brief paper a numerical sufficiency test for the asymptotic stability of linear time varying systems a numerical sufficiency test for the asymptotic stability of linear time varying hurwitz systems is proposed the algorithmic procedure constructs a bounding tube in which the state is guaranteed to stay the continuous time system is evaluated at discrete time instants for which successive quadratic lyapunov functions are generated the tube is constructed based on i a conservative estimate of the state evolution from a discrete time instant to the next obtained from the corresponding lyapunov function and ii re evaluation of the tube diameter at each discrete time instant to account for variations in the plant matrix the numerical test is illustrated in simulation via both a stable and an unstable system

new stability conditions for a class of linear time varying systems this paper considers the problem of asymptotic stability for linear time varying systems of the form x t a t x t some new stability conditions are proposed first two stability conditions for nonlinear time varying systems are given by using non monotonic lyapunov functions then the results obtained are extended to the linear case two stability conditions with infinite integral are derived furthermore by using the top floor function a linear matrix inequalities lmi condition and an eigenvalue criterion for asymptotic stability of systems are presented comparing with the existing results the conditions obtained allow both a t and a t are unbounded at t some numerical examples are provided to show the effectiveness of the theoretical results

new sufficient conditions for the stability of slowly varying linear systems the frozen time approach is used to state some new sufficient conditions for the stability of linear time varying systems an upper bound on the norm of the time derivative of system matrix which under different assumptions on frozen time system eigenvalues guarantees asymptotic stability or exponential stability of the system is established

enlargement of obstacles for the simple random walk we consider a continuous time simple random walk moving among obstacles which are sites resp bonds of the lattice z d we derive in this context a version of the technique of enlargement of obstacles developed by sznitman in the brownian case this method gives controls on exponential moments of certain death times as well as good lower bounds for certain principal eigenvalues we give an application to recover an asymptotic result of donsker and varadhan on the number of sites visited by the random walk and another application to the number of bonds visited by the random walk

an alternate stability analysis framework for adaptive control n abstract a proof is given for the uniform asymptotic stability of a class of pointwise in time stable systems of time varying ordinary differential equations the sufficient conditions for stability are shown to be naturally testable in a general adaptive control context a weak form of robust identification is found to imply robust stability of the overall closed loop adaptive control system

assessing asymptotic stability of linear continuous time varying systems by computing the envelope of all trajectories in this note necessary and sufficient numerical conditions for asymptotic stability and for uniform asymptotic stability of linear continuous time varying systems are derived for a given set of initial conditions a tube containing all the trajectories of the system is constructed in the state space at each instant of time there exists an initial condition inside the set such that the resulting trajectory attains the border of the tube based on the above formulation necessary and sufficient conditions for asymptotic stability and for uniform asymptotic stability are expressed through the solution of a linear differential lyapunov equation the conditions can deal with the stability of periodic systems as well one of the main characteristics of the proposed necessary and sufficient conditions is that the only assumption on the dynamical matrix of the time varying system is continuity examples from the literature illustrate the superiority of the proposed conditions when compared to other methods

fuzzy hypervector spaces based on fuzzy singletons we introduce and study fuzzy hypervector spaces based on fuzzy singletons in this regard by considering the notion of fuzzy singletons we characterize a fuzzy hypervector space fuzzily spanned by a fuzzy subset then we use these results to introduce the concept of fuzzy freeness of a fuzzy subset m of a hypervector space v and finally we characterize it in terms of linear independence in the usual sense

relaxed conditions for the exponential stability of a class of linear time varying systems this technical note states new sufficient conditions for the exponential stability of linear time varying ltv systems of the form aeligmacr ldr a t aelig t the approach proposed derives and uses the notion of perturbed frozen time pft form that can be associated to any ltv system exploiting the bellman gronwall lemma relaxed stability conditions are then stated in terms of ldquoaveragerdquo parameter variations salient features of the approach are pointwise stability of a ldr is not required amacr ldr may not be bounded the stability conditions also apply to uncertain systems the approach is illustrated by numerical examples

limit theorems for sums of random exponentials we study limiting distributions of exponential sums open image in new window as t n where x i are i i d random variables two cases are considered a ess sup x i 0 and b ess sup x i we assume that the function h x log p x i x case b or h x log p x i 1 x case a is regularly varying at with index 1 case b or 0 case a the appropriate growth scale of n relative to t is of the form open image in new window where the rate function h0 t is a certain asymptotic version of the function open image in new window case b or open image in new window case a we have found two critical points 1 2 below which the law of large numbers and the central limit theorem respectively break down for 0 2 under the slightly stronger condition of normalized regular variation of h we prove that the limit laws are stable with characteristic exponent 0 2 and skewness parameter 1

quenched to annealed transition in the parabolic anderson problem we study limit behavior for sums of the form frac 1 lambda l sum x in lambda l u t x where the field lambda l left x in bf z d x le l right is composed of solutions of the parabolic anderson equation u t x 1 kappa mathop int 0 t delta u s x rm d s mathop int 0 t u s x partial b x s the index set is a box in zd namely lambda l left x in bf z bf d x leq l right and l l t is a nondecreasing function l 0 infty rightarrow bf r we identify two critical parameters eta 1 eta 1 and l t e t the sums frac 1 lambda l sum x in lambda l u t x satisfy a law of large numbers or put another way they exhibit annealed behavior for gamma eta 2 and l t e t one has sum x in lambda l u t x when properly normalized and centered satisfies a central limit theorem for subexponential scales that is when lim t rightarrow infty frac 1 t ln l t 0 quenched asymptotics occur that means lim t rightarrow infty frac 1 t ln left frac 1 lambda l sum x in lambda l u t x right gamma kappa where gamma kappa is the almost sure lyapunov exponent i e lim t rightarrow infty frac 1 t ln u t x gamma kappa we also examine the behavior of frac 1 lambda l sum x in lambda l u t x for l e t with in the transition range 0 eta 1

fuzzy ideals and fuzzy subalgebras of lie algebras abstract a fuzzy idea l of a lie algebra l factors it into a lie algebra l l called a fuzzy quotient lie algebra this fuzzy algebra lie algebra is always a fuzzy partition of l and a fuzzy partition of l will be a fuzzy quotient lie algebra if and only if its associated fuzzy similarity relation is compatible with the lie algebra operations relationship between the operations of the lie algebras l i t and zadeh s extension principle are studied we also study homomorphisms of lie algebras and the relationship between them and fuzzy ideals and fuzzy subalgebras of the domains and the co domains of these homomorphisms finally solvability of fuzzy ideals and studied in defining these solvable fuzzy ideals we use zadeh s extension principle

unified stability criteria for slowly time varying and switched linear systems this paper presents a unified approach to formulating stability conditions for slowly time varying linear systems and switched linear systems the concept of total variation is generalized to the case of matrix valued functions using this generalized concept a result extending existing stability conditions for slowly time varying linear systems is derived as special cases of this result two sets of stability conditions are derived for switched linear systems which match known results in the literature a numerical example is included to further illustrate the application of the main result

parabolic problems for the anderson model the objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics in particular in hydrodynamics on a qualitative level intermittent random fields are distinguished by the appearance of sparsely distributed sharp peaks which give the main contribution to the formation of the statistical moments the paper deals with the cauchy problem t u t x hu t x u 0 x t0 x 0 t x d for the anderson hamiltonianh x x d where is a generally unbounded spatially homogeneous random potential this first part is devoted to some basic problems using percolation arguments a complete answer to the question of existence and uniqueness for the cauchy problem in the class of all nonnegative solutions is given in the case of i i d random variables necessary and sufficient conditions for intermittency of the fieldsu t ast are found in spectral terms ofh rough asymptotic formulas for the statistical moments and the almost sure behavior ofu t x ast are also derived

precise large deviation estimates for a one dimensional random walk in a random environment suppose that the integers are assigned i i d random variables f xg taking values in the interval 1 2 1 which serve as an environment thisenvironmentdenesarandomwalk fxkg calledarwre which when at x moves one step to the right with probability x and one step to the left withprobability1 x solomon 1975 determinedthealmost sureasymp totic speed rate of escape of a rwre in a more general set up dembo peres and zeitouni 1996 following earlier work by greven and den hol lander 1994 on the quenched case have computed rough tail asymptotics for the empirical mean of the annealed rwre they conjectured the form of the rate function in a full ldp we prove in this paper their conjecture the proof is based on a icoarse graining schemei together with comparison techniques

transition from the annealed to the quenched asymptotics for a random walk on random obstacles in this work we study a natural transition mechanism describing the passage from a quenched almost sure regime to an annealed in average one for a symmetric simple random walk on random obstacles on sites having an identical and independent law the transition mechanism we study was first proposed in the context of sums of identical independent random exponents by ben arous bogachev and molchanov in probab theory related fields 132 2005 579 612 let p x t be the survival probability at time t of the random walk starting from site x and let l t be some increasing function of time we show that the empirical average of p x t over a box of side l t has different asymptotic behaviors depending on l t there are constants 0 1 a law of large numbers is satisfied and the empirical survival probability decreases like the annealed one if l t e td d 2 with y 2 also a central limit theorem is satisfied if l t t the averaged survival probability decreases like the quenched survival probability if t l t and log l t t d d 2 we obtain an intermediate regime furthermore when the dimension d 1 it is possible to describe the fluctuations of the averaged survival probability when l t e td d 2 with y 2 it is shown that they are infinitely divisible laws with a levy spectral function which explodes when x 0 as stable laws of characteristic exponent a 2 these results show that the quenched and annealed survival probabilities correspond to a low and high temperature behavior of a mean field type phase transition mechanism

sufficient conditions for stability of linear time varying systems abstract in this paper we consider sufficient conditions for the exponential stability of linear time varying systems of the form dot x t a t x t t 0 stability guaranteeing upper bounds for different measures of parameter variations are derived

paper an approach to stable indirect adaptive control stable indirect adaptive control of minimum and nonminimum phase plants is established for cases where a priori bounds on the unknown plant parameters are known and where for each set of parameter values within these bounds the plant has no unstable pole zero cancellation by incorporating this partial parameter knowledge in the adaptive law and using a nonminimal representation of the plant it is shown that the adaptive closed loop control system can be written as an exponentially stable system driven by the identification error the stability of the adaptive control system is then shown using techniques similar to those known from the model reference adaptive control approach

large deviation principle for random walk in a quenched random environment in the low speed regime we consider a one dimensional random walk x n n n in a random environment of zero or strictly positive drifts we establish a full large deviation principle for x n n of the correct order n log n 2 in the low speed regime valid for almost every environment this completes the large deviation picture obtained earlier by greven and den hollander and gantert and zeitouni in the case of zero and positive drifts the proof uses coarse graining along with concentration of measure techniques

parabolic problems for the anderson model i intermittency and related topics the objective of this paper is a mathematically rigorous investigation of intermittency and related questions intensively studied in different areas of physics in particular in hydrodynamics on a qualitative level intermittent random fields are distinguished by the appearance of sparsely distributed sharp peaks which give the main contribution to the formation of the statistical moments the paper deals with the cauchy problem t u t x hu t x u 0 x t 0 x 0 t x d for the anderson hamiltonianh x x d where is a generally unbounded spatially homogeneous random potential this first part is devoted to some basic problems using percolation arguments a complete answer to the question of existence and uniqueness for the cauchy problem in the class of all nonnegative solutions is given in the case of i i d random variables necessary and sufficient conditions for intermittency of the fieldsu t ast are found in spectral terms ofh rough asymptotic formulas for the statistical moments and the almost sure behavior ofu t x ast are also derived

control of slowly varying linear systems state feedback control of slowly varying linear continuous time and discrete time systems with bounded coefficient matrices is studied in terms of the frozen time approach this study centers on pointwise stabilizable systems these are systems for which there exists a state feedback gain matrix placing the frozen time closed loop eigenvalues to the left of a line re s gamma

fuzzy logic based generalized decision theory with imperfect information the existing decision models have been successfully applied to solving many decision problems in management business economics and other fields but nowadays arises a need to develop more realistic decision models the main drawback of the existing utility theories starting from von neumann moregnstern expected utility to the advanced non expected models is that they are designed for laboratory examples with simple well defined gambles which do not adequately enough reflect real decision situations in real life decision making problems preferences are vague and decision relevant information is imperfect as described in natural language nl vagueness of preferences and imperfect decision relevant information require using suitable utility model which would be fundamentally different to the existing precise utility models precise utility models cannot reflect vagueness of preferences vagueness of objective conditions and outcomes imprecise beliefs etc the time has come for a new generation of decision theories in this study we propose a decision theory which is capable to deal with vague preferences and imperfect information the theory discussed here is based on a fuzzy valued non expected utility model representing linguistic preference relations and imprecise beliefs

analytic feedback control and the algebraic riccati equation the central result of this correspondence is lemma 1 1 which states that the stabilizing solution p to the algebraic riccati equation in a b c depends analytically on a b c in the remainder of the correspondence various control and system theoretic ramifications of the analyticity lemma are considered an important consequence of lemma 1 1 is that any smooth state feedback control law for a finite dimensional plant may be implemented using dynamic input output compensators whose transfer functions depend smoothly on the plant transfer function

parameter information content of measurable signals in direct adaptive control it is postulated that available parameter information is a functional of all past history of measurable signals from this point of view direct model reference adaptive controllers become functional differential equations a modified model reference adaptive control structure and functional adaptation algorithm are presented it is shown that the system is well defined stable and achieves asymptotic model transfer function matching under weaker excitation conditions than those required by earlier model reference adaptive systems it is claimed that the information content perspective developed in this paper has implications in robust adaptive control theory

biased random walks on galton watson trees with leaves we consider a biased random walk xn on a galton watson tree with leaves in the sub ballistic regime we prove that there exists an explicit constant 0 1 depending on the bias such that xn is of order n denoting n the hitting time of level n we prove that n n1 is tight moreover we show that n n1 does not converge in law at least for large values of we prove that along the sequences n k k n n1 converges to certain infinitely divisible laws key tools for the proof are the classical harris decomposition for galton watson trees a new variant of regeneration times and the careful analysis of triangular arrays of i i d heavy tailed random variables

stability of linear nonautonomous multivariable systems with differentiable matrices abstract we consider linear nonautonomous multivariable systems with differentiable matrices explicit stability conditions are derived in the appropriate situations our results improve the traditional freezing method

fuzzy linear spaces over valued fields abstract the concept of fuzzy linear spaces was introduced by nanda 3 the purpose of the present paper is to introduce some further concepts such as convex fuzzy sets etc in fuzzy linear spaces over any valued field

convex fuzzy mappings abstract in this note the concept of convexity and logarithmic convexity for fuzzy mappings are introduced and some applications to optimization are discussed