the pth moment exponential stability and almost surely exponential stability of stochastic differential delay equations with poisson jump abstract this paper is devoted to study a class of nonlinear stochastic differential delay equations with poisson jump in comparison to the brownian motion the jump leads to the discontinuity of sample paths which makes the analysis more difficult we first introduce the local lipschitz condition and a new nonlinear growth condition which is weaker than those in the previous literature then by virtue of lyapunov function and semi martingale convergence theorem we prove that the considered stochastic system has a unique global solution moreover we also investigate the pth moment exponential stability and the almost surely exponential stability of solutions finally an example is given to illustrate the effectiveness of our theoretical results

moment lyapunov exponent and stability index for linear conservative system with small random perturbation asymptotic expansion series for the moment lyapunov exponent and stability index are constructed and justified for the two dimensional linear stochastic system close to a harmonic oscillator as an example a one degree of freedom mechanical system parametrically excited in stiffness and damping is considered and several terms of the expansion are obtained

on the estimation of optical flow relations between different approaches and some new results abstract a common basis is suggested for the optical flow estimation approaches of nagel 1983 haralick and lee 1983 and tretiak and pastor 1984 based on a discussion of these approaches an exact solution for the system of partial differential equations proposed by horn and schunck 1981 is given at gray value corners and extrema the insight gained by this solution results in a modification of the oriented smoothness approach of nagel 1983 which thereby becomes considerably simpler in addition the optical flow estimation approach of hildreth 1983 1984 can be shown to represent a kind of special case of this modified oriented smoothness approach in a more direct manner than discussed in nagel 1984

lyapunov exponents and rotation number of two dimensional systems with telegraphic noise exact expressions for the exponential growth rates lyapunov exponents and rotation numbers of two dimensional systems perturbed by telegraphic noise are derived asymptotic expansions for small large slow and fast noise and the white noise limit are constructed then results are applied to the random oscillator stochastic stability in particular stabilization by noise and stochastic bifurcation

asymptotic analysis of the lyapunov exponent and rotation number of the random oscillator and application we construct asymptotic expansions for the exponential growth rate lyapunov exponent and rotation number of the random oscillator when the noise is large small rapidly varying or slowly varying we then apply our results to problems in the stability of the random oscillator the spectrum of the one dimensional random schr6dinger operator and wave propagation in a one dimensional random medium

on the stability properties of a van der pol duffing oscillator that is driven by a real noise abstract in this paper we consider a van der pol duffing oscillator that is excited parametrically by a small intensity real noise which is assumed to be an integrable function of an n dimensional ornstein uhlenbeck vector process that is an output of a linear filter system the stability properties include the moment lyapunov exponent g p x 0 and the maximal lyapunov exponent and the stability in probability are examined to study a model of enhanced generality we remove both the detailed balance condition and the strong mixing condition in the case of an arbitrary finite real number p we employ the perturbation method and a spectrum representation of the fokker planck operator of the linear filter system to construct asymptotic expansions of the pth moment lyapunov exponent and the top lyapunov exponent the same methods are also used for a nonlinear stochastic system to obtain the fpk fokker planck kolmogonov equation for the amplitude process which is identical to the one that is derived from the stochastic averaging method in the case of a broadband noise excitation on the basis of this fpk equation we also examine the almost sure stability condition of the ito stochastic differential equation for the amplitude process which matches the result that is derived from the maximal lyapunov exponent finally the method proposed by lin and cai probabilistic structural dynamics advanced theory and application mcgraw hill new york 1995 is adopted to examine the stability in probability of the amplitude process for the nonlinear ito differential equation

almost sure instability of the random harmonic oscillator the problem of almost sure stability of the random harmonic oscillator with a jump process coefficient is studied it is shown that the sample paths are almost surely unstable and an asymptotic series expansion in the powers of the noise strength for the asymptotic exponential growth rate is obtained

a stabilization algorithm for a class of uncertain linear systems abstract this paper presents an algorithm for the stabilization of a class of uncertain linear systems the uncertain systems under consideration are described by state equations which depend on time varying unknown but bounded uncertain parameters the construction of the stabilizing controller involves solving a certain algebraic riccati equation furthermore the solution to this riccati equation defines a quadratic lyapunov function which is used to establish the stability of the closed loop system this leads to a notion of quadratic stabilizability it is shown that the stabilization procedure will succeed if and only if the given uncertain linear system is quadratically stabilizable the paper also deals with a notion of overbounding for uncertain linear systems this procedure enables the stabilization algorithm to be applied to a larger class of uncertain linear systems also included in the paper are results which indicate the degree of conservativeness introduced by this overbounding process

almost sure stability of linear stochastic differential equations with jumps under the nondegenerate condition as in the diffusion case see 14 21 6 the linear stochastic jump diffusion process projected on the unit sphere is a strong feller process and has a unique invariant measure which is also ergodic using the relation between the transition probabilities of jump diffusions and the corresponding diffusions due to 22 the unique deterministic lyapunov exponent can be represented by the furstenberg khas minskii formula as an integral over the sphere or the projective space with respect to the ergodic invariant measure so that the almost sure asymptotic stability of linear stochastic systems with jumps depends on its sign the critical case of zero lyapunov exponent is discussed and a large deviations result for asymptotically stable systems is further investigated several examples are treated for illustration

computation of discontinuous optical flow by domain decomposition and shape optimization a well known method for the reconstruction of motion fields from noisy image data is to determine flow fields by the minimization of a quadratic functional the first approach of this class has been proposed by horn and schunck 1981 a drawback of such approaches is that an explicit representation of the discontinuities of the motion field is lacking and that in general the resulting flow fields approximate the motion fields only badly at the corresponding locations in the image plane in this article we discuss the possibility to improve the results by hypothesizing the qualitative structure of the motion field in terms of certain parameters we decompose the image plane into disjoint sets restrict the domain of definition of the functionals to these sets and use the hypotheses to deform and to move the boundaries of the sets within the image plane we discuss the range of applicability of this new technique and illustrate the algorithm by numerical examples this article is a revised and extended version of schnorr 1990

almost sure stability of dynamical systems under combined harmonic and stochastic excitations abstract the almost sure asymptotic stability and the associated sample behavior of mechanical and structural systems under combined harmonic and stochastic excitations are examined the method of extended stochastic averaging developed by the author is used to obtain a lower dimensional markov processes for multi degree of freedom structures subjected to both harmonic and stochastic excitations provided that the intensities of these excitations are small the approach in this paper formulated for the study of almost sure asymptotic stability is based on the well developed concept of lyapunov exponents the largest lyapunov exponent is obtained explicitly by using the lower dimensional approximate ito equations the results from this analysis are applied to study the almost sure asymptotic stability of uncoupled flapping motion of rotor blades in forward flight under the effect of atmospheric turbulence

a formula connecting sample and moment stability of linear stochastic systems given the linear stochastic system dot x a xi t x x in mathbb r d xi t some nice diffusion sample and moment stability of x equiv 0 are studied via the sample lyapunov exponent lambda and the lyapunov exponent of the pth mean g p of a solution generalizing a result of molchanov for the undamped linear oscillator it is shown that g p is a smooth convex function of p in mathbb r with g 0 0 and g 0 lambda for trace a 0 a second zero of g at p d is detected this allows one to draw simple but quite complete conclusions about the relation between sample and moment stability

nonlinear filtering for discrete time linear systems with non gaussian initial data the optimal minimum mean square error filtering problem is discussed for a linear system with non gaussian initial distribution an input output realization is derived using an absolutely continuous change of probability measure a representation result is presented which facilitates the derivation of optimal filter realization

determining optical flow for irregular domains by minimizing quadratic functionals of a certain class snyder 1989 has recently classified all smoothness terms which involve first order derivatives of the flowfield u x t and of the image grey value function g x t the physically plausible smoothness terms belonging to this class are known from the work of horn and schunck 1981 and nagel 1987 in this paper we discuss the possibilities of approximating the solutions to the minimization problems of horn schunk 1981 and nagel 1987 in particular it is shown that these solutions exist are unique and depend continuously on the input data these properties make it possible while taking into consideration arbitrary models of the grey value function to approximate efficiently the weak solutions of the associated boundary value problems in irregularly shaped domains with a sufficiently smooth boundary using finite elements experiments with image sequences from synthetic as well as outdoor scenes show how the orientation dependency of the smoothness term in nagel s approach influences the results

on the rate at which a homogeneous diffusion approaches a limit an application of large deviation theory to certain stochastic integrals soit x t la solution d une equation differentielle stochastique dont les coefficients sont homogenes de degre 1 sous des conditions douces on montre que des limites comme lim t 1 t log p ix t x o r existe et on donne une formule pour leur calcul

stochastic dynamics of parametrically excited two d o f systems with symmetry in this paper we investigate the non linear dynamics of a two degree of freedom system with symmetries subject to random parametric excitation the study of this non linear near hamiltonian system is simplified by using the symmetry and separation of scales present in the problem to this end we study the equations as a random perturbation of a four dimensional weakly dissipative hamiltonian system we achieve the model reduction through stochastic averaging and the reduced process is simply a markov process on a line examination of the reduced markov process on the line yields many important results namely probability density functions and stochastic bifurcations the steady state dynamics is computed explicitly phenomenological and dynamical bifurcations are investigated the approach adopted in this paper can in principle be applied to any four dimensional integrable system

a limit formula for joint spectral radius with p radius of probability distributions abstract in this paper we show a characterization of the joint spectral radius of a set of matrices as the limit of the p radius of an associated probability distribution when p tends to allowing the set to have infinitely many matrices the obtained formula extends the results in the literature based on the formula we then present a novel characterization of the stability of switched linear systems for an arbitrary switching signal via the existence of stochastic lyapunov functions of any higher degrees numerical examples are presented to illustrate the results

almost sure and moments stability of jump linear systems abstract the stability of piecewise deterministic linear systems driven by an underlying finite markov chain is analyzed necessary and sufficient conditions for moment stability are obtained by means of an explicit formula for the corresponding liapunov exponent the relationship between almost sure and moment stability is elucidated revealing the possible occurrence of high order moment instability and large deviations from a stable sample path behavior

a result on almost sure stability of linear continuous time markovian switching systems this work investigates the almost sure stability for linear markovian switching systems in continuous time by using lyapunov function method the distribution of switching points is combined into constructing the lyapunov function which gives rise to the fluctuation in bounding the transient phase over the time interval confined between two successive switching points due to the randomness of their locations showing that the influence of the accumulated fluctuations by averaging it out will be negligible is the key step in proving our stability result illustrative examples are included to show the effectiveness of the theoretical result

almost sure stability of linear stochastic systems with poisson process coefficients we consider the problem of determining the sample path stability of a class of linear stochastic differential equations with point process coefficients necessary and sufficient conditions are obtained which are similar in spirit to those derived by khas minskii and pinsky for diffusion processes the conditions are based on the deep theorems of furstenburg on the asymptotic behavior of products of random matrices estimates on the probabilities of large deviations for stable processes are also given together with a result on the stabilization of unstable systems by feedback controls

the moment lyapunov exponent of a co dimension two bifurcation system driven by non gaussian colored noise in the present paper based on the concept of the pth moment lyapunov exponent the stochastic stability of a typical co dimension two bifurcation system that is on a three dimensional center manifold and possesses two pure imaginary eigenvalues and one zero eigenvalue and is excited by a non gaussian colored noise is investigated the non gaussian colored noise is treated as an ornstein uhlenbeck process by means of the path integral approach based on the perturbation approach and the green s functions method the second differential eigenvalue equation which governing the moment lyapunov exponent is established by solving the eigenvalue problem the weak noise asymptotic expansions for the finite pth moment lyapunov exponent are obtained and which matches the approximation of the numerical monte carlo simulations finally the conclusions are given

large deviations and stochastic flows of diffeomorphisms previous results in the theory of large deviations for additive functionals of a diffusion process on a compact manifold m are extended and then applied to the analysis of the lyapunov exponents of a stochastic flow of diffeomorphisms of m an approximation argument relates these results to the behavior near the diagonal in m2 of the associated two point motion finally it is shown under appropriate non degeneracy conditions that the two point motion is ergodic on m2 if the top lyapunov exponent is positive

robust wiener filtering with non parametric spectral uncertainty in this article robust least squares filtering problems are considered for non parametric multivariate spectral uncertainty defined by the so called spectral band and generalised moment constraints its major aim is to provide a basis for computing approximate solutions to worst case wiener filtering optimisation problems involving causal filters and multivariate signals it hinges upon associating upper and lower bounds on the minimum worst case performance achievable with causal filters with linear cost linear matrix inequality lc lmi constraint optimisation problems on the basis of a lagrangean duality formulation for the worst case least squares performance of a given filter upper bounds on it are obtained as the optimal values of lc lmi problems then for linearly parameterised classes of filter transfer functions a causal filter which optimises such an upper bound on worst case performance can also be obtained from an lc lmi optimisation problem to estimate the amount of conservatism incur

almost sure and moment lyapunov exponents for a stochastic beam equation the transverse vibrations of an euler bernoulli beam with axial tension p and axial white noise forcing are given by mytt m yt eiyxxxx pyxx 0yxxw t 0 x l with hinged endpoints y 0 t yxx 0 t y l t yxx l t 0 the solution may be written y x t n 1 sin n xl cn t where the amplitude cn t of the nth mode of vibration is given by a two dimensional linear stochastic ordinary differential equation the main results give formulas for the almost sure and moment lyapunov exponents for the spde in terms of the almost sure and moment lyapunov exponents for each of the sdes corresponding to modes which are present in the initial condition it is shown that the almost sure and moment lyapunov exponents for the spde depend sensitively on the initial distribution of energy amongst the infinitely many modes of vibration and that they cannot be well approximated using only finitely many modes of vibration

a theoretical framework for convex regularizers in pde based computation of image motion many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy typically these energy functionals consist of two terms a data term which requires e g that a brightness constancy assumption holds and a regularizer that encourages global or piecewise smoothness of the flow field in this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images this taxonomy provides a unifying framework for data driven and flow driven isotropic and anisotropic as well as spatial and spatio temporal regularizers while some of these techniques are classic methods from the literature others are derived here for the first time we prove that all these methods are well posed they posses a unique solution that depends in a continuous way on the initial data an interesting structural relation between isotropic and anisotropic flow driven regularizers is identified and a design criterion is proposed for constructing anisotropic flow driven regularizers in a simple and direct way from isotropic ones its use is illustrated by several examples

reliable estimation of dense optical flow fields with large displacements in this paper we show that a classic optical flow technique by nagel and enkelmann 1986 ieee trans pattern anal mach intell vol 8 pp 565 593 can be regarded as an early anisotropic diffusion method with a diffusion tensor we introduce three improvements into the model formulation that i avoid inconsistencies caused by centering the brightness term and the smoothness term in different images ii use a linear scale space focusing strategy from coarse to fine scales for avoiding convergence to physically irrelevant local minima and iii create an energy functional that is invariant under linear brightness changes applying a gradient descent method to the resulting energy functional leads to a system of diffusion reaction equations we prove that this system has a unique solution under realistic assumptions on the initial data and we present an efficient linear implicit numerical scheme in detail our method creates flow fields with 100 density over the entire image domain it is robust under a large range of parameter variations and it can recover displacement fields that are far beyond the typical one pixel limits which are characteristic for many differential methods for determining optical flow we show that it performs better than the optical flow methods with 100 density that are evaluated by barron et al 1994 int j comput vision vol 12 pp 43 47 our software is available from the internet

robust reduced order nonstrictly proper state estimation via the optimal projection equations with petersen hollot bounds a state estimation design problem involving parametric plant uncertainties is considered an error bound suggested by recent work of petersen and hollot is utilized for guaranteeing robust estimation necessary conditions which generalize the optimal projection equations for reduced order state estimation are used to characterize the estimator which minimizes the error bound the design equations thus effectively serve as sufficient conditions for synthesizing robust estimators an additional feature is the presence of a static estimation gain in conjunction with the dynamic kalman estimator i e a nonstrictly proper estimator

almost sure enhanced dissipation and uniform in diffusivity exponential mixing for advection diffusion by stochastic navier stokes we study the mixing and dissipation properties of the advection diffusion equation with diffusivity 0 kappa ll 1 and advection by a class of random velocity fields on mathbb t d d 2 3 including solutions of the 2d navier stokes equations forced by sufficiently regular in space non degenerate white in time noise we prove that the solution almost surely mixes exponentially fast uniformly in the diffusivity kappa namely that there is a deterministic exponential rate independent of kappa such that all mean zero h 1 initial data decays exponentially fast in h 1 at this rate with probability one this implies almost sure enhanced dissipation in l 2 specifically that there is a deterministic uniform in kappa exponential decay in l 2 after time t rsim left log kappa right both the mathcal o left log kappa right time scale and the uniform in kappa exponential mixing are optimal for lipschitz velocity fields this work is also a major step in our program on scalar mixing and lagrangian chaos necessary for a rigorous proof of the batchelor power spectrum of passive scalar turbulence

robust h sub 2 filtering for uncertain systems with measurable inputs this paper deals with the robust minimum variance filtering problem for linear time varying systems subject to a measurable input and to norm bounded parameter uncertainty in the state and or the output matrices of the state space model the problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty and any input of bounded energy three types of input signals are considered a signal that is a priori known for the whole time interval an unknown signal of very large bandwidth that is perfectly measured on line and a large bandwidth signal that is measured ahead of time in a fixed preview time interval both the time varying finite horizon and stationary infinite horizon cases are treated

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

almost sure stability of linear gyroscopic systems this paper studies the stability behaviour of a linear gyroscopic system parametrically perturbed by a multiplicative real noise of small intensity to this end its maximal lyapunov exponent is calculated using the method of sri namachchivaya et al 1 the results derived are suitable for cases where the response frequencies 1 2are non commensurable and the infinitesimal generator associated with the noise process t has a simple zero eigenvalue these results are then employed to determine the almost sure stability boundaries of a rotating shaft subjected to random axial loading

the existence and asymptotic estimations of solutions to stochastic pantograph equations with diffusion and levy jumps in this paper we consider a class of stochastic pantograph differential equations with levy jumps spdewljs by using the burkholder davis gundy inequality and the kunita s inequality we prove the existence and uniqueness of solutions to spdewljs whose coefficients satisfying the lipschitz conditions and the local lipschitz conditions meantime we establish the p th exponential estimations and almost surely asymptotic estimations of solutions to spdewljs

a unified approach for stochastic and mean square stability of continuous time linear systems with markovian jumping parameters and additive disturbances necessary and sufficient conditions for stochastic stability ss and mean square stability mss of continuous time linear systems subject to markovian jumps in the parameters and additive disturbances are established we consider two scenarios regarding the additive disturbances one in which the system is driven by a wiener process and one characterized by functions in l 2 m omega cal f mathbb p which is the usual scenario for the h infty approach the markov process is assumed to take values in an infinite countable set mathcal s it is shown that ss is equivalent to the spectrum of an augmented matrix lying in the open left half plane to the existence of a solution for a certain lyapunov equation and implies is equivalent for mathcal s finite asymptotic wide sense stationarity awss it is also shown that ss is equivalent to the state x t belonging to l 2 n omega cal f mathbb p whenever the disturbances are in l 2 m omega cal f mathbb p for the case in which mathcal s is finite ss and mss are equivalent and the lyapunov equation can be written down in two equivalent forms with each one providing an easier to check sufficient condition

optical flow with an intensity weighted smoothing matching algorithms which use image structure such as edges and junctions cannot perform well on unstructured images for such images global gradient based methods may be more appropriate some of the assumptions involved in applying discretized conservation equations such as the optical flow equation are discussed and an intensity weighted method of estimating dense displacement fields is presented which attempts to avoid some of the problems of the standard methods the only derivative required is the intensity gradient and the method includes procedures for automatic parameter evaluation the algorithm is expected to perform better than conventional algorithms on images without strong texture as is demonstrated on the test set of images

stability of nonlinear regime switching jump diffusion abstract motivated by networked systems stochastic control optimization and a wide variety of applications this work is devoted to systems of switching jump diffusions treating such nonlinear systems we focus on stability issues one of the distinct features considered here is that the switching process depends on the jump diffusions first asymptotic stability in the large is obtained then the study on exponential p stability is carried out connection between almost surely exponential stability and exponential p stability is exploited also presented are smooth dependence on the initial data using the smooth dependence necessary conditions for exponential p stability are derived then criteria for asymptotic stability in distribution are provided a couple of examples are given to illustrate our results

almost sure stability and instability for switching jump diffusion systems with state dependent switching abstract this work develops almost sure stability criteria for switching jump diffusion systems with state dependent switching by means of introducing certain auxiliary markov chains and constructing certain order preserving couplings upper and lower stability envelops are constructed which lead to systems with upper and lower approximating markov chains using these approximations sufficient conditions that are relatively easily verifiable for the almost sure stability and instability are obtained when the jump process is missing it is demonstrated that the techniques work equally well and provide a way to analyze the corresponding switching diffusion systems with x dependent switching in addition stochastic stabilization and destabilization are examined moreover illustrative examples are provided for demonstration

on functionals with greyvalue controlled smoothness terms for determining optical flow the modification by h h nagel 1987 of the approach developed by b k p horn and b g schunck 1981 for determining optical flow is generalized to the case where local motion information is given by more than one constraint equation applying this scheme to three constraint equations reported in the literature as a special case a generalization of nagel s approach is obtained an existence and uniqueness result of solutions under very general conditions that in turn ensures the applicability of standard techniques to compute an approximate solution is presented

on the mathematical foundations of smoothness constraints for the determination of optical flow and for surface reconstruction gradient based approaches to the computation of optical flow often use a minimization technique incorporating a smoothness constraint on the optical flow field the author derives the most general form of such a smoothness constraint that is quadratic in first derivatives of the grey level image intensity function based on three simple assumptions about the smoothness constraint 1 it must be expressed in a form that is independent of the choice of cartesian coordinate system in the image 2 it must be positive definite and 3 it must not couple different component of the optical flow it is shown that there are essentially only four such constraints any smoothness constraint satisfying 1 2 or 3 must be a linear combination of these four possibly multiplied by certain quantities invariant under a change in the cartesian coordinate system beginning with the three assumptions mentioned above the author mathematically demonstrates that all best known smoothness constraints appearing in the literature are special cases of this general form and in particular that the weight matrix introduced by h h nagel is essentially modulo invariant quantities the only physically plausible such constraint

reducing the sensitivity to parameter variations of a minimum order reduced order observer a quantitative upper hound is established which defines the extent to which a minimum order reduced order non adaptive observer may be rendered insensitive to parameter variations that upper bound depends on the number of measurements and the location of questionable parameters within the system matrices an integral squared error objective function is explicitly solved that objective function may be used to assess the sensitivity of the system to parameter errors a numerical example is presented for a continuous observer the results are extended to the discrete ease

robust discrete time minimum variance filtering the bounded variance filtered estimation of the state of an uncertain linear discrete time system with an unknown norm bounded parameter matrix is considered an upper bound on the variance of the estimation error is found for all admissible systems and estimators are derived that minimize the latter bound we treat the finite horizon time varying case and the infinite time case where the nominal system model is time invariant in the special stationary case where it is known that the uncertain system is time invariant we provide a robust filter for all uncertainties that still keep the system asymptotically stable

numerical solutions of regime switching jump diffusions abstract this work develops numerical algorithms for approximating the solutions of stochastic differential equations that involve switching jump diffusion processes in which the switching is a random process that depends on the jump diffusion being non standard due to the jump diffusion dependent switching makes the problem far more difficult to deal with using decreasing step sizes we construct the algorithm which is in the spirit of euler maruyama method to prove the convergence we first derive the tightness of the algorithm then we establish the strong convergence the strong convergence is in the sense of usual numerical consideration for solutions of stochastic differential equations that is we consider uniform mean square convergence in a finite interval finally numerical examples are provided for demonstration

the optimal projection equations for reduced order state estimation first order necessary conditions for optimal steady state reduced order state estimation for a linear time invariant plant in the presence of correlated disturbance and nonsingular measurement noise are derived in a new and highly simplified form in contrast to the lone matrix riccati equation arising in the full order kalman filter case the optimal steady state reduced order estimator is characterized by three matrix equations one modified riccati equation and two modified lyapunov equations coupled by a projection whose rank is precisely equal to the order of the estimator and which determines the optimal estimator gains this coupling is a graphic reminder of the suboptimality of proposed approaches involving either model reduction followed by full order estimator design or full order estimator design followed by estimator reduction techniques the results given here complement recently obtained results which characterize the optimal reduced order model by means of a pair of coupled modified lyapunov equations 7 and the optimal fixed order dynamic compensator by means of a coupled system of two modified riceati equations and two modified lyapunov equations 6

almost sure asymptotic stability of a general four dimensional system driven by real noise in the first part of this paper we construct an asymptotic expansion for the maximal lyapunov exponent the exponential growth rate of solutions to a linear stochastic system and the rotation numbers for a general four dimensional dynamical system driven by a small intensity real noise process stability boundaries are obtained provided the natural frequencies are noncommensurable and the infinitesimal generator associated with the noise process has an isolated simple zero eigenvalue this work is an extension of the work of sri namachchivaya and van roessel and is general in the sense that general stochastic perturbations of nonautonomous systems with two noncommensurable natural frequencies are considered

an investigation of smoothness constraints for the estimation of displacement vector fields from image sequences a mapping between one frame from an image sequence and the preceding or following frame can be represented as a displacement vector field in most situations the mere gray value variations do not provide sufficient information in order to estimate such a displacement vector field supplementary constraints are necessary for example the postulate that a displacement vector field varies smoothly as a function of the image position taken as a general requirement this creates difficulties at gray value transitions which correspond to occluding contours nagel therefore introduced the oriented smoothness requirement which restricts variations of the displacement vector field only in directions with small or no variation of gray values this contribution reports results of an investigation about how such an oriented smoothness constraint may be formulated and evaluated

stability indices for randomly perturbed power systems this paper considers the stability of moments of stochastic systems such as stability of the mean or mean square stability the exponential growth behavior of moments is compared to almost sure exponential growth via lyapunov exponents we develop a series of indices that are useful to describe system performance under random perturbations the theory is applied to two examples including an electric power system

optimal linear filtering under parameter uncertainty this paper addresses the problem of designing a guaranteed minimum error variance robust filter for convex bounded parameter uncertainty in the state output and input matrices the design procedure is valid for linear filters that are obtained from the minimization of an upper bound of the error variance holding for all admissible parameter uncertainty the results provided generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured assuming the order of the uncertain system is known the optimal robust linear filter is proved to be of the same order as the order of the system in the present case of convex bounded parameter uncertainty the basic numerical design tools are linear matrix inequality lmi solvers instead of the riccati equation solvers used for the design of robust filters available in the literature to date the paper that contains the most important and very recent results on robust filtering is used for comparison purposes in particular it is shown that under the same assumptions our results are generally better as far as the minimization of a guaranteed error variance is considered some numerical examples illustrate the theoretical results

a stochastic hopf bifurcation let x t t 0 be the solution of a stochastic differential equation sde in d which fixes 0 and let denote the lyapunov exponent for the linear sde obtained by linearizing the original sde at 0 it is known that under appropriate conditions the sign of controls the stability instability of 0 and the transience recurrence of x t t 0 on d 0 in particular if the coefficients in the sde depend on some parameterz which is varied in such a way that the corresponding lyapunov exponent z changes sign from negative to positive the almost surely stable fixed point at 0 is replaced by an almost surely unstable fixed point at 0 together with an attracting invariant probability measure z on d 0 in this paper we investigate the limiting behavior of z as z converges to 0 from above the main result is that the rescaled measures 1 z z converge in an appropriate weak sense to a non trivial finite measure on d 0

generalized joint spectral radius and stability of switching systems abstract this paper extends the notion of generalized joint spectral radius with exponents originally defined for a finite set of matrices to probability distributions we show that under a certain invariance condition the radius is calculated as the spectral radius of a matrix that can be easily computed extending the classical counterpart using this result we investigate the mean stability of switching systems in particular we establish the equivalence of mean square stability simultaneous contractibility in square mean and the existence of a quadratic lyapunov function also the stabilization of positive switching systems is studied numerical examples are given to illustrate the results

a computational framework and an algorithm for the measurement of visual the robust measurement of visual motion from digitized image sequences has been an important but difficult problem in computer vision this paper describes a hierarchical computational framework for the determination of dense displacement fields from a pair of images and an algorithm consist ent with that framework our framework is based on the separation of the image intensity information as well as the process of measuring motion according to scale the large scale intensity information is first used to obtain rough estimates of image motion which are then refined by using intensity information at smaller scales the estimates are in the form of displacement or velocity vectors for pixels and are accompanied by a direction dependent confidence measure a smoothness constraint is employed to propagate the measurements with high confidence to their neigboring areas where the confidences are low at all levels the computations are pixel parallel uniform across the image and based on information from a small neighborhood of a pixel for our algorithm the local displacement vectors are determind by mini mizing the sum of squared differences ssd of intensities the confidence measures are derived from the shape of the ssd surface and the smoothness constraint is cast in the form of energy minimization results of applying our algorithm to pairs of real images are included in addition to our own

turbulence effects on fluidelastic instability of a cylinder in a shear flow abstract fluidelastic instability is the main mechanism that causes severe damages in flow induced vibration experiments show that grid generated turbulence can affect the stability of the system which is modeled as an ornstein uhlenbeck process the dynamic stability of a four dimensional system under real noise excitation is studied through the determination of the p th moment lyapunov exponent and the lyapunov exponent the partial differential eigenvalue equation governing the moment lyapunov exponent is established for small noise amplitudes a method of regular perturbation is used to determine analytical expansions of the moment lyapunov exponents and lyapunov exponents which are shown to be in good agreement with those obtained using numerical approaches the analytical method is applied to study the stability of a cylinder in a shear flow where fluidelastic instability is known to occur the results demonstrate that the unstable system can be stabilized under certain conditions and the effect of stabilization is proportional to the turbulence intensity which agrees with experimental observations

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

scattering of a wave packet by an interval of random medium this paper deals with the scattering theory for the one dimensional discrete schrodinger equation with a random potential having large support the main result is that a fluctuation deep within the scattering region has a very small effect on the scattering of wave packets the region of random potential is effectively opaque

first order dynamics driven by rapid markovian jumps the effect of rapid random jumps on the behavior of deterministically stable dynamics is considered the random driving force noise is taken to be a state dependent markov jump process with either finite or infinite state space while the jump rate is high o 1 varepsilon the jump size is assumed to be o 1 for a particle that is deterministically confined to a potential well the stationary joint probability density function of the state and noise variables the probability distribution of the exit points and the mean first passage time from the well are computed in contrast to the case of white noise where these quantities depend on a barrier height determined solely by the potential here they depend on an effective barrier height determined by both the potential and the noise process the method used here is to introduce the small parameter varepsilon where 1 varepsilon is a measure of the rapid jump rate and to employ singular perturbation methods to solve the forward and

robust observers for systems with parameters abstract in many cases linear multivariable models which describe physical systems contain structured parametric type uncertainties specifically it may be that the state space model is expressed in a form which involves parameters we first consider circumstances in which a parameter independent observer can be constructed for the system and suggest conditions that guarantee its existence we also give conditions under which such a robust observer can be subsequently used with additional dynamics in a parameter free configuration for regulation

on the asymptotic stability and numerical analysis of solutions to nonlinear stochastic differential equations with jumps this paper is concerned with the stability and numerical analysis of solution to highly nonlinear stochastic differential equations with jumps by the ito formula stochastic inequality and semi martingale convergence theorem we study the asymptotic stability in the p th moment and almost sure exponential stability of solutions under the local lipschitz condition and nonlinear growth condition on the other hand we also show the convergence in probability of numerical schemes under nonlinear growth condition finally an example is provided to illustrate the theory

stability radius for structured perturbations and the algebraic riccati equation abstract in this paper we generalize the notion of stability radius introduced in 1 to allow for structured perturbations we then relate the stability radius to the existence of hermitian solutions of an algebraic riccati equation and give some applications of this result

robust minimum variance filtering this paper deals with the robust minimum variance filtering problem for linear systems subject to norm bounded parameter uncertainty in both the state and the output matrices of the state space model the problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty two methods for designing robust filters are investigated the first one deals with constant parameter uncertainty and focuses on the design of steady state filters that yield an upper bound to the worst case asymptotic error variance this bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system and it can be made tighter if a tight bound on the latter power spectrum can be obtained the second method allows for time varying parameter uncertainty and for general time varying systems and is more systematic we develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

lyapunov exponent and rotation number of two dimensional linear stochastic systems with telegraphic noise in this paper the lyapunov exponent and rotation number of a family of two dimensional systems with general telegraphic noise where the unperturbed system has oscillatory behavior are studied using a martingale approach an iterative computational procedure is derived and analytic expansions in the noise strength are obtained for the lyapunov exponent and the rotation number these expansions are convergent in a nonmarginal way the positivity of the exponent is also established for the random harmonic oscillator with zero mean telegraphic noise and lower and upper bounds are derived for the exponent when the noise is the random telegraph process

almost sure and δmoment stability of jump linear systems abstract in this paper we study the almost sure stability and moment stability of discrete time jump linear systems with a finite state form process criteria for almost sure and moment stability which are necessary and sufficient conditions for scalar one dimensional systems are derived the relationship between almost sure and 6 moment stability for scalar one dimensional systems is also presented if the system matrices commute necessary and sufficient conditions for almost sure stability are obtained

modulational instability induced by randomly varying coefficients for the nonlinear schrodinger equation abstract we introduce the theory of modulational instability mi of electromagnetic waves in optical fibers the model at hand is the one dimensional nonlinear schrodinger equation with random group velocity dispersion and random nonlinear coefficient we compute the mi gain which reads as the lyapunov exponent of a random linear system we show that the distribution of the mi gain can be expressed in terms of the log normal statistics the heavy tail of this probability distribution function involves very different behaviors for the sample and moment mi gains in the anomalous dispersion regime random fluctuations of the nonlinear coefficient reduces the sample mi gain peak although the moment mi peak is enhanced and the unstable bandwidth is widened still in the anomalous dispersion regime random fluctuations of the group velocity dispersion reduces both the sample mi gain peak and the moment mi peak finally in the normal dispersion regime randomness extends the mi domain to the whole spectrum of modulations and increases the mi gain peak the linear stability analysis is confirmed by numerical simulations of the full stochastic nonlinear schrodinger equation

optic flow in harmony most variational optic flow approaches just consist of three constituents a data term a smoothness term and a smoothness weight in this paper we present an approach that harmonises these three components we start by developing an advanced data term that is robust under outliers and varying illumination conditions this is achieved by using constraint normalisation and an hsv colour representation with higher order constancy assumptions and a separate robust penalisation our novel anisotropic smoothness is designed to work complementary to the data term to this end it incorporates directional information from the data constraints to enable a filling in of information solely in the direction where the data term gives no information yielding an optimal complementary smoothing behaviour this strategy is applied in the spatial as well as in the spatio temporal domain finally we propose a simple method for automatically determining the optimal smoothness weight this method bases on a novel concept that we call optimal prediction principle opp it states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence the benefits of our optic flow in harmony ofh approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used middlebury optic flow benchmark

moment lyapunov exponent for two coupled oscillators driven by real noise in this paper an approximation for the moment lyapunov exponent the asymptotic growth rate of the moments of the response of two coupled oscillators driven by real noise is constructed a perturbation approach is used to obtain explicit expressions for these exponents in the presence of small intensity noise the results are applied to study the moment stability of the stationary solutions of structural and mechanical systems subjected to stochastic excitation

robust reduced order modeling via the optimal projection equations with peterson hollot bounds an optimal reduced order modeling problem with parametric plant uncertainty is considered a model reduction bound suggested by recent work of i r petersen and c v hollot is utilized for guaranteeing robust reduced order modeling over a specified range of uncertain parameters necessary conditions which generalize the optimal projection equations for model reduction are used to characterize the reduced order model which minimizes the model reduction bound the optimality equations thus effectively serve as sufficient conditions for characterizing robust reduced order models