weyl manifolds and connections a study is made of weyl connections and their associated holonomy groups the extent to which a weyl connection determines its associated metric and 1 form structures is also discussed finally the related concept of a locally metric connection is introduced and some relations between metric locally metric and weyl connections are established

approximate labeling via graph cuts based on linear programming a new framework is presented for both understanding and developing graph cut based combinatorial algorithms suitable for the approximate optimization of a very wide class of markov random fields mrfs that are frequently encountered in computer vision the proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state of the art techniques like the alpha expansion algorithm which is included merely as a special case moreover contrary to alpha expansion the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems for example even for mrfs with nonmetric potentials in addition they are capable of providing per instance suboptimality bounds in all occasions including discrete mrfs with an arbitrary potential function these bounds prove to be very tight in practice that is very close to 1 which means that the resulting solutions are almost optimal our algorithms effectiveness is demonstrated by presenting experimental results on a variety of low level vision tasks such as stereo matching image restoration image completion and optical flow estimation as well as on synthetic problems

structure propagation for image registration mosaicing is a commonly used technique in many medical imaging applications where subimages are stitched together in order to obtain a larger field of view however stitching which involves alignment or registration in overlapping regions is often challenging when the information shared by subimages is absent or small while it is not possible to perform an alignment without overlap using existing techniques imaging artifacts such as distortions towards image boundaries present further complications during registration by decreasing the reliability of available information without taking these into consideration a registration approach might violate the continuity and the smoothness of structures across subimages in this paper we propose a novel registration approach for the stitching of subimages in such challenging scenarios by using a perceptual grouping approach we extend subimages beyond their boundaries by propagating available structures in order to obtain structural maps in the extended regions these maps are then used to establish correspondences between subimages when the shared information is absent small or unreliable using our approach ensures the continuity and the smoothness of structures across subimage boundaries furthermore since only structures are used the proposed method can also be used for the stitching of multi modal images our approach is unique in that it also enables contactless stitching we demonstrate the effectiveness of the proposed method by performing several experiments on synthetic and medical images moreover we show how stitching is possible in the presence of a physical gap between subimages

stability and stabilizability of chemical reactors modelled with stochastic parameters abstract chemical reactors are considered where unknown parameter variations are model led by stochastic parameters the continuous time process is transformed to an equivalent discrete time system with stochastic parameters which is a natural approach in the context of digital control making the analysis much easier a stabilizability test for this discrete time model is used to analyse three cases from the chemical engineering literature it is shown that stability in a mean sense is too weak from an engineering point of view one should study stability at least in a mean square sense which is the approach given here

scale and rotation invariant matching using linearly augmented trees we propose a novel linearly augmented tree method for efficient scale and rotation invariant object matching the proposed method enforces pairwise matching consistency defined on trees and high order constraints on all the sites of a template the pairwise constraints admit arbitrary metrics while the high order constraints use l1 norms and therefore can be linearized such a linearly augmented tree formulation introduces hyperedges and loops into the basic tree structure but different from a general loopy graph its special structure allows us to relax and decompose the optimization into a sequence of tree matching problems that are efficiently solvable by dynamic programming the proposed method also works on continuous scale and rotation parameters we can match with a scale up to any large value with the same efficiency our experiments on ground truth data and a variety of real images and videos show that the proposed method is efficient accurate and reliable

interactive image segmentation based on synthetic graph coordinates in this paper we propose a framework for interactive image segmentation the goal of interactive image segmentation is to classify the image pixels into foreground and background classes when some foreground and background markers are given the proposed method minimizes a min max bayesian criterion that has been successfully used on image segmentation problem and it consists of several steps in order to take into account visual information as well as the given markers without any requirement of training first we partition the image into contiguous and perceptually similar regions superpixels then we construct a weighted graph that represents the superpixels and the connections between them an efficient algorithm for graph clustering based on synthetic coordinates is used yielding an initial map of classified pixels this method reduces the problem of graph clustering to the simpler problem of point clustering instead of solving the problem on the graph data structure as most of the known algorithms from literature do finally having available the data modeling and the initial map of classified pixels we use a markov random field mrf model or a flooding algorithm to get the image segmentation by minimizing a min max bayesian criterion experimental results and comparisons with other methods from the literature are presented on lhi gulshan and zhao datasets demonstrating the high performance and accuracy of the proposed scheme

global minimization for continuous multiphase partitioning problems using a dual approach this paper is devoted to the optimization problem of continuous multi partitioning or multi labeling which is based on a convex relaxation of the continuous potts model in contrast to previous efforts which are tackling the optimal labeling problem in a direct manner we first propose a novel dual model and then build up a corresponding duality based approach by analyzing the dual formulation sufficient conditions are derived which show that the relaxation is often exact i e there exists optimal solutions that are also globally optimal to the original nonconvex potts model in order to deal with the nonsmooth dual problem we develop a smoothing method based on the log sum exponential function and indicate that such a smoothing approach leads to a novel smoothed primal dual model and suggests labelings with maximum entropy such a smoothing method for the dual model also yields a new thresholding scheme to obtain approximate solutions an expectation maximization like algorithm is proposed based on the smoothed formulation which is shown to be superior in efficiency compared to earlier approaches from continuous optimization numerical experiments also show that our method outperforms several competitive approaches in various aspects such as lower energies and better visual quality

on the compatibility of lorentz metrics with linear connections on four dimensional manifolds this paper considers four dimensional manifolds upon which there is a lorentz metric h and a symmetric connection which are originally assumed unrelated it then derives sufficient conditions on h and expressed through the curvature tensor of for to be the levi civita connection of some local lorentz metric g and calculates the relationship between g and h some examples are provided which help to assess the strength of the sufficient conditions derived

technical communique discrete time optimal control with control dependent noise and generalized riccati difference equations the optimal control law is derived for discrete time linear stochastic systems with quadratic performance criterion and control dependent noise the analysis includes the study of a generalized riccati difference equation and of the asymptotic behavior of its solutions

compensatability and optimal compensation of systems with white parameters the optimal compensation problem is considered in the case of linear discrete time systems with stationary white parameters and quadratic criteria a generalization of the notion of mean square stabilizability namely mean square compensatability is introduced it is shown that suitable mean square compensatability and detectability conditions are sufficient and necessary in general for the existence of a unique optimal mean square stabilizing compensator tests are given to determine whether or not a system is mean square compensatable it is indicated how to calculate numerically the tests and the optimal mean square stabilizing compensator the results are illustrated with examples

static output feedback control of markov jump linear systems without mode observation in this paper we address infinite horizon optimal control of markov jump linear systems mjls via static output feedback because the jump parameter is assumed not to be observed the optimal control law is nonlinear and intractable therefore we assume the regulator to be linear under this assumption we first present sufficient feasibility conditions for static output feedback stabilization of mjls with nonobserved mode in the mean square sense in terms of linear matrix inequalities lmis however these conditions depend on the particular state space representation i e a coordinate transform can make the lmis feasible while the original lmis are infeasible to avoid the issues with the ambiguity of the state space representation we therefore present an iterative algorithm for the computation of the regulator gain the algorithm is shown to converge if the mjls is stabilizable via mode independent static output feedback however convergence of the algorithm is not sufficient for the stability of the closed loop which requires an additional stability check after the regulator gains have been computed a numerical example demonstrates the application of the presented results

linearization of expectation based inequality conditions in control for discrete time linear systems represented with random polytopes abstract a technique of linearizing what we call expectation based inequality conditions is proposed for control of discrete time linear systems with stochastic dynamics in particular the coefficient random matrices of the systems are assumed to be represented with random polytopes and the linearization technique is discussed so as to appropriately deal with associated uncertainties our expectation based inequality is an inequality that involves decision variables contained in the expectation operation and has a unique difficulty in direct linearization in general hence two key lemmas are provided so that the decision variables can be taken out from the expectation operation the combinational use of such lemmas and the conventional linear matrix inequality lmi techniques which is nothing but our linearization technique is expected to be useful for transforming various kinds of expectation based nonlinear inequality into numerically solvable standard lmis as a demonstration new robust stability conditions are derived with the technique whose effectiveness is confirmed numerically

controller design of systems with multiplicative noise general linear continuous stochastic systems are considered with multiplicative noise in the control and state channels and stabilizing optimal inputs are synthesized for both time varying and time invariant situations in the nonstationary case a set of nonlinear matrix differential equations has to be solved in the stationary problem a set of nonlinear matrix algebraic equations provides the solution the separation principle is not valid and both the state filtering and the control synthesis problem should be treated simultaneously

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

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

some remarks on metric and weyl connections a discussion is given regarding those lie subgroups of gl n r which contain so n or so n 1 1 as lie subgroups the result is applied to the theory of holonomy groups and in particular to metric and weyl connections some general remarks regarding the relationship between metric connections and curvature tensors are given

exploiting unsupervised and supervised constraints for subspace clustering data in many image and video analysis tasks can be viewed as points drawn from multiple low dimensional subspaces with each subspace corresponding to one category or class one basic task for processing such kind of data is to separate the points according to the underlying subspace referred to as subspace clustering extensive studies have been made on this subject and nearly all of them use unconstrained subspace models meaning the points can be drawn from everywhere of a subspace to represent the data in this paper we attempt to do subspace clustering based on a constrained subspace assumption that the data is further restricted in the corresponding subspaces e g belonging to a submanifold or satisfying the spatial regularity constraint this assumption usually describes the real data better such as differently moving objects in a video scene and face images of different subjects under varying illumination a unified integer linear programming optimization framework is used to approach subspace clustering which can be efficiently solved by a branch and bound bb method we also show that various kinds of supervised information such as subspace number outlier ratio pairwise constraints size prior and etc can be conveniently incorporated into the proposed framework experiments on real data show that the proposed method outperforms the state of the art algorithms significantly in clustering accuracy the effectiveness of the proposed method in exploiting supervised information is also demonstrated

stationary optimal control of stochastically sampled continuous time systems abstract this paper solves the digital stationary optimal control problem in the case of linear stochastic continuous time systems long term average integral criteria complete state information and where the sampling periods are independent identically distributed stochastic variables using the notions of mean square stabilizability and mean square detectability it is shown that stochastic sampling may increase or restore stabilizability and may decrease or destroy stability if the presence of stochastic sampling is not taken into account in the determination of the optimal controller

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

sufficient conditions for a curvature tensor to be riemannian and for determining its metric a simple necessary and sufficient condition that a curvature tensor be riemannian i e that its symmetric connection be metric is found in very general conditions for a four dimensional space time manifold this enables existing uniqueness results for the metric tensor and an associated algebraic procedure for obtaining the metric tensor components from the curvature tensor components when the curvature tensor is known to be a riemannian tensor to be extended to the situation where it is not known a priori whether the curvature tensor has come from a lorentz metric

an efficient optimization framework for multi region segmentation based on lagrangian duality we introduce a multi region model for simultaneous segmentation of medical images in contrast to many other models geometric constraints such as inclusion and exclusion between the regions are enforced which makes it possible to correctly segment different regions even if the intensity distributions are identical we efficiently optimize the model using a combination of graph cuts and lagrangian duality which is faster and more memory efficient than current state of the art as the method is based on global optimization techniques the resulting segmentations are independent of initialization we apply our framework to the segmentation of the left and right ventricles myocardium and the left ventricular papillary muscles in magnetic resonance imaging and to lung segmentation in full body x ray computed tomography we evaluate our approach on a publicly available benchmark with competitive 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

parametrization of all linear compensators for discrete time stochastic parameter systems abstract for discrete time stochastic parameter systems this paper presents a characterization of all state covariances assignable by a linear controller and a parametrization of all controllers that achieves a desired covariance these results indirectly provide the parametrization of all linear fixed order compensators which are mean square stabilizing for this class of systems the paper also includes robustification of the derived compensators and an example to illustrate the results

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

the equivalent discrete time optimal control problem for continuous time systems with stochastic parameters this paper considers the transformation of the digital optimal control problem to an equivalent discrete time optimal control problem for linear continuous time systems with continuous time white stochastic parameters and additive continuous time white noise the observations available at the sampling instants are in general non linear and corrupted by discrete time noise the equivalent discrete time system has white stochastic parameters expressions are derived for the first and second moments of these parameters and for the cost criterion parameters which are explicit in the parameters and the statistics of the continuous time system

collective inference for extraction mrfs coupled with symmetric clique potentials many structured information extraction tasks employ collective graphical models that capture inter instance associativity by coupling them with various clique potentials we propose tractable families of such potentials that are invariant under permutations of their arguments and call them symmetric clique potentials we present three families of symmetric potentials max sum and majority we propose cluster message passing for collective inference with symmetric clique potentials and present message computation algorithms tailored to such potentials our first message computation algorithm called pass is sub quadratic in the clique size outputs exact messages for max and computes 13 15 approximate messages for potts a popular member of the sum family empirically it is upto two orders of magnitude faster than existing algorithms based on graph cuts or belief propagation our second algorithm based on lagrangian relaxation operates on majority potentials and provides close to exact solutions while being two orders of magnitude faster we show that the cluster message passing framework is more principled accurate and converges faster than competing approaches we extend our collective inference framework to exploit associativity of more general intra domain properties of instance labelings which opens up interesting applications in domain adaptation our approach leads to significant error reduction on unseen domains without incurring any overhead of model retraining

the influence of finite word length on digital optimal control this paper is concerned with the performance of linear discrete time systems controlled by a finite word length computer with floating point arithmetic and of which the state is directly measurable with an a d converter of the same word length the effect of using finite word length is twofold first roundings are made after addition or multiplication of two rounded numbers second the control parameters are represented in the controller s memory by rounded numbers the first effect can be accounted for by considering the control parameters stochastic the second effect is deterministic after a description of the stochastlcs of the roundoff errors has been derived the influence of both effects on the optimality and stability of digital control systems in the steady state in relation to a quadratic cost function is considered

brief paper optimal estimation of linear discrete time systems with stochastic parameters this paper considers optimal linear state estimation in the general case of linear discrete time systems with stochastic parameters which are statistically independent with respect to time the estimator is derived by transforming the system to one with deterministic parameters and state dependent additive system and observation noise it is shown that mean square stability of the system is a sufficient and almost necessary condition for the existence uniqueness and stability of the time invariant estimator

generalized flows for optimal inference in higher order mrf map use of higher order clique potentials in mrf map problems has been limited primarily because of the inefficiencies of the existing algorithmic schemes we propose a new combinatorial algorithm for computing optimal solutions to 2 label mrf map problems with higher order clique potentials the algorithm runs in time o 2 kn 3 in the worst case k is size of clique and n is the number of pixels a special gadget is introduced to model flows in a higher order clique and a technique for building a flow graph is specified based on the primal dual structure of the optimization problem the notions of the capacity of an edge and a cut are generalized to define a flow problem we show that in this flow graph when the clique potentials are submodular the max flow is equal to the min cut which also is the optimal solution to the problem we show experimentally that our algorithm provides significantly better solutions in practice and is hundreds of times faster than solution schemes like dual decomposition 1 trws 2 and reduction 3 4 5 the framework represents a significant advance in handling higher order problems making optimal inference practical for medium sized cliques

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

continuation methods theory and applications this paper surveys in a tutorial fashion theoretical and applications aspects of the confirmation method for the solution of large scale system engineering problems the continuation method is motivated and defined the existence of the method is formulated in terms of degree theory a la algebraic topology examples are given throughout the paper and applications to engineering and economic problems are cited and described

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

optimal projection equations for discrete time fixed order dynamic compensation of linear systems with multiplicative white noise the optimal projection equations for discrete time reduced order dynamic compensation are generalized to include the effects of state control and measurement dependent noise in addition the discrete time static output feedback problem with multiplicative disturbances is considered for both problems the design equations are presented in a concise unified manner to facilitate their accessibility for developing numerical algorithms for practical applications

robust controller synthesis using the maximum entropy design equations this note presents an application of the optimality conditions obtained in 1 for dynamic compensation in the presence of state control and measurement dependent noise by solving these equations which represent a fundamental generalization of standard steady state lqg theory a series of increasingly robust control designs is obtained for the example considered in 2

approximation algorithms for classification problems with pairwise relationships metric labeling and markov random fields in a traditional classification problem we wish to assign one of k labels or classes to each of n objects in a way that is consistent with some observed data that we have about the problem an active line of research in this area is concerned with classification when one has information about pairwise relationships among the objects to be classified this issue is one of the principal motivations for the framework of markov random fields and it arises in areas such as image processing biometry and document analysis in its most basic form this style of analysis seeks to find a classification that optimizes a combinatorial function consisting of assignment costs based on the individual choice of label we make for each object and separation costs based on the pair of choices we make for two related objects we formulate a general classification problem of this type the metric labeling problem we show that it contains as special cases a number of standard classification frameworks including several arising from the theory of markov random fields from the perspective of combinatorial optimization our problem can be viewed as a substantial generalization of the multiway cut problem and equivalent to a type of uncapacitated quadratic assignment problem we provide the first nontrivial polynomial time approximation algorithms for a general family of classification problems of this type our main result is an o log k log log k approximation algorithm for the metric labeling problem with respect to an arbitrary metric on a set of k labels and an arbitrary weighted graph of relationships on a set of objects for the special case in which the labels are endowed with the uniform metric all distances are the same our methods provide a 2 approximation algorithm

joint sulcal detection on cortical surfaces with graphical models and boosted priors in this paper we propose an automated approach for the joint detection of major sulci on cortical surfaces by representing sulci as nodes in a graphical model we incorporate markovian relations between sulci and formulate their detection as a maximum a posteriori map estimation problem over the joint space of major sulci to make the inference tractable a sample space with a finite number of candidate curves is automatically generated at each node based on the hamilton jacobi skeleton of sulcal regions using the adaboost algorithm we learn both individual and pairwise shape priors of sulcal curves from training data which are then used to define potential functions in the graphical model based on the connection between adaboost and logistic regression finally belief propagation is used to perform the map inference and select the joint detection results from the sample spaces of candidate curves in our experiments we quantitatively validate our algorithm with manually traced curves and demonstrate the automatically detected curves can capture the main body of sulci very accurately a comparison with independently detected results is also conducted to illustrate the advantage of the joint detection approach

robust static and dynamic output feedback stabilization deterministic and stochastic perspectives three parallel gaps in robust feedback control theory are examined sufficiency versus necessity deterministic versus stochastic uncertainty modeling and stability versus performance deterministic and stochastic output feedback control problems are considered with both static and dynamic controllers the static and dynamic robust stabilization problems involve deterministically modeled bounded but unknown measurable time varying parameter variations while the static and dynamic stochastic optimal control problems feature state control and measurement dependent white noise general sufficiency conditions for the deterministic problems are obtained using lyapunov s direct method while necessary conditions for the stochastic problems are derived as a consequence of minimizing a quadratic performance criterion the sufficiency tests are then applied to the necessary conditions to determine when solutions of the stochastic optimization problems also solve the deterministic robust stability problems as an additional application of the deterministic result the modified riccati equation approach of petersen and hollot is generalized in the static case and extended to dynamic compensation

stabilizing compensator design for discrete time non linear stochastic systems with incomplete state information in this work an approach to stabilizing compensator design is presented that is suitable for a large class of discrete time non linear stochastic systems with incomplete state information the non linearity is contained either in the state or the measurement equation and it involves a white noise vector sequence the proposed compensator is a combination of a constant gain observer and a constant feedback control gain the stabilizability conditions depend upon the system and chosen design parameter characteristics and are given for both mean square and almost sure stochastic boundedness and stability of the controlled system a specific subclass of these systems subject to certain control laws is shown to possess stabilizability conditions that can be tested a priori

on variance neutrality of systems within general random parameters a necessary condition for variance neutrality of discrete time linear systems within general random parameters and with arbitrary observations is established it is proved that this condition is sufficient as well if the observations are linear this result is of importance in connection with separability of optimal control and state estimation