phase margins for multivariable control systems this paper presents a new definition for the phase margin of multivariable systems the properties of the phase margin are such that a stable closed loop multi input multi output system will remain stable for all unitary perturbations in the feedback path whose phases are less than the phase margin of the system it is also shown that the definition of phase margin is invariant under unitary transformations of the system

guided image completion by confidence propagation this paper presents a new guided image completion method which fills any missing values by considering information from a guidance image we develop a confidence propagation scheme that allows the filling process to be carried out simultaneously without the need of deciding the filling order we conduct experiments in several applications where the problem can be formulated into a guided image completion problem such as interactive segmentation and colorization the experimental results show that our method provides good results and succeeds in situations where conventional methods fail in addition as all building blocks are parallel processes our method is much suitable for hardware acceleration highlightswe proposed an image completion method based on a new formulation filling process was carried out simultaneously without deciding the filling order good results were obtained in a variety of applications

on eigenvalues eigenvectors and singular values in robust stability analysis abstract recent papers have examined the problem of robustness of the stability of multi variable feedback systems to perturbations g in matrix form attention has been primarily focused on the use of the maximal singular value g this paper considers how structured information on the uncertainty in each element 9 con be used in a similar way based on eigenvalue and singular value analysis

analysis and design of linear multivariable feedback systems in the presence of additive perturbations the paper introduces the concept of normal approximations to the analysis of uncertain linear multivariable feedback systems in order to derive a new criterion for the stability of plants subject to additive perturbations this criterion permits a complete assessment of stability margins in that it provides a measure of tolerance to uncertainty as well as providing a measure of gain phase margins the proposed approach leads to a systematic design procedure which minimizes the effects of uncertainty by attaining the condition of normality or which improves the stability margins by robust gain phase sharing the results presented in this paper are insensitive to small perturbations on the nominal plant model and provide the means for a consideration of information concerning the structure of uncertainty

robust stability of additively perturbed interconnected systems the concept of generalized block diagonal dominance is used to derive robust stability results for additively perturbed interconnected systems these results characterize the robustness of interconnected systems by putting upper bounds on the spectral norms of the various subblocks of admissible perturbations

simultaneous structure and texture image inpainting an algorithm for the simultaneous filling in of texture and structure in regions of missing image information is presented in this paper the basic idea is to first decompose the image into the sum of two functions with different basic characteristics and then reconstruct each one of these functions separately with structure and texture filling in algorithms the first function used in the decomposition is of bounded variation representing the underlying image structure while the second function captures the texture and possible noise the region of missing information in the bounded variation image is reconstructed using image inpainting algorithms while the same region in the texture image is filled in with texture synthesis techniques the original image is then reconstructed adding back these two sub images the novel contribution of this paper is then in the combination of these three previously developed components image decomposition with inpainting and texture synthesis which permits the simultaneous use of filling in algorithms that are suited for different image characteristics examples on real images show the advantages of this proposed approach

algebraic theory for robust stability of interconnected systems necessary and sufficient conditions we consider an interconnected system s o made of linear mulrivariable subsystems which are specified by matrix fractions with elements in a ring of stable scalar transfer functions h given that the k th subsystem is perturbed from g k n rk d k 1 to tilde g k n rk delta n rk d k delta d k 1 and that the system s o is h stable we derive a computationally efficient necessary and sufficient condition for the h stability of the perturbed system these fractional perturbations are more general than the conventional additive and multiplicative perturbations the result is generalized to handle simultaneous perturbations of two or more subsystems

adaptive support weight approach for correspondence search we present a new window based method for correspondence search using varying support weights we adjust the support weights of the pixels in a given support window based on color similarity and geometric proximity to reduce the image ambiguity our method outperforms other local methods on standard stereo benchmarks

technical communique an algorithm for the computation of the transfer function matrix for singular systems for singular systems i e for systems of the form ex ax bu with e singular the problem of computing the transfer function matrix has been solved an algorithm is developed which uses the souriau frame faddeev algorithm for regular systems the final expression is suitable for computer use

robust stabilization of linear multivariable systems relations to approximation the stabilization of a linear system modelled as g a where g is a known rational transfer function and a is a perturbation satisfying w a2 g1 or equivalently there does not exist g with fewer poles in c than g such that w1 g g w2 a simple characterization of all robustly stabilizing controllers is then derived and state space formulae for maximally robust controllers are given finally reduced order controllers are considered

multivariable feedback a personal reminiscence my involvement in the development of linear multivariable feedback theory and its applications is described from a highly personal point of view concentrating on the origin of key ideas and their development in association with many colleagues detailed references are given to all my papers and books and explanatory notes provided where further material may be found

on the relationship between lehtomaki s robustness test and an inverse nyquist based test in this note we show that lehtomaki s robustness test 1 is simply a special case of the inverse nyquist based test in 2

contour detection and hierarchical image segmentation this paper investigates two fundamental problems in computer vision contour detection and image segmentation we present state of the art algorithms for both of these tasks our contour detector combines multiple local cues into a globalization framework based on spectral clustering our segmentation algorithm consists of generic machinery for transforming the output of any contour detector into a hierarchical region tree in this manner we reduce the problem of image segmentation to that of contour detection extensive experimental evaluation demonstrates that both our contour detection and segmentation methods significantly outperform competing algorithms the automatically generated hierarchical segmentations can be interactively refined by user specified annotations computation at multiple image resolutions provides a means of coupling our system to recognition applications

linear stable unity feedback system necessary and sufficient conditions for stability under nonlinear plant perturbations the authors consider a linear not necessarily time invariant stable unity feedback system where the plant and the compensator have normalized right coprime factorizations they study two cases of nonlinear plant perturbations additive and feedback with four subcases resulting from 1 allowing exogenous input to delta p or not 2 allowing the observation of the output of delta p or not the plant perturbation delta p is not required to be stable using the factorization approach the authors obtain necessary and sufficient conditions for all cases in terms of two pairs of nonlinear pseudostate maps simple physical considerations explain the form of these necessary and sufficient conditions finally the authors obtain the characterization of all perturbations delta p for which the perturbed system remain stable

effective recursive algorithm for judging the positive definiteness of matrices of high dimension this paper presents a new efficient recursive algorithm for judging the positive definiteness of a matrix with this algorithm both a simpler computation process and a decreased memory requirement can be obtained

method of robust stability analysis with highly structured uncertainties this paper presents a method of analyzing the stability of linear time invariant interconnected systems with uncertainties each subsystem is single input single output and its vector locus lies inside a polygon at each frequency it is shown that the convex closure of the image of the cartesian product of these polygons under the mapping phi det i fh agrees with the convex closure of the image of the vertices of these polygons under the mapping from this result the image can be estimated by a finite dumber of calculations a sufficient stability condition is obtained by applying this result to the multivariable nyquist stability criterion

the numerical range a tool for robust stability studies the use of numerical range concepts for assessing robust stability of multivariable feedback systems is investigated the characterization of perturbations by their numerical range allows a more detailed description of their gains and phases and allows a robust stability theorem similar in structure to that of postlethwaite et al with the possibility of arbitrary large perturbations

computation of transfer function matrices of generalized state space models a reliable computational algorithm is proposed for the evaluation of the transfer function matrices of linear multivariable systems described by generalized state space models the algorithm is based on a new efficient and numerically stable procedure for computing irreducible state space realizations of generalized state space models for each input output channel the proposed algorithm computes an irreducible realization using this procedure then the parameters of the corresponding transfer function gain poles zeros are determined from the resulting irreducible model

improved design technique for uncertain multiple input multiple output feedback systems this paper presents a synthesis technique for linear time invariant n n multiple input multiple output mimo feedback systems with constrained plant p and output feedback due to uncertainty p is known only to be a member of a set x1d4ab p it is required for all pep the n2 system transfer functions tuv be members of specified sets of acceptable outputs a uv u v 1 tdot n the problem is rigorously converted into a number of single input single output siso uncertainty problems whose solutions are guaranteed to solve the original mimo problem the technique has several advantages over previous ones 1 fixed point theory is not needed to rigorously justify the theory the justification is very simple 2 there is significantly less overdesign inherent in the method and 3 if arbitrary small sensitivity is desired over arbitrary large bandwidth then the set p must satisfy certain constraints as 8 it is shown that these constraints are inherent in all linear time invariant compensat

on closed form solutions to the generalized sylvester conjugate matrix equation abstract in this paper several explicit parametric solutions to the generalized sylvester conjugate matrix equation are given the proposed solutions can provide all the degrees of freedom which are represented by a free parameter matrix in addition the approaches adopted in this paper do not require that the coefficient matrices are in any canonical forms

the problem of guaranteeing robust disturbance rejection in linear multivariable feedback systems abstract this paper considers a linear time invariant lumped multivariable feedback system consisting of a plant which is subjected to perturbations a precompensator and a feedback compensator given that the nominal feedback system is exponentially stable and achieves considerable disturbance rejection this paper establishes necessary and sufficient conditions on the nominal feedback system so that over the prescribed class of additive multiplicative perturbations all perturbed feedback systems preserve stability and considerable disturbance rejection the generalization to distributed systems and the extension to discrete systems are indicated

a linearization algorithm for optimizing control systems subject to singular value inequalities the design of feedback linear multivariable systems subject to inequality constraints frequently leads to nonlinear programming problems involving singular values of matrix transfer functions we present a readily implementable and globally convergent algorithm for solving such problems it exploits the structure inherent in singular values differently than do other existing methods

inverse of polynomial matrices in the irreducible form an algorithm is developed for finding the inverse of polynomial matrices in the irreducible form the computational method involves the use of the left right matrix division method and the determination of linearly dependent vectors of the remainders the obtained transfer function matrix has no nontrivial common factor between the elements of the numerator polynomial matrix and the denominator polynomial

matrix wa atw and its applications for matrix a with off diagonal elements not necessarily of the same sign conditions are obtained for the existence of a positive definite diagonal matrix w such that matrix wa atw is positive definite and the applications of the latter to the determination of the stability of interval matrices are considered

stereo matching using tree filtering matching cost aggregation is one of the oldest and still popular methods for stereo correspondence while effective and efficient cost aggregation methods typically aggregate the matching cost by summing averaging over a user specified local support region this is obviously only locally optimal and the computational complexity of the full kernel implementation usually depends on the region size in this paper the cost aggregation problem is re examined and a non local solution is proposed the matching cost values are aggregated adaptively based on pixel similarity on a tree structure derived from the stereo image pair to preserve depth edges the nodes of this tree are all the image pixels and the edges are all the edges between the nearest neighboring pixels the similarity between any two pixels is decided by their shortest distance on the tree the proposed method is non local as every node receives supports from all other nodes on the tree the proposed method can be naturally extended to the time domain for enforcing temporal coherence unlike previous methods the non local property guarantees that the depth edges will be preserved when the temporal coherency between all the video frames are considered a non local weighted median filter is also proposed based on the non local cost aggregation algorithm it has been demonstrated to outperform all local weighted median filters on disparity depth upsampling and refinement

image inpainting by patch propagation using patch sparsity this paper introduces a novel examplar based inpainting algorithm through investigating the sparsity of natural image patches two novel concepts of sparsity at the patch level are proposed for modeling the patch priority and patch representation which are two crucial steps for patch propagation in the examplar based inpainting approach first patch structure sparsity is designed to measure the confidence of a patch located at the image structure e g the edge or corner by the sparseness of its nonzero similarities to the neighboring patches the patch with larger structure sparsity will be assigned higher priority for further inpainting second it is assumed that the patch to be filled can be represented by the sparse linear combination of candidate patches under the local patch consistency constraint in a framework of sparse representation compared with the traditional examplar based inpainting approach structure sparsity enables better discrimination of structure and texture and the patch sparse representation forces the newly inpainted regions to be sharp and consistent with the surrounding textures experiments on synthetic and natural images show the advantages of the proposed approach

fast image and video colorization using chrominance blending colorization the task of coloring a grayscale image or video involves assigning from the single dimension of intensity or luminance a quantity that varies in three dimensions such as red green and blue channels mapping between intensity and color is therefore not unique and colorization is ambiguous in nature and requires some amount of human interaction or external information a computationally simple yet effective approach of colorization is presented in this paper the method is fast and it can be conveniently used on the fly permitting the user to interactively get the desired results promptly after providing a reduced set of chrominance scribbles based on the concepts of luminance weighted chrominance blending and fast intrinsic distance computations high quality colorization results for still images and video are obtained at a fraction of the complexity and computational cost of previously reported techniques possible extensions of the algorithm introduced here included the capability of changing the colors of an existing color image or video as well as changing the underlying luminance and many other special effects demonstrated here

on the phases of a complex matrix abstract in this paper we define the phases of a complex sectorial matrix to be its canonical angles which are uniquely determined from a sectorial decomposition of the matrix properties of matrix phases are studied including those of compressions schur complements matrix products and sums in particular by exploiting a notion known as the compound numerical range we establish a majorization relation between the phases of the eigenvalues of ab and the phases of a and b this is then applied to investigate the rank of i a b with phase information of a and b which plays a crucial role in feedback stability analysis a pair of problems banded sectorial matrix completion and decomposition is studied the phases of the kronecker and hadamard products are also discussed

control parameterization and robustness of feedback systems an asymptotic analysis the problem of robust design is regarded as a parameterization problem and the choice of parameters to satisfy with respect to a class of bounded perturbations is considered application areas for the general results derived include multivariate root locus robustness design based on simplified or reduced plant models and singular perturbation analysis the results are based on asymptotic analysis of feedback structures and a proof of the existence of parameter ranges for robust stability

stability conditions for a class of delay differential systems in this paper necessary and sufficient conditions of asymptotic stability independent of delay of a certain class of both the retarded and neutral types of delay differential systems are obtained the stability conditions reduce to positivity of a quartic equation conditions for the latter in explicit form are given by the authors in an earlier publication in addition sufficient conditions for stability for a general order delay differential system independent of delay are also obtained such conditions are ascertained from the fact that a sufficient condition for any algebraic equation to have no positive real roots is that all its coefficients be positive

robust stabilization with positive real uncertainty beyond the small gain theory in many applications of feedback control phase information is available concerning the plant uncertainty for example lightly damped flexible structures with colocated rate sensors and force actuators give rise to positive real transfer functions closed loop stability is thus guaranteed by means of negative feedback with strictly positive real compensators in this paper the properties of positive real transfer functions are used to guarantee robust stability in the presence of positive real but otherwise unknown plant uncertainty these results are then used for controller synthesis to address the problem of robust stabilization in the presence of positive real uncertainty one of the principal motivations for these results is to utilize phase information in guaranteeing robust stability in this these sense results go beyond the usual limitations the small gain theorem and quadratic lyapunov functions which may be conservative when phase information is available the results of this paper are based upon a riccati equation formulation of the positive real lemma and thus are in the spirit of recent riccati based approaches to bounded real h control

principal gains and principal phases in the analysis of linear multivariable feedback systems the concepts of principal gain and principal phase are introduced for linear multivariable systems and their use in the analysis of feedback behavior is demonstrated a sufficient nyquist type stability criterion is presented in terms of these quantities and is used to characterize the robustness of the closed loop stability property when the system model is subjected to a linear perturbation either multiplicative or additive at any point in the feedback configuration the results presented are less conservative than those obtained via the small gain theorem

paper sensitivity integrals for multivariable discrete time systems the purpose of this paper is to develop integral formulae for singular values of the sensitivity function to express design constraints in multivariable discrete time systems we present extensions to both the classical poisson integral and bode s sensitivity integral formulae the main utility of these results is that they can be used to quantify design limitations that arise in multivariable discrete time systems due to such system characteristics as open loop unstable poles and nonminimum phase zeros and to such design requirements as stability and bandwidth constraints these formulae are similar to those for multivariable continuous time systems obtained elsewhere and they reveal that feedback design limitations depend on directionality properties of the sensitivity function and on those of unstable poles and nonminimum phase zeros in the open loop transfer function

fundamental relationship between bilateral filtering adaptive smoothing and the nonlinear diffusion equation in this paper the relationship between bilateral filtering and anisotropic diffusion is examined the bilateral filtering approach represents a large class of nonlinear digital image filters we first explore the connection between anisotropic diffusion and adaptive smoothing and then the connection between adaptive smoothing and bilateral filtering previously adaptive smoothing was considered to be an inconsistent approximation to the nonlinear diffusion equation we extend adaptive smoothing to make it consistent thus enabling a unified viewpoint that relates nonlinear digital image filters and the nonlinear diffusion equation

design sensitivity analysis of structures based upon the singular value decomposition the singular value decomposition svd is employed for design sensitivity analysis of structures as the squares of singular values are the bounds of power energy and power spectral density ratios between the input and output vectors shaping the singular values of a structure is equivalent to shaping the response of the structure comparison is made of the proposed sensitivity analysis based upon the svd with the conventional techniques the issues such as structural robustness worst loading case and multiple load cases are studied as shown design sensitivity analysis based upon the svd can give good insight into static and dynamic response characteristics of structures it is more informative than eigenvalue design sensitivity analysis and in particular computationally advantageous in case of multiple load cases numerical examples are presented to illustrate the proposed approach

robust stability of lure systems with multiple nonlinearities the stability of a perturbed lure system is studied through the popov lyapunov approach the multivariable popov criterion is used to guarantee the stability of the nominal system and then the stability of the perturbed system is investigated by using the lyapunov function developed for the nominal system a robustness measure which gives some bounds on allowable perturbations for the system is derived evading the use of norm forms a feature of the proposed measure is that the observation of the range for individual parameter deviation is feasible

stability conditions of delay differential systems sufficient conditions of asymptotic stability independent of delay of both the retarded and neutral types of delay differential systems are obtained the main results are based on the sufficient conditions under which the roots of the determinant of a given l l complex matrix polynomial lie either in the open left half plane or inside the unit circle therefore the explicit computation of the determinant polynomial is not required

on interconnections of mixed systems using classical stability theory abstract in this paper we derive stability results for large scale interconnections of mixed linear time invariant systems using classical nyquist arguments we compare our results with moylan and hill 1978 8 our results indicate that if one relaxes assumptions on the subsystems in an interconnection from assumptions of passivity or small gain to assumptions of mixedness then the moylan and hill like conditions on the interconnection matrix become more stringent finally we explore a condition for the stability of large scale time varying interconnections of strictly positive real systems this condition mirrors the condition obtained in 8 for time invariant interconnections and is thus an extension of this work

nonlocal image and movie denoising neighborhood filters are nonlocal image and movie filters which reduce the noise by averaging similar pixels the first object of the paper is to present a unified theory of these filters and reliable criteria to compare them to other filter classes a ccd noise model will be presented justifying the involvement of neighborhood filters a classification of neighborhood filters will be proposed including classical image and movie denoising methods and discussing further a recently introduced neighborhood filter nl means in order to compare denoising methods three principles will be discussed the first principle method noise specifies that only noise must be removed from an image a second principle will be introduced noise to noise according to which a denoising method must transform a white noise into a white noise contrarily to method noise this principle which characterizes artifact free methods eliminates any subjectivity and can be checked by mathematical arguments and fourier analysis noise to noise will be proven to rule out most denoising methods with the exception of neighborhood filters this is why a third and new comparison principle the statistical optimality is needed and will be introduced to compare the performance of all neighborhood filters the three principles will be applied to compare ten different image and movie denoising methods it will be first shown that only wavelet thresholding methods and nl means give an acceptable method noise second that neighborhood filters are the only ones to satisfy the noise to noise principle third that among them nl means is closest to statistical optimality a particular attention will be paid to the application of the statistical optimality criterion for movie denoising methods it will be pointed out that current movie denoising methods are motion compensated neighborhood filters this amounts to say that they are neighborhood filters and that the ideal neighborhood of a pixel is its trajectory unfortunately the aperture problem makes it impossible to estimate ground true trajectories it will be demonstrated that computing trajectories and restricting the neighborhood to them is harmful for denoising purposes and that space time nl means preserves more movie details

convergence in the boundary layer for singularly perturbed equations a singularly perturbed linear finite dimensional ordinary differential equation is considered on the half line 0 the reduced system is assumed to have a unique solution in the sense of distributions it is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense and the order of the limiting distribution is computed an application to the optimal linear quadratic regulator with cheap control is described

uncertain multiple input multiple output systems with internal variable feedback there is given a linear time invariant multiple input multiple output mimo plant p with internal variables xi and outputs yi available for feedback due to uncertainty p is known only to be in a set p there are given tolerances on the overall system response functions tuv system output yu in response to command input ru to be satisfied pep it is shown how this mimo uncertainty problem may be replaced by a number of single input single output siso multiple loop uncertainty problems a suitable fixed point theorem guarantees that the solution of the siso problems solves the original mimo problem plant elements which appear singly in the mimo structure also appear singly in the siso structures a design example demonstrates how inner loop feedback may enormously decrease the effect of sensor noise at the mimo plant inputs extensions to disturbance attenuation under uncertainty and to uncertain time varying and non linear mimo plants are discussed

the robustness optimization of a multivariable feedback system in hankel norm space this paper is concerned with the optimization of robustness in a multi input multi output linear time invariant finite dimensional feedback system the objective is to derive a closed form solution to the problems of the synthesis of optimal controllers that either minimize the weighted sensitivity function or maximize the excess robust ness with respect to hankel norm criterion an all pass solution for the minimum hankel norm is employed to treat our problems finally the infinite norm case is also discussed

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

a feedback theory of two degree of freedom optimal wiener hopf design the design of linear two degree of freedom stabilizing controllers is treated in a quadratic cost setting the class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance tracking cost sensitivity and stability margins is discussed

an algorithm for obtaining the redundancy equations of lti systems in the context of model based failure detection and diagnosis there is a residual generation which can be obtained through a generalized parity space concept this paper presents a new algorithm involving the generation of redundancy or parity equations for dynamic linear time invariant systems the proposed scheme involves the successive elimination of state sub vectors and their replacement by output values as well as the processing of an output done one at a time to avoid matrix inversion some examples point out the numerical efficiency of the proposed procedure

reduced conservative singular value analysis for robustness in recent years many studies have been reported on methods of examining the problems of the robustness of multi input and multi output systems in the frequency domain using the singular value technique however since the conventional criteria have been derived as sufficient conditions for stability or sensitivity reduction they are more than sufficient or so called conservative conditions and therefore they have the disadvantage that they cannot be used for the evaluation of stability and or sensitivity reduction in this paper we propose new criteria for robust stability and sensitivity reduction with reduced conservatism which utilize equivalent systems with the same transfer function as that of the plant in order to illustrate the effectiveness of these criteria examples of the longitudinal and lateral motion of aircraft are analysed by both the conventional and the proposed methods and the results are compared to show the advantage of the proposed method

effects of mode localization on input output directional properties of structures abstract the singular value decomposition svd is employed to study the effects of localization phenomena on input output relationships and power and energy transmission ratios of structures for weakly and strongly coupled systems existence of strong localization of singular vectors and abrupt veering of singular value loci are shown occurrence of strong localization causes abrupt changes in input output directional properties in contrast to eigenvalues singular values do not veer away by introducing a disorder in weakly coupled systems in particular the use of singular values and vectors is computationally advantageous in considering multiple load cases while eigenvalue based analyses give information about the resonance frequencies and vibration modes of a structure singular values of the structure are related to the forced response characteristics and give the dynamic behavior in the frequency domain representative examples in structural dynamics are presented

multivariable gain phase and sensitivity integral relations and design trade offs we present several extensions of the classical bode integral relations to multivariable systems the main contributions are an extended gain phase integral formula and an extended sensitivity integral relation these results are useful for analyzing fundamental design limitations that arise in linear multivariable feedback systems in particular they provide important insights into feedback properties which are unique to multivariable systems and which cannot be inferred from the previously known integral relations applicable to single input single output systems both results show that design limitations in multivariable systems depend strongly upon certain directionality properties

robustness of feedback stabilized systems in the presence of non linear and random perturbations the general robustness problem is discussed for a controlled discrete time system subject to a lur e type feedback non linearity together with random multiplicative noises effective on state input and the non linearity a sufficient condition is given utilizing the discrete stochastic version of the second method of lyapunov to guarantee that any stabilizing controller designed for the deterministic linear part of the system renders the closed loop system with perturbations asymptotically stable with probability one then specializations to systems given in controllability and controller canonical forms are made independent noise signals are assumed to be effective on individual parameters of these canonical forms whose inputs are designed to assign the closed loop poles to zero in these cases stronger results are obtained in terms of system parameters and known characteristics of perturbations

depth video enhancement based on weighted mode filtering this paper presents a novel approach for depth video enhancement given a high resolution color video and its corresponding low quality depth video we improve the quality of the depth video by increasing its resolution and suppressing noise for that a weighted mode filtering method is proposed based on a joint histogram when the histogram is generated the weight based on color similarity between reference and neighboring pixels on the color image is computed and then used for counting each bin on the joint histogram of the depth map a final solution is determined by seeking a global mode on the histogram we show that the proposed method provides the optimal solution with respect to l1 norm minimization for temporally consistent estimate on depth video we extend this method into temporally neighboring frames simple optical flow estimation and patch similarity measure are used for obtaining the high quality depth video in an efficient manner experimental results show that the proposed method has outstanding performance and is very efficient compared with existing methods we also show that the temporally consistent enhancement of depth video addresses a flickering problem and improves the accuracy of depth video

robustness under bounded uncertainty with phase information the authors consider uncertain linear systems where the uncertainties in addition to being bounded also satisfy constraints on their phase in this context the authors define the phase sensitive structured singular value ps ssv of a matrix and show that sufficient and sometimes necessary conditions for stability of such uncertain linear systems can be rewritten as conditions involving ps ssv they then derive upper bounds for ps ssv computable via convex optimization they extend these results to the case where the uncertainties are structured diagonal or block diagonal for instance

algorithms for the computation of the transfer function matrix for two dimensional regular and singular general state space models the problem of computing the transfer function matrices for regular and singular discrete two dimensional general state space models 2d gm is discussed and some programmable algorithms are developed that generalize the well known leverrier algorithm to 2d systems of general form the results also show that the transfer function matrices for regular and singular 2d gm can also be formulated via the state transition matrices of the systems

efficient algorithms for globally optimal trajectories we present serial and parallel algorithms for solving a system of equations that arises from the discretization of the hamilton jacobi equation associated to a trajectory optimization problem of the following type a vehicle starts at a prespecified point x sub o and follows a unit speed trajectory x t inside a region in spl rscr sup m until an unspecified time t that the region is exited a trajectory minimizing a cost function of the form spl int sub 0 sup t r x t dt q x t is sought the discretized hamilton jacobi equation corresponding to this problem is usually solved using iterative methods nevertheless assuming that the function r is positive we are able to exploit the problem structure and develop one pass algorithms for the discretized problem the first algorithm resembles dijkstra s shortest path algorithm and runs in time o n log n where n is the number of grid points the second algorithm uses a somewhat different discretization and borrows some ideas from a variation of dial s shortest path algorithm 1969 that we develop here it runs in time o n which is the best possible under some fairly mild assumptions finally we show that the latter algorithm can be efficiently parallelized for two dimensional problems and with p processors its running time becomes o n p provided that p o spl radic n log n

gain margin and time lag tolerance constraints applied to the stabilization problem and robust servomechanism problem definitions of gain margin tolerance and time lag tolerance for a multivariable linear time invariant system are given which correspond to a generalization of the notions of gain and phase margin of classical control system theory existence conditions are then given to solve the stabilization problem and the robust servomechanism problem with gain margin and time lag tolerance constraints in particular the following is shown for a system described in terms of a state state model 1 generically there exists a controller to stabilize an unstable m input r output system so that the resultant closed loop system possesses a nonzero gain margin if and only if min r m 1 2 for stable plants there always exists a controller to solve the robust servomechanism problem so that it has an arbitrary specified gain margin time lag tolerance constraint if and only if there exists a solution to the robust servomechanism problem for the plant a controller synthesis method is then given which solves the robust servomechanism problem so that it has a specified gain margin time lag tolerance various examples of the proposed algorithm are given to illustrate the type of results that may be obtained

stability of interval matrix polynomial in continuous and discrete cases abstract sufficient conditions of asymptotic stability of interval matrix polynomial of both continuous and discrete cases are given these conditions are presented in terms of the positive definiteness of either an ln ln or l l hermitian and interval matrix therefore the computation of the determinant interval polynomial is avoided

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

robust stability under additive perturbations we consider a mimo linear time invariant feedback system1 s p c which is assumed to be u stable the plant p is subjected to an additive perturbation delta p which is proper but not necessarily stable we prove that the perturbed system is u stable if and only if delta p i q delta p 1 is u stable here q c i pc 1

on the relationship between the stability margin and the phase margin for multivariable systems one of the main concerns in the area of control theory is the ability of a system to remain stable in the presence of unknown perturbations consequently it is important to be able to measure relative stability of systems and thus be able to determine if they are robust and will remain stable when subjected to various perturbations for single input single output feedback systems relative stability in the frequency domain is typically measured in terms of the phase margin and the gain margin for multivariable systems however relative stability in the frequency domain is typically measured at some point in the control loop in terms of the size of the smallest destabilizing perturbation either multiplicative or additive the stability margin is a standard technique used to measure relative stability for unstructured perturbations while the doyle function is a common method used to measure relative stability for structured perturbations the problems with these measurements is that they are based upo

robust stability of interconnected systems the concept of generalized block diagonal dominance is used to extend a number of recently developed robust stability results for multivariable systems to large scale interconnected systems

a criterion of approximation for the method of inequalities a criterion of approximation is derived for replacing a plant transfer function which is either non rational or is rational but large or is not accurately known by a convenient rational approximant for the purposes of designing a control system the criterion provides simple sufficient conditions on the accuracy of approximation to ensure that designs carried out with the approximant are valid

the design of servomechanism controllers for uncertain plants abstract the design of multivariable servomechanism controllers is considered here for plants whose parameters are uncertain or perturbed within a cone bounding criterion the solution comes from a controller design problem as an lq optimal control problem in which the gain matrices result in a quadratic performance upper bound similar to that described by gilman and rhodes 1976 which depends on the uncertainty under conditions on the nominal plant and on the uncertainty a resulting linear time invariant controller is guaranteed to achieve the objectives of robust tracking and regulation with closed loop stability

a performance criterion a natural measure of performance is defined for control systems the input to the system is known to the extent that it belongs to a known function space lack of performance is then defined as the least upper bound of the absolute error that occurs over all time and all inputs the main problems of computing a value of the controller parameter that satisfies prescribed performance are considered and useful expressions are derived for such computations in particular a simple formula is derived for calculating performance the paper discusses the implications of the new measure of performance in control theory and design

graph cuts and efficient n d image segmentation combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics this paper focusses on possibly the simplest application of graph cuts segmentation of objects in image data despite its simplicity this application epitomizes the best features of combinatorial graph cuts methods in vision global optima practical efficiency numerical robustness ability to fuse a wide range of visual cues and constraints unrestricted topological properties of segments and applicability to n d problems graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes geodesic active contours and level sets the segmentation energies optimized by graph cuts combine boundary regularization with region based properties in the same fashion as mumford shah style functionals we present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s t graph cuts after the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in boykov and jolly 2001 this idea was widely studied in computer vision and graphics communities we provide links to a large number of known extensions based on iterative parameter re estimation and learning multi scale or hierarchical approaches narrow bands and other techniques for demanding photo video and medical applications

multivariable circle criteria an approach based on sector conditions the definition and properties of sector conditions introduced by zames for scalar systems can be extended to the multivariable case the present paper makes use of appropriate forms of sector conditions in conjunction with the decomposition of a linear operator into two linear operators and g where has a normal transfer function matrix and proposes a useful stability criterion for a class of multivariable non linear feedback systems the relevant stability result is developed further by a suitable interpretation of sector conditions in the frequency domain a particular choice for leads to a generalization of the circle criterion in which the nyquist plot of the frequency response of scalar systems is replaced by bands swept by circles whose centres and radii are related in a direct manner to the numerical range of g j the result has a simple graphical interpretation and lends itself to a computer implementation which can be shown to be numerically stable the approach is also suitable for

robustness with simultaneous pole and zero movement across the jω axis in this paper we present some new tests for assessing the robustness of the stability property of a feedback design the tests offer a wider scope of application than those previously described in the literature the main result is a robustness test which can be used to assess closed loop stability when the nominal plant model and perturbed plant model representing uncertainty have different numbers of poles and zeros in the right half plane this test also indicates over which frequencies good sensitivity and robust stability are compatible objectives and over which frequencies a compromise has to be made contrary to popular belief if there are no uncertain zeros which can move across the imaginary axis then good sensitivity and robust stability are compatible objectives over the same frequencies

an extension of the characteristic sequences method to the case of repeated roots an extension of the characteristic sequences method to the case of repeated roots has been investigated the aim of the present note is to complete the study and the related design of systems whose mathematical modeling in state space form or transfer function form is not available a comparative study between the characteristic sequences method and the characteristic locus method shows that the two methods are closely related to each other and the former one is a time domain counterpart of the latter one

an m matrix and majorant approach to robust stability and performance analysis for systems with structured uncertainty uncertain multiinput multioutput systems described in the frequency domain are discussed the theory of nonnegative matrices and m matrices is used along with majorant bounding techniques to develop robust stability and performance results for two types of uncertainty the first type is uncertainty with norm bounded subblocks the second type is uncertainty that has subblocks with known patterns but unknown gains this latter uncertainty representation allows the elements of a given uncertainty block to be correlated for uncertainties of this type a recursive analysis methodology is developed which yields increasingly nonconservative results throughout this paper the performance analysis determines norm bounds on the deviations of the outputs from their nominal values the results are illustrated by a numerical example

stability of a matrix polynomial in continuous systems two sufficient conditions under which the roots of the determinant of a given m times m matrix polynomial of n th order lie in the open left half plane have been obtained the first condition is given in terms of the positive definiteness of an mn times mn symmetric matrix while the second condition is given in terms of the positive definiteness of an m times m matrix that is a function of s re s leq 0 these conditions are represented in terms of rational functions of the coefficient matrices of the given matrix polynomial therefore the explicit computation of the determinant polynomial is not required

technical communique controller synthesis with guaranteed closed loop phase constraints in this paper we present an analysis and synthesis approach for guaranteeing that the phase of a single input single output closed loop transfer function is contained in the interval a a for a given a 0 at all frequencies specifically we first derive a sufficient condition involving a frequency domain inequality for guaranteeing a given phase constraint next we use the kalman yakubovich popov theorem to derive an equivalent time domain condition in the case where a p2 we show that frequency and time domain sufficient conditions specialize to the positivity theorem furthermore using linear matrix inequalities we develop a controller synthesis approach for guaranteeing a phase constraint on the closed loop transfer function finally we extend this synthesis approach to address mixed gain and phase constraints on the closed loop transfer function

stability of a matrix polynomial in discrete systems two sufficient conditions that the determinant of a nonsingular real m times m matrix polynomial of n th order has all its roots inside the unit circle have been obtained these conditions are represented in terms of rational functions of the coefficient matrices therefore these conditions do not require the computation of the determinant polynomial the first condition is given in terms of the positive definiteness of an mn times mn symmetric matrix while the second condition is expressed by the positive definiteness of an m times m hermitian matrix which is a function of z z leq 1 the first condition implies the second and hence is more restrictive than the second

gain phase structures for linear multivariate systems a general gain phase structure for linear multivariable systems is proposed and related to the ideas of quasi nyquist loci and singular value decompositions the analysis of absolute stability using positive real conditions and eigenvalue estimation using gershgorin s theorem and the numerical range

algebraic theory of linear multivariable feedback systems this paper presents an algebraic theory for analysis and design of linear multivariable feedback systems the theory is developed in an algebraic setting sufficiently general to include as special cases continuous and discrete time systems both lumped and distributed designs are implemented by construction of a controller with two vector inputs and one vector output use of controllers of this type is shown to generate convenient stability results and convenient global parametrizations of all i o maps and all disturbance to output maps achievable for a given plant by a stabilizing compensator these parametrizations are then used to show that any such i o map and any such disturbance to output map may be simultaneously realized by choice of an appropriate controller in the special case of lumped systems it is shown that the design theory can be reduced to manipulations involving polynomial matrices only the resulting design procedure is thus shown to be more efficient computationally finally the problem of asymptotically tracking a class of input signals is considered in the general algebraic setting it is shown that the classical results on asymptotic tracking can be generalized to this setting additionally sufficient conditions for robustness of asymptotic tracking and robustness of stability are developed

the structured phase margin for robust stability analysis of linear systems with phase and time delay uncertainties in this paper we introduce the notion of the structured phase margin for characterising stability margins for a dynamical system with block structured phase uncertainty since the structured phase margin may in general be difficult to compute we derive an easily computable lower bound in terms of a generalised eigenvalue problem this bound is constructed by choosing stability multipliers that are tailored to the structure of the phase uncertainty the results in this paper complement and generalise phase information results presented in the literature involving principal phases multivariable phase margin phase spread phase envelope phase matching and phase sensitive structured singular value finally using the structured phase margin we present new and improved delay dependent stability criteria for stability analysis of time delay systems