bilinear system identification by volterra kernels estimation this note considers the identification of bilinear discrete time dynamic systems from sequences of input and noise corrupted output measurements in contrast to other approaches the proposed algorithm is simple and does not require knowledge of the noise statistics it is also shown that the obtained estimates are unbiased and consistent which is not shown in the previous papers

comments on stochastic stability of jump linear systems for original paper see ibid vol 47 p 1204 8 2002 the purpose of the article is to show that the conjecture presented in remark 3 of the above paper by y fang and k loparo 2002 is actually true

robustness of stochastic discrete time switched linear systems with application to control with shared resources motivated by control applications relying on shared resources such as computation time or bandwidth we analyze the stability and robustness of discrete time switched linear systems with stochastic commutations we show that a wide class of shared resources control strategies can be modeled by a stochastic jump linear system involving two stochastic processes the class of systems we study encompasses markov chains and independent and identically distributed switching processes for these systems we recall existing definitions of stability and robustness by relying on the input to state stability iss property we show that for the class of systems under concern delta moment stability is equivalent to delta moment iss and that they both imply almost sure iss several sufficient conditions are provided to guarantee these properties anytime control design for a translational oscillator rotational actuator tora system is used to illustrate all these concepts

exact location of the multicritical point for finite dimensional spin glasses a conjecture we present a conjecture on the exact location of the multicritical point in the phase diagram of spin glass models in finite dimensions by generalizing our previous work we combine duality and gauge symmetry for replicated random systems to derive formulae which make it possible to understand all the relevant available numerical results in a unified way the method applies to non self dual lattices as well as to self dual cases in the former case of which we derive a relation for a pair of values of multicritical points for mutually dual lattices the examples include the j and gaussian ising spin glasses on the square hexagonal and triangular lattices the potts and zq models with chiral randomness on these lattices and the three dimensional j ising spin glass and the random plaquette gauge model

applications of the generalized singular value decomposition method on the eigenproblem using the incomplete boundary element formulation in this paper four incomplete boundary element formulations including the real part singular boundary element the real part hypersingular boundary element the imaginary part boundary element and the plane wave element methods are used to solve the free vibration problem among these incomplete boundary element formulations the real part singular and the hypersingular boundary elements are of the singular type and the other two are of the regular type when the incomplete formulation is used the spurious eigensolution may be encountered an auxiliary system whose boundary conditions are linearly independent of those of the original system is required in the proposed method in order to eliminate the spurious eigensolution a mathematical proof is given to show that the spurious eigensolution will appear in both the original and auxiliary systems as a result one can eliminate spurious eigensolution by means of the generalized singular value decomposition method in addition to the spurious eigensolution problem the regular boundary element formulation further suffers ill conditioned behaviors in the problem solver it is explained analytically using a circular domain why ill conditioned behaviors exist two main ill conditioned problems are the numerical instability of solution and the nonexistence of solution to solve the numerical instability of solution problem existing in these proposed regular formulations the tikhonov s regularization technique is used to improve the condition number of the leading coefficient matrix further the generalized singular value decomposition method is used to eliminate spurious eigensolutions numerical examples are given to verify the performance of these proposed methods and the results match the analytical values well

mean square stability for discrete bounded linear systems in hilbert space the asymptotic behaviour for infinite dimensional discrete linear systems driven by white noise is considered in this paper both the evolution and convergence of the state correlation operators sequence are analysed mean square stability conditions are investigated including a comparison with the deterministic stability problem the particular case of compact operators is considered in some detail

multicritical dynamics for the j ising model exact dynamical properties are discussed for the j ising model around the multicritical point mcp it is found that the relation of relaxations between the non equilibrium remanent magnetization m t and the equilibrium autocorrelation function q t at the mcp is different from that at the pure critical point the dynamic critical exponent for the ferromagnetic ordering defined by and that for the spin glass ordering defined by become identical at the mcp accurate numerical calculations for them are performed in two and three dimensions using the non equilibrium relaxation analysis the mcp is located at and the exponent is estimated as for the square lattice they are estimated as and for the simple cubic lattice

stabilization of networked stochastic time delay fuzzy systems with data dropout this paper deals with the problem of stabilization for networked stochastic systems with transmitted data dropout the plant in the networked control system ncs under consideration is a discrete stochastic time delay nonlinear system represented by a takagi sugeno fuzzy model exponential stability criteria of the ncs are developed by using a common quadratic lyapunov function and a fuzzy lyapunov function respectively a stabilization controller with convergence rate constraint can be designed by solving a set of linear matrix inequalities that is numerically feasible with commercially available software three numerical examples are presented to demonstrate the effectiveness of the proposed methods

mean square stability conditions for discrete stochastic bilinear systems necessary and sufficient conditions for mean square stability are proved for the following class of nonlinear dynamical systems finite dimensional bilinear models evolving in discrete time and driven by random sequences the stochastic environment under consideration is characterized only by independence wide sense stationarity and second order properties thus we do not assume random sequences to be gaussian zero mean or ergodic the probability distributions involved are allowed to be arbitrary and unknown limiting state moments are given in terms of the model parameters and disturbances moments

the dynamical critical exponent of the two three and five dimensional kinetic ising model abstract we present monte carlo simulation results for the dynamical critical exponent z of the two three and five dimensional kinetic ising model we used glauber as well as metropolis dynamics both type of dynamics lead to the same z values in two and three dimensions the z values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at tc for very large systems up to 169984 2 3072 3 and 48 5 for the two dimensional case we obtain z 2 21 0 03 and for the three dimensional case z 2 08 0 03 for the five dimensional glauber case the requirement z 2 gives a critical point j kbtc 0 11391 from monte carlo simulations whereas new series expansions with four more terms give 0 113935 0 000015 for this ratio

short time dynamics and magnetic critical behavior of the two dimensional random bond potts model the critical behavior in the short time dynamics for the random bond potts ferromagnet in two dimensions is investigated by short time dynamic monte carlo simulations the numerical calculations show that this dynamic approach can be applied efficiently to study the scaling characteristic which is used to estimate the critical exponents straight theta beta nu and z for quenched disordered systems from the power law behavior of the kth moments of magnetization

on line parameter identification of bilinear systems in this correspondence an on line identification scheme for bilinear systems is presented this algorithm is a direct extension of the stochastic approximation algorithm proposed by saridis and stein to bilinear systems the properties of the algorithm are that it does not require knowledge of the noise statistics and that it converges to the true value of the parameters volterra kernals in the mean square sense

control under stochastic multiplicative uncertainties part ii optimal design for performance this paper studies the optimal control design problem for linear discrete time systems with stochastic multiplicative uncertainties these uncertainties are assumed to be present in the control inputs and modeled as independent and identically distributed i i d random processes the optimal performance under study is defined in the mean square sense referred to as the mean square optimal h 2 performance it is shown that the mean square optimal h 2 control problem via state feedback can be solved using a mean square stabilizing solution to a modified algebraic riccati equation mare a necessary and sufficient condition for the existence of this solution is presented which constitutes a generalization of the solution to the classic optimal h 2 state feedback design problem whereas the latter can be obtained by solving an algebraic riccati equation are it is also proven that the optimal control design problem can be cast as an eigenvalue problem evp for the output feedback case with possible input delays we show that the mean square optimal h 2 control problem also amounts to solving an mare when the plant has no nonminimum phase zeros from the inputs to the measurement outputs that is the global optimal solution is obtained by solving an mare incorporating the delays the implication is that in this case a separation principle still holds

adaptive lattice bilinear filters two fast least squares lattice algorithms for adaptive nonlinear filters equipped with bilinear system models are presented the lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem thus using multichannel lattice filtering algorithms to solve the nonlinear filtering problem the computational complexity of the algorithms is an order of magnitude smaller than that of previously available methods the first of the two approaches is an equation error algorithm that uses the measured desired response signal directly to compute the adaptive filter outputs this method is conceptually very simple but results in biased system models in the presence of measurement noise the second is an approximate least squares output error solution the past samples of the output of the adaptive system itself are used to produce the filter output at the current time results indicate that the output error algorithm is less sensitive to output measurement noise than the equation error method

short time critical dynamics and universality on a two dimensional triangular lattice abstract the critical scaling and universality in the short time dynamics for spin models on a two dimensional triangular lattice are investigated by using a monte carlo simulation emphasis is placed on the dynamic evolutions from fully ordered initial states to show that universal scaling exists already in the short time regime in forms of power law behavior of the magnetizations and binder cumulant the results estimated for the dynamic and static critical exponents z and confirm explicitly that the potts models on the triangular lattice and square lattice belong to the same universality classes our critical scaling analysis strongly suggests that the simulation for the dynamic relaxations can be used to determine the universality

cal h representation and applications to generalized lyapunov equations and linear stochastic systems this paper introduces an h representation method to express an n2 1 vector x as x h x tilde based on the introduced h representation approach several topics are extensively discussed including the generalized lyapunov equations gles arising from stochastic control stochastic observability generalized d stability and d stabilization weak stability and stabilization a necessary and sufficient condition for the existence and uniqueness of the symmetric and skew symmetric solutions of gles is presented respectively moreover the solution structure of gles is also clarified through the h representation method several necessary and sufficient conditions are also obtained for stochastic observability generalized d stability and d stabilization weak stability and stabilization

multicritical points for spin glass models on hierarchical lattices the locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis the results are compared with an analytical conjecture derived by using the duality the gauge symmetry and the replica method we find that the conjecture does not give the exact answer but leads to locations slightly away from the numerically reliable data we propose an improved conjecture to give more precise predictions of the multicritical points than the conventional one this improvement is inspired by a different point of view coming from the renormalization group and succeeds in deriving very consistent answers with many numerical data doi 10 1103 physreve 77 061116

discrete time mean field stochastic linear quadratic optimal control problems this paper firstly presents necessary and sufficient conditions for the solvability of discrete time mean field stochastic linear quadratic optimal control problems secondly the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method thirdly by introducing several sequences of bounded linear operators the problem is formulated as an operator stochastic linear quadratic optimal control problem by the kernel range decomposition representation of the expectation operator and its pseudo inverse the optimal control is derived using solutions to two algebraic riccati difference equations finally by completing the square the two riccati equations and the optimal control are also obtained

stability of discrete deterministic and stochastic nonlinear systems abstract in this paper we derive some sufficient conditions for local asymptotic stability and instability for discrete nonlinear deterministic and stochastic systems these theorems are easy to apply to specific discrete nonlinear systems some applications of our theorems to bilinear systems illustrate the above

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

identification of discrete time stochastic bilinear systems this paper considers the problem of identifying unknown parameters appearing in discrete time varying bilinear models the system is assumed to operate in a stochastic environment where the input disturbance and the noise observation have unknown probability distribution identifiability conditions are investigated in the light of a state covariance analysis for stochastic bilinear systems by assuming that the only accessible process is supplied by the noisy observation sequence a recursive identification procedure is proposed which is suitable for on line applications stochastic approximation algorithms are used for identifying time invariant bilinear systems

lyapunov equation for infinite dimensional discrete bilinear systems abstract mean square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences such a convergence preserving property holds for an infinite dimensional bilinear system if and only if the associate lyapunov equation has a unique strictly positive solution

an asymmetric indirect trefftz method for solving free vibration problems in this paper a new asymmetric indirect trefftz method aitm has been developed to solve free vibration problems the proposed method is categorized into a regular type of boundary element methods bems such that no singular or hypersingular integration is necessary however like other regular bems the proposed approach encounters the numerical instability as the number of elements increases to deal with such an ill posed behavior tikhonov s regularization method in conjunction with the generalized singular value decomposition gsvd is adopted it is proved that the degeneracy of the proposed indirect trefftz method has the same mathematical structure as the direct trefftz method thus no special effort should be paid in programming besides such an equivalency indicates that the current method does not have spurious eigensolutions furthermore the proposed approach can easily treat a multiply connected domain of genus 1 as shown in fig 1 due to its indirect nature the present approach can also represent the mode shapes within its own mathematical formulations several numerical examples are given to show the validity of the proposed approach

finite size scaling and critical exponents in critical relaxation we simulate the critical relaxation process of the two dimensional ising model with the initial state both completely disordered or completely ordered results of a new method to measure both the dynamic and static critical exponents are reported based on the finite size scaling for the dynamics at the early time from the time dependent binder cumulant the dynamical exponent z is extracted independently while the static exponents beta nu and nu are obtained from the time evolution of the magnetization and its higher moments

non equilibrium dynamics of the ising model for t less than equal totc the growth of order in ising models with nonconserved order parameter is considered for quenches to final temperatures tf 0 and tf tc the results of numerical simulations in spatial dimension d 2 are presented in all cases a scaling regime is entered for sufficiently long times where the characteristic length scale is the domain size l t approximately t12 for tf 0 and the nonequilibrium correlation length xi t approximately t1z for tf tc the equal time correlation function has the expected scaling forms f r l t and r d 2 eta fc r xi t for tf 0 and tc respectively the scaling function fc x has interesting short distance behaviour which is elucidated using scaling arguments and by in and 1 n expansions the t 0 scaling function f x depends on whether the spin correlations present in the initial conditions are of long or short range as does the exponent which describes the decay of the autocorrelation function a t si t si o approximately l t results for a quench from the equilibrium critical state to tf 0 are consistent with theoretical predictions

non equilibrium critical relaxation of the three dimensional ising model abstract the non equilibrium relaxation process at the critical point is studied using monte carlo simulation for the ferromagnetic ising model on a cubic lattice it was observed that the time dependent magnetization decayed following a power law t from the all up initial condition three kinds of single spin flip dynamics were studied for several lattices up to 1536 3 the system size dependences are also studied the value of was estimated to be 0 250 2 this value of leads to the estimation of the dynamical exponent z to be 2 06 2 if we assume z where and denote the critical exponents for spontaneous magnetization and correlation length in equilibrium state respectively and 0 515 the result of the non equilibrium relaxation in the ordered phase is also given

locations of multicritical points for spin glasses on regular lattices we present an analysis leading to precise locations of the multicritical points for spin glasses on regular lattices the conventional technique for determination of the location of the multicritical point was previously derived using a hypothesis emerging from duality and the replica method in the present study we propose a systematic technique by an improved technique giving more precise locations of the multicritical points on the square triangular and hexagonal lattices by carefully examining the relationship between two partition functions related with each other by the duality we can find that the multicritical points of the ifmmode pm else textpm fi j ising model are located at p c 0 890 phantom rule 0 2em 0ex 813 on the square lattice where p c means the probability of j ij j g0 at p c 0 835 phantom rule 0 2em 0ex 985 on the triangular lattice and at p c 0 932 phantom rule 0 2em 0ex 593 on the hexagonal lattice these results are in excellent agreement with recent numerical estimations

critical exponents of the dilute ising model from four loop expansions four loop expansions of the coefficients of the callan symanzik equation for 3d and 2d dilute ising models are calculated fixed point coordinates and critical exponents are estimated by two methods of summation of double series a generalisation of the pade borel approximation and the first confluent form of the e algorithm of wynn summation of the double series for the 2d dilute ising model gives exponents very close to exponents of the pure ising model in accordance with the exact solution

symmetry complexity and multicritical point of the two dimensional spin glass we analyse models of spin glasses on the two dimensional square lattice by exploiting symmetry arguments the replicated partition functions of the ising and related spin glasses are shown to have many remarkable symmetry properties as functions of the edge boltzmann factors it is shown that the applications of homogeneous and hadamard inverses to the edge boltzmann matrix indicate reduced complexities when the elements of the matrix satisfy certain conditions suggesting that the system has special simplicities under such conditions using these duality and symmetry arguments we present a conjecture on the exact location of the multicritical point in the phase diagram

non equilibrium relaxation and interface energy of the ising model abstract from the non equilibrium critical relaxation study of the two dimensional ising model the dynamical critical exponent z is estimated to be 2 165 0 010 for this model the relaxation in the ordered phase of this model is consistent with exp t behavior the interface energy of the three dimensional ising model is studied and the critical exponent of the correlation length and the critical amplitude of the surface tension 0 are estimated to be 0 6250 0 0025 and 1 42 0 04 respectively a dynamic monte carlo renormalization group method is successfully applied to the equilibrium properties of the three dimensional ising model

dynamical rushbrooke s inequality for nonequilibrium relaxation process an inequality for dynamic critical exponents is proved for relaxation processes of arbitrary magnetic systems this is a dynamical extension of rushbrooke s inequality it can be applied to any continuous transition systems with various dynamics the relation is demonstrated on the result of nonequilibrium relaxation analysis of fluctuations applied to the three dimensional ferromagnetic ising model

volterra integral approach to impulsive renewal systems application to networked control we analyze impulsive systems with independent and identically distributed intervals between transitions our approach involves the derivation of novel results for volterra integral equations with positive kernel we highlight several applications of these results and show that when applied to the analysis of impulsive systems they allow us to i provide necessary and sufficient conditions for mean square stability stochastic stability and mean exponential stability which can be equivalently tested in terms of a matrix eigenvalue computation an lmi feasibility problem and a nyquist criterion condition ii assess performance of the impulsive system by computing a second moment lyapunov exponent the applicability of our results is illustrated in a benchmark problem considering networked control systems with stochastically spaced transmissions for which we can guarantee stability for inter sampling times roughly twice as large as in previous papers

helmholtz eigenvalue analysis by boundary element method abstract a new and robust scheme for the eigenvalue analysis of the helmholtz differential equation by the boundary element method bem is developed in this paper unlike the existing methods in which a highly complicated transcendental equation including the unknown wavenumbers appears the present method can reduce the computational task greatly with the help of the multiple reciprocity boundary element formulation in terms of the fundamental solution for the laplace equation and related simple calculations for polynomials the newton method is employed for determination of the desired eigenvalues two dimensional problems with various homogenous boundary conditions are solved to show the versatility of the proposed scheme

spectral properties of sums of certain kronecker products we introduce two kinds of sums of kronecker products and their induced operators we study the algebraic properties of these two kinds of matrices and their associated operators the properties include their eigenvalues their eigenvectors and the relationships between their spectral radii or spectral abscissae furthermore two projected matrices of these kronecker products and their induced operators are also studied

self averaging distribution of pseudocritical temperatures and finite size scaling in critical disordered systems we evaluate by monte carlo simulations various singular thermodynamic quantities x for ensembles of quenched random ising and ashkin teller models the measurements are taken at t c and we study how the distributions p x and in particular their relative squared width r x over the ensemble depend on the system size l the ashkin teller model was studied in the regime where bond randomness is irrelevant and we found weak self averaging r x ensuremath sim l ensuremath alpha ensuremath nu ensuremath rightarrow 0 where ensuremath alpha l0 and ensuremath nu are the exponents of the pure model fixed point governing the transition for the site dilute ising model on a cubic lattice known to be governed by a random fixed point we find that r x tends to a constant as predicted by aharony and harris we tested whether this constant is universal however this constant is different for canonical and grand canonical disorder we identify the pseudocritical temperature of each sample i t c i l as the temperature at which the susceptibility reaches its maximal value ensuremath chi mathrm max the distribution of these sample dependent t c i l was investigated we found that its variance scales as ensuremath delta t c l 2 ensuremath sim l ensuremath 2 ensuremath nu our previously proposed finite size scaling ansatz for disordered systems was tested and found to hold we did observe deviations from a single function which imply that sample dependent scaling functions are needed these deviations are however relatively small and hence to obtain a fixed statistical error it may be more computationally efficient to measure ensuremath chi mathrm max than the commonly used ensuremath chi t c ensuremath infty

quadratic and h switching control for discrete time linear systems with multiplicative noises the goal of this paper is to study the switched stochastic control problem of discrete time linear systems with multiplicative noises we consider both the quadratic and the h criteria for the performance evaluation initially we present a sufficient condition based on some lyapunov metzler inequalities to guarantee the stochastic stability of the switching system moreover we derive a sufficient condition for obtaining a metzler matrix that will satisfy the lyapunov metzler inequalities by directly solving a set of linear matrix inequalities and not bilinear matrix inequalities as usual in the literature of switched systems we believe that this result is an interesting contribution on its own in the sequel we present sufficient conditions again based on lyapunov metzler inequalities to obtain the state feedback gains and the switching rule so that the closed loop system is stochastically stable and the quadratic and h performance costs are bounded above by a constant value these results are illu

iterative solutions of coupled discrete markovian jump lyapunov equations in this paper two iterative methods are given to solve coupled discrete markovian jump lyapunov equations arising from the stability analysis of discrete time markovian jump systems when such equations have unique positive definite solutions a sufficient condition for the convergence of iterates for one iterative method is derived when such equations only have unique solutions but not necessarily positive definite the above iterative method may fail and an alterative iterative method is provided by using the solutions of discrete time lyapunov equations as its intermediate steps a sufficient condition is also presented for the convergence of the iterates

filtering s coupled algebraic riccati equations for discrete time markov jump systems abstract this paper deals with a set of s coupled algebraic riccati equations that arises in the study of filtering of discrete time linear jump systems with the markov chain in a general borel space s by s coupled it is meant that the algebraic riccati equations are coupled via an integral over s conditions for the existence and uniqueness of a positive semi definite solution to the filtering s coupled algebraic riccati equations are obtained in terms of the concepts of stochastic detectability and stochastic stabilizability this result is then applied to solve the infinite horizon minimum mean square linear markov jump filtering problem the obtained results generalize previous ones in the literature which considered only the case of the markov chain taking values in a finite state space

recursive identification of bilinear systems methods of identifying bilinear systems from recorded input output data are discussed in this article a short survey of the existing literature on the topic is given standard methods from linear systems identification such as least squares extended least squares recursive prediction error and instrumental variable methods are transferred to bilinear input output model structures and tested in simulation special attention is paid to problems of stabilizing the model predictor and it is shown how a time varying kalman filter and associated parameter estimation algorithm can deal with this problem

mean square small gain theorem for stochastic control discrete time case this paper presents a small gain theorem in the mean square sense for multiple interconnected linear systems with multiplicative noises the small gain theorem is proposed in terms of the spectral radius of a matrix whose elements are the squares of h sub 2 norms of the involved transfer functions both robust stability and performance conditions are characterized by the new small gain theorem

damage spreading and critical exponents for model a ising dynamics using damage spreading and heat bath dynamics we study the ising model in 2 and 3 dimensions with non conservative dynamics our algorithm differs in some important points from previous ones which makes it rather efficient we give estimates for the exponent z which seem to be the most precise published so far 2 172 0 006 for d 2 2 032 0 004 for d 3 we also give precise estimates of the exponent introduced by janssen et al z phys b 73 1989 539 and of analogous but in principle independent exponents we find surprisingly that some of the latter agree with and give an explanation for this

duality in finite dimensional spin glasses we present an analysis leading to a conjecture on the exact location of the multicritical point in the phase diagram of spin glasses in finite dimensions the conjecture in satisfactory agreement with a number of numerical results was previously derived using an ansatz emerging from duality and the replica method in the present paper we carefully examine the ansatz and reduce it to a hypothesis on analyticity of a function appearing in the duality relation thus the problem is now clearer than before from a mathematical point of view the ansatz somewhat arbitrarily introduced previously has now been shown to be closely related to the analyticity of a well defined function

moment stability of nonlinear discrete stochastic systems with time delays based on h representation technique in this paper mean square stability of nonlinear discrete stochastic systems with time delays is investigated we obtain the second order moment equations of discrete stochastic systems by virtue of the h representation technique by the comparison principle and the established moment equations some moment stability theorems for nonlinear discrete stochastic systems with time delays are established a numerical example is presented to illustrate the efficiency of our results at the end of the paper

an alternating iterative algorithm for the cauchy problem associated to the helmholtz equation in this paper the iterative algorithm proposed by kozlov et al comput maths math phys 31 1991 45 for obtaining approximate solutions to the ill posed cauchy problem for the helmholtz equation is analysed the technique is then numerically implemented using the boundary element method bem the numerical results confirm that the iterative bem produces a convergent and stable numerical solution with respect to increasing the number of boundary elements and decreasing the amount of noise added into the input data an efficient stopping regularising criterion is also proposed

damage spreading and critical exponents for model a ising dynamics abstract recent simulations by grassberger gave very precise estimates of the dynamical critical exponent z via damage spreading techniques we confirm these results using a slightly altered method and we examine larger systems up to 18161 2 and 695 2 giving z 2 18 0 02 and 2 04 0 01 respectively

nonequilibrium relaxation study on spin glass model ferromagnetic fm transition point and universality class of the j ising model on cubic lattice are studied by computer simulation using the nonequilibrium relaxation ner method at fm bond density p between multicritical one pmc and 1 static exponents take universal values which are different from those of p 1 or p pmc and they are consistent with the values of the random fixed point and of the simulations and experiments for diluted ising systems the dynamical exponent however seems to depend on p and not to be universal although it may be due to finite time correction the estimation of pmc on square lattice is also refined to be 0 8894 9 which is consistent with the nishimori and nemoto s conjecture 0 889972

on discrete stochastic bilinear systems stability abstract mean square stability conditions for discrete time bilinear systems operating in a stochastic environment are given in this paper only independence and wide sense stationarity are required for the second order disturbance sequences involved thus dismissing ergodicity and zero mean assumptions stochastic stability conditions are derived by using a deterministic stability result for a class of separable nonlinear dynamical systems evolving in a banach space

brief stability radii of discrete time stochastic systems with respect to blockdiagonal perturbations we consider stochastic discrete time systems with multiplicative noise which are controlled by dynamic output feedback and subjected to blockdiagonal stochastic parameter perturbations stability radii for these systems are characterized via scaling techniques and it is shown that for real data the real and the complex stability radii coincide in a second part of the paper we investigate the problem of maximizing the stability radii by dynamic output feedback necessary and sufficient conditions are derived for the existence of a stabilizing compensator which ensures that the stability radius is above a prespecified level these conditions consist of parametrized matrix inequalities and a coupling condition

brief paper detectability and observability of discrete time stochastic systems and their applications this paper studies detectability and observability of discrete time stochastic linear systems based on the standard notions of detectability and observability for time varying linear systems corresponding definitions for discrete time stochastic systems are proposed which unify some recently reported detectability and exact observability concepts for stochastic linear systems the notion of observability leads to the stochastic version of the well known rank criterion for observability of deterministic linear systems by using these two concepts the discrete time stochastic lyapunov equation and riccati equations are studied the results not only extend some of the existing results on these two types of equation but also indicate that the notions of detectability and observability studied in this paper take analogous functions as the usual concepts of detectability and observability in deterministic linear systems it is expected that the results presented may play important roles in many design problems in stochastic linear systems