleton type linguistic fuzzy control system are addressed first stability theorems are given for both continuous time case and discrete time case and they are recast in the formulation of bilinear matrix inequalities bmis continuous and discrete iterative linear matrix inequality methods are presented to obtain the feasible solution for the stability conditions represented as the bmi the interesting feature of this paper is that the suggested method can be applied not only to the stability analysis but also to the controller synthesis when it is applied to the synthesis of the type ii fuzzy logic controller the resulting one can theoretically guarantee the stability of the closed loop system finally the effectiveness of the suggested method is illustrated via computer simulation

singular continuous spectra in a pseudointegrable billiard the pseudointegrable barrier billiard invented by hannay and mccraw j phys a 23 887 1990 a rectangular billiard with line segment barrier placed on a symmetry axis is generalized it is demonstrated that the fourier spectrum of a typical function on the phase space exhibits a singular continuous component

the central limit theorem for markov chains started at a point the aim of this paper is to prove a central limit theorem and an invariance principle for an additive functional of an ergodic markov chain on a general state space with respect to the law of the chain started at a point no irreducibility assumption nor mixing conditions are imposed the only assumption bears on the growth of the l 2 norms of the ergodic sums for the function generating the additive functional which must be with the result holds almost surely with respect to the invariant probability of the chain

lmi based stability analysis for piecewise multi affine systems this paper provides a computational method to study the asymptotic stability of piecewise multi affine pma systems such systems stem from a class of fuzzy systems with singleton consequents and can be used to approximate any smooth nonlinear system with arbitrary accuracy based on the choice of piecewise lyapunov functions stability conditions are expressed as a feasibility test of a convex optimization with linear matrix inequality constraints the basic idea behind these conditions is to exploit the parametric expressions of pma systems by means of finsler s lemma numerical examples are given to point out the effectiveness of the proposed method

renormalisation of correlations in a barrier billiard quadratic irrational trajectories abstract we present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisation approach for quadratic irrational trajectories depending on the nature of the barrier this leads to either self similar or chaotic behaviour in the self similar case we give an analysis of the half barrier and present a detailed calculation of the locations asymptotic heights and signs of the main peaks in the autocorrelation function then we consider arbitrary barriers illustrating that typically these give rise to chaotic correlations of the autocorrelation function which we further represent by showing the invariant sets associated with these correlations our main ingredient here is a functional recurrence which has been previously derived and used in work on the harper equation strange non chaotic attractors and a quasi periodically forced two level system

golden mean renormalization for the harper equation the strong coupling fixed point we construct a renormalization fixed point corresponding to the strong coupling limit of the golden mean harper equation we give an analytic expression for this fixed point establish its existence and uniqueness and verify properties previously seen only in numerical calculations the spectrum of the linearization of the renormalization operator at this fixed point is also explicitly determined this strong coupling fixed point also helps describe the onset of a strange nonchaotic attractor in quasiperiodically forced systems

random walks in dynamic random environments a transference principle we study a general class of random walks driven by a uniquely ergodic markovian environment under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker that is the environment process we can transfer the rate of mixing in time of the environment to the rate of mixing of the environment process with a loss of at most polynomial order therefore the method is applicable to environments with sufficiently fast polynomial mixing we obtain unique ergodicity of the environment process moreover the unique invariant measure of the environment process depends continuously on the jump rates of the walker as a consequence we obtain the law of large numbers and a central limit theorem with nondegenerate variance for the position of the walk

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow