robust stability and stabilization of discrete time non linear systems the lmi approach the purpose of this paper is to convert the problem of robust stability of a discrete time system under non linear perturbation to a constrained convex optimization problem involving linear matrix inequalities lmi the nominal system is linear and time invariant while the perturbation is an uncertain non linear time varying function which satisfies a quadratic constraint we show how the proposed lmi framework can be used to select a quadratic lyapunov function which allows for the least restrictive non linear constraints when the nominal system is unstable the framework can be used to design a linear state feedback which stabilizes the system with the same maximal results regarding the class of non linear perturbations of particular interest in this context is our ability to use the lmi formulation for stabilization of interconnected systems composed of linear subsystems with uncertain non linear and time varying coupling by assuming stabilizability of the subsystems we can produce local control la

brief paper fault tolerant control for singular systems with actuator saturation and nonlinear perturbation in this paper the problem of robust fault tolerant control for a class of singular systems subject to both time varying state dependent nonlinear perturbation and actuator saturation is investigated a sufficient condition for the existence of a fixed gain controller is first proposed which guarantees the regularity impulse free and stability of the closed loop system under all possible faults an optimization problem with lmi constraints is formulated to determine the largest contractively invariant ellipsoid an adaptive fault tolerant controller is then developed to compensate for the failure effects on the system by estimating the fault and updating the design parameter matrices online both of these two controllers are in the form of a saturation avoidance feedback with the advantage of relatively small actuator capacities compared with the high gain counterpart an example is included to illustrate the proposed procedures and their effectiveness

wu s method and its application to perspective viewing abstract an algebraic method for proving a class of geometry theorems recently proposed by wu is informally discussed key concepts relevant to the method are explained an application of this method to perspective viewing in image understanding is discussed finally it is outlined how the method can be helpful to prove geometry theorems involving inequalities to capture the relation of a point being in between two given points this is also illustrated using an example from image understanding

growth of sobolev norms in time dependent semiclassical anharmonic oscillators abstract we consider the semiclassical schrodinger equation on r d given by i t 2 2 w l x v t x where w l is an anharmonic trapping of the form w l x 1 2 l j 1 d x j 2 l l 2 is an integer and is a semiclassical small parameter we construct a smooth potential v t x bounded in time with its derivatives and an initial datum such that the sobolev norms of the solution grow at a logarithmic speed for all times of order log 1 2 1 the proof relies on two ingredients first we construct an unbounded solution to a forced mechanical anharmonic oscillator then we exploit semiclassical approximation with coherent states to obtain growth of sobolev norms for the quantum system which are valid for semiclassical time scales

transfer of energy to high frequencies in the cubic defocusing nonlinear schrodinger equation we consider the cubic defocusing nonlinear schrodinger equa tion on the two dimensional torus we exhibit smooth solutions for which the support of the conserved energy moves to higher fourier modes this behavior is quantified by the growth of higher sobolev norms given any 1 k 1 s 1 we construct smooth initial data u0 withu0 h s k at some time t this growth occurs despite the hamiltonian s bound onu t h 1 and despite the conservation of the quantityu t l2

h control for descriptor systems a matrix inequalities approach abstract this paper considers the h control problem for descriptor systems that possibly have impulsive modes and or j axis zeros first we propose matrix inequalities that give a generalized stability condition and an h norm condition for descriptor systems using these matrix inequalities we show that the solvability of a set of matrix inequalities is necessary and sufficient to the existence of a proper controller that satisfies a prescribed h norm condition as well as stabilizing the closed loop system and eliminating all impulsive modes these inequalities are equivalent to certain linear matrix inequalities to which we can get solutions whenever they exist using efficient polynomial time algorithms

an abstract birkhoff normal form theorem and exponential type stability of the 1d nls we study stability times for a family of parameter dependent nonlinear schrodinger equations on the circle close to the origin imposing a suitable diophantine condition first introduced by bourgain we prove a rather flexible birkhoff normal form theorem which implies e g exponential and sub exponential time estimates in the sobolev and gevrey class respectively

asymptotic behavior of the nonlinear schrodinger equation with harmonic trapping we consider the cubic nonlinear schrodinger equation with harmonic trapping on d 1 d 5 in the case when all directions but one are trapped aka cigar shaped trap we prove modified scattering and construct modified wave operators for small initial and final data respectively the asymptotic behavior turns out to be a rather vigorous departure from linear scattering and is dictated by the resonant system of the nls equation with full trapping on d 1 in the physical dimension d 3 this system turns out to be exactly the cr equation derived by faou germain and the first author as the large box limit of the resonant nls equation in the homogeneous zero potential setting the special dynamics of the latter equation combined with the above modified scattering results allow us to justify and extend some physical approximations in the theory of bose einstein condensates in cigar shaped traps 2015 wiley periodicals inc

long time stability of small finite gap solutions of the cubic nonlinear schrodinger equation on t2 abstract in this paper we study long time stability of a class of nontrivial quasi periodic solutions depending on one spacial variable of the cubic defocusing non linear schrodinger equation on the two dimensional torus we prove that these quasi periodic solutions are orbitally stable for finite but long times provided that their fourier support and their frequency vector satisfy some complicated but explicit condition which we show holds true for most solutions the proof is based on a normal form result more precisely we expand the hamiltonian in a neighborhood of a quasi periodic solution we reduce its quadratic part to diagonal constant coefficients through a kam scheme and finally we remove its cubic terms with a step of nonlinear birkhoff normal form the main difficulty is to impose second and third order melnikov conditions this is done by combining the techniques of reduction in order of pseudo differential operators with the algebraic analysis of resonant quadratic hamiltonians

robust stabilization for a class of discrete time non linear systems via output feedback the unified lmi approach this paper discusses a robust stabilization problem for a class of multi input and multi output mimo discrete time non linear systems with both state and control inputs containing non linear perturbations the problem is solved via static output feedback and dynamic output feedback respectively a unified approach is used to cast the problem into a convex optimization involving linear matrix inequalities lmi all the controllers can robustly stabilize the systems and maximize the bound on the non linear perturbations this paper also extends the output feedback centralized design approach to a class of discrete time mimo non linear decentralized systems both robust static and dynamic output feedback controllers are obtained

conservative integrators for a toy model of weak turbulence abstract weak turbulence is a phenomenon by which a system generically transfers energy from low to high wave numbers while persisting for all finite time it has been conjectured by bourgain that the 2d defocusing nonlinear schrodinger equation nls on the torus has this dynamic and several analytical and numerical studies have worked towards addressing this point in the process of studying the conjecture colliander keel staffilani takaoka and tao introduced a toy model dynamical system as an approximation of nls which has been subsequently studied numerically in this work we formulate and examine several numerical schemes for integrating this model equation the model has two invariants and our schemes aim to conserve at least one of them we prove convergence in some cases and our numerical studies show that the schemes compare favorably to others such as trapezoidal rule and fixed step fourth order runge kutta the preservation of the invariants is particularly important in the study of weak turbulence as the energy transfer tends to occur on long time scales

analysis of stability robustness for generalized state space systems with structured perturbations abstract a new approach is proposed to analyze the stability robustness of generalized state space systems with structured perturbations the presented method is computationally simple to use and can easily be calculated by computer as far as we are aware this paper seems to be the first one to solve the robust stability problems for generalized state space systems with structured uncertainties the robust stability problem of generalized state space systems is more complicated than that of regular state space systems because it needs consideration of not only stability robustness but also system regularity and impulse elimination the latter two ones need not be considered in regular state space systems

robustness analysis of uncertain linear singular systems with output feedback control the robustness analysis for a linear singular system with uncertain parameters and static output feedback control is considered the problem is transformed into a robust nonsingularity problem based on the linear fractional transformation lft approach the robustness bounds to preserve regularity impulse immunity and stability are found in terms of the structured singular value spl mu with respect to parametric uncertainties the lft approach provides a unified framework for robustness analysis of both uncertain linear continuous discrete time singular systems

on quadratic stability of systems with structured uncertainty this paper considers the problem of stability robustness with respect to a class of nonlinear time varying perturbations which are bounded in a component wise rather than aggregated manner a family of robustness bounds is parameterized in terms of a non singular symmetric matrix it is shown that the problem of computing the largest robustness bound over the set of non singular symmetric matrices can be approximated by a smooth minimization problem over a compact set a convergent algorithm for computing an optimal robustness bound is proposed in the form of a gradient flow

robust stability and stabilization for singular systems with state delay and parameter uncertainty considers the problems of robust stability and stabilization for uncertain continuous singular systems with state delay the parametric uncertainty is assumed to be norm bounded the purpose of the robust stability problem is to give conditions such that the uncertain singular system is regular impulse free and stable for all admissible uncertainties while the purpose of the robust stabilization is to design a state feedback control law such that the resulting closed loop system is robustly stable these problems are solved via the notions of generalized quadratic stability and generalized quadratic stabilization respectively necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are derived a strict linear matrix inequality lmi design approach is developed an explicit expression for the desired robust state feedback control law is also given finally a numerical example is provided to demonstrate the application of the proposed method

state estimation and sliding mode control of markovian jump singular systems this paper is concerned with the state estimation and sliding mode control problems for continuous time markovian jump singular systems with unmeasured states firstly a new necessary and sufficient condition is proposed in terms of strict linear matrix inequality lmi which guarantees the stochastic admissibility of the unforced markovian jump singular system then the sliding mode control problem is considered by designing an integral sliding surface function an observer is designed to estimate the system states and a sliding mode control scheme is synthesized for the reaching motion based on the state estimates it is shown that the sliding mode in the estimation space can be attained in a finite time some conditions for the stochastic admissibility of the overall closed loop system are derived finally a numerical example is provided to illustrate the effectiveness of the proposed theory

an are approach to semi global stabilization of discrete time descriptor linear systems with input saturation the semi global stabilization problem of discrete time descriptor linear systems with input saturation is considered by exploring the properties of the solutions to a class of parametric discrete time riccati equations for discrete time descriptor linear system and their associated feedback gains both the state feedback and output feedback semi global stabilization problem are solved by linear feedback without any system decomposition on the original descriptor linear system a numerical example is used to show the effectiveness of the proposed approach

bilinear estimates and applications to 2d nls the three bilinearities uv uv uv for functions u v r2 0 t 7 c are sharply estimated in function spaces xs b associated to the schrodinger operator i t these bilinear estimates imply local wellposedness results for schrodinger equations with quadratic nonlinearity improved bounds on the growth of spatial sobolev norms of finite energy global in time and blow up solutions of the cubic nonlinear schrodinger equation and certain generalizations are also obtained

unbounded sobolev trajectories and modified scattering theory for a wave guide nonlinear schrodinger equation we consider the following wave guide nonlinear schrodinger equation begin aligned i partial t partial xx vert d y vert u vert u vert 2u end aligned ws on the spatial cylinder mathbb r x times mathbb t y we establish a modified scattering theory between small solutions to this equation and small solutions to the cubic szeg equation the proof is an adaptation of the method of hani et al modified scattering for the cubic schrodinger equation on product spaces and applications 2015 arxiv 1311 2275v3 combining this scattering theory with a recent result by gerard and grellier on the growth of sobolev norms for the cubic szeg equation 2015 we infer existence of global solutions to ws which are unbounded in the space l 2 xh s y mathbb r times mathbb t for every s frac 1 2

growth of sobolev norms for the analytic nls on t2 we consider the completely resonant non linear schrodinger equation on the two dimensional torus with any analytic gauge invariant nonlinearity fix s 1 we show the existence of solutions of this equation which achieve arbitrarily large growth of hs sobolev norms we also give estimates for the time required to attain this growth

cylindrical algebraic decomposition i the basic algorithm given a set of r variate integral polynomials a cylindrical algebraic decomposition cad of euclidean r space e r partitions e r into connected subsets compatible with the zeros of the polynomials by compatible with the zeros of the polynomials we mean that on each subset of e r each of the polynomials either vanishes everywhere or nowhere for example consider the bivariate polynomial y 4 2 y 3 y 2 3 x 2 y 2 x 4

long time instability and unbounded sobolev orbits for some periodic nonlinear schrodinger equations we study the energy cascade problematic for some nonlinear schrodinger equations on mathbb t 2 in terms of the growth of sobolev norms we define the notion of long time strong instability and establish its connection to the existence of unbounded sobolev orbits this connection is then explored for a family of cubic schrodinger nonlinearities that are equal or closely related to the standard polynomial one u 2u most notably we prove the existence of unbounded sobolev orbits for a family of hamiltonian cubic nonlinearities that includes the resonant cubic nls equation a k a the first birkhoff normal form

the growth in time of higher sobolev norms of solutions to schrodinger equations on compact riemannian manifolds abstract in this paper we shall estimate the growing speed for higher sobolev norms of the solutions to schrodinger equations on riemannian manifolds d 2 under some bilinear strichartz estimate assumptions

improved quantitative measures of robustness for multivariable systems asymptotically stable linear systems subject to unstructured time varying perturbations are considered allowable perturbation bounds are obtained such that the perturbed systems remain stable these bounds are derived iteratively by means of adjusting a sequence of lyapunov matrices in comparison with existing methods less conservative quantitative measures of robustness are obtained

optimal bounds for the growth of sobolev norms of solutions of a quadratic szegő equation in this paper we study a quadratic equation on the one dimensional torus involving the szeg projector onto functions with nonnegative frequencies thanks to a lax pair structure we construct a flow on bmo t im which propagates h s regularity for any s 0 whereas the energy level corresponds to s 1 2 then for each s 1 2 we exhibit solutions whose h s norm goes to exponentially fast and we show that this growth is optimal

the weakly nonlinear large box limit of the 2d cubic nonlinear schrodinger equation we consider the cubic nonlinear schrodinger nls equation set on a two dimensional box of size l with periodic boundary conditions by taking the large box limit l to infty in the weakly nonlinear regime characterized by smallness in the critical space we derive a new equation set on r 2 that approximates the dynamics of the frequency modes this nonlinear equation turns out to be hamiltonian and enjoys interesting symmetries such as its invariance under fourier transform as well as several families of explicit solutions a large part of this work is devoted to a rigorous approximation result that allows to project the long time dynamics of the limit equation into that of the cubic nls equation on a box of finite size

comments on improved quantitative measures of robustness for multivariable systems in the above note h g chen and k w han 1994 the robust stability bound of the perturbed linear systems is derived iteratively by means of adjusting a sequence of lyapunov matrices in this short note the author shows that the above result can be improved

interpreting line drawings of curved objects in this thesis we study the problem of interpreting line drawings of scenes composed or opaque regular solid objects bounded by piecewise smooth surfaces with no markings or texture on them it is assumed that the line drawing has been formed by orthographic projection of such a scene under general viewpoint that the line drawing is error free and that there are no lines due to shadows or specularities our definition implicitly excludes laminae wires and the apices of cones a major component of the interpretation of line drawings is line labelling by line labelling we mean a classification of each image curve as corresponding to either a depth or orientation discontinuity in the scene and b further subclassification of each kind of discontinuity for a depth discontinuity we determine whether it is a limb a locus of points on the surface where the line of sight is tangent to the surface or an occluding edge a tangent plane discontinuity of the surface for an orientation discontinuity we determine whether it corresponds to a convex or concave edge this thesis presents the first mathematically rigorous scheme for labelling line drawings of the class of scenes described by analysing the projection of the neighborhoods of different kinds of points on a piecewise smooth surface we are able to catalog all local labelling possibilities for the different types of junctions in a line drawing an algorithm is developed which utilizes this catalog to determine all legal labellings of the line drawing a local minimum complexity rule at each vertex select those labellings which correspond to the minimum number of faces meeting at the vertex is used in order to prune highly counter intuitive interpretations the labelling scheme was implemented and tested on a number of line drawings the labellings obtained are few and by and large in accordance with human interpretations

geometric reasoning for constructing 3d scene descriptions from images abstract there are many applications for a vision system which derives a three dimensional model of a scene from one or more images and stores the model for easy retrieval and matching the derivation of a 3d model of a scene involves transformations between four levels of representation images 2d features 3d structures and 3d geometric models geometric reasoning is used to perform these transformations as well as for the eventual model matching since the image formation process is many to one the problem of deriving 3d features from 2d features is ill constrained additional constraints may be derived from knowledge of the domain from which the images were taken the 3d mosaic system has successfully used domain specific knowledge to drive the geometric reasoning necessary to acquire 3d models for complex real world urban scenes to generalize this approach a framework for the representation and use of domain knowledge for geometric reasoning for vision is proposed

a multi level geometric reasoning system for vision abstract geometry is known to play an important role in image understanding and machine vision geometric reasoning is employed in different forms in model formation and model matching problems in model based vision research geometric representations and reasoning methods are often used implicitly in the design of vision systems and algorithms used there an approach towards model based vision in which geometric and algebraic reasoning is explicit is discussed a multi level reasoning system for machine vision based on this approach is being designed and developed at general electric corporate research and development three key components of this system a hierarchical organization of geometric knowledge for its systematic and efficient use as well as to control the search space labeling algorithms and algebraic reasoning algorithms are presented the use of such a system for deriving a three dimensional model from two dimensional images as well as for using a two dimensional image for matching against another two dimensional image called view consistency problems is discussed

stability analysis and stabilization for nonlinear continuous time descriptor semi markov jump systems this paper investigates the stochastic stability and the state feedback control design for a class of nonlinear continuous time descriptor semi markov jump systems whose transition rates are time varying which are more general than the descriptor markov jump systems first by deriving the infinitesimal generator for stochastic lyapunov functional of descriptor semi markov jump systems a stochastic stability condition is established which guarantees this kind of systems are regular impulse free have a unique solution and are stochastically stable in order to design the state feedback controller a linear matrix inequality lmi stability condition is developed based on the lower and upper bounds of the time varying transition probability and singular value decomposition approach furthermore the state feedback controller design is developed in terms of lmi approach last numerical examples are given to demonstrate the effectiveness of the obtained methods

an algebraic approach to shape from image problems abstract this paper presents a new method for recovering three dimensional shapes of polyhedral objects from their single view images the problem of recovery is formulated in a constrained optimization problem in which the constraints reflect the assumption that the scene is composed of polyhedral objects and the objective function to be minimized is a weighted sum of quadric errors of surface information such as shading and texture for practical purpose it is decomposed into the two more tractable problems a linear programming problem and an unconstrained optimization problem in the present method the global constraints placed by the polyhedron assumption are represented in terms of linear algebra whereas similar constraints have usually been represented in terms of a gradient space moreover superstrictness of the constraints can be circumvented by a new concept position free incidence structure for this reason the present method has several advantages it can recover the polyhedral shape even if image data are incorrect due to vertex position errors it can deal with perspective projection as well as orthographic projection the number of variables in the optimization problem is very small three or a little greater than three and any kinds of surface information can be incorporated in a unifying manner

generalized quadratic stability for continuous time singular systems with nonlinear perturbation this note considers the generalized quadratic stability problem for continuous time singular system with nonlinear perturbation the perturbation is a function of time and system state and satisfies a lipschitz constraint in this work a sufficient condition for the existence and uniqueness of solution to the singular system is firstly presented then by using s procedure and matrix inequality approach a necessary and sufficient condition is presented in terms of linear matrix inequality under which the maximal perturbation bound is obtained to guarantee the generalized quadratic stability of the system that is the system remains exponential stable and the nominal system is regular and impulse free furthermore robust stability for nonsingular systems with perturbation can be obtained as a special case finally the effectiveness of the developed approach for both singular and nonsingular systems is illustrated by numerical examples