further results on infinity norms as lyapunov functions for linear systems this note continues on the results proposed in two previous papers for computing vector 1 or infin norm based lyapunov functions for linear discrete time systems by presenting a finitely terminating algorithm for the construction of lyapunov functions of that class the algorithm utilizes the solution of a finite sequence of feasibility linear programs lps with very few constraints or equivalently very simple algebraic tests in contrast to solving the original problem where a bilinear matrix equation with rank and norm constraint needs to be solved

on matrix structures invariant under toda like isospectral flows abstract we work in the space r n n of n by n real matrices we say that a linear transformation on this space is toda like if it maps symmetric matrices to skew symmetric matrices with such a transformation we associate a bilinear operation defined by x y x y y x where u v uv vu then r n n together with this operation is a usually not associative algebra we call any subalgebra of such an algebra a toda like algebra we classify these algebras which arise in connection with eigenvalue computations we determine the toda like algebras which are of primary interest for this application we accomplish this classification by studying certain difference weighted graphs which we associate with the algebras

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

on matrix differential equations and abstract fg algorithm abstract there is well known relationship between both the isospectral flows and the unitarily self equivalent flows and the abstract fg eigenvalue algorithm namely the values of the isospectral and self equivalent flows at integer times coincide with the iterates of fg algorithm we show that such a relation is characteristic of a whole class of matrix differential equations all these equations are built by means of various representations of an arbitrary lie algebra on k n n

iso spectral deformations of general matrix and their reductions on lie algebras we study an iso spectral deformation of the general matrix which is a natural generalization of the nonperiodic toda lattice equation this deformation is equivalent to the cholesky flow a continuous version of the cholesky algorithm introduced by watkins we prove the integrability of the deformation and give an explicit formula for the solution to the initial value problem the formula is obtained by generalizing the orthogonalization procedure of szego using the formula the solution to the lu matrix factorization can the constructed explicitly based on the root spaces for simple lie algebras we consider several reductions of the equation this leads to generalized toda equations related to other classical semi simple lie algebras which include the integrable systems studied by bogoyavlensky and kostant we show these systems can be solved explicitly in a unified way the behaviors of the solutions are also studied generically there are two types of solutions having either sorting property or blowing up to infinity in finite time

3d free form surface registration and object recognition a new technique to recognise 3d free form objects via registration is proposed this technique attempts to register a free form surface represented by a set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d sensed data points to the model surface represented by another set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d model data points without prior knowledge of correspondence or view points between the two point sets with an initial assumption that the sensed surface be part of a more complete model surface the algorithm begins by selecting three dispersed reliable points on the sensed surface to find the three corresponding model points the method uses the principal curvatures and the darboux frames to restrict the search over the model space invariably many possible model 3 typles will be found for each hypothesized model 3 tuple the transformation to match the sensed 3 tuple to the model 3 tuple can be determined a heuristic search is proposed to single out the optimal transformation in low order time for realistic object recognition or registration where the two range images are often extracted from different view points of the model the earlier assumption that the sensed surface be part of a more complete model surface cannot be relied on with this the sensed 3 tuple must be chosen such that the three sensed points lie on the common region visible to both the sensed and model views we propose an algorithm to select a minimal non redundant set of 3 tuples such that at least one of the 3 tuples will lie on the overlap applying the previous algorithm to each 3 tuple within this set the optimal transformation can be determined experiments using data obtained from a range finder have indicated fast registration for relatively complex test cases if the optimal registrations between the sensed data candidate and each of a set of model data are found then for 3d object recognition purposes the minimal best fit error can be used as the decision rule

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

isospectral flows and abstract matrix factorizations a general framework for constructing isospectral flows in the space operatorname gl n of n by n matrices is proposed depending upon how operatorname gl n is split this framework gives rise to different types of abstract matrix factorizations when sampled at integer times these flows naturally define special iterative processes and each flow is associated with the sequence generated by the corresponding abstract factorization the proposed theory unifies as special cases the well known matrix decomposition techniques used in numerical linear algebra and is likely to offer a broader approach to the general matrix factorization problem

statistical approaches to feature based object recognition this paper examines statistical approaches to model based object recognition evidence is presented indicating that in some domains normal gaussian distributions are more accurate than uniform distributions for modeling feature fluctuations this motivates the development of new maximum likelihood and map recognition formulations which are based on normal feature models these formulations lead to an expression for the posterior probability of the pose and correspondences given an image several avenues are explored for specifying a recognition hypothesis in the first approach correspondences are included as a part of the hypotheses search for solutions may be ordered as a combinatorial search in correspondence space or as a search over pose space where the same criterion can equivalently be viewed as a robust variant of chamfer matching in the second approach correspondences are not viewed as being a part of the hypotheses this leads to a criterion that is a smooth function of pose that is amenable to local search by continuous optimization methods the criteria is also suitable for optimization via the expectation maximization em algorithm which alternates between pose refinement and re estimation of correspondence probabilities until convergence is obtained recognition experiments are described using the criteria with features derived from video images and from synthetic range images

brief paper nonlinear control design for linear differential inclusions via convex hull of quadratics this paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions ldis a recently introduced non quadratic lyapunov function the convex hull of quadratics will be used for the construction of nonlinear state feedback laws design objectives include stabilization with maximal convergence rate disturbance rejection with minimal reachable set and least l 2 gain conditions for stabilization and performances are derived in terms of bilinear matrix inequalities bmis which cover the existing linear matrix inequality lmi conditions as special cases numerical examples demonstrate the advantages of using nonlinear feedback control over linear feedback control for ldis it is also observed through numerical computation that nonlinear control strategies help to reduce control effort substantially

point signatures a new representation for 3d object recognition few systems capable of recognizing complex objects with free form sculptured surfaces have been developed the apparent lack of success is mainly due to the lack of a competent modelling scheme for representing such complex objects in this paper a new form of point representation for describing 3d free form surfaces is proposed this representation which we call the point signature serves to describe the structural neighbourhood of a point in a more complete manner than just using the 3d coordinates of the point being invariant to rotation and translation the point signature can be used directly to hypothesize the correspondence to model points with similar signatures recognition is achieved by matching the signatures of data points representing the sensed surface to the signatures of data points representing the model surface the use of point signatures is not restricted to the recognition of a single object scene to a small library of models instead it can be extended naturally to the recognition of scenes containing multiple partially overlapping objects which may also be juxtaposed with each other against a large model library no preliminary phase of segmenting the scene into the component objects is required in searching for the appropriate candidate model recognition need not proceed in a linear order which can become prohibitive for a large model library for a given scene signatures are extracted at arbitrarily spaced seed points each of these signatures is used to vote for models that contain points having similar signatures inappropriate models with low votes can be rejected while the remaining candidate models are ordered according to the votes they received in this way efficient verification of the hypothesized candidates can proceed by testing the most likely model first experiments using real data obtained from a range finder have shown fast recognition from a library of fifteen models whose complexities vary from that of simple piecewise quadric shapes to complicated face masks results from the recognition of both single object and multiple object scenes are presented

criteria for robust absolute stability of time varying nonlinear continuous time systems the present paper establishes results for the robust absolute stability of a class of nonlinear continuous time systems with time varying matrix uncertainties of polyhedral type and multiple time varying sector nonlinearities by using the variational method and the lyapunov second method criteria for robust absolute stability are obtained in different forms for the given class of systems specifically the parametric classes of lyapunov functions are determined which define the necessary and sufficient conditions of robust absolute stability the piecewise linear lyapunov functions of the infinity vector norm type are applied to derive an algebraic criterion for robust absolute stability in the form of solvability conditions of a set of matrix equations several simple sufficient conditions of robust absolute stability are given which become necessary and sufficient for special cases two examples are presented as applications of the present results to a particular second order system and to a specific class of systems with time varying interval matrices in the linear part

lie algebra representations nilpotent matrices and the c numerical range abstract in this paper we survey some applications of the representation theory of lie algebras to linear algebra this includes the derivation of the jordan form for tensor products of invertible matrices the study of normal form problems for nilpotent matrices as well as the derivation of explicit formulas for the c numerical radius of certain nilpotent block shift matrices arising in quantum mechanics and nuclear magnetic resonance nmr spectroscopy in this latter case a conjecture concerning an explicit formula for the c numerical radius is stated we show the existence of unitary transformations that realize the prospective maxima our approach depends on the clebsch gordan decomposition for unitary representations of su 2 c

on infinity norms as lyapunov functions for linear systems the note presents a construction of the lyapunov function defined by l sub spl infin sup n vector norm for both continuous and discrete time linear systems in contrast to the previous results no restrictions on the positions or multiplicity of system matrix eigenvalues are required

switching controller design via convex polyhedral lyapunov functions in this paper we propose a systematic switching control design method for a class of nonlinear discrete time hybrid systems the novelty of the adopted approach is in the fact that unlike conventional control the control burden is shifted to a logical level thus creating the need for the development of new analysis design methods

general isospectral flows for linear dynamic systems the matrix a a0 a1 2a2 kak lal with matrix coefficients a0 a1 a2 al cm n defines a linear dynamic system of dimension m n when m n and when det a 0 for some values of the eigenvalues of this system are well defined a one parameter trajectory of such a system a0 a1 a2 al is an isospectral flow if the eigenvalues and the dimensions of the associated eigenspaces are the same for all parameter values ir this paper presents the most general form for isospectral flows of linear dynamic systems of orders l 2 3 4 and the forms for isospectral flows for even higher order systems are evident from the patterns emerging based on the definition of a class of coordinate transformations called structure preserving transformations the concept of isospectrality and the associated flows is seen to extend to cases where m n

zero preserving iso spectral flows based on parallel sums abstract driessel k r driessel computing canonical forms using flows linear algebra appl 379 2004 353 379 introduced the notion of quasi projection onto the range of a linear transformation from one inner product space into another inner product space here we introduce the notion of quasi projection onto the intersection of the ranges of two linear transformations from two inner product spaces into a third inner product space as an application we design a new family of iso spectral flows on the space of symmetric matrices that preserves zero patterns we discuss the equilibrium points of these flows we conjecture that these flows generically converge to diagonal matrices we perform some numerical experiments with these flows which support this conjecture we also compare our zero preserving flows with the toda flow

on the continuous realization of iterative processes many important mathematical problems are solved by iterative methods many of these iterative schemes may be regarded as the discrete realization of certain continuous dynamical systems this paper summarizes some of the recent developments in the continuous realization of several popular basic iterative methods

isospectral flows that preserve matrix structure abstract the matrix a a ij s n is said to lie on a strict undirected graph g if a ij 0 i j whenever i j is not in e g if s is skew symmetric the isospectral flow a t a s maintains the spectrum of a we consider isospectral flows that maintain a matrix a t on a given graph g we review known results for a graph g that is a generalised path and construct isospectral flows for a generalised ring and a star and show how a flow may be constructed for a general graph the analysis may be applied to the isospectral problem for a lumped mass finite element model of an undamped vibrating system in that context it is important that the flow maintain other properties such as irreducibility or positivity and we discuss whether they are maintained

scaled toda like flows abstract this paper discusses the class of isospectral flows x x a x where denotes the hadamard product and is the lie bracket the presence of a allows arbitrary and independent scaling for each element in the matrix x the time 1 mapping of the scaled toda like flow still enjoys a qr like iteration the scaled structure includes the classical toda flow brockett s double bracket flow and other interesting flows as special cases convergence proof is thus unified and simplified the effect of scaling on a variety of applications is demonstrated by examples

lyapunov function construction by linear programming in this paper the lyapunov function given by the infinity norm is considered a new proof of the theorem of molchanov and pyatintskii 1986 is given the presented proof enables us to give an explicit calculation of the matrix which was only demonstrated to exist in the original paper combining the obtained result with the idea of scaling faces of a polytope gives the method of fitting the shape of level surfaces of the lyapunov function given by the infinity norm to the specified demands

using spin images for efficient object recognition in cluttered 3d scenes we present a 3d shape based object recognition system for simultaneous recognition of multiple objects in scenes containing clutter and occlusion recognition is based on matching surfaces by matching points using the spin image representation the spin image is a data level shape descriptor that is used to match surfaces represented as surface meshes we present a compression scheme for spin images that results in efficient multiple object recognition which we verify with results showing the simultaneous recognition of multiple objects from a library of 20 models furthermore we demonstrate the robust performance of recognition in the presence of clutter and occlusion through analysis of recognition trials on 100 scenes

registration of 3d points using geometric algebra and tensor voting we address the problem of finding the correspondences of two point sets in 3d undergoing a rigid transformation using these correspondences the motion between the two sets can be computed to perform registration our approach is based on the analysis of the rigid motion equations as expressed in the geometric algebra framework through this analysis it was apparent that this problem could be cast into a problem of finding a certain 3d plane in a different space that satisfies certain geometric constraints in order to find this plane in a robust way the tensor voting methodology was used unlike other common algorithms for point registration like the iterated closest points algorithm ours does not require an initialization works equally well with small and large transformations it cannot be trapped in local minima and works even in the presence of large amounts of outliers we also show that this algorithm is easily extended to account for multiple motions and certain non rigid or elastic transformations

positively invariant polyhedral sets of discrete time linear systems the problem of the existence of positively invariant polyhedral sets for linear discrete time dynamical systems is studied in the first part of the paper necessary and sufficient conditions for a

fast parametric elastic image registration we present an algorithm for fast elastic multidimensional intensity based image registration with a parametric model of the deformation it is fully automatic in its default mode of operation in the case of hard real world problems it is capable of accepting expert hints in the form of soft landmark constraints much fewer landmarks are needed and the results are far superior compared to pure landmark registration particular attention has been paid to the factors influencing the speed of this algorithm the b spline deformation model is shown to be computationally more efficient than other alternatives the algorithm has been successfully used for several two dimensional 2 d and three dimensional 3 d registration tasks in the medical domain involving mri spect ct and ultrasound image modalities we also present experiments in a controlled environment permitting an exact evaluation of the registration accuracy test deformations are generated automatically using a random hierarchical fractional wavelet based generator

the cal d q r algorithm basic theory convergence and conditional stability we describe a fast matrix eigenvalue algorithm that uses a matrix factorization and reverse order multiply technique involving three factors and that is based on the symmetric matrix factorization as well as on d orthogonal reduction techniques where d mbox diag pm1 is computed from the given matrix a it operates on a similarity reduction of a real matrix a nn to general tridiagonal form t and computes all of a s eigenvalues in frac 4 3 n 3 o n 2 operations where the o n 2 part of the operations is possibly performed over bbb c instead of the 7 8 n 3 real flops required by the qr eigenvalue algorithm potential breakdo wn of the dqr algorithm can occur in the reduction to tridiagonal form and in the d orthogonal dqr reductions both however can be monitored during the computations the former occurs rather rarely for dimensions n leq 300 and can essentially be bypassed while the latter is extremely rare and can be bypassed as well in our conditionally stable implementation of the dqr steps we prove an implicit dq theorem which allows implicit shifts give a convergence proof for the dqr algorithm and show that dqr is conditionally stable for general balanced tridiagonal matrices t rm b

necessary and sufficient stability condition for second order switched systems a phase function approach abstractto find a unified approach for the stability analysis of second order switched system the concept of phase function is proposed in this paper first the basic properties of phase function are explored following this concept and its properties the phase based stability criterion is investigated based on the lyapunov theory and a necessary and sufficient stability condition is obtained in the phase function approach moreover the connection between phase based stability conditions and algebraic condition of system matrices is also discussed finally numerical examples are provided to exemplify the main result and make necessary comparisons with the existing methods

positively invariant sets for constrained continuous time systems with cone properties this note deals with some properties of particular bounded sets w r t linear continuous time systems described by x spl dot t a 0 x t c t where c t spl isin spl omega spl sub r sup n spl omega a compact set and matrix e sup ta 0 has the property of leaving a proper cone k positively invariant that is e sup ta 0 k spl sub k the considered bounded sets spl dscr k a b are described as the intersection of shifted cones necessary and sufficient conditions are given they guarantee that such sets are positively invariant w r t the considered system the trajectories starting from x sub 0 spl isin r sup n spl dscr k a b respectively to x sub 0 spl isin r sup n are studied in terms of attractivity and contractivity of the set spl dscr k a b the results are applied to the study of the constrained state feedback regulator problem

a numerical technique for the stability analysis of linear switched systems in this paper the ray gridding approach a new numerical technique for the stability analysis of linear switched systems is presented it is based on uniform partitions of the state space in terms of ray directions which allow refinable families of polytopes of adjustable complexity to be examined for invariance in this framework the existence of a polyhedral lyapunov function that is common to a family of asymptotically stable subsystems can be checked efficiently via simple iterative algorithms the technique can be used to prove the stability of switched linear systems classes of linear time varying systems and linear differential lnclusions we also present preliminary results on another related problem namely the construction of multiple polyhedral lyapunov functions for the specification of stabilizing switching sequences for a switched system constructed from a family of stable linear subsystems

isospectral matrix flow maintaining staircase structure and total positivity of an initial matrix abstract in this paper we introduce an isospectral matrix flow lax flow that preserves some structures of an initial matrix this flow is given by d a d t a u a l a a 0 a 0 where a is a real n n matrix not necessarily symmetric a b a b b a is the matrix commutator also known as the lie bracket a u is the strictly upper triangular part of a and a l is the strictly lower triangular part of a we prove that if the initial matrix a 0 is staircase so is a t moreover we prove that this flow preserves the certain positivity properties of a 0 also we prove that if the initial matrix a 0 is totally positive or totally nonnegative with non zero codiagonal elements and distinct eigenvalues then the solution a t converges to a diagonal matrix while preserving the spectrum of a 0 some simulations are provided to confirm the convergence properties

stability and invariance analysis of uncertain discrete time piecewise affine systems this note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non invariant set x of states the approach relies on introducing fake dynamics outside x and on synthesizing a piecewise affine and possibly discontinuous lyapunov function via linear programming the existence of such a function proves stability properties of the original system and allows the determination of a region of attraction contained in x the procedure is particularly useful in practical applications for analyzing the stability of piecewise affine control systems that are only defined over a bounded subset x of the state space and to determine whether for a given set of initial conditions the trajectories of the state vector remain within the domain x

isospectral flows preserving some centrosymmetric structures abstract let g be a simple undirected graph no loops no multiple edges on n vertices let s n be the set of real symmetric matrices of order n a matrix a a i j s n is said to be a matrix on g if a i j 0 whenever i j and the vertices i j of g are not joined by an edge of g we recall that if f is a skew symmetric operator on s n then the solution a t of d a d t a f a a 0 a 0 s n maintains the spectrum of a0 the matrix a s n is said to be centrosymmetric if jaj a where j is the matrix with ones on the secondary diagonal and zeros elsewhere centrosymmetric matrices are symmetric about the secondary diagonal centrosymmetric matrices appear in fields such as finite element analysis we construct an isospectral flow on a graph g with the property that if a0 is centrosymmetric so is a t and discuss the limit of a t as t

the projected gradient methods for least squares matrix approximations with spectral constraints the problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure this paper describes a general procedure in using the projected gradient method it is shown that the projected gradient of the objective function on the manifold of constraints usually can be formulated explicitly this gives rise to the construction of a descent flow that can be followed numerically the explicit form also facilitates the computation of the second order optimality conditions examples of applications are discussed with slight modifications the procedure can be extended to solve least squares problems for general matrices subject to singular value constraints

brief on absolute stability analysis by polyhedral lyapunov functions this paper addresses the problem of computing a polyhedral lyapunov function plf for a linear differential inclusion ldi a numerically efficient algorithm is presented to compute a plf for an ldi it is also pointed out that for the case of a polyhedron defined by vertices rather than by faces one can state algebraic stability conditions analogous to those given by molchanov and pyatnitskiy 1986

self similar flows abstract large classes of self similar isospectral flows can be viewed as continuous analogues of certain matrix eigenvalue algorithms in particular there exist families of flows associated with the qr lr and cholesky eigenvalue algorithms this paper uses lie theory to develop a general theory of self similar flows which includes the qr lr and cholesky flows as special cases also included are new families of flows associated with the sr and hr eigenvalue algorithms the basic theory produces analogues of unshifted single step eigenvalue algorithms but it is also shown how the theory can be extended to include flows which are continuous analogues of shifted and multiple step eigenvalue algorithms

structural indexing efficient 3 d object recognition the authors present an approach for the recognition of multiple 3 d object models from three 3 d scene data the approach uses two different types of primitives for matching small surface patches where differential properties can be reliably computed and lines corresponding to depth or orientation discontinuities these are represented by splashes and 3 d curves respectively it is shown how both of these primitives can be encoded by a set of super segments consisting of connected linear segments these super segments are entered into a table and provide the essential mechanism for fast retrieval and matching the issues of robustness and stability of the features are addressed in detail the acquisition of the 3 d models is performed automatically by computing splashes in highly structured areas of the objects and by using boundary and surface edges for the generation of 3 d curves the authors present results with the current system 3 d object recognition based on super segments and discuss further extensions

design of stabilizing switching control laws for discrete and continuous time linear systems using piecewise linear lyapunov functions in this paper the stability of switched linear systems is investigated using piecewise linear lyapunov functions in particular we identify classes of switching sequences that result in stable trajectories given a switched linear system we present a systematic methodology for computing switching laws that guarantee stability based on the matrices of the system in the proposed approach we assume that each individual subsystem is stable and admits a piecewise linear lyapunov function based on these lyapunov functions we compose global lyapunov functions that guarantee stability of the switched linear system a large class of stabilizing switching sequences for switched linear systems is characterized by computing conic partitions of the state space the approach is applied to both discrete time and continuous time switched linear systems

further comments on vector norms as lyapunov functions for linear systems this paper deals with the conditions for a vector norm to be a lyapunov function for a linear time invariant system an error in the proof of the related theorem given in hmamed 1994 is pointed out and a counterexample proving that this theorem is generally false is provided it is demonstrated that the considered problem is related to the one of extending a linear operator without increasing its norm

constrained regulation of linear continuous time dynamical systems abstract in this paper the linear constrained regulation problem lcrp for continuous time dynamical systems is studied the first part of the paper deals with the existence of linear state feedback control laws that transfer asymptotically to the origin all initial states belonging to a given polyhedral subset of the state space while respecting linear constraints on both state and control vectors then the lcrp is formulated as an optimization problem which can be solved by applying linear programming techniques

comprehensive lyapunov functions for linear switching systems abstract for a linear dynamical switching system we analyse maximal asymptotic growth of trajectories depending on the initial point both discrete and continuous time systems in r d are considered we prove the existence of a lyapunov norm in r d with the following property for every invariant linear subspace l r d of the system the restriction of the norm on l provides a tight upper bound for the growth of trajectories on l for this we introduce the concept of the spectral normal form of a family of matrices properties of the comprehensive lyapunov norms are analysed and methods of their construction are discussed

destabilizing strategies for uncertain linear systems the paper the problem of determining destabilizing strategies for uncertain linear systems was researched sufficient conditions for the existence of a destabilizing strategy were presented and an algorithm for computation of the destabilizing strategy was given the approach elaborated in the paper develops some of the previous results which did not provide methods for calculation of destabilizing switching

a continuous jacobi like approach to the simultaneous reduction of real matrices abstract the problem of simultaneous reduction of real matrices by either orthogonal similarity or orthogonal equivalence transformations is considered based on the jacobi idea of minimizing the sum of squares of the complementary part of the desired form to which matrices are reduced the projected gradient method is used in this paper it is shown that the projected gradient of the objective function can be formulated explicitly this gives rise to a system of ordinary differential equations that can be readily solved by numerical software the advantages of this approach are that the desired form to which matrices are reduced can be almost arbitrary and that if a desired form is not attainable then the limit point of the corresponding differential equation gives a way of measuring the distance from the best reduced matrices to the nearest matrices that have the desired form the general procedure for deriving these differential equations is discussed the framework can be generalized to the complex valued case some applications are given

a convex condition for robust stability analysis via polyhedral lyapunov functions in this paper we study the robustness analysis problem for linear continuous time systems subject to parametric time varying uncertainties making use of piecewise linear polyhedral lyapunov functions a given class of lyapunov functions is said to be universal for the uncertain system under consideration if the robust stability of the system is equivalent to the existence of a lyapunov function belonging to the class in the literature it has been shown that the class of polyhedral functions is universal while for instance the class of quadratic functions is not this fact justifies the effort of developing efficient algorithms for the construction of polyhedral lyapunov functions in this context we provide a low computational cost procedure based on a novel convex condition for the construction of a polyhedral lyapunov function in the section on the numerical examples we consider some benchmark problems for the robust stability analysis and we show that the proposed low computational cost approach though only sufficient is less conservative than all the other approaches presented so far in the literature

robust point correspondence applied to two and three dimensional image registration accurate and robust correspondence calculations are very important in many medical and biological applications often the correspondence calculation forms part of a rigid registration algorithm but accurate correspondences are especially important for elastic registration algorithms and for quantifying changes over time in this paper a new correspondence calculation algorithm csm correspondence by sensitivity to movement is described a robust corresponding point is calculated by determining the sensitivity of a correspondence to movement of the point being matched if the correspondence is reliable a perturbation in the position of this point should not result in a large movement of the correspondence a measure of reliability is also calculated this correspondence calculation method is independent of the registration transformation and has been incorporated into both a 2d elastic registration algorithm for warping serial sections and a 3d rigid registration algorithm for registering pre and postoperative facial range scans these applications use different methods for calculating the registration transformation and accurate rigid and elastic alignment of images has been achieved with the csm method it is expected that this method will be applicable to many different applications and that good results would be achieved if it were to be inserted into other methods for calculating a registration transformation from correspondences

vector norms as lyapunov functions for linear systems a unified theory of quadratic and piecewise linear lyapunov functions for continuous and discrete time linear systems is presented the key to this work is the description of these lyapunov functions by vector norms the main results are sufficient and necessary conditions for a vector norm to be a lyapunov function as well as a method based on these conditions of constructing such lyapunov functions