descriptor discrete time systems with random abrupt changes stability and stabilisation this paper deals with the class of linear discrete time systems with random abrupt changes also known as class of markovian jump singular systems the problems of stochastic stability and the stochastic stabilisation using state feedback control and static output feedback control are tackled conditions in the lmi setting to design the appropriate gains of the controllers are developed it is shown that all the addressed problems can be solved if the corresponding developed linear matrix inequalities lmis are feasible numerical examples are employed to show the usefulness of the proposed results

the structured distance to the nearest system without property mathcal p for a system matrix m this paper explores the smallest frobenius norm additive structured perturbation delta m for which a system property mathcal p e g controllability observability stability etc fails to hold i e delta m is the structured perturbation with smallest frobenius norm such that there exists a property matrix r in mathcal p for which m delta m r drops rank the frobenius norm is used because of its direct dependence on the magnitude of each entry in the perturbation matrix necessary conditions on a locally minimum norm structured rank reducing perturbation delta m and associated property matrix r are set forth and proven an iterative algorithm is also set forth that computes a locally minimum norm structured perturbation and associated property matrix satisfying the necessary conditions algorithm convergence is proven using a discrete lyapunov function

a survey of exact algorithms for the simple assembly line balancing problem in this survey paper we discuss the development of the simple assembly line balancing problem salbp modifications and generalizations over time present alternate 0 1 programming formulations and a general integer programming formulation of the problem discuss other well known problems related to salbp describe and comment on a number of exact i e optimum seeking methods and present a summary of the reported computational experiences all models discussed here are deterministic i e all input parameters are assumed to be known with certainty and all the algorithms discussed are exact the problem is termed simple in the sense that no mixed models subassembly lines zoning restrictions etc are considered due to the richness of the literature we exclude from discussion here a the inexact i e heuristic approximate algorithms for salpb and b the algorithms for the general assembly line balancing problem including the stochastic models

fault detection filter design for markovian jump singular systems with intermittent measurements this paper addresses the problem of fault detection filter design for discrete time markovian jump singular systems with intermittent measurements the measurement transmission from the plant to the fault detection filter is assumed to be imperfect and a stochastic variable is utilized to model the phenomenon of data missing our attention is focused on the design of a fault detection filter such that the residual system is stochastically markovian jump admissible and satisfies some expected performances a new necessary and sufficient condition for a class of discrete time markovian jump singular systems to be stochastically markovian jump admissible is proposed in the form of strict linear matrix inequalities sufficient conditions are established for the existence of the fault detection filter finally a numerical example is provided to demonstrate the usefulness and applicability of the developed theoretical results

computation of the real controllability radius and minimum norm perturbations of higher order descriptor and time delay lti systems a linear time invariant lti system s controllability radius measures the norm of the smallest parametric perturbation such that the perturbed system is uncontrollable and is of practical importance in this note we study the real controllability radii of i higher order systems ii descriptor systems and iii time delay systems where the perturbations are restricted to the set of real values and the spectral norm is considered formulas for these radii are presented using a framework involving generalized real perturbation values which has certain computational advantages over other formulations found in the literature in particular the formulas are readily more computable especially for higher dimensional systems and a minimum norm perturbation can also easily be obtained numerical examples are presented

between controllable and uncontrollable the distance between a system a b and the set of uncontrollable systems is the minimum of the smallest singular value of i a b with respect to

mean square stochastic stability of linear time delay system with markovian jumping parameters this paper deals with the mean square stochastic stability of the class of linear time delay systems with markovian jumping parameters a delay independent sufficient condition for checking the stochastic stability of this class of systems is established a numerical example is given to show the usefulness of the proposed theoretical results

branch and bound algorithms for the multi product assembly line balancing problem abstract this paper considers a flexible manufacturing system for several products each requiring a number of sequential nonpreemptive tasks some of which may be common to many products work stations are capable of handling any task the objective is to minimize the number of work stations necessary to manufacture all products so that tasks are performed in the proper order and so that all tasks assigned to any given station can be executed within a prescribed time frame a new branch and bound approach for this problem is presented it contains two main improvements over previously published tree search algorithms an improved lower bounding procedure and a more powerful partitioning scheme the algorithm can be used either as a heuristic in its truncated version or as an exact method in its full version tests performed on randomly generated problems confirm the effectiveness of the proposed improvements

computing the radius of controllability for state space systems abstract in this paper we discuss the problem of computing the nearest uncontrollable system to a given control system represented by a matrix pair a b in order to do so we construct a sequence of structured matrices from given system matrices a and b controllability of the pair a b is equivalent to a condition on the null space dimension of an appropriate matrix in this sequence we show that the dimension of the reachability space is also related to the above condition further it is shown that the nearest structured low rank approximation slra of this structured matrix corresponds to a nearest uncontrollable system to the pair a b

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

absalom balancing assembly lines with assignment restrictions abstract assembly line balancing problems albps arise whenever an assembly line is configured redesigned or adjusted an albp consists of distributing the total workload for manufacturing products among the work stations along the line on the one hand research has focussed on developing effective and fast solution methods for exactly solving the simple assembly line balancing problem salbp on the other hand a number of real world extensions of salbp have been introduced but solved with straight forward and simple heuristics in many cases therefore there is a lack of procedures for exactly solving such generalized albp in this paper we show how to extend the well known solution procedure s alome scholl a klein r 1997 s alome a bidirectional branch and bound procedure for assembly line balancing informs j comput 9 319 334 which is able to solve even large salbp instances in a very effective manner to a problem extension with different types of assignment restrictions called aralbp the extended procedure referred to as a bsalom employs a favorable branching scheme an arsenal of bounding rules and a variety of logical tests using ideas from constraint programming computational experiments show that a bsalom is a very promising exact solution approach although the additional assignment restrictions complicate the problem considerably and necessitate a relaxation of some components of s alome

algebraic riccati equations and the distance to the nearest uncontrollable pair a connection is established between nearness to unstabilizability of a stabilizable pair a b of matrices and nearness to singularity of the symmetric positive definite solution to an associated algebraic riccati equation from this result computable upper and lower bounds are derived for the distance of a b to the nearest uncontrollable pair numerical tests confirm the validity of the method and potential applications are discussed

on the structured distance to uncontrollability this article is concerned with the structured distance to uncontrollability of a linear time invariant system and relates this concept to a variation of the value the developed framework is applied to derive computational expressions for the class of real perturbations as well as for hermitian symmetric and skew symmetric perturbations in a relatively simple manner examples demonstrate that the structured distance can differ from the standard unstructured distance to uncontrollability by an arbitrary amount it is also shown how systems of higher order can be addressed

an algorithm for computing the distance to uncontrollability in this paper we present an algorithm to compute the distance to uncontrollability the problem of computing the distance is an optimization problem of minimizing sigma x y over the complete plane this new approach is based on finding zero points of grad sigma x y we obtain the explicit expression of the derivative matrix of grad sigma x y the newton s method and the bisection method are applied to approach these zero points numerical results show that these methods work well

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

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

real controllability stabilizability radius of lti systems in this note we present a simple and readily computable formula for the calculation of the real controllability stabilizability and observability detectability radii for linear time invariant systems

estimating the distance to uncontrollability a fast method and a slow one abstract for a linear control system a b the distance to uncontrollability is characterized by min ec n a i b where n a i b is the smallest singular value of the augmented matrix a i b two methods are developed to estimate the distance to uncontrollability giving both a lower bound and an upper bound one method is fast requiring only one spectral decomposition of a and computations of three smallest singular values and being used for well conditioned a the other is slow requiring computations of a large number of the smallest singular values but it produces bounds as tight as possible and also a region containing global minimizers newton s method can be used to compute the global minimizers if one really wants

structured low rank approximation this paper concerns the construction of a structured low rank matrix that is nearest to a given matrix the notion of structured low rank approximation arises in various applications ranging from signal enhancement to protein folding to computer algebra where the empirical data collected in a matrix do not maintain either the specified structure or the desirable rank as is expected in the original system the task to retrieve useful information while maintaining the underlying physical feasibility often necessitates the search for a good structured lower rank approximation of the data matrix this paper addresses some of the theoretical and numerical issues involved in the problem two procedures for constructing the nearest structured low rank matrix are proposed the procedures are flexible enough that they can be applied to any lower rank any linear structure and any matrix norm in the measurement of nearness the techniques can also be easily implemented by utilizing available optimization packages the special case of symmetric toeplitz structure using the frobenius matrix norm is used to exemplify the ideas throughout the discussion the concept rather than the implementation details is the main emphasis of the paper

a global minimum search algorithm for estimating the distance to uncontrollability abstract let a r n n and b r n m we suggest a new search algorithm for estimating the distance a b of a controllable pair a b to the set of uncontrollable pairs by estimating the global minimum of the function min a i b c where min denotes the smallest singular value of a matrix using simple properties of this function due to ralph byers one first observes that provided rank b n the minimization problem can be transformed to a minimization problem in the bounded region x z x a 2 z a 2 in the two dimensional real plane the algorithm then progressively partitions this region into simplexes and by determining whether their vertices x j z j satisfy z j min y r min a x j iy i b it computes after a finite number of steps upper and lower bounds for a b the difference between the two is small if a b is small while the lower bound is larger if a b is large thus ensuring safe decisions an error analysis numerical examples and an operation count are all presented only simple modifications of the search region are necessary to extend the applicability of the algorithm to the case when rank b n

properties of numerical algorithms related to computing controllability the numerical properties of some methods for computing controllability are used in an expository way to motivate a wider understanding of numerical computations in particular the numerical rank of a matrix the numerical stability of algorithms the sensitivity of problems and the scaling of problems are discussed a numerically stable algorithm is given for computing controllability but it is pointed out that a measure of the distance of the given system from the nearest uncontrollable system would be more useful and this appears to be an open computational problem

robust admissibility of uncertain switched singular systems this article investigates the robust admissibility of uncertain discrete time switched singular systems first the admissibility is introduced by using the switched lyapunov function for singular systems sufficient conditions for robust admissibility of uncertain switched singular systems are presented in strict linear matrix inequalities formulation robust admissibility condition designs for both state feedback and static output control feedback are then derived numerical examples are provided to illustrate our approach

stochastic and exponential stability of discrete time markov jump linear singular systems abstract in this paper stochastic and almost sure stability of a markov jump linear singular system are analyzed first it is given a set of coupled generalized lyapunov equations to characterize the stochastic stability of the system second it is introduced a top lyapunov exponent to give a sufficient condition for almost sure stability our approach captures the solvability issue arising in this class of systems leading to lyapunov equations whose parameters reflex the solvability in an explicit manner two examples are presented in order to show the effectiveness of the proposed stability analysis

the feedback search algorithm estimating the distance of semi explicit systems to r uncontrollability abstract we show that the distance of a special descriptor system termed semi explicit from the nearest r uncontrollable system can be estimated by the global minimum of a specific real valued univariate function with variable we study this function for both real and complex and then develop a novel global optimization algorithm called the feedback search algorithm the algorithm is initially developed for one variable and then it is extended to two variables we implement the algorithm and apply it to the above function when varies on the real axis and also on the complex plane in addition to this we apply the algorithm to another relevant function from the literature for the numerical applications several random examples as well as examples from the literature were used

numerical linear algebra aspects of control design computations the interplay between recent results and methodologies in numerical linear algebra and mathematical software and their application to problems arising in systems control and estimation theory is discussed the impact of finite precision finite range arithmetic including the implications of the proposed ieee floating point standard s on control design computations is illustrated with numerous examples as are pertinent remarks concerning numerical stability and conditioning basic tools from numerical linear algebra such as linear equations linear least squares eigenproblems generalized eigenproblems and singular value decomposition are then outlined a selected list of applications of the basic tools then follows including algorithms for solution of problems such as matrix exponentials frequency response system balancing and matrix riccati equations the implementation of such algorithms as robust mathematical software is then discussed a number of issues are addressed including characteristics of reliable mathematical software availability and evaluation language implications fortran ada etc and the overall role of mathematical software as a component of computer aided control system design

the algebraic structure of pencils and block toeplitz matrices abstract we restate several results on the kronecker structure obtainable after a given matrix pencil is affected by an arbitrarily small perturbation and state some new results on the kronecker structure after a new row is appended or a column deleted the results are simple consequences of a theory of majorization for semi infinite integer sequences the bounds after a new row is appended correspond to bounding the controllability indices after adding a single input to a linear time invariant dynamical system we illustrate the known relations between the kronecker indices the segre characteristics and the nullities of certain block toeplitz matrices constructed from the original pencils and discuss how those nullities change when the pencil is affected by a perturbation or a new row

an linear programming based lower bound for the simple assembly line balancing problem the simple assembly line balancing problem is a classical integer programming problem in operations research a set of tasks each one being an indivisible amount of work requiring a number of time units must be assigned to workstations without exceeding the cycle time we present a new lower bound namely the lp relaxation of an integer programming formulation based on dantzig wolfe decomposition we propose a column generation algorithm to solve the formulation therefore we develop a branch and bound algorithm to exactly solve the pricing problem we assess the quality of the lower bound by comparing it with other lower bounds and the best known solution of the various instances from the literature computational results show that the lower bound is equal to the best known objective function value for the majority of the instances moreover the new lp based lower bound is able to prove optimality for an open problem c 2004 elsevier b v all rights reserved

survey paper structured low rank approximation and its applications fitting data by a bounded complexity linear model is equivalent to low rank approximation of a matrix constructed from the data the data matrix being hankel structured is equivalent to the existence of a linear time invariant system that fits the data and the rank constraint is related to a bound on the model complexity in the special case of fitting by a static model the data matrix and its low rank approximation are unstructured we outline applications in system theory approximate realization model reduction output error and errors in variables identification signal processing harmonic retrieval sum of damped exponentials and finite impulse response modeling and computer algebra approximate common divisor algorithms based on heuristics and local optimization methods are presented generalizations of the low rank approximation problem result from different approximation criteria e g weighted norm and constraints on the data matrix e g nonnegativity related problems are rank minimization and structured pseudospectra

regularity and stability analysis of discrete time markov jump linear singular systems abstract in this paper the regularity and stability analysis of discrete time markov jump linear singular systems mjlss is performed when dealing with singular systems a primary concern is related to the existence and uniqueness of a solution to the system this problem that is called regularity problem has a known solution when the linear singular system is not subject to jumps lss it turns out that when the pair of matrices that describes the dynamics of the lss satisfies a certain condition then it is regular by extending this condition to mjlss a unique solution for this class of systems is derived indeed through the idea of mode to mode regularity which is stronger than the mode by mode notion that can be found in the literature the existence of a unique solution of an mjlss is shown furthermore for systems that are mode to mode regular it is shown how to obtain recursive second moment models whose complexity depends on how anticipative the systems is the derived results on regularity and second moment modeling enable us to study stability of an mjlss by following the literature on markov jump linear systems mjls four different concepts of stability are introduced and their relationship is established the results presented in this paper generalize well known results concerning the stability given in the mjls theory for instance it is shown that the stability of the system is equivalent to the spectral radius of an augmented matrix being less than one as happens in the theory of mjls

the mixed and multi model line balancing problem a comparison abstract the balancing problem deals with the assignment of tasks to work stations we can distinguish two approaches in the literature on the mixed model line balancing problem that both transform this problem into a single model line balancing problem these approaches use combined precedence diagrams and adjusted task processing times respectively an experiment was carried out to compare several heuristics based on the combined precedence diagram a new optimisation method has been developed the results indicate that the position of common tasks in the precedence diagram of the different models has a significant effect on both the cpu time and the unequal distribution of the total work content of single models among work stations moreover good solutions with respect to the number of required stations go together with long cpu times for several instances we decreased the cpu times considerably without deteriorating the performance of the methods by using a reversed combined precedence diagram

measuring how far a controllable system is from an uncontrollable one the main goal of this note is to explore some of the properties of a controllable system which in a precise sense to be defined is near an uncontrollable pair to do this we first discuss the notion of the distance between a controllable system and the nearest uncontrollable one in both real and complex cases 2 5 when this distance is relatively small we show to what extent this distance corresponds to certain properties of the uncontrollability matrix and the reachability grammian

capacitated vehicle routing on trees t v e is a tree with nonnegative weights associated with each of its vertices a fleet of vehicles of capacity q is located at the depot represented by vertex v1 the capacitated vehicle routing problem on trees tcvrp consists of determining vehicle collection routes starting and ending at the depot such that the weight associated with any given vertex is collected by exactly one vehicle the sum of all weights collected by a vehicle does not exceed q a linear combination of the number of vehicles and of the total distance traveled by these vehicles is minimized the tcvrp is shown to be np hard this paper presents lower bounds for the tcvrp based on the solutions of associated bin packing problems we develop a linear time heuristic upper bound procedure and present a bound on its worst case performance these lower and upper bounds are then embedded in an enumerative algorithm numerical results follow