tracing the equilibrium path beyond compound critical points a unified presentation of some popular continuation procedures used in the non linear finite element analysis of structural mechanics is introduced an extension of the elliptical constraint equation proposed by crisfield is given it is shown that in the proposed procedure real roots can always be obtained in solving the iterative change of the load parameter updated weighting factors are introduced in the constraint equation in order to get better convergence characteristics in the case when localized deformations occur for bifurcation points a modification of rheinboldt s branching procedure is presented post critical response after limit and bifurcation points is determined in some numerical examples

infinite horizon stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper studies the infinite horizon mixed h 2 h control for discrete time stochastic systems with state and disturbance dependent noise we shall first establish a version of stochastic bounded real lemma sbrl which by itself has theoretical importance based on the sbrl it is shown that under the condition of exact observability the existence of a static state feedback h 2 h controller is equivalent to the solvability of four coupled matrix valued equations a suboptimal h 2 h controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix valued equations

exact observability conditions for hilbert space dynamical systems connected with riesz basis of divided differences abstract in the paper we consider the problem of exact observability of a general class of distributed parameter systems in hilbert spaces we show that under some conditions on asymptotic behavior of the spectrum of the differential operator the system is not exact observable in default topologies and find a stronger topology for state observation for which the system becomes exactly observable we illustrate this result with a vibrating clamped free timoshenko beam model

convergence cones near bifurcation the performance of predictor solver continuation methods near bifurcation points is considered a general theory is developed for the convergence of two commonly used solvers namely newton s method and the chord method near singular points of a nonlinear equation this theory provides a uniform treatment of continuation for simple bifurcation multiple bifurcation and multiple limit point bifurcation problems for these types of bifurcation it is shown that there are conical domains of attraction for the above iterative methods centred on solution branches which correspond to isolated roots of the algebraic bifurcation equations

hopf bifurcation near a double singular point with z 2 symmetry and x 0 breaking this paper deals with nonlinear equations f x 0 and the corresponding odes xt f x satisfying f 0 0 and a z2 symmetry in particular we are interested in hopf points which indicate the bifurcation of periodic solutions of xt f x from steady state solutions of f x 0 it is shown that under suitable nondegeneracy conditions there bifurcate two paths of hopf points from a double singular point where x 0 and fx 0 has a double zero eigenvalue with one eigenvector symmetric and one anti symmetric this result gives a new example of finding hopf points through local singular points our main tools for analysis are some extended systems which also provide easily implemented algorithms for the numerical computation of the bifurcating hopf points a supporting numerical example for a brusselator model is also presented

robust stability and robust stabilization of a class of discrete time time varying linear stochastic systems in this paper a small gain result is presented for a class of discrete time time varying markovian jump systems with state dependent and input dependent noise using the stabilizing solutions of some generalized riccati equations the result is obtained based on a lyapunov type argument as an application of the proposed small gain result we discuss the problem of robust stability and robust state feedback stabilization of the considered class of stochastic systems via the stability radius concept

robust h sub spl infin filtering of stationary continuous time linear systems with stochastic uncertainties the problem of applying h sub spl infin filters on stationary continuous time linear systems with stochastic uncertainties in the state space signal model is addressed these uncertainties are modeled via white noise processes the relevant cost function is the expected value of the standard h sub spl infin performance index with respect to the uncertain parameters the solution is obtained via a stochastic bounded real lemma that results in a modified riccati inequality this inequality is expressed in the form of a linear matrix inequality whose solution provides the filter parameters the method proposed is also applied to the case where in addition to the stochastic uncertainty other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope the problem of mixed h sub 2 h sub spl infin filtering for the above system is also treated the theory developed is demonstrated by a practical example

non criticality criteria for abelian sandpile models with sources and sinks we prove that the abelian sandpile model on a random binary and binomial tree as introduced in redig ruszel and saada j stat phys 147 653 677 2012 is not critical for all branching probabilities p 1 by estimating the tail of the annealed survival time of a random walk on the binary tree with randomly placed traps we obtain some more information about the exponential tail of the avalanche radius next we study the sandpile model on zd with some additional dissipative sites we provide examples and sufficient conditions for non criticality we also make a connection with the parabolic anderson model finally we initiate the study of the sandpile model with both sources and sinks and give a sufficient condition for non criticality in the presence of a finite number of sources using a connection with the homogeneous pinning model

an explicit equivalent positive semidefinite program for nonlinear 0 1 programs we consider the general nonlinear optimization problem in 0 1 variables and provide an explicit equivalent positive semidefinite program in 2n 1 variables the optimal values of both problems are identical from every optimal solution of the former one easily finds an optimal solution of the latter and conversely from every solution of the latter one may construct an optimal solution of the former for illustration the equivalent positive semidefinite program is explicated for quadratic 0 1 programs and max cut in mathbb r 3 for unconstrained 0 1 programs a special representation in terms of a weighted sum of squares is provided

transport properties of the one dimensional stochastic lorentz model i velocity autocorrelation function point scatterers are placed on the real line such that the distances between scatterers are independent identically distributed random variables stationary renewal process for a fixed configuration of scatterers a particle performs the following random walk the particle starts at the pointx with velocity 1 in between scatterers the particle moves freely at a scatterer the particle is either transmitted or reflected both with probability 1 2 for given initial conditions of the particle the velocity autocorrelation function is a random variable on the scatterer configurations if this variable is averaged over the distribution of scatterers it decays not faster thant 3 2

a small gain theorem for linear stochastic systems abstract a well known result in linear control theory is the so called small gain theorem stating that if given two plants with transfer matrix functions t 1 and t 2 in h such that t 1 and t 2 when coupling t 2 to t 1 such that u 2 y 1 and u 1 y 2 one obtains an internally stable closed system the aim of the present paper is to describe a corresponding result for stochastic systems with state dependent white noise

robust kalman filters for linear time varying systems with stochastic parametric uncertainties we present a robust recursive kalman filtering algorithm that addresses estimation problems that arise in linear time varying systems with stochastic parametric uncertainties the filter has a one step predictor corrector structure and minimizes an upper bound of the mean square estimation error at each step with the minimization reduced to a convex optimization problem based on linear matrix inequalities the algorithm is shown to converge when the system is mean square stable and the state space matrices are time invariant a numerical example consisting of equalizer design for a communication channel demonstrates that our algorithm offers considerable improvement in performance when compared with conventional kalman filtering techniques

discrete time mean field stochastic linear quadratic optimal control problems ii infinite horizon case this paper first presents results on the equivalence of several notions of l2l2 stability for linear mean field stochastic difference equations with random initial value then it is shown that the optimal control of a mean field linear quadratic optimal control with an infinite time horizon uniquely exists and the optimal control can be expressed as a linear state feedback involving the state and its mean via the minimal nonnegative definite solution of two coupled algebraic riccati equations as a byproduct the open loop l2l2 stabilizability is proved to be equivalent to the closed loop l2l2 stabilizability moreover the minimal nonnegative definite solution the maximal solution the stabilizing solution of the algebraic riccati equations and their relations are carefully investigated specifically it is shown that the maximal solution is employed to construct the optimal control and value function to another infinite time horizon mean field linear quadratic optimal control in addition the maximal solution being the stabilizing solution is completely characterized by properties of the coefficients of the controlled system this enriches the existing theory about stochastic algebraic riccati equations finally the notion of exact detectability is introduced with its equivalent characterization of stochastic versions of the popov belevitch hautus criteria it is then shown that the minimal nonnegative definite solution is the stabilizing solution if and only if the uncontrolled system is exactly detectable

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

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

robust h spl infin control for uncertain stochastic systems with state delay this note deals with the problems of robust stochastic stabilization and robust h control for uncertain stochastic systems with a time varying delay in the state the parameter uncertainties are assumed to be time varying norm bounded appearing in both the state and input matrices the purpose of the robust stochastic stabilization problem is the design of a memoryless state feedback controller such that the closed loop system is mean square asymptotically stable for all admissible uncertainties in the robust h control problem in addition to the mean square asymptotic stability requirement a prescribed h performance is required to be achieved in terms of a linear matrix inequality sufficient conditions for the solvability of these problems are proposed respectively the expressions of desired state feedback controllers are given an example illustrating the proposed approach is provided

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

stabilizability of linear time varying and uncertain linear systems feedback stabilization of linear time varying and uncertain linear systems is considered it is proved that given a stabilizing dynamic linear state feedback controller one can always construct a stabilizing nondynamic linear state feedback controller a similar result is shown for uncertain linear systems a linear time varying system can be stabilized by dynamic output feedback if and only if it admits a coprime factorization

optimal filtering for discrete time linear systems with multiplicative white noise perturbations and periodic coefficients in this technical brief the problem of the estimation of a remote signal generated by a discrete time dynamical system with periodic coefficients subject to multiplicative and additive white noise perturbations is investigated to measure the quality of the estimation achieved by an admissible filter we introduced a performance criterion described by the cesaro limit of the mean square of the deviation between the estimated signal zf t and the remote signal z t the dimension of the state space of the admissible filters is not prefixed the state space representation of the optimal filter is constructed based on the unique periodic solution of a discrete time linear equation together with the stabilizing solution of a suitable discrete time riccati equation with periodic coefficients

minimal representation of matrix valued white stochastic processes and u d factorisation of algorithms for optimal control two different descriptions are used in the literature to formulate the optimal dynamic output feedback control problem for linear dynamical systems with white stochastic parameters and quadratic criteria called the optimal compensation problem one describes the matrix valued white stochastic processes involved using a sum of deterministic matrices each one multiplied by a scalar stochastic process that is independent of the others another that is more general and concise uses kronecker products instead this article relates the statistics of both descriptions and shows their advantages and disadvantages as to the first description an important result that comes out is the minimum number of matrices multiplied by scalar independent stochastic processes needed to represent a certain matrix valued white stochastic process together with an associated minimal representation as to the second description an important result concerns the generation of all kronecker products that represent relevant st

exact detectability and exact observability of discrete time linear stochastic systems with periodic coefficients abstract this paper is devoted to the problem of detectability and observability of a class of time varying stochastic systems the main contribution of this note is to propose a pbh type test which is equivalent to the detectability of the considered stochastic systems in the sense that all unstable modes produce some non zero output then we apply the obtained results in order to derive a criterion of exponential stability in mean square sense as well as existence conditions for the stabilizing solution of a class of discrete time time varying riccati equations

regional observability for distributed semi linear hyperbolic systems the objective of this paper is to study the notion of regional observability of hyperbolic semilinear systems for the state reconstruction in a given subregion we give a first approach which combines the extension of the hum method and the fixed point techniques the analytical case is then explored using sectorial property of the considered dynamic operator and converted to a fixed point problem the two approaches lead to algorithms which are successfully implemented numerically and illustrated with examples and simulations

properties of the solutions of rational matrix difference equations abstract we prove a comparison theorem for the solutions of a rational matrix difference equation generalizing the riccati difference equation and existence and convergence results for the solutions of this equation moreover we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing or almost stabilizing solution

long time tails in a random diffusion model letw w x x zd be a positive random field with i i d distribution given its realization letxt be the position at timet of a particle starting at the origin and performing a simple random walk with jump rate w 1 xt the processx xt t 0 combined withw on a common probability space is an example of random walk in random environment we consider the quantities t d dt e x t 2 m 1t and t w d dt ew x t 2 m 1t here ew is expectation overx at fixedw and e ew dw is the expectation over bothx andw we prove the following long time tail results 1 limt td 2 t v2md 2 3 d 2 d 2 and 2 limt td 4 st w zs weakly in path space with zs s 0 the gaussian process with ezs 0 and ezrzs v2md 2 4 d d 2 r s d 2 herem and v2 are the mean and variance of w 0 under the main surprise is that fixingw changes the power of the long time tail fromd 2 tod 4 since delta t me mu 0 w 1 x 0 m 1 w 1 x t m 1 with 0 the stationary measure for the environment process our result 1 exhibits a long time tail in an equilibrium autocorrelation function

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

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

global observability and detectability analysis of uncertain reaction systems and observer design observation issues are of fundamental importance for reaction systems due to the limited availability of on line sensors and the uncertainties related to the mathematical model the objective of this work is to propose a methodology to make a global analysis of observability and detectability of such systems with a particular concern about the design of robust observers for this the uncertainties of the reaction system are modelled as arbitrary unknown inputs these results include and generalize the standard asymptotic observers well known in the biotechnology moreover the observability properties required for the existence of such observers and for the assignability of their convergence dynamics are clarified

time varying state feedback stabilisation of stochastic feedforward nonlinear systems with unknown growth rate abstractwe consider the time varying state feedback stabilisation problem for a class of stochastic feedforward nonlinear systems with unknown growth rate in this paper a new lasalle type theorem for stochastic time varying systems is firstly established by using the generalized weakly positive definite function as an application to deal with serious uncertainties in the unknown growth rate a time varying approach rather than an adaptive one is adopted to design the scheme of a state feedback controller for stochastic feedforward systems based on the established lasalle type theorem it is shown that all signals of the resulting closed loop system converge to zero almost surely illustrative examples are given to verify the theoretical findings

switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in odes the paper provides full algorithmic details on switching to the continuation of all possible codim 1 cycle bifurcations from generic codim 2 equilibrium bifurcation points in n dimensional odes we discuss the implementation and the performance of the algorithm in several examples including an extended lorenz 84 model and a laser system

infinite horizon optimal control of linear discrete time systems with stochastic parameters the infinite horizon optimal control problem is considered in the general case of linear discrete time systems and quadratic criteria both with stochastic parameters which are independent with respect to time a stronger stabilizability property and a weaker observability property than usual for deterministic systems are introduced it is shown that the infinite horizon problem has a solution if the system has the first property if in addition the problem has the second property the solution is unique and the control system is stable in the mean square sense a simple necessary and sufficient condition explicit in the system matrices is given for the system to have the stronger stabilizability property this condition also holds for deterministic systems to be stabilizable in the usual sense the stronger stabilizability and weaker observability properties coincide with the usual ones if the parameters are deterministic

hopf bifurcation near a double singular point abstract the nonlinear equation f x 0 f x r2 x where x is a banach space and f satisfies a z2 symmetry relation is considered interest centres on a certain type of double singular point where the solution x is symmetric and fx has a double zero eigenvalue with one eigenvector symmetric and one antisymmetric we show that under certain nondegeneracy conditions which are stated both algebraically and geometrically there exists a path of hopf bifurcations or imaginary hopf bifurcations passing through the double singular point and for which x is not symmetric except at the double singular point an easy geometrical test is found to decide which type of phenomenon occurs a biproduct of the analysis is that explicit expressions are obtained for quantities which help to provide a reliable numerical method to compute these paths a pseudo spectral method was used to obtain numerical results for the brusselator equations to illustrate the theory

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

on stabilizability and exact observability of stochastic systems with their applications this paper mainly studies the stabilizability and exact observability of stochastic linear controlled systems and their applications with the aid of the operator spectrum a necessary and sufficient condition is given for the stabilizability of stochastic systems some new concepts such as unremovable spectrum and strong solution are introduced an unremovable spectral theorem and a stochastic popov belevith hautus criterion for exact observability are presented as applications a comparison theorem for stochastic algebraic riccati equations and a result on lyapunov type equations are obtained

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

optimal stabilization control for discrete time mean field stochastic systems this paper will investigate the stabilization and optimal linear quadratic lq control problems for infinite horizon discrete time mean field systems unlike the previous works for the first time the necessary and sufficient stabilization conditions are explored under mild conditions and the optimal lq controller for infinite horizon is designed with a coupled algebraic riccati equation are more specifically we show that under the exact detectability exact observability assumption the mean field system is stabilizable in the mean square sense with the optimal controller if and only if a coupled are has a unique positive semidefinite positive definite solution the presented results are parallel to the classical results for the standard lq control

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

corrigendum addendum to sets of matrices all infinite products of which converge abstract this corrigendum addendum supplies corrected statements and proofs of some results in our paper appearing in linear algebra appl 161 1992 227 263 these results concern special kinds of bounded semigroups of matrices it also reports on progress on the topics of this paper made in the last eight years

optimal filtering for discrete time linear systems with time correlated multiplicative measurement noises in this note the filtering problem for discrete time linear systems with time correlated multiplicative measurement noises is considered where the vector consisting of all the multiplicative measurement noises can be described by a linear system model with white noise by introducing several new recursive terms a novel algorithm for optimal filtering of the system under consideration is proposed in the sense of linear minimum mean square error the proposed algorithm is recursive and has time independent complexity computer simulations are provided to illustrate the performance of the proposed algorithm

generalized lyapunov equation approach to state dependent stochastic stabilization detectability criterion in this paper the generalized lyapunov equation approach is used to study stochastic stabilization detectability with state multiplicative noise some practical test criteria for stochastic stabilization and detectability such as stochastic popov belevitch hautus criterion for exact detectability are obtained moreover useful properties of the generalized lyapunov equation are derived based on critical stability and exact detectability introduced in this paper as applications first the stochastic linear quadratic regulator as well as the related generalized algebraic riccati equation are discussed extensively second the infinite horizon stochastic h 2 h infin control with state and control dependent noise is also investigated which extends and improves the recently published results

brief paper optimal reduced order compensation of time varying discrete time systems with deterministic and white parameters the finite horizon optimal compensation problem is considered in the case of linear time varying discrete time systems with deterministic and white stochastic parameters and quadratic criteria the dimensions of the compensator are a priori fixed and may be time varying also the dimensions of the system may be time varying strengthened discrete time optimal projection equations sdope are developed which within the class of minimal compensators are equivalent to the first order necessary optimality conditions based on the sdope and their associated boundary conditions two numerical algorithms are presented to solve the two point boundary value problem one is a homotopy algorithm while the second iterates the sdope repeatedly forward and backward in time the latter algorithm is much more efficient and constitutes a generalization of the single iteration of the control and estimation riccati equations associated with the full order problem for systems with deterministic parameters the algorithms are illustrated with a numerical example the case of systems with deterministic parameters will be treated as a special case of systems with white parameters

on solving nonlinear equations with simple singularities or nearly singular solutions the paper begins with a review of the convergence theory for newton s method near simple and other regular singularities followed by a brief discussion of the inherent difficulty of singular problems and the effect of rounding errors on the achievable solution accuracy then several ways to accelerate the slow convergence of newton s method are described in some detail these are richardson extrapolation overrelaxation bordering by a singularity condition and appending the usual linear model by a quadratic term the last two approaches require limited second derivative information which can be obtained analytically by differencing or through secant updating numerical comparisons reported in the final sections lead to the conclusion that the collection of the additional information pays off in terms of speed and accuracy

on stability of linear time varying infinite dimensional discrete time systems the asymptotic behaviour of linear time varying infinite dimensional discrete lime systems is considered the introduced notions are weak power equistability power equistability uniform power equistability l p equistability uniform l p equistability and l p x equistability it is shown that they are identical a generalization of the concept of spectral radius of a single operator is also proposed it is proven that any time varying system is uniformly power equistable if and only if the generalized spectral radius of the sequence of the operators which define the system considered is less than one

uniform stabilization of discrete time switched and markovian jump linear systems the uniform stability of discrete time switched linear systems possibly with a strongly connected switching path constraint and the existence of finite path dependent dynamic output feedback controllers uniformly stabilizing such a system are both shown to be characterized by the existence of a finite dimensional feasible system of linear matrix inequalities this characterization is based on the observation that a linear time varying system is uniformly stable only if there exists a finite path dependent quadratic lyapunov function the synthesis of a uniformly stabilizing controller is done without conservatism by solving any feasible system of linear matrix inequalities among an increasing family of systems of linear matrix inequalities the result carries over to the almost sure uniform stabilization of markovian jump linear systems

multiple bifurcations in a reaction diffusion problem abstract we study multiple bifurcations in a system of reaction diffusion equations defined on the unit square first we investigate linear stability of the system at the uniform steady state solution then we discuss necessary conditions for mode interactions in particular we show that a corank four bifurcation point of the system can be easily generated by the mode interactions of two double bifurcation points we also study the possibilities of preserving the multiplicity of bifurcation points in the discrete system a continuation bcg algorithm proposed by chien et al is exploited to trace the solution branches finally sample numerical results are reported

adaptive impulsive observers for nonlinear systems this paper revisits the design of adaptive impulsive observers aios for nonlinear systems the dynamics of observer state of the proposed aio is modelled by an impulsive differential equation by which the observer state is updated in an impulsive fashion the parameter estimation law is modelled by an impulse free time varying differential equation associated with the impulse time sequence for determining when the observer state is updated unlike the previous work the convergence analysis of the estimation error system is performed by applying a time varying lyapunov function based method in conjunction with the application of a generalized version of barbalat s lemma a sufficient condition for the existence of aios is also derived for some special cases it is shown that the sufficient condition can be formulated in terms of linear matrix inequalities lmis and the observer matrices can be attained by solving a set of lmis furthermore with an additional persistence of excitation type constraint it is proved that the sufficient condition can guarantee the convergence of parameter estimation two examples of chaotic oscillators are provided to illustrate the design procedure of the proposed aios

detectability observability and lyapunov type theorems of linear discrete time varying stochastic systems with multiplicative noise abstractthe objective of this paper is to study detectability observability and related lyapunov type theorems of linear discrete time time varying stochastic systems with multiplicative noise some new concepts such as uniform detectability k exact detectability resp kwft exact detectability kft exact detectability kn exact detectability and k exact observability resp kwft exact detectability kft exact detectability kn exact detectability are introduced respectively and nice properties associated with uniform detectability exact detectability and exact observability are also obtained moreover some lyapunov type theorems associated with generalised lyapunov equations and exponential stability in mean square sense are presented under uniform detectability kn exact observability and kn exact detectability respectively

nash estimates and the asymptotic behavior of diffusions afin d analyser le comportement asymptotique d une particule diffusant dans un champ de derive a partir d un potentiel borne lisse on developpe des estimations a priori du type de nash sur la densite de transition du processus

finite dimensional approximation of nonlinear problems in the first two papers of this series 4 5 we have studied a general method of approximation of nonsingular solutions and simple limit points of nonlinear equations in a banach space we derive here general approximation results of the branches of solutions in the neighborhood of a simple bifurcation point the abstract theory is applied to the galerkin approximation of nonlinear variational problems and to a mixed finite element approximation of the von karman equations

on unified concepts of detectability and observability for continuous time stochastic systems this paper is concerned with detectability and observability of continuous time stochastic linear systems by adopting the idea used in defining these two concepts for time varying systems and markovian jump linear systems that have been studied in the literature corresponding definitions for continuous time stochastic linear systems are proposed these two definitions are not only able to unify some recent definitions on these two concept reported in the literature but also allow us to propose an efficient rank criterion to test observability of continuous time stochastic linear systems it seems that this rank criterion is quite analogous to the rank criterion for deterministic linear systems with the help of these two concepts and the new criteria the stochastic lyapunov equation is revisited and some recent published work on this equation are generalized numerical examples are given to illustrate the effectiveness of the proposed approach

global optimization with polynomials and the problem of moments we consider the problem of finding the unconstrained global minimum of a real valued polynomial p x mathbb r n to mathbb r as well as the global minimum of p x in a compact set k defined by polynomial inequalities it is shown that this problem reduces to solving an often finite sequence of convex linear matrix inequality lmi problems a notion of karush kuhn tucker polynomials is introduced in a global optimality condition some illustrative examples are provided

brief paper on detectability of stochastic systems we discuss notions of detectability for stochastic linear control systems of ito type a natural concept of detectability requires a non zero output if the state process is unstable we show that this property can equivalently be characterized by a generalized version of the hautus test the proof is based on spectral theory for positive operators

dynamic structure factor in a random diffusion model let xt 0 denote random walk in the random waiting time model i e simple random walk with jump ratew 1 xt where w x x d is an i i d random field we show that under some mild conditions theintermediate scattering functionf q t e0 e iqx l q d is completely monotonic int e0 denotes double expectation w r t walk and field we also show that thedynamic structure factors q w 2 0 cos t f q t exists for 0 and is strictly positive ind 1 2 it diverges as 1 1 2 resp ln in the limit 0 ind 3 its limit value is strictly larger than expected from hydrodynamics this and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that d q 2 whered is the diffusion constant

characterization and computation of generalized turning points a minimal set of augmenting equations is given so that general parameter dependent problems together with these equations will be nonsingular at points of simple rank deficiency applications to de

folds in solutions of two parameter systems and their calculation part i this paper is concerned with paths of turning points in solutions of nonlinear systems having two parameters it is well known that these paths are solutions of a particular extended system of nonlinear equations in this paper both regular points and simple turning points in the extended system are related to the local geometry of the solution surface of the original nonlinear system a description is given of numerical methods both for solving the extended system and for calculating certain quantities which determine the local geometry of the solution surface applications to perturbed bifurcation to the formation of isolas and to the calculation of the multiplicity of solutions are also discussed numerical examples are given

lie algebraic stability criteria for switched systems it was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable lie algebra possesses a quadratic common lyapunov function which implies that the corresponding switched linear system is exponentially stable for arbitrary switching in this paper we prove that the same properties hold under the weaker condition that the lie algebra generated by given matrices can be decomposed into a sum of a solvable ideal and a subalgebra with a compact lie group the corresponding local stability result for nonlinear switched systems is also established moreover we demonstrate that if a lie algebra fails to satisfy the above condition then it can be generated by a family of stable matrices such that the corresponding switched linear system is not stable relevant facts from the theory of lie algebras are collected at the end of the paper for easy reference

detectability of linear discrete time systems with stochastic parameters abstract the paper introduces the concept of mean square detectability and relates this to the recently introduced concept of mean square observability it is shown that under appropriate mean square detectability and stabilizability conditions the infinite horizon optimal control problem for the general case of linear discrete time systems and quadratic criteria both with stochastic parameters which are statistically independent of time has a unique solution when the control system is mean square stable a simple necessary and sufficient condition explicit in the system matrices is given to determine if a system is mean square detectable this condition also holds for deterministic systems to be detectable in the usual sense the mean square detectability property coincides with the usual one if the parameters are deterministic

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

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

on the detectability and observability of continuous stochastic markov jump linear systems abstract this paper is concerned with the detectability and observability of continuous linear stochastic systems subject to markov jump by introducing some operators we investigate the relationship between some different concepts of detectability and observability and obtain their sufficient and necessary conditions continuous time stochastic lyapunov equations and stochastic continuous algebraic riccati equations are also discussed to serve as analysis tools

a long time tail for random walk in random scenery consider a simple random walk on d whose sites are colored black or white independently with probabilityq resp 1 q walk and coloring are independent letn k be the number of steps by the walk between itskth and k 1 th visits to a black site i e the length of itskth white run and let k e n k q 1 our main result is a proof that lim k k d 2 k 1 q q d 2 2 d 2 d 2 since it is known thatq 1 k e n 1 n k 1 b e n 1 b e n k 1 b withb the event that the origin is black exhibits a long time tail in the run length autocorrelation function numerical calculations of k 1 k 100 ind 1 2 and 3 show that there is an oscillatory behavior of k for smallk this damps exponentially fast following which the power law sets in fairly rapidly we prove that if the coloring is not independent but is convex in the sense of fkg then the decay of k cannot be faster than

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

stochastic observability in network state estimation and control a hidden markov model for the traffic congestion control problem in transmission control protocol tcp networks is developed and the question of observability of this system is posed of specific interest are the dependence of observability on the congestion control law and the interaction between observability ideas and the effectiveness of feedback control analysis proceeds with a survey of observability concepts and an extension of some available definitions for linear and nonlinear stochastic systems the key idea is to link the improvement of state estimator performance to the conditioning on the output data sequence the observability development proceeds from linear deterministic systems to linear gaussian systems nonlinear systems etc with backwards compatibility to deterministic ideas the principal concepts relate to the entropy decrease of scalar functions of the state which in the linear case are describable in terms of covariance matrices a feature of nonlinear systems is that the estimator properties may affect the closed loop control performance results are derived linking stochastic reconstructibility to strict improvement of the optimal closed loop control performance over open loop control for the hidden markov model the entropy provides a means to quantify and thus order simulation results for a simplified tcp network motivated by the link between feedback control and reconstructibility the entropy formulation is also explored as a means to discriminate between different control strategies for improving estimator performance this approach has connections to dual adaptive control ideas where the control has the simultaneous and opposing goals of regulating the system and of exciting the system to prevent estimator divergence

on a class of rational matrix differential equations arising in stochastic control we prove a monotonicity and a comparison theorem for the solutions of a rational matrix differential equation appearing in stochastic control and derive existence and convergence results for the solutions of this differential equation moreover in the time invariant case we present conditions ensuring that the corresponding algebraic matrix equation has a stabilizing solution

on the detectability and observability of discrete time markov jump linear systems abstract this paper presents a new detectability concept for discrete time markov jump linear systems with finite markov state which generalizes the ms detectability concept found in the literature the new sense of detectability can similarly assure that the solution of the coupled algebraic riccati equation associated to the quadratic control problem is a stabilizing solution in addition the paper introduces a related observability concept that also generalizes previous concepts a test for detectability based on a coupled matrix equation is derived from the definition and a test for observability is presented which can be performed in a finite number of steps the results are illustrated by examples including one that shows that a system may be detectable in the new sense but not in the ms sense

finite size scaling of the time dependent structure factor in the one dimensional glauber model abstract we study the time dependent structure factor of the one dimensional glauber model upon instantaneous cooling results obtained earlier by reiss mazenko and widom and bray are linked together next finite size scaling in the limit of zero temperature long times small wave vectors and large systems is established the scaling function is compared with numerical simulation results obtained by vinals and jasnow in the case of a two dimensional glauber model quenched into the region of phase separation

asymptotic height optimization for topical ifs tetris heaps and the finiteness conjecture given an iterated function system ifs of topical maps verifying some conditions we prove that the asymptotic height optimization problems are equivalent to finding the extrema of a continuous functional the average height on some compact space of measures we give general results to determine these extrema and then apply them to two concrete problems first we give a new proof of the theorem that the densest heaps of two tetris pieces are sturmian second we construct an explicit counterexample to the lagarias wang finiteness conjecture

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