controlled invariance for discrete time nonlinear systems with an application to the disturbance decoupling problems invariant distributions are defined for discrete time nonlinear control systems and necessary and sufficient conditions are given for their controlled invariance this extends to discrete time systems the basic tool which has been so important in solving the various synthesis problems for continuous time systems to indicate their utility in the discrete time setting they are used to locally solve the disturbance decoupling problem

self calibration of a 1d projective camera and its application to the self calibration of a 2d projective camera we introduce the concept of self calibration of a 1d projective camera from point correspondences and describe a method for uniquely determining the two internal parameters of a 1d camera based on the trifocal tensor of three 1d images the method requires the estimation of the trifocal tensor which can be achieved linearly with no approximation unlike the trifocal tensor of 2d images and solving for the roots of a cubic polynomial in one variable interestingly enough we prove that a 2d camera undergoing planar motion reduces to a 1d camera from this observation we deduce a new method for self calibrating a 2d camera using planar motions both the self calibration method for a 1d camera and its applications for 2d camera calibration are demonstrated on real image sequences

recursive identification using feedforward neural networks the paper is concerned with the identification of an unknown nonlinear dynamical system when only the inputs and outputs are accessible for measurement under certain assumptions it is shown that generically the system can be realized by a recursive input output model furthermore relying on the approximation properties of neural networks and the existence of effective training algorithms it is demonstrated how an effective identification model can be constructed simulation results are presented to complement the theoretical discussions

analysis of discrete time linear switched systems a variational approach a powerful approach for analyzing the stability of continuous time switched systems is based on using tools from optimal control theory to characterize the most unstable switching law this reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific most unstable switching law more generally this so called variational approach was successfully applied to derive nice reachability type results for both linear and nonlinear continuous time switched systems motivated by this we develop in this paper an analogous approach for discrete time linear switched systems we derive and prove a necessary condition for optimality of the most unstable switching law this yields a type of discrete time maximum principle mp we demonstrate by an example that this mp is in fact weaker than its continuous time counterpart to overcome this we introduce the auxiliary system of a discrete time linear switched system and show that regularity properties of time optimal controls for the auxiliary system imply nice reachability results for the original discrete time linear switched system using this approach we derive several new lie algebraic conditions guaranteeing nice reachability results these results and their proofs turn out to be quite different from their continuous time counterparts

smooth time varying stabilization of driftless systems over communication channels abstract we address the problem of smooth time varying stabilization of port interconnected driftless passive systems the benchmark that we study is reminiscent of driftless systems interconnected over communication channels and constitutes a generalization of the well known chained form nonholonomic systems our contribution consists in proposing a smooth time varying controller that guarantees uniform global asymptotic stability moreover a necessary condition is also stated both the sufficient and necessary conditions are formulated in terms of the so called persistency of excitation previously used in set point control of nonholonomic systems the proof of sufficiency relies on a recently reported extended matrosov s theorem which may be regarded as an extension of krasovski i la salle s invariance principle to the case of nonautonomous systems

ergodic theorems for discrete time stochastic systems using a stochastic lyapunov function sufficient conditions are established under which the law of large numbers and related ergodic theorems hold for nonlinear stochastic systems operating under feedback it is shown that these conditions hold whenever a moment condition is satisfied this may be interpreted as a generalizaton of the martingale property if in addition a stochastic controllability condition holds then it is shown that the underlying distributions governing the system converge to an invariant probability at a geometric rate the key assumption used is that a markov chain with stationary transition probabilities exists that serves as a state process for the closed loop system

minimal realization of nonlinear systems described by input output difference equations we consider a general class of nonlinear discrete time systems described by their input output i o relationship we first present the necessary and sufficient conditions for existence of a local observable state space realization of the system and an explicit algorithm for computing it in cases where the i o map and its resulting realization are nonminimal we formulate an algorithm for extracting its minimal realization whenever possible the developed theory and algorithms are illustrated by means of several examples

on uncontrollable discrete time bilinear systems which are nearly controllable in this note for a class of uncontrollable discrete time bilinear systems it is shown that the controllable region nearly covers the whole space while the uncontrollable region is only a hypersurface as a result for almost any initial state and any terminal state of the system the former can be transferred to the latter in addition the two dimensional controllability counterexamples in are generalized to arbitrary finite dimensional cases

asymptotic stability and stabilizability of special classes of discrete time positive switched systems abstract in this paper we consider discrete time positive switched systems switching among autonomous subsystems characterized either by monomial matrices or by circulant matrices necessary and sufficient conditions are provided guaranteeing either global uniform asymptotic stability or stabilizability i e the possibility of driving to zero the state trajectory corresponding to any initial state by resorting to some switching sequence such conditions lead to simple algorithms that allow to easily detect under suitable conditions whether a given positive switched system is not stabilizable

on near controllability and stabilizability of a class of discrete time bilinear systems in this paper the near controllability and stabilizability of a class of discrete time bilinear systems are studied a necessary and sufficient condition for the near controllability of the systems is first derived then on the basis of the corresponding near controllability criterion the stabilizability problem of the systems is solved in turn

two way ambiguity in 2d projective reconstruction from three uncalibrated 1d images we show that there is in general a two way ambiguity for 2d projective reconstruction from three uncalibrated 1d views independent of the number of point correspondences the two distinct projective reconstructions are exactly related by a quadratic transformation with the three camera centers as fundamental points unique 2d reconstruction is possible only when the three camera centers are aligned by carlsson duality 1995 there is a dual two way ambiguity for 2d projective reconstruction from six point correspondences independent of the number of 1d views the theoretical results are demonstrated on numerical examples

on controllability and near controllability of discrete time inhomogeneous bilinear systems without drift in this paper controllability and near controllability of discrete time inhomogeneous bilinear systems without drift are studied necessary and sufficient conditions for controllability and near controllability of the systems are respectively presented in particular algorithms for computing the control inputs to achieve the transition of a given pair of states for the controllable systems and nearly controllable systems are also provided examples are shown to demonstrate the conceptions and results of the paper

invariant codistributions and the feedforward form for discrete time nonlinear systems the goal of this paper is two fold first given an arbitrary n dimensional discrete time nonlinear dynamical system necessary and sufficient conditions for the existence of a one dimensional invariant codistribution are obtained second it is shown that the previous conditions can be used iteratively to obtain a nested sequence of n invariant codistributions with the properties that each codistribution contains the previous one and the last one coincides with the cotangent bundle of the state manifold as a byproduct necessary and sufficient conditions are obtained for a discrete time nonlinear dynamical system to be equivalent to the so called feedforward form

minimum time control of boolean networks boolean networks bns are discrete time dynamical systems with boolean state variables bns have recently been attracting considerable interest as computational models for biological systems and in particular gene regulating networks boolean control networks bcns are boolean networks with boolean inputs we consider the problem of steering a bcn from a given state to a desired state in minimal time using the algebraic state space representation assr of bcns we derive several necessary conditions stated in the form of maximum principles mps for a control to be time optimal in the assr every state and input vector is a canonical vector using this special structure yields an explicit state feedback formula for all time optimal controls to demonstrate the theoretical results we develop a bcn model for the genetic switch controlling the lambda phage development upon infection of a bacteria our results suggest that this biological switch is designed in a way that guarantees minimal time respon

brief paper a second order maximum principle for discrete time bilinear control systems with applications to discrete time linear switched systems a powerful approach for analyzing the stability of continuous time switched systems is based on using optimal control theory to characterize the most unstable switching law this reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific most unstable switching law for discrete time switched systems the variational approach received considerably less attention this approach is based on using a first order necessary optimality condition in the form of a maximum principle mp and typically this is not enough to completely characterize the most unstable switching law in this paper we provide a simple and self contained derivation of a second order necessary optimality condition for discrete time bilinear control systems this provides new information that cannot be derived using the first order mp we demonstrate several applications of this second order mp to the stability analysis of discrete time linear switched systems

on near controllability nearly controllable subspaces and near controllability index of a class of discrete time bilinear systems a root locus approach this paper studies near controllability of a class of discrete time bilinear systems via a root locus approach a necessary and sufficient criterion for the systems to be nearly controllable is given in particular by using the root locus approach the control inputs which achieve the state transition for the nearly controllable systems can be computed furthermore for the non nearly controllable systems nearly controllable subspaces are derived and near controllability index is defined accordingly the controllability properties of such a class of discrete time bilinear systems are fully characterized finally examples are provided to demonstrate the results of the paper

discrete time transitivity and accessibility analytic systems a basic open question for discrete time nonlinear systems is that of determining when in analogy with the classical continuous time positive form of chow s lemma accessibility follows from transitivity of a natural group action this paper studies the problem and establishes the desired implication for analytic systems in several cases i compact state space ii under a poisson stability condition and iii in a generic sense in addition the paper studies accessibility properties of the controllability sets recently introduced in the context of dynamical systems studies finally various examples and counterexamples are provided relating the various lie algebras introduced in past work

non linear non interacting control with stability in discrete time a geometric framework the aim of the paper is to set the non linear non interacting control problem with stability in discrete time in a correct geometric framework so providing a solution which recalls the continuous approach and to point out the peculiarities of discrete time dynamics geometric necessary and sufficient conditions for the solvability of the problem are given and a constructive method figures out the regular static state feedback solution it is shown that if the given dynamics is feedback equivalent to a decoupled system characterized by an invertible drift the computation of the distributions involved can be carried out in a simple and elegant way the main results are thus proved exhaustively in this case and then generalized to submersive systems

brief paper controllability of boolean control networks via the perron frobenius theory boolean control networks bcns are recently attracting considerable interest as computational models for genetic and cellular networks addressing control theoretic problems in bcns may lead to a better understanding of the intrinsic control in biological systems as well as to developing suitable protocols for manipulating biological systems using exogenous inputs we introduce two definitions for controllability of a bcn and show that a necessary and sufficient condition for each form of controllability is that a certain nonnegative matrix is irreducible or primitive respectively our analysis is based on a result that may be of independent interest namely a simple algebraic formula for the number of different control sequences that steer a bcn between given initial and final states in a given number of time steps while avoiding a set of forbidden states

observability of autonomous discrete time non linear systems a geometric approach in this paper the observability of autonomous discrete time systems is studied from a purely differential geometric point of view as with continuous time systems this approach leads to a local canonical form for an observable system a proposal for the generalization of an invariant subspace is made

stabilisation of discrete time bilinear systems by constant control inputs abstractin this paper the stabilisation problem of discrete time bilinear systems by using constant control inputs is considered it is shown that the spectrum of a matrix derived from the system

affine structure from line correspondences with uncalibrated affine cameras this paper presents a linear algorithm for recovering 3d affine shape and motion from line correspondences with uncalibrated affine cameras the algorithm requires a minimum of seven line correspondences over three views the key idea is the introduction of a one dimensional projective camera this converts 3d affine reconstruction of line directions into 2d projective reconstruction of points in addition a line based factorization method is also proposed to handle redundant views experimental results both on simulated and real image sequences validate the robustness and the accuracy of the algorithm

invariants of six points and projective reconstruction from three uncalibrated images there are three projective invariants of a set of six points in general position in space it is well known that these invariants cannot be recovered from one image however an invariant relationship does exist between space invariants and image invariants this invariant relationship is first derived for a single image then this invariant relationship is used to derive the space invariants when multiple images are available this paper establishes that the minimum number of images for computing these invariants is three and the computation of invariants of six points from three images can have as many as three solutions algorithms are presented for computing these invariants in closed form the accuracy and stability with respect to image noise selection of the triplets of images and distance between viewing positions are studied both through real and simulated images applications of these invariants are also presented both the results of faugeras 1992 and hartley et al 1992 for projective reconstruction and sturm s method 1869 for epipolar geometry determination from two uncalibrated images with at least seven points are extended to the case of three uncalibrated images with only six points

on controllability near controllability controllable subspaces and nearly controllable subspaces of a class of discrete time multi input bilinear systems abstract this paper considers a class of discrete time multi input inhomogeneous bilinear systems the structure of such systems is most close to linear time invariant systems but they own a strong property that is if the systems are uncontrollable they can still be nearly controllable necessary and sufficient conditions for controllability and near controllability of the systems are established by using a classical decomposition furthermore a geometric characterization is given for the systems such that controllable subspaces and nearly controllable subspaces are derived and characterized similar results on controllability are also obtained for the continuous time counterparts of the systems finally examples are provided to demonstrate the conceptions and results of this paper

control of systems without drift via generic loops this paper proposes a simple numerical technique for the steering of arbitrary analytic systems with no drift it is based on the generation of nonsingular loops which allow linearized controllability along suitable trajectories once such loops are available it is possible to employ standard newton or steepest descent methods as classically done in numerical control the theoretical justification of the approach relies on results establishing the genericity of nonsingular controls as well as a simple convergence lemma

controllability and near controllability of a class of discrete time inhomogeneous bilinear systems in this paper a class of discrete time inhomogeneous bilinear systems whose controllability cannot be checked by the classical results is considered by using an algebraic technique it is shown t

commutative algebraic methods for controllability of discrete time polynomial systems abstractin this paper we consider controllability of discrete time polynomial systems first we present a forward accessibility local reachability condition that can be verified in finite time in contrast to conventional conditions second we give a backward accessibility local controllability condition for an invertible system and a condition to verify invertibility finally we derive sufficient conditions to test whether the forward accessible system is reachable and to test the backward accessible system is controllable

controllability of nonlinear discrete time systems a lie algebraic approach this paper presents a geometric study of controllability for discrete time nonlinear systems various accessibility properties are characterized in terms of lie algebras of vector fields some of the results obtained are parallel to analogous ones in continuous time but in many respects the theory is substantially different and many new phenomena appear

on controllability of discrete time bilinear systems by near controllability abstract in this paper controllability of discrete time bilinear systems is studied by applying a recent result on near controllability a new sufficient condition for controllability of the systems is presented where controllability is proved by approximation with near controllability the new condition is algebraically verifiable and is hence easy to apply compared with a classical result on controllability of discrete time bilinear systems which can be effective even when the classical result does not work furthermore the control inputs to achieve the transition of the systems between any given pair of states are approximately computable according to near controllability therefore near controllability can be used to not only better characterize the system properties but also prove controllability with computable control inputs the new condition is then generalized to derive similar results on controllability and near controllability of the systems finally examples are given to illustrate the results of this paper

from chronological calculus to exponential representations of continuous and discrete time dynamics a lie algebraic approach in this paper formal exponential representations of the solutions to nonautonomous nonlinear differential equations are derived it is shown that the chronological exponential admits an ordinary exponential representation the exponent being given by an explicitly computable lie series expansion the results are then used to describe controlled dynamics dynamics under sampling and forced discrete time dynamics the study emphasizes the role of lie algebra techniques in nonlinear control theory and specifies structural similarities between nonautonomous differential equations dynamics under sampling and forced discrete time dynamics up to hybrid ones

partial controllability concepts the main results in theory of controllability are formulated for deterministic or stochastic control systems given in a standard form i e given as a first order differential equation driven by an infinitesimal generator of strongly continuous semigroup in an abstract hilbert or banach space and disturbed by a deterministic function or by a white noise process at the same time some deterministic or stochastic linear systems can be written in a standard form if the state space is enlarged respectively the ordinary controllability conditions for them are too strong since they assume extended state space it is reasonable to introduce partial controllability concepts which assume original state space in this paper we study necessary and sufficient conditions of partial controllability for deterministic and stochastic linear control systems given in a standard form and their implications to particular cases

new bad lines in r x y and optimization of the epimorphism theorem we give necessary and sufficient conditions on a commutative ring with unity r so that the following holds any polynomial f in r x y such that r x y f similar or equal to r 1 a line for short is a variable alpha x for some automorphism alpha r x y r x y the main ingredient here is the construction of new bad lines lines which are not variables

brief paper explicit construction of a barabanov norm for a class of positive planar discrete time linear switched systems we consider the stability under arbitrary switching of a discrete time linear switched system a powerful approach for addressing this problem is based on studying the most unstable switching law musl if the solution of the switched system corresponding to the musl converges to the origin then the switched system is stable for any switching law the musl can be characterized using optimal control techniques this variational approach leads to a hamilton jacobi bellman equation describing the behavior of the switched system under the musl the solution of this equation is sometimes referred to as a barabanov norm of the switched system although the barabanov norm was studied extensively it seems that there are few examples where it was actually computed in closed form in this paper we consider a special class of positive planar discrete time linear switched systems and provide a closed form expression for a corresponding barabanov norm and a musl the unit circle in this norm is a parallelogram

on the solvability of polynomial systems arising in control we consider a compactification of a general system of polynomial equations in weighted projective space and give some sufficient conditions about the solvability of a polynomial system over c and r we also prove that for generic linear subspaces the inverse eigenvalue problem with perturbations in the linear subspace always has n solutions

on small controllability and controllability of a class of nonlinear systems in this paper small controllability and controllability of a class of nonlinear systems are studied both the discrete time case and continuous time case are considered by proposing an implicit function approach sufficient conditions for the systems respectively to be small controllable and controllable are obtained examples are also provided to illustrate the results of the paper

on controllability of homogeneous and inhomogeneous discrete time multi input bilinear systems in dimension two abstractin this paper the controllability problem of two dimensional discrete time multi input bilinear systems is completely solved the homogeneous and the inhomogeneous cases are studied separately and necessary and sufficient conditions for controllability are established by using a linear algebraic method which are easy to apply moreover for the uncontrollable systems near controllability is considered and similar necessary and sufficient conditions are also obtained finally examples are provided to demonstrate the results of this paper

controllability is harder to decide than accessibility this article compares the difficulties of deciding controllability and accessibility these are standard properties of control systems but complete algebraic characterizations of controllability have proved elusive the article shows in particular that for subsystems of bilinear systems accessibility can be decided in polynomial time but controllability is np hard

stability of discrete time switched homogeneous systems on cones and conewise homogeneous inclusions this paper presents a stability analysis of switched homogeneous systems on cones under arbitrary and optimal switching rules with extensions to conewise homogeneous or linear inclusions several interrelated approaches such as the joint spectral radius approach and the generating function approach are exploited to derive necessary and sufficient stability conditions and to develop suitable algorithms for stability tests specifically the generalized joint spectral radius and the generalized joint lower spectral radius are introduced to characterize the radii of domains of strong and weak attraction furthermore strong and weak generating functions and their radii of convergence are employed to derive stability conditions their analytic properties numerical approximations and convergence analysis are established extensions to conewise homogeneous or linear inclusions are made to address state dependent switching dynamics relations between different stability notions in the strong or weak sense ar

reconstruction from projections using grassmann tensors in this paper a general procedure is given for reconstruction of a set of feature points in an arbitrary dimensional projective space from their projections into lower dimensional spaces this extends the methods applied in the well studied problem of reconstruction of scene points in 3 given their projections in a set of images in this case the bifocal trifocal and quadrifocal tensors are used to carry out this computation it is shown that similar methods will apply in a much more general context and hence may be applied to projections from n to m which have been used in the analysis of dynamic scenes and in radial distortion correction for sufficiently many generic projections reconstruction of the scene is shown to be unique up to projectivity except in the case of projections onto one dimensional image spaces lines in which case there are two solutions projections from n to 2 have been considered by wolf and shashua in international journal of computer vision 48 1 53 67 2002 where they were applied to several different problems in dynamic scene analysis they analyzed these projections using tensors but no general way of defining such tensors and computing the projections was given this paper settles the general problem showing that tensor definition and retrieval of the projections is always possible

quadratic forms and approximate feed back linearization in discrete time quadratic feedback linearization is discussed for discrete time systems i e approximate feedback linearization up to the second order with respect to input and state variables after introducing in discrete time two equivalence classes invariant under quadratic static state feedback and diffeomorphism two canonical quadratic representations are proposed then it is shown that any nonlinear discrete time dynamics which are controllable in their first approximations can be linearized up to the second order under dynamic feedback the results stated here can be considered as the general discrete time analogues of the continuous time ones kang and krener 1992

identification of a discrete planar symmetric shape from a single noisy view in this paper we propose a method for identifying a discrete planar symmetric shape from an arbitrary viewpoint our algorithm is based on a newly proposed notion of a view s skeleton we show that this concept yields projective invariants which facilitate the identification procedure it is furthermore shown that the proposed method may be extended to the case of noisy data to yield an optimal estimate of a shape in question substantiating examples are provided

dual computation of projective shape and camera positions from multiple images given multiple image data from a set of points in 3d there are two fundamental questions that can be addressed what is the structure of the set of points in 3d what are the positions of the cameras relative to the points in this paper we show that for projective views and with structure and position defined projectively these problems are dual because they can be solved using constraint equations where space points and camera positions occur in a reciprocal way more specifically by using canonical projective reference frames for all points in space and images the imaging of point sets in space by multiple cameras can be captured by constraint relations involving three different kinds of parameters only coordinates of 1 space points 2 camera positions 3 image points the duality implies that the problem of computing camera positions fromp points in q views can be solved with the same algorithm as the problem of directly reconstructing q 4 points in p 4 views this unifies different approaches to projective reconstruction methods based on external calibration and direct methods exploiting constraints that exist between shape and image invariants

a controllability counterexample simulation by time discretizations can be qualitatively misleading as counterexamples a class of noncontrollable single input two dimensional bilinear control systems is presented whose euler discretizations are controllable on the punctured plane

identification and control of a nonlinear discrete time system based on its linearization a unified framework this paper presents a unified theoretical framework for the identification and control of a nonlinear discrete time dynamical system in which the nonlinear system is represented explicitly as a sum of its linearized component and the residual nonlinear component referred to as a higher order function this representation substantially simplifies the procedure of applying the implicit function theorem to derive local properties of the nonlinear system and reveals the role played by the linearized system in a more transparent form under the assumption that the linearized system is controllable and observable it is shown that 1 the nonlinear system is also controllable and observable in a local domain 2 a feedback law exists to stabilize the nonlinear system locally and 3 the nonlinear system can exactly track a constant or a periodic sequence locally if its linearized system can do so with some additional assumptions the nonlinear system is shown to have a well defined relative degree delay and zero dynamics if the zero dynamics of the linearized system is asymptotically stable so is that of the nonlinear one and in such a case a control law exists for the nonlinear system to asymptotically track an arbitrary reference signal exactly in a neighborhood of the equilibrium state the tracking can be achieved by using the state vector for feedback or by using only the input and the output in which case the nonlinear autoregressive moving average narma model is established and utilized these results are important for understanding the use of neural networks as identifiers and controllers for general nonlinear discrete time dynamical systems

coordinates in two variables over a q algebra this paper studies coordinates in two variables over a q algebra it gives several ways to characterize such coordinates also various results about coordinates in two variables that were previously only known for fields are extended to arbitrary q algebras

algebraic functions for recognition in the general case a trilinear relationship between three perspective views is shown to exist the trilinearity result is shown to be of much practical use in visual recognition by alignment yielding a direct reprojection method that cuts through the computations of camera transformation scene structure and epipolar geometry moreover the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection the proof of the central result may be of further interest as it demonstrates certain regularities across homographics of the plane and introduces new view invariants experiments on simulated and real image data were conducted including a comparative analysis with epipolar intersection and the linear combination methods with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks

the output regulation problem with stability for linear switching systems a geometric approach abstract this work presents a solution for the output regulation problem with quadratic stability under arbitrary switching in linear switching systems the extension to other stability requirements like asymptotic stability in particular is also considered and it is shown to affect only few specific features of the proposed solution the main reason is that the geometric approach which is at the basis of the developed methodology establishes a neat separation between the structural aspects and the stability aspects of the problem for the same reason continuous time systems and discrete time systems are given a unified treatment as far as the structural issues are concerned while different technicalities characterize the discussion of the stability issues

analysis and stabilization for networked linear hyperbolic systems of rationally dependent conservation laws in this paper for a networked linear hyperbolic partial differential equations pdes system of conservation laws the propagation periods of which are rationally dependent with coupled boundary conditions we propose a novel approach to analyze its controllability and observability in addition we propose a design method of a stabilizing controller where a boundary input with boundary valued feedback is considered first we characterize the control properties such as controllability of such a pde system in terms of the corresponding ones of a finite dimensional discrete time system defined on the boundaries of the pde system which is derived by fully exploiting the method of characteristics since the obtained discrete time system is low dimensional its analysis is relatively easier next we propose a design method of a stabilizing controller based on this discrete time system finally numerical simulations are presented to show that the proposed method is effective

controllability analysis and control design for switched boolean networks with state and input constraints this paper investigates the controllability analysis and the control design for switched boolean networks sbns with state and input constraints by using the semi tensor product method and presents a number of new results on their controllability optimal control and stabilization first the constrained incidence matrix is proposed for sbns based on which several necessary and sufficient conditions are obtained for the controllability second using the results on the controllability two algorithms are established to design proper switching sequence and controls that minimize the cost functional in a fixed designed shortest termination time third the constrained sbn is converted to an equivalent unconstrained one based on which some necessary and sufficient conditions are presented for the stabilization of the constrained sbn with open loop and closed loop controls respectively finally a practical example of the apoptosis network is studied by using the new results obtained in this paper the s

reachability and steering of rolling polyhedra a case study in discrete nonholonomy rolling a ball on a plane is a standard example of nonholonomy reported in many textbooks and the problem is also well understood for any smooth deformation of the surfaces for nonsmoothly deformed surfaces however much less is known although it may seem intuitive that nonholonomy is conserved think e g to polyhedral approximations of smooth surfaces current definitions of nonholonomy are inherently referred to systems described by ordinary differential equations and are thus inapplicable to such systems in this paper we study the set of positions and orientations that a polyhedral part can reach by rolling on a plane through sequences of adjacent faces we provide a description of such reachable set discuss conditions under which the set is dense or discrete or has a compound structure and provide a method for steering the system to a desired reachable configuration robustly with respect to model uncertainties based on ideas and concepts encountered in this case study and in some other examples we provide we turn back to the most general aspects of the problem and investigate the possible generalization of the notion of kinematic nonholonomy to nonsmooth discrete and hybrid dynamical systems to capture the essence of phenomena commonly regarded as nonholonomic at least two irreducible concepts are to be defined of internal and external nonholonomy which may coexist in the same system these definitions are instantiated by examples

stability analysis of discrete time switched linear systems with unstable subsystems abstract the problem of stability for discrete time switched linear systems dslss with unstable subsystems is investigated unlike most existing results that require each switching mode of the system to be asymptotically stable this paper considers the case that each subsystem may be unstable first under certain hypotheses a necessary condition of stability for dslss is obtained second using the average dwell time adt strategy some sufficient conditions of exponential stability for switched linear systems are derived under two assumptions finally two examples are presented to show the effectiveness of the proposed approaches

feedback linearization of sampled data systems it is shown that feedback linearizability of a continuous time system can be destroyed through the introduction of the usual sample and hold devices a method whereby a feedback linearizable discrete time model can be recovered is given

tame and wild coordinates of z x y abstract algorithms to decide whether a polynomial is a coordinates tame coordinate respectively of z x y are given moreover if a polynomial p z x y is a coordinate tame coordinate respectively the algorithms effectively construct a concrete automorphism of z x y that sends x to p the algorithm to determine tame coordinate is applicable to r x y where r is an euclidean domain while the algorithm to determine coordinate is applicable to d x y where d is a unique factorization domain

anti windup strategies for discrete time switched systems subject to input saturation this paper deals with the design of anti windup compensator for discrete time switched systems subject to input saturation the cases of static and dynamic anti windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed loop system two aspects of the switching law are taken into account during the design either it is arbitrary or it is a part of the complete control law theoretical conditions allowing to synthesise the anti windup compensator are mainly described through linear matrix inequalities computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution

new insights on the analysis of nonlinear time delay systems application to the triangular equivalence in this paper we present recent advances towards an algebraic framework for the analysis and control of nonlinear systems with delays we show the usefulness of these results by applying them to obtain a constructive characterization of the equivalence of a given system to the so called triangular form

motion from point matches multiple of solutions in this paper we study the multiplicity of solutions of the motion problem given n point matches between two frames how many solutions are there to the motion problem we show that the maximum number of solutions is 10 when 5 point matches are available this settles a question that has been around in the computer vision community for a while we follow two tracks we show that the two approaches are compatible and yield the same result we then describe a computer implementation of the second approach that uses maple a language for symbolic computation the program allows us to compute exactly the solutions for any configuration of 5 points some experiments are described

global stabilization of discrete time homogeneous systems abstract the feedback stabilization of continuous time r homogeneous systems has been studied by several authors see for instance dayawansa and martin proceedings of the 28th c d c tampa florida december 1989 hermes j differential equations 92 1991 76 89 hermes systems control lett 24 1995 7 11 kawski proceedings of the 27th c d c texas 1988 texas kawski control theory and advanced technology vol 6 mita press tokyo 1996 pp 497 516 sepulchre and aeyels math control signal systems 9 1996 34 58 in kawski analysis of controlled dynamical systems birkhauser basel 1991 kawski proceedings of ifac nolcos 1995 kawski gave an intrinsic concept of homogeneity with respect to general smooth dilations in this note we define the homogeneity of transition maps w r t continuous dilations and we show how one can construct a global stabilizing feedback control for discrete time homogeneous systems which are locally asymptotically stabilizable