kalman decomposition for implicit linear systems the kalman decomposition for a general class of implicit systems is introduced and studied the properties of strong reachability observability acceptance of all inputs and outer sequences output uniqueness uniqueness and trajectory observability of the original system are related to the properties of its subsystems obtained via the kalman decomposition the problems of transfer relation regularizability by feedback output feedback and output injection are studied by means of this decomposition

frechet distance as a tool for diagnosing multivariate data abstract outliers can have dramatic effects on results from statistical analyses and on conclusions based on statistical analyses it is therefore important to detect outliers and influential points methods for detecting outliers in multivariate data may be based on assessments of changes in the estimate of the mean vector or changes in the estimate of the scatter matrix as data points are perturbed here we propose a method based on the frechet distance between the observed empirical distributions of the unperturbed and perturbed data as these distributions involve both the mean vector and the scatter matrix the resulting diagnostics are functions of both mean and scatter the proposed diagnostics are illustrated by two examples

on the relationship between continuous and discrete time quantum walk quantum walk is one of the main tools for quantum algorithms defined by analogy to classical random walk a quantum walk is a time homogeneous quantum process on a graph both random and quantum walks can be defined either in continuous or discrete time but whereas a continuous time random walk can be obtained as the limit of a sequence of discrete time random walks the two types of quantum walk appear fundamentally different owing to the need for extra degrees of freedom in the discrete time case

local influence in principal components analysis summary based on the definition of generalised influence function and generalised cook statistic local influence of small perturbations on the eigenvalues and eigenvectors of a covariance matrix are studied for population and sample versions the results based on the correlation matrix are also derived and some related topics are discussed finally an example is used for illustration bations although this method has been applied to many models beckman nachtsheim cook 1987 lawrance 1988 thomas cook 1990 assessing the local influence for multivariate data is still an unexplored area in this paper a method based on a generalised influence function and generalised cook statistic is introduced to assess the local influence of small perturbations on a statistic of interest and we prove that this method is equivalent to cook s work based on normal curvature in the likelihood framework since local influence on some statistics in multivariate analysis is not easy to study using the likelihood displacement of cook 1986 this method is expected to have wider applications in this paper we employ the generalised cook statistic to assess local influence in principal components analysis in 2 we introduce the definition of the generalised influ ence function and generalised cook statistic in 3 the perturbation theory of eigenvalues and eigenvectors of a real symmetric matrix is studied in 4 the local influence of small perturbations of observations on eigenvalues and the eigenvectors of sample covariance

identification of influential observations on total least squares estimates abstract it is known that total least squares tls estimates are very sensitive to outliers therefore identification of outliers is important for exploring appropriate model structures and determining reliable tls estimates of parameters in this paper we investigate sensitivities of tls estimates as observation data are perturbed and then based on perturbation theory of matrices we develop identification indices for detecting observations that highly influence the tls estimates finally numerical examples are given to illustrate the proposed detection method

disturbance decoupling of linear time varying singular systems the problem of disturbance decoupling by state feedback is defined for a linear time varying singular system it is required that the closed loop system has a unique impulse free solution and its output is not affected by disturbances an algorithm namely disturbance decoupling algorithm is proposed it is proved that the feasibility of the disturbance decoupling algorithm is invariant under any regular feedback control law based on the disturbance algorithm a constructive method is provided to design a disturbance decoupling feedback control law sufficient conditions for the solvability of the disturbance decoupling problem are derived it is proved that one of the sufficient conditions is also necessary provided that other conditions are satisfied

disturbance decoupling for descriptor systems by state feedback we study the disturbance decoupling problem for linear time invariant descriptor systems we give necessary and sufficient conditions for the existence of a solution to the disturbance decoupling problem with or without stability via a proportional and or derivative feedback that also makes the resulting closed loop system regular and or of index at most one all results are proved constructively based on condensed forms that can be computed using orthogonal matrix transformations i e transformations that can be implemented in a numerically stable way

disturbance decoupling with stability and impulse free response in singular systems abstract the problem of disturbance decoupling with stability and impulse free response in square singular systems e x ax bu gq with output y dx by applying a state feedback u fx is considered by employing van dooren s recursive algorithm for the computation of the subspace supremal a b invariant subspace in kernel d and using kalman s decomposition theorem the paper s approach presents a complete solution to the underlying problem regarding state space systems it is shown that the solution to the underlying problem is obtained almost directly from van dooren s recursive algorithm

the disturbance decoupling problem for implicit linear discrete time systems the disturbance decoupling problem for implicit linear discrete time systems is studied in detail necessary and sufficient conditions for the problem to be solved are given the results are obtained with the aid of the concepts of almost invariant sliding and coasting subspaces for implicit systems

disturbance and input output decoupling of singular systems the disturbance decoupling and the simultaneous disturbance and input output decoupling problems for singular systems are considered in the context of the matrix fraction description mfd of the system solvability conditions are obtained in terms of the composite matrix of a column reduced mfd of the system a characterisation of the fixed poles of both problems is given and it is shown that the remaining poles can be arbitrarily assigned

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

a tutorial on the geometric analysis of linear time invariant implicit systems abstract a background of recent work in nonregular and regular implicit systems of the form e x ax bu is provided then the output nulling unknown input and composite subspaces are defined for singular systems with recursions given for their computation inner subspaces that is those in the domain of e and a are distinguished from outer subspaces those in the codomain of e and a the notions of composite preimage and composite image are introduced the result is a framework that unifies some of the recent work in the geometric theory of implicit systems system properties are discussed for both regular and nonregular systems and duality is investigated

controllability of system dynamics on networks quantum walks and random walks abstract we consider a model of system dynamics on networks consisting of a certain number of stations nodes connected by edges at every time step a certain quantity leaves the stations and gets re distributed among the neighboring stations preserving an appropriate norm one has the control at every station on the relative quantity which is sent to the various neighbors controllability is achieved when every possible distribution of the given quantity in a natural set can be obtained this general model includes in particular classical and quantum walks on graphs the case of quantum walks is treated in detail and it is proved that controllability is achieved if and only if the underlying graph is not bipartite this extends to general graphs a result previously proved in the literature for the case where the underlying graph is regular then extensions are presented to general systems modeling system dynamics on networks

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

controllability and observability of grid graphs via reduction and symmetries in this paper we investigate the controllability and observability properties of a family of linear dynamical systems whose structure is induced by the laplacian of a grid graph this analysis is motivated by several applications in network control and estimation quantum computation and discretization of partial differential equations specifically we characterize the structure of the grid eigenvectors by means of suitable decompositions of the graph for each eigenvalue based on its multiplicity and on suitable symmetries of the corresponding eigenvectors we provide necessary and sufficient conditions to characterize all and only the nodes from which the induced dynamical system is controllable observable we discuss the proposed criteria and show through suitable examples how such criteria reduce the complexity of the controllability respectively observability analysis of the grid

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

noninteracting control of descriptor systems involving disturbances for m input p output descriptor systems involving disturbances it is proven that if the problem of disturbance rejection is solvable via static state feedback and the input output transfer function matrix is right invertible there always exists a static state feedback control law yielding simultaneously to disturbance rejection a triangular input output relation the structural properties of the closed loop system stability pole assignment etc are extensively studied

disturbance decoupling with closed loop modes stability in switched linear systems this work deals with the problem of rendering the output of a switched linear system insensitive to a disturbance input with the requirement that the dynamics of the closed loop system be exponentially stable for all switching signals with a sufficiently large dwell time a necessary and sufficient condition for the problem to have a solution is shown a complete computational procedure to check the solvability condition and to synthesize the compensation scheme is provided a worked out example is presented with the aim of showing the effectiveness of the devised method

on disturbance decoupling in descriptor systems the disturbance decoupling problem for a linear multivariable control system is to determine when and how a state feedback may be chosen so that some class of disturbances has no effect on the system output the development of necessary and sufficient conditions for the solvability of this problem for state space systems by wonham and his co workers has profoundly influenced geometric control theory particularly by means of the concept of an a b invariant subspace this paper develops necessary and sufficient conditions for solvability of this problem for linear systems described by a mixture of algebraic and differential equations although the argument presented has the same structure as in the state space case and incorporates a generalisation of a b invariant subspaces to descriptor systems there are some additional issues demanding particularly careful attention is the ensuring of existence and uniqueness of classical solutions of the underlying differential equations which cannot be tak

non stationary quantum walks on the cycle we consider quantum walks on the cycle in the non stationary case where the coin operation is allowed to change at each time step we characterize in algebraic terms the set of possible state transfers and prove that as opposed to the stationary case the associate probability distribution may converge to a uniform distribution among the nodes of the associated graph

an approach for pole assignment in singular systems pole assignment in a singular system edx dt ax bu is discussed it is shown that the problem of assigning the roots of det se a bf by applying a proportional feedback u fx r in a given singular system is equivalent to the problem of pole assignment of an appropriate regular system an immediate application of this result is that procedures and computational algorithms that were originally developed for assigning eigenvalues in regular systems become useful tools for pole assignment in singular systems the approach provides a useful tool for the combined problem of eliminating impulsive behavior and stabilizing a singular system

a simple procedure for the stabilization of a class of uncontrollable generalized systems this paper gives a simple procedure for the stabilization with a prescribed rate of convergence of the free motions of a class of possibly single input uncontrollable generalized continuous time time invariant linear systems preserving the impulse free property if any