two three and four dimensional diffusion limited aggregation models abstract two three and four dimensional diffusion limited aggregation dla models with noise reduction and with growth probabilities proportional to small integer powers of the harmonic measure have been investigated using improved algorithms the results obtained from these simulations provide the basis for a more decisive test of theoretical results than ordinary dla simulations alone using off lattice models effective fractal dimensionalities d of about 1 41 and 1 29 were found for 2 and 3 respectively for a two dimensional d 2 embedding space for d 3 d 2 13 for 2 and d 1 90 for 3 similarly for d 4 d 2 97 for 2 and d 2 74 for 3 for the noise reduced dla lattice models our results are consistent with the idea that d d 1 in the asymptotic s m limit where s is the cluster size and m is the noise reduction parameter however for d 4 the effective fractal dimensionality is quite close to 3 for m 30

the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

stabilization of highly nonlinear hybrid systems by feedback control based on discrete time state observations given an unstable hybrid stochastic differential equation sde can we design a feedback control based on the discrete time observations of the state at times 0 tau 2 tau ldots so that the controlled hybrid sde becomes asymptotically stable it has been proved that this is possible if the drift and diffusion coefficients of the given hybrid sde satisfy the linear growth condition however many hybrid sdes in the real world do not satisfy this condition namely they are highly nonlinear and there is no answer to the question yet if the given sde is highly nonlinear the aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid sdes under some reasonable conditions on the drift and diffusion coefficients we show how to design the feedback control function and give an explicit bound on tau the time duration between two consecutive state observations whence the new theory established in this paper is implementable

growth pattern formation in benard flows abstract the effects of benard flows on diffusion limited aggregation dla is investigated by a growth pattern formation gpf computational model the gpf introduced consists of a dla process driven by a thermal convection field in a plane viscous incompresible flow the flow regime is governed by the grashoff prandtl and schmidt dimensionless parameters moving from low to high grashoff numbers the particle motions obtained change from primarily stochastic brownian trajectories with hausdorff dimension 2 0 to mainly deterministic curvilinear trajectories with hausdorff dimension 1 0 correspondingly the resulting clusters change their hausdorff dimension from the dla fractal to 1 0

stabilization of hybrid stochastic differential equations by feedback control based on discrete time state observations recently mao 2013 discusses the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations mao 2013 also obtains an upper bound on the duration between two consecutive state observations however it is due to the general technique used there that the bound on is not very sharp in this paper we will consider a couple of important classes of hybrid sdes making full use of their special features we will be able to establish a better bound on our new theory enables us to observe the system state less frequently so costs less but still to be able to design the feedback control based on the discrete time state observations to stabilize the given hybrid sdes in the sense of mean square exponential stability

on asymptotic convergence and boundedness of stochastic systems with time delay analyzing the long term behavior of a nonlinear dynamical system is an important but challenging task especially in the presence of noise and delays this paper investigates asymptotic convergence and boundedness properties of stochastic systems with time delay we are particularly interested in asymptotic convergence that may not be exponential as observed in many practical applications general criteria for checking both moment and almost sure asymptotic convergence and boundedness are established such criteria are mainly motivated by stochastic systems with time varying coefficients and multiple delays and or different orders of nonlinearities as shown by several examples the existing results cannot be applied to analyze such systems thus we generalize the existing theory by allowing the diffusion operator associated with a lyapunov function to satisfy a weaker assumption which involves time varying coefficients and several auxiliary functions to cope with possible multiple delays and or different orders of nonlinearities the results presented in this paper provide an effective tool for checking asymptotic convergence and boundedness properties of general stochastic nonlinear systems with time delay

delay dependent exponential stability of stochastic systems with time varying delay nonlinearity and markovian switching the problem of delay dependent stability in the mean square sense for stochastic systems with time varying delays markovian switching and nonlinearities is investigated both the slowly time varying delays and fast time varying delays are considered based on a linear matrix inequality approach delay dependent stability criteria are derived by introducing some relaxation matrices which can be chosen properly to lead to a less conservative result numerical examples are given to illustrate the effectiveness of the method and significant improvement of the estimate of stability limit over some existing results in the literature

theory of fractal growth abstract the problem we consider is to understand why nature gives rise to fractal structures the first step is to formulate models of fractal growth based on physical mechanisms like the diffusion limited aggregation and the more general dielectric breakdown model they are based on a simple iterative process governed by the laplace equation and a stochastic field and they give rise to patterns that spontaneously evolve into random fractal structures of great complexity in addition one would like to achieve a theoretical understanding of these models similar to that provided by the renormalization group for ising type models recently we have introduced a new theoretical framework for intrinsically critical growth models this method is based on a fixed scale transformation with respect to the dynamical evolution that defines a functional iteration for the distribution of elementary configurations that appear in a coarse graining process this allows to include screening effects in terms of convergent series and to describe the intrinsic fluctuations of the boundary conditions this approach clarifies the origin of fractal structures in these models and provides a systematic method for the calculation of the fractal dimension and the multifractal properties it also makes clear why the usual renormalization schemes are not suitable for these problems here we describe the basic ideas of this new approach and report about recent developments including the application to the percolation cluster interpreted as a problem of fractal growth

laplacian growth as one dimensional turbulence abstract a new model of laplacian stochastic growth is formulated using conformal mappings the model describes two growth regimes stable and turbulent separated by a sharp phase transition the first few fourier components of the mapping define the web an envelope of the cluster the web is used to study the transition and the dynamics of large scale features of the cluster characterized by evolution from macro to micro scales also we derive scaling laws for the cluster size

fractal landscapes in physics and biology the purpose of this talk is to describe some recent progress in three aspects of statistical physics that overlap biology the first of these represents a discovery about the real world for which we presently have no theoretical understanding 1 the second concerns the solution of a rich model of many body physics which should apply to a wide range of biological situations but presently applies primarily to mathematical ecology 2 the third concerns what on the one hand might be a mere numerical coincidence or on the other hand might represent evidence that diffusion limited aggregation describes the physical mechanism underlying the growth of nerve cells at least the quasi two dimensional nerve cells that grow in the retina 3

phase transition of binary component dla diffusion limited aggregation sql square lattice system contacted with thermal bath in the perimeter to make the dla model associate with more realistic processes of crystal growth the authors construct and study a new model including the experimental variables required diffusion particles of multicomponents diffuse on the square lattice as in the dla model the aggregation perimeter contacts with a thermal bath of temperature t and the sticking probability p consists of a constant probability pc and the thermal one pt at a neighbouring site of the perimeter as p 1 alpha pc alpha pt alpha is a parameter which includes the non equilibrium equilibrium tendency of the system pt is evaluated by the thermodynamic distribution of the ising system including up to next nearest neighbour interactions and chemical potentials the system has the possibility of phase transitions they show the phase transitions aggregation patterns correlation functions fractal dimensions and so on

the spectrum is continuous on the set of quasi n hyponormal operators abstract in this paper it is shown that the spectrum a set valued function is continuous when the function is restricted to the set of all quasi n hyponormal operators acting on an infinite dimensional separable hilbert space where a quasi n hyponormal operator is defined to be unitarily equivalent to an n n upper triangular operator matrix whose diagonal entries are hyponormal operators

almost sure exponential stability of hybrid stochastic functional differential equations abstract this paper is concerned with the almost sure exponential stability of the n dimensional nonlinear hybrid stochastic functional differential equation sfde d x t f 1 x t t r t t d t g 2 x t t r t t d b t where x t x t u u 0 is a c 0 r n valued process b t is an m dimensional brownian motion while r t is a markov chain we show that if the corresponding hybrid stochastic differential equation sde d y t f y t r t t d t g y t r t t d b t is almost surely exponentially stable then there exists a positive number such that the sfde is also almost surely exponentially stable as long as we also describe a method to determine which can be computed numerically in practice

razumikhin method and exponential stability of hybrid stochastic delay interval systems this paper deals with the exponential stability of hybrid stochastic delay interval systems also known as stochastic delay interval systems with markovian switching the known results in this area see e g x mao exponential stability of stochastic delay interval systems with markovian switching ieee trans automat control 47 10 2002 1604 1612 require the time delay to be a constant or a differentiable function and the main reason for such a restriction is due to the analysis of mathematics the main aim of this paper is to remove this restriction to allow the time delay to be a bounded variable only the razumikhin method is developed to cope with the difficulty arisen from the nondifferentiability of the time delay

stabilisation of hybrid stochastic systems with levy noise by discrete time feedback control this paper is devoted to deal with the stabilisation problems of continuous time hybrid stochastic systems often described by stochastic differential equations with markovian switching with levy

on the fractal characteristics of the η model abstract since the or dielectric breakdown model was proposed it has been generally accepted that the fractal characteristics of the so grown clusters have a smooth behavior as increases from 0 to infinity on the basis of recent theoretical calculations on a related model we conjecture that the aggregate can become effectively branchless for larger than a critical value 1 a related possibility is that the value 1 for the fractal dimension might be reached at finite values of we have carried out a large simulation program to test these conjectures and we find evidence supporting their validity this is a preliminary report of our work on this problem

almost sure exponential stabilization by discrete time stochastic feedback control given an unstable linear scalar differential equation dot x t alpha x t alpha 0 we will show that the discrete time stochastic feedback control sigma x t tau tau db t can stabilize it that is we will show that the stochastically controlled system dx t alpha x t dt sigma x t tau tau db t is almost surely exponentially stable when sigma 2 2 alpha and tau 0 is sufficiently small where b t is a brownian motion and t tau is the integer part of t tau we will also discuss the nonlinear stabilization problem by a discrete time stochastic feedback control the reason why we consider the discrete time stochastic feedback control is because that the state of the given system is in fact observed only at discrete times say 0 tau 2 tau ldots for example where tau 0 is the duration between two consecutive observations accordingly the stochastic feedback control should be designed based on these discrete time observations namely the stochastic feedback control should be of the form sigma x t tau tau db t from the point of control cost it is cheaper if one only needs to observe the state less frequently it is therefore useful to give a bound on tau from below as larger as better

exponential stability of stochastic delay interval systems with markovian switching in the past few years a lot of research has been dedicated to the stability of interval systems as well as the stability of systems with markovian switching however little research has been on the stability of interval systems with markovian switching which is the topic of this paper the system discussed is the stochastic delay interval system with markovian switching it is a very advanced system and takes all the features of interval systems ito equations and markovian switching as well as time lag into account the theory developed is applicable in many different and complicated situations so the importance of the paper is clear

updating the inverse of a matrix the sherman morrison woodbury formulas relate the inverse of a matrix after a small rank perturbation to the inverse of the original matrix the history of these fomulas is presented and various applications to statistics networks structural analysis asymptotic analysis optimization and partial differential equations are discussed the sherman morrison woodbury formulas express the inverse of a matrix after a small rank perturbation in terms of the inverse of the original matrix this paper surveys the history of these formulas and we examine some applications where these formulas are helpful

the spectrum is continuous on the set of p hyponormal operators in this paper it is shown that the spectrum sigma a set valued function is continuous when the function is restricted to the set of all p hyponormal operators on a hilbert space

technical communique stabilization of continuous time hybrid stochastic differential equations by discrete time feedback control in this paper we are concerned with the mean square exponential stabilization of continuous time hybrid stochastic differential equations also known as stochastic differential equations with the markovian switching by discrete time feedback controls although the stabilization by continuous time feedback controls for such equations has been discussed by several authors see e g ji and chizeck 1990 mao lam and huang 2008 mao yin and yuan 2007 wu shi and gao 2010 wu su and shi 2012 there is so far no result on the stabilization by discrete time feedback controls our aim here is to initiate the study in this area by establishing some new results

harmonic measure around a linearly self similar tree the authors use the concept of random multiplicative processes to help describe and understand the distribution of the harmonic measure on growing fractal boundaries the laplacian potential around a linearly self similar square koch tree is studied in detail the multiplicative nature of this potential and the consequent multifractality of the harmonic measure are discussed on prefractal stages the density d mu of the harmonic measure and the corresponding holder alpha ln d mu are well defined along the boundary except in the folds where the tangent is undefined a regularization scheme is introduced to eliminate these local effects they then consider the probability distributions p alpha d alpha of successive stages and discuss their collapse into an f alpha curve both the left and right hand sides of this curve show good convergence other studies indicate that for dla the right hand tail does not converge a brief comparison is made between the multifractality of these two cases

stabilization of multi group models with multiple dispersal and stochastic perturbation via feedback control based on discrete time state observations abstract this paper focuses on the multi group models with multiple dispersal and stochastic perturbation mgmds the effect of both multiple dispersal among groups and stochastic perturbation are taken into consideration the stabilization of mgmds is investigated via feedback control based on the discrete time state observations in addition a systematic method is given to construct a global lyapunov function for mgmds by means of graph theory and lyapunov method some sufficient conditions are obtained to ensure the stabilization in the sense of mean square asymptotical stability an upper bound of the duration between two consecutive state observations is estimated moreover to show the applicability of our results the main theory is employed to a stochastic coupled oscillators finally a numerical example is given to illustrate the effectiveness and feasibility of the theoretical results

quasi sure exponential stabilization of stochastic systems induced by g brownian motion with discrete time feedback control abstract in this paper we aim to study quasi sure exponential stabilization of stochastic systems induced by g brownian motion with discrete time feedback control as for an unstable system we use discrete stochastic feedback control to stabilize it if stochastic differential equation driven g brownian motion g sde in short is quasi sure exponential stability it reveals that there exist the discrete step size h 0 and a positive constant h with h h and the responding stochastically controlled system is also quasi sure exponential stability finally a simple example is also provided to show the validity of the control strategy

robust stability and stabilization of linear stochastic systems with markovian switching and uncertain transition rates abstract this paper is concerned with the robust stabilization problem for a class of linear uncertain stochastic systems with markovian switching the uncertain stochastic system with markovian switching under consideration involves parameter uncertainties both in the system matrices and in the mode transition rates matrix new criteria for testing the robust stability of such systems are established in terms of bi linear matrix inequalities blmis and sufficient conditions are proposed for the design of robust state feedback controllers a numerical example is given to illustrate the effectiveness of our results

stochastic model for dielectric breakdown we discuss a model for the development of discharge patterns in dielectric breakdown based on the laplace equation associated with a probability field the model gives rise to random fractals with well defined hausdorff dimensions the relations of this model with the diffusion limited aggregation are discussed in detail the possibility of application to other stochastic phenomena like fracture propagation is proposed

a discrete model for the lightning discharge for a lightning discharge model presented by the author j s nisbet and j r kasha j comput phys 82 193 1989 we simulate lightning by letting the conductivity tend to infinity wherever the electric field reaches the breakdown threshold here we show that for this discharge model and for a one parameter family of integration schemes the backward euler scheme is the only one that leads to the equilibration of the electric potential along the discharge channel moreover the potential obtained by letting the conductivity tend to infinity in the continuous equation is identical to the potential obtained in the backward euler approximation when conductivity tends to infinity connections to diffusion limited aggregation dla to more recent schemes for simulating the lightning discharge and to experiments of williamset al are discussed

stochastic stabilization of hybrid differential equations this paper aims to determine whether or not a stochastic state feedback control can stabilize a given linear or nonlinear hybrid system new methods are developed and sufficient conditions on the stability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization by stochastic feedback controls two types of structure controls namely state feedback and output injection are discussed our stabilization criteria are in terms of linear matrix inequalities lmis whence the feedback controls can be designed more easily in practice a couple of examples and computer simulations are worked out to illustrate our theory

continuity of the spectrum on a class of upper triangular operator matrices let b h denote the algebra of operators on an infinite dimensional complex hilbert space h and let a b k denote the berberian extension of an operator a b h it is proved that the set theoretic function the spectrum is continuous on the set c i b hi of operators a for which a 0 implies a is nilpotent possibly the 0 operator and a x0b a 1 0 a 1 0 at every non zero p a for some operators x and b such that p b and a b if cs m denotes the set of upper triangular operator matrices a aij i j 1m b i 1nhi where aii c i and aii has svep for all 1 i m then is continuous on cs m it is observed that a considerably large number of the more commonly considered classes of hilbert space operators constitute sets c i and have svep

stability of a random diffusion with linear drift we consider a linear system with markovian switching which is perturbed by gaussian type noise if the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable we also show that under certain conditions the linear system with markovian switching can be stabilized by such noisy perturbation

observability and detectability of discrete time stochastic systems with markovian jump abstract this paper studies detectability and observability of markov jump discrete time linear stochastic systems with multiplicative noise mjdls for short the relations between some concepts of detectability and observability are established these relations together with equivalent expressions of observability gramian allow us to obtain some other sufficient and necessary conditions of detectability and observability as applications discrete time stochastic lyapunov equations and stochastic discrete algebraic riccati equations sdare are discussed

the evolution and discharge of electric fields within a thunderstorm a 3 dimensional electrical model for a thunderstorm is developed and finite difference approximations to the model are analyzed if the spatial derivatives are approximated by a method akin to the scheme and if the temporal derivative is approximated by either a backward difference or the crank nicholson scheme we show that the resulting discretization is unconditionally stable the forward difference approximation to the time derivative is stable when the time step is sufficiently small relative to the ratio between the permittivity and the conductivity max norm error estimates for the discrete approximations are established to handle the propagation of lightning special numerical techniques are devised based on the inverse matrix modification formula and cholesky updates numerical comparisons between the model and theoretical results of wilson and holzer saxon are presented we also apply our model to a storm observed at the kennedy space center on july 11 1978

stabilisation of hybrid stochastic differential equations by delay feedback control this paper is concerned with the exponential mean square stabilisation of hybrid stochastic differential equations also known as stochastic differential equations with markovian switching by delay feedback controls although the stabilisation by non delay feedback controls for such equations has been discussed by several authors there is so far little on the stabilisation by delay feedback controls and our aim here is mainly to close the gap to make our theory more understandable as well as to avoid complicated notations we will restrict our underlying hybrid stochastic differential equations to a relatively simple form however our theory can certainly be developed to cope with much more general equations without any difficulty

behaviour of the harmonic measure at the bottom of fjords diffusion limited aggregates are among many important fractal shapes that involve deep indentations usually called fjords to estimate the harmonic measure at the bottom of a fjord seems a prohibitive task but the authors find that a new mathematical equality due to beurling carleson and jones makes it easy they find that the harmonic measure at the bottom of a fjord as a function of its euclidean depth can exhibit a wide range of behaviours they introduce an infinite family of model fjords for which the equality takes a very simple form in this family the decay of the harmonic measure at their bottoms can be for example power law semi exponential stretched exponential and exponentially stretched exponential they show that self affinity or randomness can lead to faster than power law decays of the minimal growth probability on boundaries

worst case control of uncertain jumping systems with multi state and input delay information in this paper the problem of worst case also called h control for a class of uncertain systems with markovian jump parameters and multiple delays in the state and input is investigated the jumping parameters are modelled as a continuous time discrete state markov process and the parametric uncertainties are assumed to be real time varying and norm bounded that appear in the state input and delayed state matrices the time delay factors are unknowns and time varying with known bounds complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak delay dependent stochastic stability with a prescribed h performance the solutions are provided in terms of a finite set of coupled linear matrix inequalities lmis application of the developed theory to a typical example has been presented

on almost sure stability of hybrid stochastic systems with mode dependent interval delays this note develops a criterion for almost sure stability of hybrid stochastic systems with mode dependent interval time delays which improves an existing result by exploiting the relation between the bounds of the time delays and the generator of the continuous time markov chain the improved result shows that the presence of markovian switching is quite involved in the stability analysis of delay systems numerical examples are given to verify the effectiveness

admissibility and stabilization of stochastic singular markovian jump systems with time delays abstract this paper deals with the admissibility analysis and stabilization of stochastic singular markovian jump systems ssmjss with time delays more general conditions for the existence and uniqueness of the impulse free solution to delayed ssmjss are presented consequently by constructing stochastic lyapunov krasovskii functional and applying generalized ito formula new sufficient conditions for the stability of ssmjss and delayed ssmjss are obtained in terms of strict linear matrix inequalities state feedback controller is designed to ensure stabilization of the delayed ssmjss three illustrative examples including an r l c circuit network and an oil catalytic cracking process are employed to verify the effectiveness and usefulness of the obtained results

robust integral sliding mode control for uncertain stochastic systems with time varying delay this paper is concerned with sliding mode control for uncertain stochastic systems with time varying delay both time varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system an integral sliding surface is first constructed then by means of linear matrix inequalities lmis a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties the synthesized sliding mode controller guarantees the reachability of the specified sliding surface finally a simulation example is presented to illustrate the proposed method

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

stabilization of hybrid neutral stochastic differential delay equations by delay feedback control abstract this paper is concerned with the problem of exponential mean square stabilization of hybrid neutral stochastic differential delay equations with markovian switching by delay feedback control a delay feedback controller is designed in the drift part so that the controlled system is mean square exponentially stable we discussed two types of structure controls that is state feedback and output injection the stabilization criteria are derived in terms of linear matrix inequalities

approximations to the multiplier method we analyze approximations to the multiplier method for solving an equality constrained optimization problem the multiplier method replaces the constrained problem by the unconstrained optimization of a penalized lagrangian over a hilbert space we consider the effect of replacing this hilbert space by a subspace the analysis is closely connected to an analysis of the galerkin approximation to the original optimization problem our estimates are essentially corollaries of a theorem which bounds the error in the galerkin approximation to a nonlinear equation some applications to problems in optimal control are discussed

quasi sure exponential stability and stabilisation of stochastic delay differential equations under g expectation framework in this work we obtain the sufficient conditions to examine quasi sure exponential stability of stochastic delay differential equation under g expectation framework in short g sdde our argumen

concept of complexity in random dynamical systems we introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system in dynamical systems with small random perturbations this indicator coincides with the rate k of divergence of nearby trajectories evolving under two different noise realizations the meaning of k is discussed in the context of the information theory and it is shown that it can be determined from real experimental data in the presence of strong dynamical intermittency the value of k is very different from the standard lyapunov exponent ensuremath lambda mathrm ensuremath sigma computed considering two nearby trajectories evolving under the same realization of the randomness however the former is much more relevant than the latter from a physical point of view as illustrated by some numerical computations for noisy maps and sandpile models textcopyright 1996 the american physical society

exponential mean square stability of time delay singular systems with markovian switching and nonlinear perturbations abstract this paper considers exponential stability in mean square of singular markovian jump systems the systems under consideration involve nonlinear perturbation and time varying delays by using the lyapunov krasovskii functional delay dependent stability conditions in terms of linear matrix inequality lmi are addressed which guarantee exponential mean square stability and a prescribed h performance index for the considered systems two numerical examples are given to illustrate the effectiveness of the proposed main results

stabilization of stochastic differential equations driven by g brownian motion with feedback control based on discrete time state observation abstract this paper mainly concerns the stability of the solutions for stochastic differential equations driven by g brownian motion g sdes via feedback control based on discrete time state observation more precisely the discrete time state feedback control is included in the drift coefficient of the g sdes by constructing an appropriate g lyapunov function a set of conditions is obtained for the h stability asymptotic stability and mean square exponential stability of the controlled systems finally an example with numerical simulation is presented to illustrate the effectiveness of the proposed control design technique

delay dependent stability of highly nonlinear hybrid stochastic systems abstract there are lots of papers on the delay dependent stability criteria for differential delay equations ddes stochastic differential delay equations sddes and hybrid sddes a common feature of these existing criteria is that they can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions namely satisfy the linear growth condition in other words there is so far no delay dependent stability criterion on nonlinear equations without the linear growth condition we will refer to such equations as highly nonlinear ones this paper is the first to establish delay dependent criteria for highly nonlinear hybrid sddes it is therefore a breakthrough in the stability study of highly nonlinear hybrid sddes

theory of laplacian fractals diffusion limited aggregation and dielectric breakdown model abstract we describe a new theoretical approach that clarifies the origin of fractal structures in irreversible growth models based on the laplace equation and a stochastic field this new theory provides a systematic method for the calculation of the fractal dimension d and of the multifractal spectrum of the growth probability a detailed application to the dielectric breakdown model and diffusion limited aggregation in two dimensions is presented our approach exploits the scale invariance of the laplace equation that implies that the structure is self similar both under growth and scale transformation this allows one to introduce a fixed scale transformation instead of coarse graining as in the renormalization group theory that defines a functional equation for the fixed point of the distribution of basic diagrams used in the coarse graining process for the calculation of the matrix elements of this transformation one has to consider an infinite but rapidly convergent number of processes that occurs outside a considered diagram

stabilization and destabilization of hybrid systems of stochastic differential equations this paper aims to determine whether or not a stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system new methods are developed and sufficient conditions on the stability and instability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization and destabilization

a note on delay dependent stability of ito type stochastic time delay systems different from the existing delay dependent stability criteria which depend on the size of the delays in both the drift and diffusion parts of stochastic time delay systems stdss this paper shows that the delay dependent stability criterion depends only on the drift part and works for arbitrary large delays of the diffusion part of stdss by developing the stochastic version descriptor system approach simple stability criterion is further derived for aperiodic sampled data stochastic systems the theoretical results are illustrated by means of a numerical example

brief paper robust exponential stabilization for markovian jump systems with mode dependent input delay this paper is concerned with the problem of exponential stabilization for uncertain linear systems with markovian jump parameters and mode dependent input delays sufficient stabilization conditions are developed in terms of matrix inequalities which can be solved by a proposed iterative algorithm based on the cone complementarity linearization ccl method memory controllers are also designed such that the closed loop system is exponentially mean square stable for all admissible uncertainties numerical examples are given to show that the developed method is efficient and less conservative

theoretical concepts for fractal growth abstract after the introduction of fractal geometry by benoit mandelbrot the key problem is to understand why nature gives rise to fractal structures this implies the formulation of models of fractal growth based on physical phenomena and the subsequent understanding of their mathematical structure in the same sense as the renormalization group has allowed to understand sing type models the models of diffusion limited aggregation and the more general dielectric breakdown model based on iterative processes governed by the laplace equation and a stochastic field have a clear physical meaning and they spontaneously evolve into random fractal structures of great complexity from a theoretical point of view however it is not possible to describe them within usual concepts recently we have introduced a new theoretical framework for this class of problems this clarifies the origin of fractal structures in these models and provides a systematic method for the calculation of the fractal dimension and the multifractal properties here we summarize the basic ideas of this new approach and report about recent developments