stochastic stabilization and destabilization of nonlinear differential equations abstract this paper is concerned with the stochastic stabilization and destabilization of nonlinear differential equations which more precisely further develops the general theory of stochastic stabilization and destabilization that was studied by mao 1994 4 and appleby et al 2008 1 the proposed results are of substantial improvements and reveal the more fundamental principle for stochastic stabilization and destabilization of dynamical systems which is also verified with examples of application to mass action systems

exponential p convergence analysis for stochastic bam neural networks with time varying and infinite distributed delays we discuss exponential p convergence for stochastic bam neural networks the delays here are multiple time varying and infinite distributed delays we establish a new l operator delay differential integral inequality delay dependent criteria ensuring exponential p convergence are obtained giving the detail estimations of the exponential p convergence ball this paper is concerned with the problem of global exponential p convergence for stochastic bam neural networks with time varying and infinite distributed delays by constructing a new delay differential integral inequality and a novel l operator differential integral inequality and coupling with stochastic analysis techniques some delay dependent sufficient conditions are derived to guarantee exponential p convergence and the state variables of the discussed stochastic bam neural networks are globally exponentially convergent to a ball in the state space with a pre specified convergence rate meanwhile the exponential p convergent balls are also estimated here the existence and the uniqueness of the equilibrium point needs not to be considered finally two examples with numerical simulations are given to illustrate the effectiveness of the theoretical results

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

the stability with a general decay of stochastic delay differential equations with markovian switching abstract this paper considers the problems on the existence and uniqueness the pth p 1 moment and the almost sure stability with a general decay for the global solution of stochastic delay differential equations with markovian switching when the drift term and the diffusion term satisfy the locally lipschitz condition and the monotonicity condition by using the lyapunov function approach the barbalat lemma and the nonnegative semi martingale convergence theorem some sufficient conditions are proposed to guarantee the existence and uniqueness as well as the stability with a general decay for the global solution of such equations it is mentioned that in this paper the time varying delay is a bounded measurable function the derived stability results are more general which not only include the exponential stability but also the polynomial stability as well as the logarithmic one at last two examples are given to show the effectiveness of the theoretical results obtained

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

technical communique a note on asymptotic stabilization of linear systems by periodic piecewise constant output feedback this note studies the asymptotic stabilization problem for controllable and observable single input single output linear time invariant continuous time systems by means of memoryless output feedback of the form u t k t y t with k t periodic and piecewise constant a necessary and sufficient condition together with a simpler to test sufficient condition given in terms of a bilinear matrix inequality is presented a few illustrative examples complete the paper

stochastic maximum principle for stochastic recursive optimal control problem under volatility ambiguity we study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by g brownian motion some of the economic and financial optimization problems with volatility ambiguity can be formulated as such problems unlike the classical variational approach we establish the maximum principle by the linearization and weak convergence methods

analysis of chemical kinetic systems over the entire parameter space i the sal nikov thermokinetic oscillator in this series of papers we re examine using recently developed techniques some chemical kinetic models that have appeared in the literature with a view to obtaining a complete description of all the qualitatively distinct behaviour that the system can exhibit each of the schemes is describable by two coupled ordinary differential equations and contain at most three independent parameters we find that even with these relatively simple chemical schemes there are regions of parameter space in which the systems display behaviour not previously found quite often these regions are small and it seems unlikely that they would be found via classical methods in part i of the series we consider one of the thermally coupled kinetic oscillator models studied by sal nikov he showed that there is a region in parameter space in which the system would be in a state of undamped oscillations because the relevant phase portrait consists of an unstable steady state surrounded by a stable limit cycle our analysis has revealed two further regions in which the phase portraits contain respectively two limit cycles of opposite stability enclosing a stable steady state and three limit cycles of alternating stability surrounding an unstable steady state this latter region is extremely small so much so that it could be reasonably neglected in any predictions made from the model

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

convergence and stability of the compensated split step theta method for stochastic differential equations with piecewise continuous arguments driven by poisson random measure abstract this paper deals with the numerical solutions of stochastic differential equations with piecewise continuous arguments sdepcas driven by poisson random measure in which the coefficients are highly nonlinear it is shown that the compensated split step theta csst method with 0 1 is strongly convergent in p th p 2 moment under some polynomially lipschitz continuous conditions it is also obtained that the convergence order is close to 1 p in terms of the stability it is proved that the csst method with 1 2 1 reproduces the exponential mean square stability of the underlying system under the monotone condition and some restrictions on the step size without any restriction on the step size there exists 1 2 1 such that the csst method with 1 is exponentially stable in mean square moreover if the drift and jump coefficients satisfy the linear growth condition the csst method with 0 1 2 also preserves the exponential mean square stability some numerical simulations are presented to verify the conclusions

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

almost sure exponential stability of dynamical systems driven by levy processes and its application to control design for magnetic bearings abstracta lyapunov type theorem is developed to study well posedness and almost surely k exponential stability of dynamical systems driven by levy processes sufficient conditions imposed by the t

unstable asymptotics for nonstationary queues we relate laws of large numbers and central limit theorems for nonstationary counting processes to corresponding limits for their inverse processes we apply these results to develop approximations for queues that are unstable in a nonstationary manner we obtain unstable nonstationary analogs of the queueing relation l w and associated central limit theorem versions for modeling and to obtain the first limits we can construct nonstationary point processes as random time transformations of familiar point processes such as renewal processes and stationary point processes we deduce the asymptotic behavior of the nonstationary point process from the asymptotic behavior of the familiar point process and the time transformation

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

the asymptotic efficiency of simulation estimators a decision theoretic framework is proposed for evaluating the efficiency of simulation estimators the framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate the cost of obtaining the estimate and the estimate itself are represented as realizations of jointly distributed stochastic processes in this context the efficiency of a simulation estimator based on a given computational budget is defined as the reciprocal of the risk the overall expected cost this framework is appealing philosophically but it is often difficult to apply in practice e g to compare the efficiency of two different estimators because only rarely can the efficiency associated with a given computational budget be calculated however a useful practical framework emerges in a large sample context when we consider the limiting behavior as the computational budget increases a limit theorem established for this model supports and extends a fairly well known efficiency principle

structured robust stability and boundedness of nonlinear hybrid delay systems taking different structures in different modes into account the paper has developed a new theory on the structured robust stability and boundedness for nonlinear hybrid stochastic differential delay equations sddes without the linear growth condition a new lyapunov function is designed in order to deal with the effects of different structures as well as those of different parameters within the same modes moreover a lot of effort is put into showing the almost sure asymptotic stability in the absence of the linear growth condition

stability analysis for a class of stochastic delay nonlinear systems driven by g brownian motion abstract this paper is devoted to study the p th moment exponential stability problem for a class of stochastic delay nonlinear systems sdnss driven by g brownian motion the delays considered in this paper are time varying delays i t 0 1 i 3 and they are not required to be differentiable different from the traditional methods we use a new approach stochastic delay feedback controls we firstly compare the sdns with the corresponding stochastic nonlinear system sns instead of studying the stability of the sdns directly then we impose the condition on the sns to ensure the p th moment exponential stability of the sns furthermore we show that there is a positive constant such that the sdns is also p th moment exponentially stable provided in particular we give an implicit lower bound for which can be computed numerically

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

recursive algorithms for stock liquidation a stochastic optimization approach this work develops stochastic optimization algorithms for a class of stock liquidation problems the stock liquidation rules are based on hybrid geometric brownian motion models allowing regime changes that are modulated by a continuous time finite state markov chain the optimal selling policy is of threshold type and can be obtained by solving a set of two point boundary value problems the total number of equations to be solved is the same as the number of states of the underlying markov chain to reduce the computational burden using a stochastic optimization approach recursive algorithms are constructed to approximate the optimal threshold values convergence and rates of convergence of the algorithm are studied simulation examples are presented and the computation results are compared with the analytic solutions finally the algorithms are tested using real market data

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

ergodic control of switching diffusions we study the ergodic control problem of switching diffusions representing a typical hybrid system that arises in numerous applications such as fault tolerant control systems flexible manufacturing systems etc under fairly general conditions we establish the existence of a stable nonrandomized markov policy which almost surely minimizes the pathwise long run average cost we then study the corresponding hamilton jacobi bellman hjb equation and establish the existence of a unique solution in a certain class using this we characterize the optimal policy as a minimizing selector of the hamiltonian associated with the hjb equations as an example we apply the results to a failure prone manufacturing system and obtain closed form solutions for the optimal policy

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

stability analysis for semi markovian switched singular stochastic systems abstract the stability problem is investigated for switched singular stochastic systems with semi markovian switching signals considering the inherent mode dependent state jumps at the switching instants sufficient conditions of stochastic stability exponential stability in the mean square and almost surely exponential stability are obtained by using the stochastic analysis theory and lyapunov function method finally an example is provided to illustrate the effectiveness of the proposed results

stochastic stabilization of singular systems with markovian switchings this paper studies the stochastic stabilization problem for a class of singular markovian jump system the aim is to determine whether or not there is a stochastic feedback controller stabilizing a given singular markovian jump system smjs a new kind of stochastic controller only in the diffusion part is proposed such that the closed loop system has a unique solution and is almost surely exponentially admissible new sufficient condition for the existence of such a controller is given as linear matrix inequalities lmis based on this more extensions to transition probability matrix tpm with elements partially unknown and system states partially observable are developed a numerical example is used to demonstrate the effectiveness of the proposed methods

on preservation of strong stabilizability under sampling it is shown that a sampled data system remains strongly stabilizable if the original continuous time system is so and if the sampling period is sufficiently small at the same time it is also shown that a sampled data system can be strongly stabilizable even if the original continuous time system is not so and some sufficient conditions guaranteeing this does not happen are derived

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

state estimation and sliding mode control of markovian jump singular systems this paper is concerned with the state estimation and sliding mode control problems for continuous time markovian jump singular systems with unmeasured states firstly a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic admissibility of the unforced markovian jump singular system then the sliding mode control problem is considered by designing an integral sliding surface function an observer is designed to estimate the system states and a sliding mode control scheme is synthesized for the reaching motion based on the state estimates it is shown that the sliding mode in the estimation space can be attained in a finite time some conditions for the stochastic admissibility of the overall closed loop system are derived finally a numerical example is provided to illustrate the effectiveness of the proposed theory

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

almost sure exponential stabilization of hybrid stochastic coupled systems via intermittent noises a higher order nonlinear growth condition abstract in this paper the almost sure exponential stabilization problem of hybrid coupled systems with two independent noises is investigated wherein one of the noises exists periodically intermittently different from existing literature on coupled systems the functions in the system we addressed are nonlinear without the linear growth condition by employing graph theory and lyapunov method almost sure exponential stabilization criterion of hybrid coupled systems with two independent noises is derived the criterion is closely associated with the noise strength the number of vertex systems the coupling strength the existence interval and period of intermittent noises meanwhile the theoretical results are applied to a higher order nonlinear stochastic coupled electronic oscillators system and the corresponding numerical example is presented

sample path properties of g brownian motion abstract the present article is devoted to careful study of sample pathwise properties of g brownian motion i e those which quasi surely hold for all paths we develop a comparison machinery to analyze the irregular functional of g brownian paths and to characterize their zero sets the key ingredient of our approach is an estimate of solutions to g heat equations as a result we prove that the g brownian motion path is nowhere differentiable

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

a finite difference method for the numerical solution of the sal nikov thermokinetic oscillator problem a finite difference method is developed for solving two coupled ordinary differential equations that model a sequence of chemical reactions the initial value problem is highly nonlinear and involves three parameters various types of theoretical solution of this problem the sal nikov thermokinetic oscillator problem may be found depending on these parameters this is because the stationary point is surrounded by up to two limit cycles the well known first order explicit euler method and an implicit finite difference method of the same order are used to compute the solution it is shown that this implicit method may in fact be used explicitly and extensive numerical experiments are made to confirm the superior stability properties of the alternative method

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

stabilization of linear systems by noise it is proved that the biggest lyapunov number lambda max of the system dot x a f t x where a is a fixed d times d matrix and f t is a zero mean strictly stationary matrix valued stochastic process satisfies 1 d trace a leqq lambda max on the other hand for each varepsilon 0 there is a process f t for which lambda max leqq 1 d trace a varepsilon in particular the system dot x ax can be stabilized by zero mean stationary parameter noise if and only if trace a 0 the stabilization can be accomplished by a one dimensional noise source the results carry over to the case where a is a stationary process they are also true for f t white noise

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

lyapunov type conditions and stochastic differential equations driven by g brownian motion abstract this paper studies the solvability and the stability of stochastic differential equations driven by g brownian motion gsdes in particular the existence and uniqueness of the solution for locally lipschitz gsdes are obtained by localization methods also the stability of such gsdes is discussed with lyapunov type conditions

necessary and sufficient conditions for 2p th moment stability of several classes of linear stochastic systems this technical note presents necessary and sufficient conditions for 2p th moment stability of several widely used linear stochastic systems by the matrix derivative operator and vectorial ito s formula we first derive two extended systems one is described by stochastic differential equation sde and the other by ordinary differential equation ode it is shown that the stochastic system is 2p th moment exponentially stable if and only if the sde is mean square exponentially stable or the ode is exponentially stable subsequently combining the quasi periodic homogeneous polynomial lyapunov function methods with the proposed techniques a series of nonconservative stability criteria are established for linear impulsive sampled data and switched stochastic systems under dwell time constraints a numerical example illustrates the proposed theoretical results

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

two time scale markov chains and applications to quasi birth death queues aiming at reduction of complexity this work is concerned with two time scale markov chains and applications to quasi birth death queues asymptotic expansions of probability vectors are constructed and justified lumping all states of the markov chain in each subspace into a single state an aggregated process is shown to converge to a continuous time markov chain whose generator is an average with respect to the stationary measures then a suitably scaled sequence is shown to converge to a switching diffusion process extensions of the results are presented together with examples of quasi birth death queues

the novel sufficient conditions of almost sure exponential stability for semi markov jump linear systems abstract this paper discusses the almost sure exponential stability problem for semi markov jump linear systems by comprehensively utilizing the coupled lyapunov matrices and the ergodic property of semi markov switching process the novel sufficient stability conditions for the considered systems are obtained which are expressed in terms of linear matrix inequalities and the probability structure of semi markov switching process finally an example is given to illustrate the effectiveness of our results

extensions of the queueing relations l λw and h λg this paper extends the fundamental queueing relations l w and h g that relate customer averages the customer average waiting time w or cost g to associated time averages the time average queue length l or cost h given an arrival process with arrival rate these relations can be established by focusing on a two dimensional cumulative input process that has the two one dimensional cumulative input processes of interest as marginals relations between the marginal averages are established for cumulative input processes that may not be representable as integrals or sums the general framework includes the continuous versions of l w and h g due to t rolski and s stidham as well as the standard version of h g and can be extended to higher dimensions inequalities are also established when some of the conditions for equality do not hold moreover central limit theorem versions of h g are established extending our recent results for l w

mean square exponential stability for stochastic control systems with discrete time state feedbacks and their numerical schemes in simulation aiming at the qualitative numerical simulation this article concerns the mean square exponential stability mses of the stochastic systems with discrete time state feedbacks and their numerical schemes a time delay dependent stability criterion is obtained for the underlying system the euler maruyama and backward euler maruyama schemes are established and their mses are proved under the same criterion which means that the numerical schemes preserve the stability of the continuous model the illustrative example at the end of this letter shows that the theoretical upper bound for the sampling period limited in the stability criterion is much greater than that obtained by the stability criteria from the literature

stabilization of regime switching processes by feedback control based on discrete time observations this work aims to extend x r mao s work automatica j ifac 49 2013 pp 3677 3681 on stabilization of hybrid stochastic differential equations by discrete time feedback control in x r mao s work the feedback control depends on discrete time observation of the state process but on continuous time observation of the switching process while in this work we study the feedback control depending on discrete time observations of the state process and the switching process our criteria depend explicitly on the regular conditions of the coefficients of the stochastic differential equation and on the stationary distribution of the switching process the sharpness of our criteria is shown through studying the stability of linear systems which also shows explicitly that the stability of hybrid stochastic differential equations depends essentially on the long time behavior of the switching process

ordinary clt and wlln versions of l λw the familiar queueing principle expressed by the formula l w little s law can be interpreted as a relation among strong laws of large numbers sllns here we prove central limit theorem clt and weak law of large numbers wlln versions of l w for example if the sequence of ordered pairs of interarrival times and waiting times is strictly stationary and satisfies a joint clt then the queue length process also obeys a clt with a related limiting distribution in a previous paper we proved a functional central limit theorem version of l w without stationarity by very different arguments the two papers highlight the differences between establishing ordinary limit theorems and their functional limit theorem counterparts

a method for the complete qualitative analysis of two coupled ordinary differential equations dependent on three parameters in this paper recent advances in bifurcation theory are specialized to systems describable by two coupled ordinary differential equations odes containing at most three independent parameters for such systems by plotting in the relevant parameter plane the locus of successively degenerate singular points a complete description of all the qualitatively distinct behaviour of the system can be obtained the description is in terms of phase portraits and bifurcation diagrams even though much use is made of existing results obtained via local analyses the results of this technique cover the entire parameter space furthermore because the information is built up in successive stages the question of whether the parameters universally unfold a given degeneracy does not arise this can mean a major saving in effort particularly for degenerate hopf points finally if as is often the case the parameters appear in the system in a simple way the procedure can be applied analytically because the variables which will appear nonlinearly can be used to parametrize the relevant loci

stochastic stabilisation of functional differential equations in this paper we investigate the problem of stochastic stabilisation for a general nonlinear functional differential equation given an unstable functional differential equation dx t dt f t xt we stochastically perturb it into a stochastic functional differential equation dx t f t xt dt x t db t where is a matrix and b t a brownian motion while xt x t 0 under the condition that f satisfies the local lipschitz condition and obeys the one side linear bound we show that if the time lag is sufficiently small there are many matrices for which the stochastic functional differential equation is almost surely exponentially stable while the corresponding functional differential equation dx t dt f t xt may be unstable

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

asymptotic analysis of the time dependent m m 1 queue using operator analytic techniques we develop a nonstationary markovian queueing theory starting with the mt mt 1 queue we employ an asymptotic approach quite different from the usual large time analysis instead we uniformly accelerate the queue length process that is we divide the arrival and service rate by a common parameter e then for a fixed time interval we consider the asymptotics for the distribution mean and variance of the queue length process as e goes to zero the effects of e can be quite different for the given time interval this gives us a dynamic asymptotic behavior for the queue length process we can formulate a time dependent traffic intensity parameter that determines when the process is asymptotically stable and when it is asymptotically unstable

brief constrained quadratic state feedback control of discrete time markovian jump linear systems in this paper we consider the quadratic optimal control problem of a discrete time markovian jump linear system subject to constraints on the state and control variables it is desired to find a state feedback controller which may also depend on the jump variable that minimizes a quadratic cost and satisfies some upper bounds on the norms of some random variables related to the state and control variables of the system the transition probability of the markov chain and initial condition of the system may belong to appropriate convex sets we obtain an approximation for the optimal solution of this problem in terms of linear matrices inequalities so that convex programming can be used for numerical calculations examples are presented to illustrate the usefulness of the developed results

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

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

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

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

estimating customer and time averages in this paper we establish a joint central limit theorem for customer and time averages by applying a martingale central limit theorem in a markov framework the limiting values of the two averages appear in the translation terms this central limit theorem helps to construct confidence intervals for estimators and perform statistical tests it thus helps determine which finite average is a more asymptotically efficient estimator of its limit as a basis for testing for pasta poisson arrivals see time averages we determine the variance constant associated with the central limit theorem for the difference between the two averages when pasta holds

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

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

the pointwise stationary approximation for m 1 m 1 s green kolesar and svoronos in press and green and kolesar in press use numerical methods to investigate the behavior of multiserver markov queues with a poisson arrival process having a sinusoidal arrival rate for this model they propose an approximation for long run average performance measures called the pointwise stationary approximation psa which consists of an appropriate weighted average of the performance measure that would result at each point in time if the system were stationary with the arrival rate that applies at that point in time in this paper we verify their conjecture that psa is asymptotically correct as the service and arrival rates increase with the instantaneous traffic intensity held fixed corresponding to long arrival rate cycles we actually establish both pointwise and average versions of this result for general time dependent birth and death processes

brief paper almost sure exponential stabilisation of stochastic systems by state feedback control so far a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability this paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean square sense the results are expressed in terms of linear matrix inequalities lmis which are easy to be checked in practice by using matlab toolbox moreover the control structure in this paper appears not only in the drift part but also in the diffusion part of the underlying stochastic system

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

review lecture instabilities and oscillations in chemical reactions in closed and open systems this lecture is chiefly concerned with isothermal oscillations in homogeneous systems and with finding and validating self consistent models emphasis is laid on satisfying basic physical principles and on preserving chemical reasonableness in as simple a manner as possible the goal is to devise a scheme that can be applied to a wide variety of circumstances to predict new behaviour as well as to interpret what is known and to form a foundation for later developments and elaborations this core of the scheme called the autocatalator combines an autocatalytic step a 2b rightarrow 3b rate k 1 ab 2 with catalyst decay b rightarrow c rate k 2 b these core reactions may display reversibility and they may be accompanied by uncatalysed conversion a rightarrow b text rate k u a particular stress is given to the problem of closed systems in closed systems oscillations cannot be indefinitely sustained in former days it was customary to ignore this inconvenience and to repeal the law of conservation of matter today a less unsatisfactory account is possible

convergence and stability of the split step theta method for stochastic differential equations with piecewise continuous arguments abstract in this paper we consider the stochastic differential equations with piecewise continuous arguments sdepcas in which both the drift and the diffusion coefficients do not satisfy the global lipschitz and linear growth conditions especially the diffusion coefficients are highly non linear growing it is proved that the split step theta sst method with 1 2 1 is strongly convergent to sdepcas under the local lipschitz monotone and one sided lipschitz conditions it is also obtained that the sst method with 1 2 1 preserves the exponential mean square stability of sdepcas under the monotone condition and some condition on the step size without any restriction on the step size there exists 1 2 1 such that the sst method with 1 is exponentially stable in mean square moreover for sufficiently small step size the rate constant can be reproduced some numerical simulations are presented to illustrate the analytical theory

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

optimal control of switching diffusions with application to flexible manufacturing systems a controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems the existence of a homogeneous markov nonrandomized optimal policy is established by a convex analytic method using the existence of such a policy the existence of a unique solution in a certain class to the associated hamilton jacobi bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate hamiltonian

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

stabilization of hybrid systems by feedback control based on discrete time state observations recently mao automatica j ifac 49 2013 pp 3677 3681 initiated the study the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations in the same paper mao also obtains an upper bound on the duration tau between two consecutive state observations however it is due to the general technique used there that the bound on tau is not very sharp in this paper we will be able to establish a better bound on tau making use of lyapunov functionals we will discuss the stabilization not only in the sense of exponential stability as mao does in automatica j ifac 49 2013 pp 3677 3681 but also in other sense that of h infty stability or asymptotic stability we will consider not only the mean square stability but also the almost sure stability

strong approximations for time dependent queues a time dependent mt mt 1 queue alternates through periods of under over and critical loading we derive period dependent pathwise asymptotic expansions for its queue length within the framework of strong approximations our main results include time dependent fluid approximations supported by a functional strong law of large numbers and diffusion approximations supported by a functional central limit theorem this complements and extends previous work on asymptotic expansions of the queue length transition probabilities

mean square convergence of explicit two step methods for highly nonlinear stochastic differential equations abstract in this paper we propose the projected two step euler maruyama method and the projected two step milstein method for highly nonlinear stochastic differential equations under a global monotonicity condition we first examine the strong convergence in mean square sense for these two explicit schemes based on the notions of stochastic stability and b consistency for two step methods we prove that the convergence rates of the projected two step euler maruyama method and the projected two step milstein method are 1 2 and 1 respectively in particular our results can be applied to equations with super linearly growing drift and diffusion coefficients finally we numerically verify the optimal mean square convergence orders of these two schemes by a series of examples