invariant subspaces for lpv systems and their applications the aim of this paper is to extend the notion of invariant subspaces known in the geometric control theory of the linear time invariant systems to the linear parameter varying lpv systems by introducing the concept of parameter varying invariant subspaces for lpv systems affine in their parameters algorithms are given to compute many parameter varying subspaces relevant in the solution of state feedback and observer design problems

dead beat functional observers for discrete time lpv systems with unknown inputs this technical note deals with functional observers for discrete time linear parameter varying lpv systems more specifically dead beat observers for reconstructing linear combinations of the state are proposed the system inputs are assumed to be unknown and the observers reduce to functions of the output over a finite number of time steps the existence of such observers is proven by resorting to the notion of inverse system together with the concepts of maximal robust invariant subspaces and nilpotent semigroups a constructive approach to derive the explicit equations of the observer is provided an example illustrates the efficiency and the computational aspects of the method

arcs cords and felts six instances of the linearization principle it is shown how a selection of prominent results in singularity theory and differential geometry can be deduced from it one theorem the rank theorem for maps between spaces of power series

stable internally positive representations of continuous time systems an internally positive representation ipr of a non positive system is a positive system that under suitable input state and output transformations exactly replicates the behavior of the original system any construction method of an ipr necessarily introduces additional natural modes which in some cases are unstable in a previous paper the authors have presented a method that provides a stable ipr if and only if the eigenvalues of the original system lie in a specific sector of the open left half complex plane in this technical note a new technique is proposed that overcomes such a limitation and provides a stable ipr for any stable system although in some cases the dimension of the ipr must be large in order to guarantee its stability although for simplicity the method is only illustrated for single input single output systems with distinct eigenvalues it also applies to multi input multi output systems with multiple eigenvalues

on a hyperplane section theorem of gurjar a hyperplane section theorem by r v gurjar 3 is given a short proof power series in any number at least three of variables satsifying the condition of the theorem are explicitly constructed in the course of the proof the restrictive looking condition of the theorem is given an easy sufficient condition from the view point of the weighted projective spaces

an algorithmic approach to simultaneous triangularization abstract we present and prove the validity of an algorithm constructing a simultaneous triangularization of a set on n matrices in c n n to do so we first prove that if a set of matrices has a common block decomposition then the set of matrices has a simultaneous triangularization if and only if the blocks on the diagonal have a simultaneous triangularization

lemme d artin rees theoreme d izumi et fonction de artin abstract we interpret the artin rees lemma and the izumi theorem in term of artin function and we obtain a stable version of the artin rees lemma we present different applications of these interpretations first we show that the artin function of x 1 x 2 x 3 x 4 as a polynomial in the ring of power series in more than three variables is not bounded by an affine function then we prove that the artin functions of a class of polynomials are bounded by affine functions and we use this to compute approximated integral closures of ideals

a new approach to the internally positive representation of linear mimo systems the problem of representing linear systems through combination of positive systems is relevant when signal processing schemes such as filters state observers or control laws are to be implemented using positive technologies such as charge routing networks and fiber optic filters this problem well investigated in the siso case can be recasted into the more general problem of internally positive representation ipr of systems this paper presents a methodology for the construction of such iprs for mimo systems based on a suitable convex positive representation of complex vectors and matrices the stability properties of the iprs are investigated in depth achieving the important result that any stable system admits a stable ipr of finite dimension a main algorithm and three variants all based on the proposed methodology are presented for the construction of stable iprs all of them are straightforward and are characterized by a very low computational cost the first and second may require a large state space dimension to provide a stable ipr while the third and the fourth are aimed to provide stable iprs of reduced order

nilpotent semigroups for the characterization of flat outputs of switched linear and lpv discrete time systems abstract this paper addresses the problem of flat output characterization for switched linear systems the characterization is also extended to lpv systems the characterization is based on the notion of nilpotent semigroups a complete corresponding recursive algorithm is provided it stops after a finite number of steps bounded by the dimension of the system illustrative examples for the respective class of switched linear and lpv systems highlight the efficiency of the characterization

germs of arcs on singular algebraic varieties and motivic integration we study the scheme of formal arcs on a singular algebraic variety and its images under truncations we prove a rationality result for the poincare series of these images which is an analogue of the rationality of the poincare series associated to p adic points on a p adic variety the main tools which are used are semi algebraic geometry in spaces of power series and motivic integration a notion introduced by m kontsevich in particular we develop the theory of motivic integration for semi algebraic sets of formal arcs on singular algebraic varieties we prove a change of variable formula for birational morphisms and we prove a geometric analogue of a result of oesterle

partial state observers for linear systems with unknown inputs we consider the problem of constructing partial state observers for discrete time linear systems with unknown inputs specifically for any given system we develop a design procedure that characterizes the set of all linear functionals of the system state that can be reconstructed through a linear observer with a given delay by treating the delay as a design parameter we allow greater flexibility in estimating state functionals and are able to obtain a procedure that directly produces the corresponding observer parameters our technique is also applicable to continuous time systems by replacing delayed outputs with differentiated outputs

on the approximation property of excellent rings where d is a smooth finite type a algebra a theorem which would imply the existence of an embedding of the above type yields the positive solution of the bass quillen conjecture so far this theorem is only known in special cases there is the following result by artin 3 4

holomorphic arcs on singularities the study of formal arcs was initiated by nash in a 1967 preprint arc spaces of smooth varieties have a rather transparent structure but difficult problems arise for arcs passing through singularities the nash conjecture on the irreducible components of such arc spaces was proved for surfaces by fernandez de bobadilla and pe pereira and for toric singularities by ishii and kollar but counter examples were found in higher dimensions by ishii and kollar de fernex and johnson and kollar here we start the study of holomorphic arcs these are holomorphic maps from the closed unit disk to a complex analytic space as one expects there is not much conceptual difference between the set of formal arcs and the set of holomorphic arcs since every formal arc can be approximated by holomorphic arcs however a formal deformation of an arc is a much more local object than a holomorphic deformation thus in many cases the space of holomorphic arcs has infinitely many connected components while the space of formal arcs always has only finitely many for a complex analytic space we define two variants the space of arcs and the space of short arcs and we study their connected components for short arcs we obtain complete answers for surface singularities and for isolated quotient singularities in all dimensions

on the observer problem for discrete time control systems this paper studies the construction of observers for nonlinear time varying discrete time systems in a general context where a certain function of the states must be estimated appropriate notions of robust complete observability are proposed under which a constructive proof of existence of an observer is developed moreover a transitive observer property is proven according to which a state observer can be generated as the series connection of two observers the analysis and the results are developed in general normed linear spaces to cover both finite dimensional and infinite dimensional systems

exact almost and optimal input decoupled delayed observers the core of this paper deals with the construction of input decoupled observers which seek asymptotic estimation of a desired output variable a linear combination of state and input of a time invariant either continuous or discrete time system driven by unknown inputs and disturbances exact almost optimal suboptimal and constrained optimal estimation or filtering problems are formulated and studied all the problems defined and studied here are inherently interconnected and have a strong common thread of estimation and filtering in the face of the unknown input and external disturbance signals they are interconnected from a variety of angles e g they are motivated by one another methods of obtaining the solvability conditions and their methods of solution rely on one another etc thus a hierarchy of problems and their solutions is built on top of one another some of the problems studied here are known in the literature but not in as general a form as is given here while a majority of the

on the robust controlled invariant abstract the robust controlled invariant is defined as a tool to characterize systems subject to parameter changes and to set up a geometric approach to robustness in the large in multi variable control problems as a typical application the robust disturbance decoupling problem an extended version of the well known disturbance decoupling is presented and a necessary and sufficient condition for it to have a solution is derived

controllability and reachability criteria for discrete time positive systems discrete time positive systems have been the object of widespread interest in the literature in the last decade particular attention has been devoted to the analysis and characterization of the different notions of reachability and controllability which in this context make their appearance in this paper the properties of ordinary and essential controllability and reachability are analysed based on a graph theoretic approach we provide practical criteria to verify whether a given positive system f g is endowed with these properties together with canonical forms for describing reachable controllable pairs

arithmetic theory of q difference equations the q analogue of grothendieck katz s conjecture on p curvatures grothendieck s conjecture on p curvatures predicts that an arithmetic differential equation has a full set of algebraic solutions if and only if its reduction in positive characteristic has a full set of rational solutions for almost all finite places it is equivalent to katz s conjectural description of the generic galois group in this paper we prove an analogous statement for arithmetic q difference equation

existence and design of functional observers for linear systems this paper presents straightforward derivations of the functional observers design for linear time invariant multivariable systems the order of these observers is equal to the dimension spl tau of the vector to be estimated necessary and sufficient conditions for the existence and stability of these observers are given illustrative examples are included

convergence and divergence of formal cr mappings let m subset mathbb c n be a generic real analytic submanifold of finite type m subset mathbb c n be a real analytic set and p in m where we assume that n n geqslant 2 let h mathbb c n p to mathbb c n be a formal holomorphic mapping sending m into m and let mathcal e m denote the set of points in m through which there passes a complex analytic subvariety of positive dimension contained in m we show that if h does not send m into mathcal e m then h must be convergent as a consequence we derive the convergence of all formal holomorphic mappings when m does not contain any complex analytic subvariety of positive dimension answering by this a long standing open question in the field more generally we establish necessary conditions for the existence of divergent formal maps even when the target real analytic set is foliated by complex analytic subvarieties allowing us to settle additional convergence problems such as e g for transversal formal maps between levi non degenerate hypersurfaces and for formal maps with range in the tube over the light cone