on stabilization of bilinear uncertain time delay stochastic systems with markovian jumping parameters in this paper we investigate the stochastic stabilization problem for a class of bilinear continuous time delay uncertain systems with markovian jumping parameters specifically the stochastic bilinear jump system under study involves unknown state time delay parameter uncertainties and unknown nonlinear deterministic disturbances the jumping parameters considered here form a continuous time discrete state homogeneous markov process the whole system may be regarded as a stochastic bilinear hybrid system that includes both time evolving and event driven mechanisms our attention is focused on the design of a robust state feedback controller such that for all admissible uncertainties as well as nonlinear disturbances the closed loop system is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are established to guarantee the existence of desired robust controllers which are given in terms of the solutions to a set of either linear matrix inequalities lmis or coupled quadratic matrix inequalities the developed theory is illustrated by numerical simulation

robust finite time h control of singular stochastic systems via static output feedback abstract this paper addresses the problem of robust finite time stabilization of singular stochastic systems via static output feedback firstly sufficient conditions of singular stochastic finite time boundedness on static output feedback are obtained for the family of singular stochastic systems with parametric uncertainties and time varying norm bounded disturbance then the results are extended to singular stochastic h finite time boundedness for the class of singular stochastic systems designed algorithm for static output feedback controller is provided to guarantee that the underlying closed loop singular stochastic system is singular stochastic h finite time boundedness in terms of strict linear matrix equalities with a fixed parameter finally an illustrative example is presented to show the validity of the developed methodology

brief paper control for discrete singular hybrid systems the problems of stability state feedback control and static output feedback control for a class of discrete time singular hybrid systems are investigated in this paper a new sufficient and necessary condition for a class of discrete time singular hybrid systems to be regular causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict lmis respectively finally two illustrative examples are provided to demonstrate the applicability of the proposed approach

ito type stochastic fuzzy differential equations with delay abstract in the paper we give some foundations for the studies of stochastic fuzzy delayed differential equations we prove the existence and uniqueness of solutions to such the equations to obtain our result we assume that the coefficients of the equation satisfy the lipschitz condition together with linear growth condition we estimate the distance between approximate solution and exact solution also the stability of solution with respect to the initial history is shown an application of stochastic fuzzy delayed differential equations in the modeling of population growth is indicated

finite group extensions and the atiyah conjecture the atiyah conjecture for a discrete group g states that the l 2 betti numbers of a finite cw complex with fundamental group g are integers if g is torsion free and in general that they are rational numbers with denominators determined by the finite subgroups of g here we establish conditions under which the atiyah conjecture for a torsion free group g implies the atiyah conjecture for every finite extension of g the most important requirement is that h g z p is isomorphic to the cohomology of the p adic completion of g for every prime p an additional assumption is necessary e g that the quotients of the lower central series or of the derived series are torsion free we prove that these conditions are fulfilled for a certain class of groups which contains in particular artin s pure braid groups and more generally fundamental groups of fiber type arrangements free groups fundamental groups of orientable compact surfaces certain knot and link groups primitive positive one relator groups and products of these therefore every finite in fact every elementary amenable extension of these groups satisfies the atiyah conjecture as a consequence if such an extension h is torsion free then the group ring ch contains no non trivial zero divisors i e h fulfills the zero divisor conjecture in the course of the proof we prove that if these extensions are torsionfree then they have plenty of non trivial torsion free quotients which are virtually nilpotent all of this applies in particular to artin s full braid group therefore answering question b6 on www grouptheory org our methods also apply to the baum connes conjecture this is discussed in 47 where for example the baum connes conjecture is proved for the full braid groups msc 55n25 homology with local coecients 16s34 group rings laurent rings 57m25 knots and links

brief paper robustness of exponential stability of a class of stochastic functional differential equations with infinite delay we regard the stochastic functional differential equation with infinite delay dx t f x t dt g x t dw t as the result of the effects of stochastic perturbation to the deterministic functional differential equation email protected t f x t where x t x t q c 0 r n is defined by x t q x email protected email protected 0 we assume that the deterministic system with infinite delay is exponentially stable in this paper we shall characterize how much the stochastic perturbation can bear such that the corresponding stochastic functional differential system still remains exponentially stable

adaptive output feedback control for a class of uncertain stochastic non linear systems with time delays in this paper we investigate the adaptive output feedback stabilisation for a class of stochastic non linear systems with time varying time delays first we give some sufficient conditions to ensure the existence and uniqueness of the solution process for stochastic non linear systems with time delays and introduce a new stability notion and the related criterion then for a class of stochastic non linear systems with time varying time delays uncertain parameters in both drift and diffusion terms and general constant virtual control coefficients we present a systematic design procedure for a memoryless adaptive output feedback control law by using the backstepping method it is shown that under the control law based on a memoryless observer the closed loop equilibrium of interest is globally stable in probability and moreover the solution process can be regulated to the origin almost surely

sofic groups and diophantine approximation we prove the algebraic eigenvalue conjecture of j dodziuk p linnell v mathai t schick and s yates see 2 for sofic groups moreover we give restrictions on the spectral measure of elements in the integral group ring finally we define integer operators and prove a quantization of the operator norm below 2 to the knowledge of the author there is no group known that is not sofic

technical communique sliding mode control of singular stochastic hybrid systems this paper is concerned with the sliding mode control smc of nonlinear singular stochastic systems with markovian switching an integral sliding surface function is designed and the resulting sliding mode dynamics is a full order markovian jump singular stochastic system by introducing some specified matrices a new sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic stability of the sliding mode dynamics then a smc law is synthesized for reaching motion moreover when there exists an external disturbance the 2 disturbance attenuation performance is analyzed for the sliding mode dynamics some related sufficient conditions are also established

dyson s spike for random schroedinger operators and novikov shubin invariants of groups we study one dimensional schroedinger operators with random edge weights and their expected spectral measures mu h near zero we prove that the measure exhibits a spike of the form mu h varepsilon varepsilon sim frac c mid rm log varepsilon mid 2 first observed by dyson without assuming independence or any regularity of edge weights we also identify the limiting local eigenvalue distribution which is different from poisson and the usual random matrix statistics we then use the result to compute novikov shubin invariants for various groups including lamplighter groups and lattices in the lie group sol

quantum feedback control of linear stochastic systems with feedback loop time delays in a quantum feedback control loop one is often confronted with time delays that mainly originated from the transition delay of signals which may cause the quantum feedback control system unstable the purpose of this paper is to deal with a problem of quantum measurement based feedback control subject to feedback loop time delays a quantum version of delay independent stability criterion as well as an upper bound on a cost function is derived based on quantum it rules we propose one numerical procedure for quantum feedback controller designs which is then illustrated by an example

sliding mode variable structure control for parameter uncertain stochastic systems with time varying delay in this paper the variable structure control problem for a class uncertain of stochastic system with time varying delay is investigated firstly a new concept of the subordinated reachability of the sliding motion is introduced to approach approximately the specified sliding surface the variable structure control law is then proposed to ensure that the sliding motion is subordinated reachable furthermore a sufficient condition for mean square asymptotical stability of the sliding motion is given finally a numerical example is presented to demonstrate the effectiveness of the obtained results

mean square stability of stochastic volterra integro differential equations abstract the mean square stability of a non linear stochastic volterra integro differential equation is studied non convolution volterra terms arise in both the drift and the dispersion term moreover for the convolution case we determine the rate of convergence in terms of an integrability condition on the volterra kernels

hybrid filtering for linear systems with non gaussian disturbances this paper is concerned with hybrid filtering of a non gaussian system coupled by a hidden switching process an optimal control approach is used to derive a finite dimensional recursive filter that is optimal in the sense of the most probable trajectory mpt estimate an approximate scheme is obtained when the probability distribution of the switching process converges to a limiting distribution which is often easier to obtain numerical examples are considered and computational experiments are reported in these examples our schemes outperform popular filtering schemes available in the literature

robust observer design for ito stochastic time delay systems via sliding mode control this paper deals with the output feedback sliding mode control for ito stochastic time delay systems the system states are unmeasured and the uncertainties are unmatched a sliding mode control scheme is proposed based on the state estimates by utilizing a novel switching function the derivative of the switching function is ensured to be finite variation it is shown that the sliding mode in the estimation space can be attained in finite time the sufficient condition for the asymptotic stability in probability of the overall closed loop stochastic system is derived finally a simulation example is shown to illustrate the proposed method

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

correlation theory of delayed feedback in stochastic systems below andronov hopf bifurcation here we address the effect of large delay on the statistical characteristics of noise induced oscillations in a nonlinear system below andronov hopf bifurcation in particular we introduce a theory of these oscillations that does not involve the eigenmode expansion and can therefore be used for arbitrary delay time in particular we show that the correlation matrix cm oscillates on two different time scales on the scale of the main period of noise induced oscillations and on the scale close to the delay time at large values of the delay time the cm is shown to decay exponentially only for large values of its argument while for the arguments comparable with the value of the delay the cm remains finite disregarding the delay time the definition of the correlation time of the system with delay is discussed

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product

robustness of general decay stability of nonlinear neutral stochastic functional differential equations with infinite delay this paper establishes the existence and uniqueness theorem of neutral stochastic functional differential equations with infinite delay and examines the almost sure stability of this solution with general decay rate this result may be used to examine almost sure robust stability to illustrate our idea more carefully we carefully discuss a scalar stochastic integro differential equation with neutral type and its asymptotic stability including the exponential stability and the polynomial stability

technical communique stabilization of a class of uncertain large scale stochastic systems with time delays this paper focuses on a class of large scale interconnected bilinear stochastic systems with time delays and time varying parameter uncertainties the problem we address is to design a robust decentralized controller such that the closed loop interconnected stochastic system is globally asymptotically stable in probability for all admissible uncertainties and time delays first robust stability analysis is given in terms of a set of linear matrix inequalities lmis then it is shown that the robust decentralized stabilization can be solved by an lmi based design method

exact statistics for linear time delayed oscillators subjected to gaussian excitation abstract large classes of stochastic systems of interest to acoustics and vibrations have time delays the presence of these time delays hinders efforts to provide physical insight into the system behavior because of the difficulty of finding exact solutions this paper addresses this issue by presenting exact steady state solutions for the probability density functions pdf s for linear time delayed oscillators subjected to gaussian excitation of arbitrary correlation a key parameter influencing these pdf s is shown to be the ratio of mean generalized kinetic energy to the mean generalized potential energy in a single damped harmonic oscillator this ratio is unity which implies an equi partition of generalized energy time delays cause deviations in the equi partition of generalized energy which creates regions of preferential total phase and causes the amplitude pdf to shift from a rayleigh distribution to a hoyt distribution

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied 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 uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are 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 theory

stability of stochastic interval systems with time delays abstract consider a given exponentially stable system undergoing a random perturbation which is dependent on a past state of the solution of the system suppose this stochastically perturbed system is described by a stochastic differential functional equation in this paper we establish a sufficient condition that the perturbed system remains exponentially stable using a specific example we show how this condition may be used and we extend it to deal with multiple time delays

approximating l2 invariants and the atiyah conjecture let g be a torsion free discrete group and let denote the field of algebraic numbers in we prove that g fulfills the atiyah conjecture if g lies in a certain class of groups d which contains in particular all groups that are residually torsion free elementary amenable or are residually free this result implies that there are no nontrivial zero divisors in g the statement relies on new approximation results for l2 betti numbers over g which are the core of the work done in this paper another set of results in the paper is concerned with certain number theoretic properties of eigenvalues for the combinatorial laplacian on l2 cochains on any normal covering space of a finite cw complex we establish the absence of eigenvalues that are transcendental numbers whenever the covering transformation group is either amenable or in the linnell class we also establish the absence of eigenvalues that are liouville transcendental numbers whenever the covering transformation group is either residually finite or more generally in a certain large bootstrap class 2003 wiley periodicals inc

stability conditions for linear retarded functional differential equations abstract the purpose of this note is to study the exponential stability for the linear retarded functional differential equation x t 1 0 d x t r where the delay function r 0 is continuous and is of bounded variation on the interval 1 0 it is shown that the spectral limit function for the equation above has a continuous dependence on the pair r the set of all functions of bounded variation for which the equation above is exponentially stable for every delay function r the so called region of stability globally in the delays is a cone therefore for a fixed r the set of all which make our equation exponentially stable that is the region of stability for the delay function r contains a cone a discussion of the characterization of these regions of stability as well as of the largest cone contained in each region of stability for a fixed delay function r is given some remarks are made with respect to a similar question for the equation x t ax t 1 0 d x t r where a is a real n by n matrix is bounded variation on 1 0 and r as before several examples illustrate the results obtained

stability of stochastic systems with uncertain time delays abstract for linear delay systems with bilinear noise sufficient conditions are given for the global asymptotic stochastic stability independent of the length of the delay s for linear stochastic noise terms sufficient conditions for the existence of an invariant distribution for all values of the delay are given it is shown that the gaussian distribution is the unique invariant distribution the covariance and correlation matrix function of the resulting stationary process are completely characterized by a lyapunov type equation all these sufficient conditions are obtained in the form of the existence of some positive definite matrices satisfying certain riccati type equations

quasi poles of linear time varying systems in an intrinsic algebraic approach abstract in a previous piece of work it has been shown that the exponential stability of a linear time varying ltv system can be evaluated using new definitions of the poles of such a system the latter are given by a fundamental set of roots of the skew polynomial p which defines the autonomous part of the system such a set may not exist over the initial field k of definition of the coefficients of the system but can exist over a suitable field extension k k it is shown here that conditions for stability can also be obtained using linear factors of the polynomial p over another field extension k which may be smaller k k k the roots of these factors are called the quasi poles of the system the necessary condition for system stability expressed in function of these quasi poles is more restrictive than the one involving a fundamental set of roots

stability of stochastic functional differential systems using degenerate lyapunov functionals and applications motivated by the seminal work of dupire 2009 on functional ito formulas this work investigates asymptotic properties of systems represented by stochastic functional differential equations sfdes stability of general delay dependent sfdes is investigated using degenerate lyapunov functionals which are only positive semi definite rather than positive definite as used in the classical work this paper first establishes boundedness and regularity of sfdes by using degenerate lyapunov functionals then moment and almost sure exponential stabilities are obtained based on degenerate lyapunov functionals and the semi martingale convergence theorem as an application of the stability criteria consentability of stochastic multi agent systems with nonlinear dynamics is studied

robust fuzzy design for nonlinear uncertain stochastic systems via sliding mode control this paper deals with the sliding mode control smc problem for nonlinear stochastic time delay systems by means of fuzzy approach the takagi sugeno t s fuzzy stochastic time delay model with parametric uncertainties and unknown nonlinearities is presented a sufficient condition for the exponential stability in mean square of the sliding motion is also derived moreover it is shown that when the linear matrix inequalities lmis with equality constraint are feasible the designs of both sliding surface and sliding mode controller can be easily obtained via convex optimization a simulation example illustrating the proposed method is given

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

stability of semilinear stochastic evolution equations stability of moments of the mild solution of a semilinear stochastic evolution equation is studied and sufficient conditions are given for the exponential stability of the pth moment in terms of liapunov function sufficient conditions for sample continuity of the solution are also obtained and the exponential stability of sample paths is proved three examples are given to illustrate the theory

stability of singular stochastic systems with markovian switching in recent years singular hybrid systems have received considerable attention however few results are concerned with stability of singular hybrid stochastic systems based on a stability result for singular hybrid systems this note studies mean square stability of singular hybrid stochastic systems it is found that the diffusions and the markov chain may play important roles in system analysis in mean square sense as a special case a criterion for mean square stability of hybrid stochastic systems is developed by the frequency domain approach

robustness of stability of nonlinear systems with stochastic delay perturbations abstract suppose there exist random disturbances to a given exponentially stable system and the stochastically perturbed system is described by a stochastic differential functional equation in this paper a sufficient condition is given so that the perturbed system remains exponentially stable in the case where the perturbation depends only on several states of the past we obtain a condition under which the perturbed system is absolutely exponentially stable

large time behaviour for a class of turbulence models stochastic burgers equations the aim of this paper is to investigate large time behaviour i e stability and growth bounds of the solutions for a class of stochastic burgers equations the analysis is based on some robustness analysis involved with an infinite dimensional stochastic evolution equation various sufficient conditions for a stochastic burgers equation are obtained to ensure its asymptotic properties lastly several examples are given to illustrate our theory

normal generation and ell 2 betti numbers of groups the normal rank of a group is the minimal number of elements whose normal closure coincides with the group we study the relation between the normal rank of a group and its first ell 2 betti number and conjecture the inequality beta 1 2 g le mathrm nrk g 1 for torsion free groups the conjecture is proved for limits of left orderable amenable groups on the other hand for every n ge 2 and every varepsilon 0 we give an example of a simple group q with torsion such that beta 1 2 q ge n 1 varepsilon these groups also provide examples of simple groups of rank exactly n for every n ge 2 existence of such examples for n 3 was unknown until now

mean dimension mean rank and von neumann luck rank we introduce an invariant called mean rank for any module m of the integral group ring of a discrete amenable group as an analogue of the rank of an abelian group it is shown that the mean dimension of the induced action on the pontryagin dual of m the mean rank of m and the von neumann luck rank of m all coincide as applications we establish an addition formula for mean dimension of algebraic actions prove the analogue of the pontryagin schnirelmnn theorem for algebraic actions and show that for elementary amenable groups with an upper bound on the orders of finite subgroups algebraic actions with zero mean dimension are inverse limits of finite entropy actions

on the spectrum of lamplighter groups and percolation clusters let mathfrak g be a finitely generated group and x its cayley graph with respect to a finite symmetric generating set s furthermore let mathfrak h be a finite group and mathfrak h wr mathfrak g the lamplighter group wreath product over mathfrak g with group of lamps mathfrak h we show that the spectral measure plancherel measure of any symmetric switch walk switch random walk on mathfrak h wr mathfrak g coincides with the expected spectral measure integrated density of states of the random walk with absorbing boundary on the cluster of the group identity for bernoulli site percolation on x with parameter mathsf p 1 mathfrak h the return probabilities of the lamplighter random walk coincide with the expected annealed return probabilities on the percolation cluster in particular if the clusters of percolation with parameter mathsf p are almost surely finite then the spectrum of the lamplighter group is pure point this generalizes results of grigorchuk and uk resp dicks and schick regarding the case when mathfrak g is infinite cyclic analogous results relate bond percolation with another lamplighter random walk in general the integrated density of states of site or bond percolation with arbitrary parameter mathsf p is always related with the plancherel measure of a convolution operator by a signed measure on mathfrak h wr mathfrak g where mathfrak h mathbb z or another suitable group

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

stability analysis of switched singular stochastic linear systems this paper is devoted to study the stability of switched singular stochastic linear systems with both stable and unstable subsystems by using the method of multiple lyapunov functions and the noti

group ring elements with large spectral density given delta 0 we construct a group g and a group ring element s in mathbb z g such that the spectral measure mu of s fulfils mu 0 varepsilon frac c log varepsilon 1 delta for small varepsilon in particular the novikov shubin invariant of any such s is 0 the constructed examples show that the best known upper bounds on mu 0 varepsilon are not far from being optimal

performance evaluation of sampled data control of markov jump linear systems abstract this technical communique extends the recent results of geromel and gabriel 2015 to h sampled data control design of markov jump linear systems mjls it fulfills a lack of a specific necessary and sufficient result in the literature of sampled data control of mjls in the context of h performance mean square stabilizability and performance determination are addressed and discussed in a unified theoretical viewpoint as a natural consequence it is shown that the previous result of geromel and gabriel 2015 is obtained as a particular case a globally uniformly convergent algorithm is proposed to solve the design conditions the theory is illustrated by means of an example

brief paper robust h filtering for nonlinear stochastic systems with uncertainties and markov delays this paper investigates the h filtering problem for a class of general nonlinear stochastic systems considering model uncertainties and random time delays governed by markov chains simultaneously the general algebraic hamilton jacobi inequality hji is established first for general nonlinear stochastic systems with uncertainties and random markovian delays then a set of sufficient conditions are derived for the filtering system to achieve stochastic stability in the sense of mean square and the prescribed disturbance attenuation level moreover the developed results are specialized for a special class of nonlinear stochastic systems by presenting the sufficient conditions in terms of matrix inequalities simulation results demonstrate the effectiveness of the proposed approach

stochastic stability of ito differential equations with semi markovian jump parameters in this note the problem of stochastic stability for linear systems with jump parameters being semi markovian rather than full markovian is further investigated in particular the system under consideration is described by ito type nonlinear stochastic differential equations with phase type semi markovian jump parameters stochastic stability conditions are presented

finite time h static output control of markov jump systems with an auxiliary approach this paper considers the finite time h static output feedback control of markov jump systems with the help of introducing two new variables related to the original system state and output sufficient conditions for the closed loop system to be stochastic finite time boundedness with the prescribed h performance level are proposed in terms of linear matrix inequalities lmis meanwhile the static output control gains are solved explicitly by the proposed conditions it is shown that the proposed method is less or at least the same conservative than the existing result lastly a numerical example is given to demonstrate the effectiveness of the proposed method

on turing dynamical systems and the atiyah problem main theorems of the article concern the problem of atiyah on possible values of l 2 betti numbers it is shown that all non negative real numbers are l 2 betti numbers and that many for example all non negative algebraic real numbers are l 2 betti numbers of simply connected manifolds with respect to a free cocompact action also an explicit example is constructed which leads to a simply connected manifold with a transcendental l 2 betti number with respect to an action of the threefold direct product of the lamplighter group mathbb z 2 mathbb z wr mathbb z the main new idea is embedding turing machines into integral group rings the main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids

hyperlinearity essentially free actions and l2 invariants the sofic property we prove that connes embedding conjecture holds for the von neumann algebras of sofic groups that is sofic groups are hyperlinear hence we provide some new examples of hyperlinearity we also show that the determinant conjecture holds for sofic groups as well we introduce the notion of essentially free actions and amenable actions and study their properties

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

mean square admissibility for stochastic ts fuzzy singular systems based on extended quadratic lyapunov function approach the mean square admissibility problem of stochastic ts fuzzy singular systems via an extended quadratic lyapunov function is investigated in this paper comparing with the existing quadratic lyapunov function method the extended quadratic lyapunov function method can relax stabilization conditions firstly the sufficient condition is given for the mean square admissibility of stochastic ts fuzzy singular systems based on an extended quadratic lyapunov function approach secondly two sufficient conditions for mean square admissibility of closed loop systems via the parallel distributed compensation pdc fuzzy controller and non parallel distributed compensation non pdc fuzzy controller are proposed furthermore through the extended quadratic lyapunov function method and non pdc fuzzy controller the less conservative mean square admissibility conditions on solving fuzzy controllers are derived in terms of linear matrix inequalities lmis finally some simulation examples are given to show the effectiveness and merits of the proposed fuzzy controller design methodology

brief paper stability and stabilization of continuous time singular hybrid systems in this paper the problems of stability and state feedback stabilization for a class of continuous time singular hybrid systems are investigated a new sufficient and necessary condition for a continuous time singular hybrid system to be regular impulse free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities lmis moreover a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities finally a numerical example is given to illustrate the effectiveness of the obtained theoretical results

a note on some differences between real and complex stability radii abstract real and complex stability radii measure the robustness of stable linear systems under real and complex parameter perturbations respectively in this note we point out some basic differences between them in particular we investigate their different behaviour with respect to system interconnections and changes in system data

moment exponential stability and integrability of stochastic functional differential equations abstract the main objective of the paper is to present sufficient conditions ensuring the p th mean and almost sure exponential stability as well as the p th mean integrability of solutions to non linear stochastic functional differential equations and especially to stochastic differential equations with time varying lags some examples are given to illustrate the theoretical considerations

some remarks on stability of stochastic singular systems with state dependent noise this paper discusses the stability for stochastic singular systems with state dependent noise in both continuous time and discrete time cases firstly the condition for the existence and uniqueness of the solution to stochastic singular systems is given based on this condition the stochastic ito singular system is transformed into a deterministic standard singular system by means of h representation method secondly new sufficient conditions for the stability of systems considered are derived in terms of strict linear matrix inequalities finally an example is given to illustrate the effectiveness of the obtained theoretical results

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

technical communique exponential stabilizability of stochastic systems with markovian jumping parameters altfn this paper was not presented at any ifac meeting this paper was recommended for publication in revised form by editor peter dorato this paper deals with the exponential stabilizability of the class of stochastic systems with jumps for the case of linear uncertain stochastic system we have designed an optimal control law that guarantees the exponential stability robustness of systems with markovian jumps for the nonlinear case with matching conditions we have established a similar result

stabilization of stochastic singular nonlinear hybrid systems abstract this paper deals with the control of the class of singular nonlinear stochastic hybrid systems under some appropriate assumptions results on stochastic stability and stochastic stabilization are developed two state feedback controllers linear and nonlinear that stochastically stabilize the class of systems we are considering are designed lmi sufficient conditions are developed to compute the gains of these controllers

sliding mode control of singular stochastic markov jump systems an investigation has been made into the sliding mode control smc problem for singular stochastic markov systems ssmss in this paper by using replacement of matrix variables a new mean square admissibility criterion of ssmss is proposed first based on this admissibility criterion the desired state feedback controller is designed to guarantee the closed loop system to be mean square admissible then the obtained results given in the form of strict linear matrix inequalities are applied to solve smc problem of ssmss in order to illustrate the workability and applicability of the theoretic results developed numerical examples are provided

stabilisation of mode dependent singular markovian jump systems with generally uncertain transition rates this paper is devoted to investigating the stability and stabilisation problems for continuous time mode dependent singular markovian jump systems smjss with generally uncertain transition rates gutrs first we establish a sufficient condition in terms of a set of coupled linear matrix inequalities lmis to ensure the systems to be regular impulse free and stochastically stable then we design a mode dependent state feedback controller to guarantee the closed loop systems stochastically admissible by applying the lmi technique finally a numerical example is presented to illustrate the effectiveness and efficiency of the proposed method