stabilization of a class of stochastic differential equations with markovian switching stability of stochastic differential equations with markovian switching has been studied quite extensively for a number of years for example by basak et al j math anal appl 202 1996 604 622 ji and chizeck ieee trans automat control 35 1990 777 788 mariton jump linear systems in automatic control marcel dekker new york 1990 mao et al stochastic process appl 79 1999 45 67 bernoulli 6 2000 73 90 and yuan and lygeros in r alur g pappas eds hybrid systems computation and control seventh international workshop hscc 2004 lecture notes in computer science vol 2993 springer berlin 2004 pp 646 659 by contrast the problem of designing controllers to stabilize systems of this type has received relatively little attention in this paper we study the problem of mean square exponential stabilization for a class of stochastic differential equations with markovian switching

reliable asynchronous sampled data filtering of t s fuzzy uncertain delayed neural networks with stochastic switched topologies abstract this paper investigates the issue of the reliable asynchronous sampled data filtering of takagi sugeno t s fuzzy delayed neural networks with stochastic intermittent faults randomly occurring time varying parameters uncertainties and controller gain fluctuation the asynchronous phenomenon occurs between the system modes and controller modes first in order to reduce the utilization rate of communication bandwidth a novel alterable sampled data terminal method is considered via variable sampling rates second based on the fuzzy model based control approach improved reciprocally convex inequality and new parameter time dependent discontinuous lyapunov approach several relaxed conditions are derived and compared with the existing work third the intermittent fault tolerance scheme is also taken into fully account in designing a reliable asynchronous sampled data controller which ensures such that the resultant neural networks is asymptotically stable finally two numerical examples are presented to illustrate the effectiveness and advantages of the theoretical results

disturbance observer based control for semi markovian jump systems with generally uncertain transition rate and saturation nonlinearity abstract this paper deals with the problem of disturbance observer based control dobc for semi markovian jump systems s mjss with generally uncertain transition rate tr and saturation nonlinearity unlike the existing theories the proposed method considers the external disturbance and saturation nonlinearity in s mjss with more general tr first of all to study this dobc problem the sufficient condition for stochastic stability of the system is derived by the use of lyapunov krasovskii functional then the design methods of the anti disturbance controller and the disturbance observer are proposed based on the given stability condition of the closed loop system furthermore the maximum domain of attraction is estimated by solving an optimization iterative algorithm finally two numerical examples are given to prove the correctness of the proposed results

stability analysis of stochastic delay differential equations with levy noise abstract this paper is concerned with p th moment exponential stability problem for a class of stochastic delay differential equations driven by levy processes several new stability theorems are obtained by developing a method proof by contradiction moreover the results are applied to investigate the p th moment exponential stability of stochastic neural networks with levy noise in particular the time varying delay in our results is not required to be differentiable even not continuous the obtained results improve greatly some previous works given in the literature in particular our method can easily correct the incorrect proofs appeared in two recent papers finally two examples are provided to show the effectiveness of the theoretical results

stabilization for switched stochastic systems with semi markovian switching signals and actuator saturation abstract in this paper the asymptotic stabilization problem is investigated for a class of switched stochastic systems with semi markovian switching signals and actuator saturation by using the stochastic analysis theory and multiple lyapunov function method sufficient conditions for the local asymptotic mean square stability of the related system are established based on the stationary distribution of the embedded markov chain moreover the mode dependent state feedback controller and estimation of domain of attraction in mean square sense are proposed in terms of a family of decoupled linear matrix inequalities lmis finally two examples are provided to illustrate the effectiveness of the proposed results

three point boundary value problems for second order discrete equations we formulate existence results for solutions to discrete equations which approximate three point boundary value problems for second order ordinary differential equations c 2003 elsevier science ltd all rights reserved

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

impulses induced p exponential input to state stability for a class of stochastic delayed partial differential equations abstractthis paper proposes a new stability concept called p exponential input to state stability piss for impulsive stochastic delayed partial differential equations isdpdes by employing the

comparison of eigenvalues for sturm liouville boundary value problems on a measure chain under consideration is a class of even ordered linear differential equations 1 m 2m t i 0m 1pi t 2i t with sturm liouville boundary conditions i 2i 0 i 2i 0 yi 1 2i 1 i 1 2i 1 0 for 0 i m 1 the derivative in this dynamic equation is the generalized delta derivative defined on a measure chain for a pair of eigenvalue problems for this dynamic equation we first verify the existence of smallest positive eigenvalues and then establish a comparison between the smallest eigenvalues of each eigenvalue problem

fixed sign solutions of second order difference equations with neumann boundary conditions in this paper we study the existence of solution of the nonlinear second order difference problem with neumann boundary conditions assuming the existence of a pair of ordered lower and upper solutions and we obtain optimal existence results for the case and even for to this end we do an exhaustive study of the values of the real parameters and for which the associated green s function to the linear operator l u u 2 2 u 1 u with neumann boundary conditions has fixed sign

higher order boundary value problems on time scales in this paper we study the existence of solutions for lidstone boundary value problems on time scale firstly by using schauder fixed point theorem in a cone we obtain the existence of solutions to a lidstone boundary value problem lbvp secondly existence result for this problem is also given by the monotone method finally by using krasnosel skii fixed point theorem it is proved that the lbvp has a positive solution

multiple fixed sign solutions for a system of difference equations with sturm liouville conditions we consider the following system of difference equations d mu i k p i k u 1 k u 2 k u n k 0 k 0 1 n i 1 2 ntogether with sturm liouville boundary conditions d ju i 0 0 0 2 n m 1 z 0 w 0 h 0 d w z w n 1 z d h w 0 by using two different fixed point theorems we develop criteria for the existence of three solutions of the system which are of fixed signs on 0 1 n m examples are also included to illustrate the results obtained

stability analysis of stochastic differential equations with markovian switching abstract this paper discusses the asymptotic stability of the nonlinear stochastic differential equations with markovian switching sdewmss the equations under consideration are more general whose transition jump rates matrix q is not precisely known by using the switching process jump times to subdivide the time and then investigate the related sequence we provide sufficient conditions for asymptotic stability of sdewmss when each subsystem is stable and a certain slow switching condition holds for the general multi dimensional linear sdewmss sufficient conditions via bi linear matrix inequalities are also proposed for the design of robust stabilization some examples are given to illustrate the effectiveness of our results

input to state stability for impulsive stochastic nonlinear systems with delayed impulses in this paper the problems of the stochastic input to state stability siss properties are investigated for impulsive stochastic nonlinear systems with delayed impulses by employing lyapunov method together with average impulsive interval approach the sufficient conditions are established to ensure properties for impulsive stochastic systems with all stable subsystems moreover the iss properties are also derived for the stochastic systems when the system is with both stable and unstable subsystems then we also study impulsive systems with multiple jumps i e there exist different impulses in a system by now there has been no papers to consider multiple jumps for stochastic cases finally two examples are provided to illustrate the effectiveness of our results

isomorphism rigidity of irreducible algebraic ℤd actions an irreducible algebraic d action on a compact abelian group x is a d action by automorphisms of x such that every closed invariant subgroup y x is finite we prove the following result if d 2 then every measurable conjugacy between irreducible and mixing algebraic d actions on compact zero dimensional abelian groups is affine for irreducible expansive and mixing algebraic d actions on compact connected abelian groups the analogous statement follows essentially from a result by katok and spatzier on invariant measures of such actions cf 4 and 3 by combining these two theorems one obtains isomorphism rigidity of all irreducible expansive and mixing algebraic d actions with d 2

eigenvalue comparisons for a class of boundary value problems of second order difference equations abstract we consider the boundary value problem for second order difference equation r i 1 y i 1 b i y i a i y i 0 1 i n y 0 y 1 y n 1 y n 0 in this study we do not require the positiveness of a k k 1 n we focus on the structure of eigenvalues of this problem and comparisons of all eigenvalues as the coefficients a i i 1 n b i i 1 n r i i 0 n and the parameters change

algebraic ℤ actions of entropy rank one we investigate algebraic z d actions of entropy rank one namely those for which each element has finite entropy such actions can be completely described in terms of diagonal actions on products of local fields using standard adelic machinery this leads to numerous alternative characterizations of entropy rank one both geometric and algebraic we then compute the measure entropy of a class of skew products where the fiber maps are elements from an algebraic z d action of entropy rank one this leads via the relative variational principle to a formula for the topological entropy of continuous skew products as the maximum of a finite number of topological pressures we use this to settle a conjecture concerning the relational entropy of commuting toral automorphisms

stability analysis for stochastic hybrid systems this survey addresses stability analysis for stochastic hybrid systems shs which are dynamical systems that combine continuous change and instantaneous change and that also include random effects we re emphasize the common features found in most of the models that have appeared in the literature which include stochastic switched systems markov jump systems impulsive stochastic systems switching diffusions stochastic impulsive systems driven by renewal processes diffusions driven by levy processes piecewise deterministic markov processes general stochastic hybrid systems and stochastic hybrid inclusions then we review many of the stability concepts that have been studied including lyapunov stability lagrange stability asymptotic stability and recurrence next we detail lyapunov based sufficient conditions for these properties and additional relaxations of lyapunov conditions many other aspects of stability theory for shs like converse lyapunov theorems and robustness theory are not fully developed hence we also formulate some open problems to serve as a partial roadmap for the development of the underdeveloped pieces

mahler measure and entropy for commuting automorphisms of compact groups we compute the joint entropy ofd commuting automorphisms of a compact metrizable group letr d u 1 1 d 1 1 be the ring of laurent polynomials ind commuting variables andm be anr d module then the dual groupx m ofm is compact and multiplication onm by each of thed variables corresponds to an action m of d by automorphisms ofx m every action of d by automorphisms of a compact abelian group arises this way iff r d our main formula shows that the topological entropy of alpha r d left langle f right rangle is given by h left alpha r d left langle f right rangle right log m left f right int limits 0 1 ldots int limits 0 1 log left f left e 2 pi it 1 ldots e 2 pi it d right right dt 1 ldots dt d where m f is the mahler measure off this reduces to the classical result for toral automorphisms via jensen s formula while the entropy of a single automorphism of a compact group is always the logarithm of an algebraic integer this no longer seems to hold for joint entropy of commuting automorphisms since values such as 7 3 4 2 occur if p is a non principal prime ideal we show h left alpha r d p right 0 using an analogue of the yuzvinskii thomas addition formula we computeh m for arbitraryr d modulesm and then the joint entropy for an action of d on a not necessarily abelian compact group using a result of boyd we characterize those m which have completely positive entropy in terms of the prime ideals associated tom and show this condition implies that m is mixing of all orders we also establish an analogue of berg s theorem proving that if m has finite entropy then haar measure is the unique measure of maximal entropy if and only if m has completely positive entropy finally we show that for expansive actions the growth rate of the number of periodic points equals the topological entropy

twin positive solutions of boundary value problems for finite difference equations with p laplacian operator abstract in this paper a new twin fixed point theorem is applied to obtain the existence of at least two positive solutions for the boundary value problem p u k a k f u k 0 k 0 n u n 1 0 u 0 b 0 u 0 0 in addition two corollaries and an example are given to illustrate the main results

noise suppresses or expresses exponential growth in this paper we will show that noise can make a given system whose solutions grow exponentially become a new system whose solutions will grow at most polynomially on the other hand we will also show that noise can make a given system whose solutions are bounded become a new system whose solutions will grow exponentially in other words we reveal that the noise can suppress or expresses exponential growth

exponential stability and instability of impulsive stochastic functional differential equations with markovian switching in this paper based on the lyapunov second method and razumikin techniques we establish some novel criteria on pth moment exponential stability almost exponential stability and instability of impulsive stochastic functional differential equations isfdes with markovian switching the findings show that impulsive stochastic functional equations with markovian switching can be exponentially stabilized by impulses finally an example is presented to illustrate the effectiveness and efficiency of the obtained results

spectral theory of second order vector difference equations abstract this paper is concerned with spectral problems of second order vector difference equations with two point boundary value conditions where the matrix valued coefficient of the leading term may be singular a concept of self adjointness of the boundary value conditions is introduced the self adjointness of the corresponding difference operator is discussed on a suitable admissible function space and fundamental spectral results are obtained the dual orthogonality of eigenfunctions is shown in a special case rayleigh s principles and the minimax theorems in two linear spaces are given as an application a comparison theorem for eigenvalues of two sturm liouville problems is presented

comparison of eigenvalues for lidstone boundary value problems on a measure chain preprint the theory of u0 positive operators with respect to a cone in a banach space is applied to the class of even order differential equation on measure chains x 2m t 0m 1 pi t x 2i t t 0 1 satisfying the lidstone boundary conditions x 2i 0 0 0 i m 1 x 2j 2 1 0 0 j m 1 the existence of a smallest positive eigenvalue is obtained and then a theorem is established comparing the smallest positive eigenvalues for two problems of this type

positive solutions for boundary value problems of second order difference equations and their computation abstract we consider the following two classes of second order boundary value problems for difference equation r i 1 y i 1 b i y i a i y i 0 1 i n y 0 y 1 y n 1 y n 0 with 0 1 and r i 1 y i 1 b i y i a i y i 0 1 i n y 0 y n y n 1 y 1 with 0 1 we establish the existence of positive solutions to both problems a solver with linear computational complexity for almost tridiagonal linear systems is developed by exploring the special structure of linear system of equations based on fast solvers for linear systems effective algorithms for the computation of positive solutions will be proposed

eigenvalue comparisons for boundary value problems for second order difference equations abstract we consider the eigenvalue problems for boundary value problems of second order difference equations 1 r i 1 y i 1 a i y i 0 1 i n y 0 y n 1 y n 0 and 2 r i 1 y i 1 b i y i 0 1 i n y 0 y n 1 y n 0 comparison results for the eigenvalues of the problem 1 and the problem 2 are established

nonuniform measure rigidity we consider an ergodic invariant measure for a smooth actionof z k k 2 on a k 1 dimensional manifold or for a locally free smooth action of r k k 2 on a 2k 1 dimensional manifold we prove that if is hyperbolic with the lyapunov hyperplanes in general position and if one element in z k has positive entropy then is absolutely continuous the main ingredient is absolute continuity of conditional measures on lyapunov foliations which holds for a more general class of smooth actions of higher rank abelian groups

the metric entropy of diffeomorphisms part i characterization of measures satisfying pesin s entropy formula soit m une variete de riemann compacte soit f m m un diffeomorphisme et soit m une mesure de probabilite de borel f invariante sur m on identifie les mesures pour lesquelles l inegalite de margulis et ruelle qui relie l entropie aux exposants de lyapunov atteint l egalite on demontre une formule valable pour toutes les mesures invariantes

existence of multiple solutions for second order discrete boundary value problems we give conditions on f involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two point boundary value problem yk 1 2yk yk 1 f k yk vk 0 for k 1 n 1 y0 0 yn where f is continuous and vk yk yk 1 for k 1 n in the special case f k t p f t greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions we give an example showing this latter result is sharp our results extend those of avery and peterson and are in the spirit of our results for the continuous analogue c 2002 elsevier science ltd all rights reserved

spectral theory of higher order discrete vector sturm liouville problems abstract this paper is concerned with spectral problems of higher order vector difference equations with self adjoint boundary conditions where the coefficient of the leading term may be singular a suitable admissible function space is constructed so that the corresponding difference operator is self adjoint in it and the fundamental spectral results are obtained rayleigh s principles and minimax theorems in two special linear spaces are given as an application comparison theorems for eigenvalues of two sturm liouville problems are presented especially the dual orthogonality and multiplicity of eigenvalues are discussed

stability for delayed switched systems with markov jump parameters and generally incomplete transition rates abstract exponential mean square stability for delayed switched systems with markov jump parameters and generally incomplete transition rates is discussed the switching dynamics among the operation modes are considered to be governed by a high level with average dwell time switching adts and a low level with stochastic markov switching many practical systems such as general economic model subject to unpredictable structural changes can be described by switching markov jump systems smjss with generally incomplete transition rates by resorting to average dwell time switching approach sufficient conditions are proposed to ensure the underlying system exponentially mean square stable finally the theoretical results are applied to a general economic model to demonstrate the effectiveness applicability and superiority of the main results

existence of positive solutions forboundary value problems of second order functional difference equations abstract we prove the existence of positive solutions for boundary value problems of second orderfunctional difference equations the result here is the generalization of a corresponding result for ordinary difference equations

eigenvalues of discrete linear second order periodic and antiperiodic eigenvalue problems with sign changing weight abstract by virtue of the eigenvalues of discrete linear second order neumann eigenvalue problems we study the eigenvalues of discrete linear second order periodic and antiperiodic eigenvalue problems with sign changing weight we find that these two problems have t real eigenvalues including the multiplicity respectively furthermore the numbers of positive eigenvalues are equal to the numbers of positive elements in the weight function and the numbers of negative eigenvalues are equal to the numbers of negative elements in the weight function furthermore these eigenvalues including the eigenvalues of neumann problem satisfy the order relation

stability analysis of markov switched stochastic differential equations with both stable and unstable subsystems abstract this paper discusses the asymptotic stability of markov switched stochastic differential equations by using the method of multiple lyapunov functions we provide sufficient conditions for stochastic asymptotic stability of markov switched stochastic differential equations with both stable and unstable subsystems via the inequality based on the multiple lyapunov functions and the stationary distribution of markovian switching process particularly our results include some existing results as special cases and improve some results in the literature two examples are given to illustrate the effectiveness of the obtained results

almost sure and moment asymptotic boundedness of stochastic delay differential systems abstract the purpose of this article is to investigate the almost sure and moment asymptotic boundedness for a class of stochastic delay differential systems using stochastic analysis techniques a generalized non autonomous l operator delay differential inequality including cross item is presented based on the obtained inequality some sufficient verifiable criteria for the almost sure and moment asymptotic boundedness of the considered systems are derived analytically two numerical examples are given to illustrate the effectiveness of our theoretical results

stability analysis and stabilization of discrete time non homogeneous semi markov jump linear systems a polytopic approach abstract this paper addresses the issues of stability analysis and stabilizing controller design for two classes of discrete time non homogeneous semi markov jump linear systems s mjlss the first class is concerned with the sojourn time probability mass functions that are independent of jump instants while the other considers the existence of probability mass functions of sojourn time depending on jump instants new techniques are developed respectively for both classes of systems by transforming their corresponding time varying semi markov kernels into more tractable forms based on the stochastic stability allowing for bounded sojourn time the derived stability and stabilization criteria containing the probability distribution information of random sojourn time can be numerically tested in order to reduce the possible conservatism of the obtained results a novel class of polytopic quadratic lyapunov function is constructed which depends on both the current mode and the elapsed time in the current mode finally the proposed control strategies are applied to an illustrative application of automotive electronic throttle valve to show the effectiveness of the theoretical results the results also reveal the significance of considering the inhomogeneity of s mjlss and the importance of our constructed lyapunov function

stabilization of stochastic functional differential systems with delayed impulses abstract this paper is concerned with the stabilization problem for a class of stochastic functional differential system with delayed impulses by applying a generalized comparison principle and the average dwell time method some sufficient criteria for input to state stable iss type and exponential stability properties are derived the coefficients of the upper bound for the diffusion operator of lyapunov functions are allowed to be time varying which improves the existing results greatly two numerical examples are presented to illustrate the effectiveness of the proposed results

a note on two types of lyapunov exponents and entropies for zk actions abstract in this paper two types of lyapunov exponents random lyapunov exponents and directional lyapunov exponents and the corresponding entropies random entropy and directional entropy are considered for smooth z k actions the close relation among these quantities are investigated and the formulas of them are given via the lyapunov exponents of the generators

dynamic threshold probe of stochastic sir model with saturated incidence rate and saturated treatment function abstract in this discourse we establish and investigate the pervasive of environmental variability in a deterministic epidemic model with saturated incidence rate and saturated treatment function we exemplify that the proposed stochastic model reveals an exclusive and universal positive solution we deal with equilibrium solution of stochastic model which contribute few biological intrinsic manifestation for the model we attain the sufficient conditions for extinction of the infectious disease and persistent in the mean of the stochastic epidemic model with probability one if 0 1 and if 0 1 respectively eventually numerical probing is furnished to elucidate the analytical outcomes

higher order three point boundary value problem on time scales in this paper we consider a higher order three point boundary value problem on time scales we study the existence of solutions of a non eigenvalue problem and of at least one positive solution of an eigenvalue problem later we establish the criteria for the existence of at least two positive solutions of a non eigenvalue problem examples are also included to illustrate our results

discrete third order three point boundary value problem we are concerned with the discrete boundary value problemlx t email protected 3x t f t x t 1 t 1

exponential stability of stochastic complex networks with multi weights based on graph theory abstract in this paper a novel approach to exponential stability of stochastic complex networks with multi weights is investigated by means of the graph theoretical method new sufficient conditions are provided to ascertain the moment exponential stability and almost surely exponential stability of stochastic complex networks with multiple weights it is noted that our stability results are closely related with multi weights and the intensity of stochastic disturbance numerical simulations are also presented to substantiate the theoretical results

on sturm liouville boundary value problems for second order nonlinear functional finite difference equations motivated by the interesting paper i karaca discrete third order three point boundary value problem j comput appl math 205 2007 458 468 this paper is concerned with a class of boundary value problems for second order functional difference equations sufficient conditions for the existence of at least one solution of a sturm liouville boundary value problem for second order nonlinear functional difference equations are established we allow f to be at most linear superlinear or sublinear in obtained results

asymptotic stability in distribution of stochastic systems with semi markovian switching this paper investigates the asymptotic stability in distribution of stochastic systems with semi markovian switching whose transition rates are time varying which are more general than stochastic

on stability of randomly switched nonlinear systems this note is concerned with stability analysis and stabilization of randomly switched systems these systems may be regarded as piecewise deterministic stochastic systems the discrete switches are triggered by a stochastic process which is independent of the state of the system and between two consecutive switching instants the dynamics are deterministic our results provide sufficient conditions for almost sure stability and stability in the mean using lyapunov based methods when individual subsystems are stable and a certain ldquoslow switchingrdquo condition holds this slow switching condition takes the form of an asymptotic upper bound on the probability mass function of the number of switches that occur between the initial and current time instants this condition is shown to hold for switching signals coming from the states of finite dimensional continuous time markov chains our results therefore hold for markovian jump systems in particular for systems with control inputs we provide explicit control schemes for feedback stabilization using the universal formula for stabilization of nonlinear systems

eigenvalues of second order difference equations with coupled boundary conditions abstract this paper is concerned with coupled boundary value problems for self adjoint second order difference equations existence of eigenvalues is proved numbers of eigenvalues are calculated and relationships between the eigenvalues of a self adjoint second order difference equation with three different coupled boundary conditions are established these results extend the relevant existing results of periodic and antiperiodic boundary value problems

exponentially incremental dissipativity for nonlinear stochastic switched systems in this paper we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state dependent switching law and multiple lyapunov functio

dynamic equations on time scales a survey the study of dynamic equations on time scales which goes back to its founder stefan hilger 1988 is an area of mathematics that has recently received a lot of attention it has been created in order to unify the study of differential and difference equations in this paper we give an introduction to the time scales calculus we also present various properties of the exponential function on an arbitrary time scale and use it to solve linear dynamic equations of first order several examples and applications among them an insect population model are considered we then use the exponential function to define hyperbolic and trigonometric functions and use those to solve linear dynamic equations of second order with constant coefficients finally we consider self adjoint equations and more generally so called symplectic systems and present several results on the positivity of quadratic functionals

razumikhin type theorem for stochastic functional differential equations with levy noise and markov switching abstractthis paper is devoted to study the well known razumikhin type theorem for a class of stochastic functional differential equations with levy noise and markov switching in comparison to the standard gaussian noise levy noise and markov switching make the analysis more difficult owing to the discontinuity of its sample paths in this paper we attempt to overcome this difficulty by using the razumikhin method and lyapunov functions we obtain several razumikhin type theorems to prove the pth moment exponential stability of the suggested system based on these results we further discuss the pth moment exponential stability of stochastic delay differential equations with levy noise and markov switching in particular the results obtained in this paper improve and generalise some previous works given in the literature finally an example is provided to illustrate the effectiveness of the theoretical results

topological entropy of nonautonomous dynamical systems abstract let m x be the space of all borel probability measures on a compact metric space x endowed with the weak topology in this paper we prove that if the topological entropy of a nonautonomous dynamical system x f n n 1 vanishes then so does that of its induced system m x f n n 1 moreover once the topological entropy of x f n n 1 is positive that of its induced system m x f n n 1 jumps to infinity in contrast to bowen s inequality we construct a nonautonomous dynamical system whose topological entropy is not preserved under a finite to one extension

stabilizing randomly switched systems this article is concerned with stability analysis and stabilization of randomly switched systems under a class of switching signals the switching signal is modeled as a jump stochastic not necessarily markovian process independent of the system state it selects at each instant of time the active subsystem from a family of systems sufficient conditions for stochastic stability almost sure in the mean and in probability of the switched system are established when the subsystems do not possess control inputs and not every subsystem is required to be stable these conditions are employed to design stabilizing feedback controllers when the subsystems are affine in control the analysis is carried out with the aid of multiple lyapunov like functions and the analysis results together with universal formulae for feedback stabilization of nonlinear systems constitute our primary tools for control design

even order nonlinear eigenvalue problems on a measure chain we consider the even order nonlinear eigenvalue problem 1 mu 2m t f t u t u 2i 0 u 2i 1 0 0 i m 1 on a measure chain t results on existence and nonexistence of positive solutions are obtained for evaluated in different intervals under certain assumptions the complete scenario for all 0 is established our work develops and improves many known results in the literature even for the case that t is the real number line we also interpret our general results on measure chains to the discrete case which yields a new set of conditions for the existence and nonexistence of positive solutions of eigenvalue problems for difference equations

higher order dynamic equations on measure chains wronskians disconjugacy and interpolating families of functions this paper introduces generalized zeros and hence disconjugacy of nth order linear dynamic equations which cover simultaneously as special cases among others both differential equations and difference equations we also define markov fekete and descartes interpolating systems of functions the main result of this paper states that disconjugacy is equivalent to the existence of any of the above interpolating systems of solutions and that it is also equivalent to a certain factorization representation of the operator the results in this paper unify the corresponding theories of disconjugacy for nth order linear ordinary differential equations and for nth order linear difference equations

eigenvalue comparisons for second order difference equations with neumann boundary conditions abstract the boundary value problem for second order difference equation r i 1 y i 1 b i y i a i y i 0 1 i n y 0 y 1 y n 1 y n 0 with 0 1 and 2 was recently discussed in ji and yang 2007 j ji b yang eigenvalue comparisons for a class of boundary value problems of second order difference equations linear algebra appl 420 1 2007 218 227 in this paper we extend our earlier results to the second order difference equations with neumann boundary conditions the case of 1 as in ji and yang 2007 mentioned above we will also focus on the structure of its eigenvalues and comparisons of all eigenvalues as the coefficients a i b i and r i change