parametrization of all strictly causal stabilizing controllers within the framework of the factorization approach we present parametrizations of all strictly causal stabilizing controllers

on stabilization for discrete linear time varying systems abstract in this paper we consider the stabilization problem for discrete linear time varying systems in an operator theoretic framework by using the complete finiteness of a certain discrete nest algebra we show that a system is stabilizable if and only if it has one kind of strong representation and we also give a parametrization for all the stabilizing controllers in terms of this strong representation this result extends the youla parametrization theorem by only requiring a strong left or a strong right representation but not both the strong stabilization problem is also discussed

on stabilization and the existence of coprime factorizations shows that any transfer function matrix whose elements belong to the quotient field of h sub infinity and which is stabilizable has a matrix fraction representation over h sub infinity which is coprime in the sense that a matrix bezout identity can be satisfied

distributed adaptive control of linear multi agent systems with event triggered communications this paper addresses the average consensus problem of multi agent systems with general linear dynamics via event triggered communications it is shown how the design of both the control law and the trigger functions depends on parameters of the overall system and an algorithm is proposed to estimate these parameters in a distributed fashion that does not imply an increase in the number of the communications between agents as a result it yields an adaptive control law and an update of the trigger functions parameters only at event times proofs of asymptotic convergence to average consensus and existence of positive lower bound for the inter event intervals are provided numerical simulations show the effectiveness of the proposed approach and how it compares to constant values of the parameters

semi cancellable fractions in system theory in this paper we propose to define the transfer function of a system in a new way namely as a semi cancellable fraction scf i e a fraction in which unstable pole zero cancellations are not allowed within this new framework it is possible to be rigorous and coherent in dealing with the stabilizability of a system from an input output viewpoint not focusing on the stabilizability of infinite dimensional input output systems

domains of undefinable solutions of some equations and systems of difference equations for some classes of difference equations and systems of difference equations we find the sets of initial values for which solutions of these equations and systems are not well defined so called domains of undefinable solutions

on the positive solutions of the difference equation xn 1 xn 1 1 x nxn 1 the positive solutions of the difference equation x n 1 x n 1 1 x nx n 1 n 0 1 2 are investigated where x 1 and x 0 are the positive real numbers

solving linear systems via pfaffians abstract an explicit solution is given for the system of linear equations e e t where are alternating matrices of pfaffian 1 which at most differ in their first row and column and e is of the form i 2 2 r e 1 i x i if v v w r r 1 with v w 1 v w then a sequence of cohn transforms with respect to the fixed w which takes v w to v w is prescribed

constrained traffic equilibrium in routing we study noncooperative routing in which each user is faced with a multicriterion optimization problem formulated as the minimization of one criterion subject to constraints on others we address the questions of existence and uniqueness of equilibrium we show that equilibria indeed exist but uniqueness may be destroyed due to the multicriteria nature of the problem we obtain uniqueness in some weaker sense under appropriate conditions we show that the link utilizations are uniquely determined at equilibrium we further study the normalized constrained equilibrium and apply it to pricing

feedback system design the tracking and disturbance rejection problems the problem of designing a compensator for a specified plant which simultaneously stabilizes the resultant feedback system and causes it to track a prescribed family of inputs and or reject prescribed disturbances is considered a set of linear design equations in the space of stable systems is formulated in a general linear systems setting and an explicit parameterization of the resultant solution space is obtained for a class of generalized multivariate systems the theory is illustrated with several single and multivariate examples

algebraic geometric aspects of feedback stabilization this paper develops a theory of feedback stabilization for siso transfer functions over a general integral domain which extends the well known coprime factorization approach to stabilization necessary and sufficient conditions for stabilizability of a transfer function in this general setting are obtained these conditions are then refined in the special cases of unique factorization domains ufds noetherian rings and rings of fractions it is shown that these conditions can be naturally interpreted geometrically in terms of the prime spectrum of the ring this interpretation provides a natural generalization to the classical notions of the poles and zeros of a plant the set of transfer functions is topologized so as to restrict to the graph topology of vidyasagar ieee trans automatic control ac 29 1984 pp 403 418 when the ring is a bezout domain it is shown that stability of a feedback system is robust in this topology when the ring is a ufd this theory is then applied to the problem of sta

feedback stabilization of mimo 3 d linear systems the authors solve the open problem of the existence of double coprime factorizations for a large class of multi input multi output mimo three dimensional 3 d linear systems it is proven that if all the unstable zeros of the contents associated with left and right matrix fraction descriptions of a given feedback stabilizable causal mimo 3 d plant are simple then the plant has a double coprime factorization the authors then give a parameterization of all stabilizing compensators for a mimo 3 d system in this class the key result developed in the paper is a novel and constructive technique of replacing an unstable polynomial with a stable polynomial step by step an illustrative example is also provided

on syzygy modules for polynomial matrices abstract in this paper we apply the theory of multivariate polynomial matrices to the study of syzygy modules for a system of homogeneous linear equations with multivariate polynomial coefficients several interesting structural properties of syzygy modules are presented and illustrated with examples

dynamics of a rational difference equation abstract in this note we investigate the solution of the difference equation x n 1 x n 1 a x n 1 x n n 0 1 2 where x 1 x 0 r and a 0 moreover we discuss the stability properties and semi cycle behavior of this solution

bezout identities and common minor zeros of 2 d polynomial matrices and applications to time delay systems this paper is concerned with factor zero coprimeness of 2 d polynomial matrices and studies relating bezout identities and some of their properties first we show that a pair of factor coprime matrices satisfies the particular bezout identities which are useful for feedback stabilization secondly we investigate the properties of the common minor zeros common zeros of all the maximum minors of factor coprime factorizations of 2 d transfer function matrices finally we apply the results to time delay systems of neutral or retarded type and provide tests for the spectrally controllability canonicality

a behavioral approach to the pole structure of one dimensional and multidimensional linear systems we use the tools of behavioral theory and commutative algebra to produce a new definition of a finite pole of a linear system this definition agrees with the classical one and allows a direct dynamical interpretation it also generalizes immediately to the case of a multidimensional nd system we make a natural division of the poles into controllable and uncontrollable poles when the behavior in question has latent variables we make a further division into observable and unobservable poles in the case of a one dimensional 1d state space model the uncontrollable and unobservable poles correspond respectively to the input and output decoupling zeros whereas the observable controllable poles are the transmission poles most of these definitions can be interpreted dynamically in both the 1d and nd cases and some can be connected to properties of kernel representations we also examine the connections between poles transfer matrices and their left and right matrix fraction descriptions mfds we find behavioral results which correspond to the concepts that a controllable system is precisely one with no input decoupling zeros and an observable system is precisely one with no output decoupling zeros we produce a decomposition of a behavior as the sum of subbehaviors associated with various poles this is related to the integral representation theorem which describes every system trajectory as a sum of integrals of polynomial exponential trajectories

polynomial filtering for fast convergence in distributed consensus in the past few years the problem of distributed consensus has received a lot of attention particularly in the framework of ad hoc sensor networks most methods proposed in the literature address the consensus averaging problem by distributed linear iterative algorithms with asymptotic convergence of the consensus solution the convergence rate of such distributed algorithms typically depends on the network topology and the weights given to the edges between neighboring sensors as described by the network matrix in this paper we propose to accelerate the convergence rate for given network matrices by the use of polynomial filtering algorithms the main idea of the proposed methodology is to apply a polynomial filter on the network matrix that will shape its spectrum in order to increase the convergence rate such an algorithm is equivalent to periodic updates in each of the sensors by aggregating a few of its previous estimates we formulate the computation of the coefficients of the optimal polynomial as a semidefinite program that can be efficiently and globally solved for both static and dynamic network topologies we finally provide simulation results that demonstrate the effectiveness of the proposed solutions in accelerating the convergence of distributed consensus averaging problems

convergence speed in distributed consensus and averaging we study the convergence speed of distributed iterative algorithms for the consensus and averaging problems with emphasis on the latter we first consider the case of a fixed communication topology we show that a simple adaptation of a consensus algorithm leads to an averaging algorithm we prove lower bounds on the worst case convergence time for various classes of linear time invariant distributed consensus methods and provide an algorithm that essentially matches those lower bounds we then consider the case of a time varying topology and provide a polynomial time averaging algorithm

causal and stable input output structures on multidimensional behaviors in this work we study multidimensional nd linear differential behaviors with a distinguished independent variable called time we define in a natural way causality and stability of input output structures with respect to this distinguished direction we make an extension of some results in the theory of partial differential equations demonstrating that causality is equivalent to a property of the transfer matrix which is essentially hyperbolicity of the p c operator defining the behavior cal b c 0 y we also quote results which in effect characterize time autonomy for the general systems case stability is likewise characterized by a property of the transfer matrix we prove this result for the 2d case and for the case of a single equation for the general case it requires solution of an open problem concerning the geometry of a particular set in mathbb c n in order to characterize input output stability we also develop new results on inclusions of kernels freeness of variables and closure with respect to cal s cal s prime and associated spaces which are of independent interest we also discuss stability of autonomous behaviors which we believe to be governed by a corresponding condition

convergence rate on periodic gossiping in a sensor network in which each sensor controls a real valued state the goal of a distributed averaging problem is to compute the global average in a decentralized way which is the average of all sensors initial state values across the entire network a t periodic gossiping protocol can solve such a problem which stipulates that each agent must gossip with each of its neighbors exactly once every t time unit the convergence rate of a t periodic gossiping protocol is determined by the magnitude of the second largest eigenvalue of the stochastic matrix associated with the gossip sequence occurring over one period an interesting result is that when the allowable gossip graph is a tree the convergence rate is independent of gossip orders within one period this paper will prove this result by developing several properties of doubly stochastic matrices the properties derived also can be used in analyzing convergence rate problems of other periodic gossip protocols

on a third order system of difference equations abstract we show that the system of difference equations x n 1 a 1 x n 2 b 1 y n z n 1 x n 2 c 1 y n 1 a 2 y n 2 b 2 z n x n 1 y n 2 c 2 z n 1 a 3 z n 2 b 3 x n y n 1 z n 2 c 3 n n 0 where the parameters a i b i c i i 1 2 3 and initial values x j y j z j j 0 1 2 are real numbers can be solved developing further the results in the literature

a necessary and sufficient condition for feedback stabilization in a factorial ring the necessity for a coprime fractional representation of a plant in order to completely parametrize all stabilizing compensators by the youla theory is examined it is shown that the coprimeness is necessary for systems in a factorial ring a class inclusive of multidimensional scalar systems some observations on partial state transfer functions in the feedback configuration are found to be useful in showing the necessity

fractional representation algebraic geometry and the simultaneous stabilization problem an explicit relationship between the fractional representation approach feedback system design and the algebro geometric approach to system theory is formulated and used to derive a global solution to the feedback system problem these techniques are then applied to the simultaneous stabilization problem yielding a natural geometric criterion for a set of plants to be simultaneously stabilized by a single compensator

parameterization of stabilizing controllers with either right or left coprime factorization a parameterization method of stabilizing controllers that requires only one of right left coprime factorizations is presented as an illustrative model we will consider the multidimensional system with structural stability for which it is not yet known in general whether or not a doubly coprime factorization always exists a parameterization of stabilizing controllers for the model is presented

brief paper stabilization of some fractional delay systems of neutral type in this note we give new stability tests which enable one to fully characterize the h stability of systems with transfer function g s r s p s q s e s h where h 0 and p q r are real polynomials in the variable s m for 0 p s q s 1

a behavioral approach to control of distributed systems this paper develops a theory of control for distributed systems i e those defined by systems of constant coefficient partial differential operators via the behavioral approach of willems the study here is algebraic in the sense that it relates behaviors of distributed systems to submodules of free modules over the polynomial ring in several indeterminates as in the lumped case behaviors of distributed arma systems can be reduced to ar behaviors this paper first studies the notion of ar controllable distributed systems following the corresponding definition for lumped systems due to willems it shows that as in the lumped case the class of controllable ar systems is precisely the class of ma systems it then shows that controllable 2 d distributed systems are necessarily given by free submodules whereas this is not the case for n d distributed systems n ge 3 this therefore points out an important difference between these two cases this paper then defines two notions of autonomous distributed systems which mimic different properties of lumped autonomous systems control is the process of restricting a behavior to a specific desirable autonomous subbehavior a notion of stability generalizing bounded input bounded output stability of lumped systems is proposed and the pole placement problem is defined for distributed systems this paper then solves this problem for a class of distributed behaviors

algebraic aspects of linear control system stability after formulating the problem of linear control system stability in very general terms the problem is resolved by 1 establishing a necessary and sufficient condition for stability 2 exploring in some detail the nature of this condition and 3 developing a parametric characterization of all controllers which stabilize a given plant the problem formulation is based on a ring theoretic setting for linear systems and is distinguished by the use of a novel control system configuration any interconnection of two distinct systems can be represented in terms of this configuration while preserving the distinction between the two systems furthermore no other configuration has this property several benefits and extensions are accrued as a result of using this configuration first a completely general yet physically meaningful problem formulation results consequently state space and operator theoretic approaches to linear control system stability are thoroughly reconciled this reconciliation embraces continuous time as well as discrete time systems lumped as well as distributed systems and 1 d as well as n d systems second the controller parametrization affords four degrees of freedom two more than any existing parametrization the additional degrees of freedom make explicit the design opportunity associated with controller implementation and thus determine several important control system characteristics this result is expected to provide a theoretical basis for the development of comprehensive control system design methodologies wherein design considerations related to controller implementation are addressed

h control of fractional linear systems abstract in this paper the standard h control problem for continuous time fractional linear time invariant single input single output systems is solved the adopted approach consists of extending to the fractional case the procedure followed within the classical solution for the integer case according to the classical route we first consider the generalization to fractional systems of the standard youla parameterization of all the stabilizing controllers the h optimal controller is then found among the class of stabilizing controllers recasting the control problem into a model matching one the results obtained naturally extend well established results to a fractional setting including both the commensurate and noncommensurate case thus providing a framework where h design can be recast along the well known and fruitful lines of the integer case a worked through example is discussed in detail to illustrate the design procedure

on the difference equation xn xn kb cxn 1 xn k abstract we describe the behavior of well defined solutions of the difference equation x n x n k b cx n 1 x n k n n 0 where k n parameters b c and the initial values x k x 1 are real numbers these results among others improve and extend our results in s stevic more on a rational recurrence relation appl math e notes 4 2004 80 85

chebyshev polynomials in distributed consensus applications in this paper we analyze the use of chebyshev polynomials in distributed consensus applications it is well known that the use of polynomials speeds up the convergence to the consensus in a significant way however existing solutions only work for low degree polynomials and require the topology of the network to be fixed and known we propose a distributed algorithm based on the second order difference equation that describes the chebyshev polynomials of first kind the contributions of our algorithm are three i since the evaluation of chebyshev polynomials is stable there is no limitation in the degree of the polynomial ii instead of the knowledge of the whole network topology it only requires a partial knowledge or an approximation to it iii it can be applied to time varying topologies in the paper we characterize the main properties of the algorithm for both fixed and time varying communication topologies theoretical results as well as experiments with synthetic data show the benefits of using our algorithm compared to existing methods

on the positive solutions of the difference equation xn 1 axn 11 bxnxn 1 we study the positive solutions of the difference equation x n 1 ax n 11 bx nx n 1 n 0 1 2 where a b x 1 and x 0 are non negative real numbers

distributed algebraic connectivity estimation for undirected graphs with upper and lower bounds the algebraic connectivity of the graph laplacian plays an essential role in various multi agent control systems in many cases a lower bound of this algebraic connectivity is necessary in order to achieve a certain performance lately several methods based on distributed power iteration have been proposed for computing the algebraic connectivity of a symmetric laplacian matrix however these methods cannot give any lower bound of the algebraic connectivity and their convergence rates are often unclear in this paper we present a distributed algorithm for estimating the algebraic connectivity for undirected graphs with symmetric laplacian matrices our method relies on the distributed computation of the powers of the adjacency matrix and its main interest is that at each iteration agents obtain both upper and lower bounds for the true algebraic connectivity both bounds successively approach the true algebraic connectivity with the convergence speed no slower than o 1 k

on strong stabilizability of mimo infinite dimensional systems abstract the strong stabilization problem i e the problem of designing a real stable stabilizing controller is considered for multi input multi output infinite dimensional real linear systems the considered systems may have infinitely many poles and zeros in the open right half plane as well as on the imaginary axis it is shown that the well known parity interlacing property pip for real rational systems is also a necessary condition in the most general case as long as the plant has coprime factorizations over h which is a necessary condition for stabilizability furthermore it is shown that pip is also sufficient under some additional mild assumptions

a constructive algorithm for the complete set of compensators for two dimensional feedback system design in the recent factorization approach to linear feedback system design it has been found that in order to completely solve a generalized stabilization problem a coprime condition in the ring of stable transfer functions must be solved in this note two dimensional 2 d systems are considered and this stable coprime condition is solved for stable rings a well known 2 d zero coprime condition is a special case of this condition this is the first constructive method for obtaining the complete set of solutions or compensators for 2 d feedback system design some examples of systems treated as 2 d systems are temporal spatial spatial spatial delay differential multipass etc

corrigendum feedback stabilization over commutative rings the matrix case in a previous paper 1 certain arguments in the proofs of proposition 1 proposition 4 and subsection 4 4 are erroneous these errors are highly regretted by this author and are corrected as follows these corrections however do not affect the main results of the paper 1 in definition 1 of a strictly causal matrix the second sentence should be corrected as a causal matrix m is called strictly causal if all entries of m are in j 2 in the sufficiency part of the proof of proposition 1 the two sentences starting in line 3 of the paragraph since it n j using units of r 1a should be replaced by the following from ny i x d and the assumption that all entries of p are in j and hence that of n since d is nonzerodivisor it follows that all entries of i x are in j hence detx det i i x is of the form 1 j where j is in j this implies that detx is a unit of r 1a as j is the jacobson s radical 3 the proof of the necessity part of proposition 4 is erroneous since this result is not needed further in the paper we replace it with the following version stating only the sufficient condition proposition 4 a strictly causal p nd 1 in f n is stabilizable if a b a

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part ii internal stabilization in this second part of the paper a quadrat siam j control optim 40 2003 pp 266 299 we show how to reformulate the fractional representation approach to synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions for internal stabilizability moreover we characterize all the integral domains a of siso stable plants such that every mimo plant defined by means of a transfer matrix whose entries belong to the quotient field k q a of a is internally stabilizable finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 s shankar and v r sule siam j control optim 30 1992 pp 11 30 v r sule siam j control optim 32 1994 pp 1675 1695 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

frequency domain robust regulation of signals generated by an infinite dimensional exosystem this paper deals with frequency domain robust regulation of signals generated by an infinite dimensional exosystem the problem is formulated and the stability types are chosen so that one can generalize the existing finite dimensional theory to more general classes of infinite dimensional systems and signals the main results of this article are extensions of the internal model principle of a necessary and sufficient solvability condition for the robust regulation problem and of davison s simple servo compensator for stable plants in the chosen algebraic framework

the fractional representation approach to synthesis problems an algebraic analysis viewpoint part i weakly doubly coprime factorizations in this paper we show how to reformulate the fractional representation approach to analysis and synthesis problems within an algebraic analysis framework in terms of modules we give necessary and sufficient conditions so that a system admits weakly left right doubly coprime factorizations moreover we explicitly characterize the integral domains a such that every plant defined by means of a transfer matrix whose entries belong to the quotient field of a admits weakly doubly coprime factorizations finally we show that this algebraic analysis approach allows us to recover on the one hand the approach developed in m c smith ieee trans automat control 34 1989 pp 1005 1007 and on the other hand the ones developed in k mori and k abe siam j control optim 39 2001 pp 1952 1973 v r sule siam j control optim 32 1994 pp 1675 1695 and 36 1998 pp 2194 2195 m vidyasagar h schneider and b a francis ieee trans automat control 27 1982 pp 880 894 m vidyasagar control system synthesis a factorization approach mit press cambridge ma 1985

average consensus on general strongly connected digraphs we study the average consensus problem of multi agent systems for general network topologies with unidirectional information flow we propose two linear distributed algorithms deterministic and gossip respectively for the cases where the inter agent communication is synchronous and asynchronous in both cases the developed algorithms guarantee state averaging on arbitrary strongly connected digraphs in particular this graphical condition does not require that the network be balanced or symmetric thereby extending previous results in the literature the key novelty of our approach is to augment an additional variable for each agent called surplus whose function is to locally record individual state updates for convergence analysis we employ graph theoretic and nonnegative matrix tools plus the eigenvalue perturbation theory playing a crucial role

approximation of linear distributed parameter systems by delay systems the present work addresses continuous time approximation of distributed parameter systems governed by linear one dimensional partial differential equations while approximation is usually realized by lumped systems that is finite dimensional systems we propose to approximate the plant by a time delay system within the graph topology we prove that if the plant admits a coprime factorization in the algebra of bibo stable systems any linear distributed parameter plant can be approximated by a time delay system governed by coupled differential difference equations considerations on stabilization and state space realization are carried out a numerical method for constructive approximation is also proposed and illustrated

feedback stabilization of multivariable two dimensional linear systems a constructive algorithm is presented for solving a two dimensional 2 d polynomial matrix equation that plays an important role in the output feedback stabilization of multivariable 2 d linear systems it is shown that this algorithm can have some computational advantages over the previous known ones based on the grobner basis approach as an application of the algorithm the class of all stabilizing strictly causal 2 d compensators is parametrized for a given stabilizable causal not necessarily strictly causal 2 d plant

on the solutions of the difference equation xn 1 xn 1 1 axnxn 1 we investigate the solutions of the difference equation x n 1 x n 1 1 ax nx n 1 n 0 1 2 where a 0 x 1 and x 0 are real numbers such that ax 1x 0 1

multi step gradient methods for networked optimization we develop multi step gradient methods for network constrained optimization of strongly convex functions with lipschitz continuous gradients given the topology of the underlying network and bounds on the hessian of the objective function we determine the algorithm parameters that guarantee the fastest convergence and characterize situations when significant speed ups over the standard gradient method are obtained furthermore we quantify how uncertainty in problem data at design time affects the run time performance of the gradient method and its multi step counterpart and conclude that in most cases the multi step method outperforms gradient descent finally we apply the proposed technique to three engineering problems resource allocation under network wide budget constraint distributed averaging and internet congestion control in all cases our proposed algorithms converge significantly faster than the state of the art

robust regulation theory for transfer functions with a coprime factorization classical frequency domain results of robust regulation are extended by requiring only a right or a left coprime factorization of a plant but not both the famous internal model principle is generalized first which leads to a necessary and sufficient solvability condition of the robust regulation problem and to a parametrization of all robustly regulating controllers in addition a procedure for constructing robustly regulating controllers is proposed

applications of grobner bases to signal and image processing a survey this paper is a tutorial and survey paper on the grobner bases method and some of its applications in signal and image processing although all the results presented in the paper are available in the literature we give an elementary treatment here in the hope that it will further bring awareness of and stimulate interest in grobner bases among researchers in signal and image processing we give first a tutorial on grobner bases and then a survey of the design of multidimensional wavelets and filter banks applications of grobner bases to other areas of signal and image processing are also briefly reviewed

controlled hopwise averaging and its convergence rate this technical note develops ideal controlled hopwise averaging icha and controlled hopwise averaging cha two asynchronous distributed averaging algorithms for wireless networks which attempt to make the most out of each iteration by fully exploiting the broadcast nature of wireless medium and incorporating feedback control of when to initiate an iteration the latter feature enabled by a common quadratic lyapunov function is novel among existing schemes and represents a new way to apply lyapunov stability theory we also derive deterministic upper bounds on the exponential convergence rate of icha on general and specific graphs express the bounds explicitly in terms of the graph invariants and show that they outperform the stochastic convergence rate of pairwise averaging on some common graphs of opposing densities finally we obtain upper bounds on the convergence rate of cha and show that cha is capable of closely mimicking the behavior of icha while being practical

quantum linear coherent controller synthesis a linear fractional representation approach abstract this paper is concerned with a linear fractional representation approach to the synthesis of linear coherent quantum controllers for a given linear quantum plant the plant and controller represent open quantum harmonic oscillators and are modelled by linear quantum stochastic differential equations the feedback interconnections between the plant and the controller are assumed to be established through quantum bosonic fields in this framework conditions for the stabilization of a given linear quantum plant via linear coherent quantum feedback are addressed using a stable factorization approach the class of all stabilizing quantum controllers is parameterized in the frequency domain coherent quantum weighted 2 and control problems for linear quantum systems are formulated in the frequency domain finally a projected gradient descent scheme is outlined for the coherent quantum weighted 2 control problem

feedback stabilization over commutative rings further study of the coordinate free approach this paper is concerned with the coordinate free approach to control systems the coordinate free approach is a factorization approach but does not require the coprime factorizations of the plant we present two criteria for feedback stabilizability for multi input multi output mimo systems in which transfer functions belong to the total rings of fractions of commutative rings both of them are generalizations of sule s results in siam j control optim 32 1994 pp 1675 1695 the first criterion is expressed in terms of modules generated from a causal plant and does not require the plant to be strictly causal it shows that if the plant is stabilizable the modules are projective the other criterion is expressed in terms of ideals called generalized elementary factors this gives the stabilizability of a causal plant in terms of the coprimeness of the generalized elementary factors as an example a discrete finite time delay system is considered

multidimensional discrete stability by serre categories and the construction and parametrization of observers via gabriel localizations immediate predecessors of this work were a paper on two dimensional deadbeat observers by bisiacco and valcher multidimens systems signal process 19 2008 pp 287 306 and one on one dimensional functional observers by blumthaler linear algebra appl 432 2010 pp 1560 1577 compare also fuhrmann s comprehensive paper linear algebra appl 428 2008 pp 44 136 the present paper extends blumthaler s results to continuous or discrete multidimensional behaviors i e constructs and parametrizes all controllable observers of a given multidimensional behavior and for this purpose also discusses the required multidimensional stability such an observer produces a signal that approximates or estimates a desired component of the behavior such that the signal difference is negligible in a suitable sense this definition thus presupposes that of negligible or stable autonomous systems in the standard one dimensional case these are the asymptotically stable behaviors we define and investigate

on a generalization of the youla kucera parametrization part i the fractional ideal approach to siso systems abstract in this paper we show how to use the theory of fractional ideals in order to study the fractional representation approach to analysis and synthesis problems for siso systems within this mathematical framework we give necessary and sufficient conditions so that a plant is internally strongly bistably stabilizable or admits a weak coprime factorization moreover we show how to generalize the youla kucera parametrization of the stabilizing controllers to any stabilizable plant which does not necessarily admit a coprime factorization this parametrization is generally affine in two free parameters

elementary proof of controller parametrization without coprime factorizability recently a controller parametrization method without coprime factorizability was presented by mori in this note we present this method using elementary matrix operations unlike in the earlier paper good knowledge of commutative algebra and module theory is not required

relationship between standard control problem and model matching problem without coprime factorizability we present the equivalence between a standard control problem and a model matching problem without coprime factorizability of plants this equivalence is well known if every stabilizable plant admit a doubly coprime factorization the result of this note does not require the coprime factorizability of plants

stabilizability representations and factorizations for time varying linear systems abstract we study the system representations factorizations and stabilizability of a discrete time time varying linear system in the framework of nest algebra we shown that every time varying linear system admits a normalized left factorization while it may possibly not have a right factorization the relationship between the system representation and factorization is studied and some new stabilizability criteria are established

consensus based distributed multiple model ukf for jump markov nonlinear systems this note studies the problem of distributed estimation for jump markov nonlinear systems jmnlss in a not fully connected sensor network based on the consensus theory a distributed unscented kalman filter ukf is first derived for nonlinear systems without jumping parameters and then it is extended to develop a distributed multiple model ukf for jmnlss the proposed filtering algorithm is illustrated via a simulation example involving tracking a maneuvering target

on the elementary factors of linear systems over unique factorization domains abstract the concept of elementary factors introduced by sule siam j control optim 32 1994 1675 1695 plays an important role in the output feedback stabilizability and stabilization of linear systems over unique factorization domains ufds this paper gives a simple proof that the elementary factors of t and w are identical where t and w are matrices associated with a right and a left matrix fraction description of a linear system over a ufd relationship between the reduced minors and the elementary factors is established an efficient method for computing the elementary factors based on the reduced minors is also proposed

accelerated distributed average consensus via localized node state prediction this paper proposes an approach to accelerate local linear iterative network algorithms asymptotically achieving distributed average consensus we focus on the class of algorithms in which each node initializes its ldquostate valuerdquo to the local measurement and then at each iteration of the algorithm updates this state value by adding a weighted sum of its own and its neighbors state values provided the weight matrix satisfies certain convergence conditions the state values asymptotically converge to the average of the measurements but the convergence is generally slow impeding the practical application of these algorithms in order to improve the rate of convergence we propose a novel method where each node employs a linear predictor to predict future node values the local update then becomes a convex weighted sum of the original consensus update and the prediction convergence is faster because redundant states are bypassed the method is linear and poses a small computational burden for a concrete theoretical analysis we prove the existence of a convergent solution in the general case and then focus on one step prediction based on the current state and derive the optimal mixing parameter in the convex sum for this case evaluation of the optimal mixing parameter requires knowledge of the eigenvalues of the weight matrix so we present a bound on the optimal parameter calculation of this bound requires only local information we provide simulation results that demonstrate the validity and effectiveness of the proposed scheme the results indicate that the incorporation of a multistep predictor can lead to convergence rates that are much faster than those achieved by an optimum weight matrix in the standard consensus framework

dynamics of a kth order rational difference equation in this article we investigate the dynamics of the difference equation x n 1 x n ka x n kx n where x k x 0 0 and a 0 k is any positive integer in some particular cases we allow for zero initial conditions

fast consensus by the alternating direction multipliers method the alternating direction multipliers method admm has been recently proposed as a practical and efficient algorithm for distributed computing we discuss its applicability to the average consensus problem in this paper by carefully relaxing admm augmentation coefficients we are able to analytically investigate its properties and to propose simple and strict analytical bounds these provide a clear indication on how to choose system parameters for optimized performance we prove both analytically and via simulations that the proposed approach exhibits convergence speed between the best in the literature classical and optimized solutions while providing the most powerful resilience to noise

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

analysis of accelerated gossip algorithms gossiping is a distributed process whose purpose is to enable the members of a group of n 1 autonomous agents to asymptotically determine in a decentralized manner the average of the initial values of their scalar gossip variables this paper analyzes the accelerated gossip algorithms first proposed in cao spielman and yeh 2006 in which local memory is exploited by installing shift registers at each agent for the two register case the existence of the desired convergence is established under a symmetry assumption by separately studying the convergence in expectation and in mean square in particular the optimal rate of convergence in expectation is derived which is faster than that of the standard gossip algorithm and a sufficient condition on the adjustable parameter for the convergence in mean square is provided these theoretical results are validated for some classes of networks by comparison with existing empirical data more general multi register cases are also discussed

adding a single state memory optimally accelerates symmetric linear maps previous papers have proposed to add memory registers to the dynamics of discrete time linear systems in order to accelerate their convergence in particular it has been proved that adding one memory slot per agent allows faster convergence towards average consensus we here prove that this situation cannot be improved by adding more memory slots when the knowledge about the self adjoint linear map to be accelerated reduces to bounds on its extreme eigenvalues

on stabilization and the existence of coprime factorizations let k be an integral domain and f its quotient field we show there are plants over f which have no stable coprime factorizations but can be stabilized in a stable closed loop this answers a question posed by vidyasagar schneider and francis

feedback stabilization over commutative rings the matrix case this paper provides a solution of the feedback stabilization problem over commutative rings for matrix transfer functions stabilizability of a transfer matrix is realised as local stabilizability over the entire spectrum of the ring for stabilizable plants certain modules generated by its fractions and that of the stabilizing controller are shown to be projective compliments of each other in the case of rings with irreducible spectrum this geometric relationship shows that the plant is stabilizable if and only if the above modules of the plant are projective of ranks equal to the number of inputs and the outputs if the maxspectrum of the ring is noetherian and of zero krull dimension then this result shows that the stabilizable plants have doubly coprime fractions over unique factorization domains the above stabilizability condition is interpreted in terms of matrices formed by the fractions of the plant certain invariants of these matrices known as elementary factors are defined and it is shown that the plant is stabilizable if and only if these elementary factors generate the whole ring this condition thus provides a generalization of the coprime factorizability as a condition for stabilizabilty a formula for the class of all stabilizing controllers is then developed that generalizes the previous well known formula in factorization theory for multidimensional transfer functions these results provide concrete conditions for stabilizabilty finally it is shown that the class of polynomial rings over principal ideal domains is an additional class of rings over which stabilizable plants always have doubly coprime fractions

optimization and analysis of distributed averaging with short node memory distributed averaging describes a class of network algorithms for the decentralized computation of aggregate statistics initially each node has a scalar data value and the goal is to compute the average of these values at every node the so called average consensus problem nodes iteratively exchange information with their neighbors and perform local updates until the value at every node converges to the initial network average much previous work has focused on algorithms where each node maintains and updates a single value every time an update is performed the previous value is forgotten convergence to the average consensus is achieved asymptotically the convergence rate is fundamentally limited by network connectivity and it can be prohibitively slow on topologies such as grids and random geometric graphs even if the update rules are optimized in this paper we provide the first theoretical demonstration that adding a local prediction component to the update rule can significantly improve the convergence rate of distributed averaging algorithms we focus on the case where the local predictor is a linear combination of the node s current and previous values i e two memory taps and our update rule computes a combination of the predictor and the usual weighted linear combination of values received from neighboring nodes we derive the optimal mixing parameter for combining the predictor with the neighbors values and conduct a theoretical analysis of the improvement in convergence rate that can be achieved using this acceleration methodology for a chain topology on n nodes this leads to a factor of n improvement over standard consensus and for a two dimensional grid our approach achieves a factor of n improvement

on a general structure of the stabilizing controllers based on stable range in this paper we prove that some stabilizing controllers of a plant which admits a left right coprime factorization have a special form where their stable and unstable parts are separated the dimension of the unstable part depends on the algebraic concept of stable range of the ring a of siso stable plants moreover we prove that if the stable range of a is equal to 1 then every plant defined by a transfer matrix with entries in the quotient field of a and admitting a left right coprime factorization can be stabilized by a stable controller strong stabilization in particular using a result of treil proving that the stable range of h infty mathbb d is equal to 1 we show that every stabilizable plant defined by a transfer matrix with entries in the quotient field of h infty mathbb d or h infty mathbb c is strongly stabilizable and equivalently every couple of stabilizable plants can be simultaneously stabilized by a controller simultaneous stabilization finally using the fact that the topological stable range of h infty mathbb d is equal to 2 a result due to suarez we show that every unstabilizable siso plant defined by a transfer function with entries in the quotient field of h infty mathbb d is as close as we want to a stabilizable plant in the product topology

global behavior of a higher order difference equation in this paper we study the global behavior of the nonnegative equilibrium points of the difference equation x n 1 ax n email protected i 02k 1x n i n 0 1 where a b c are nonnegative parameters initial conditions are nonnegative real numbers and k m are nonnegative integers email protected 2k 1 also we derive solutions of some special cases of this equation

controller parameterization of anantharam s example we consider the controller parameterization of anantharam s example 1985 it is shown that the parameterization is achieved by using only one parameter even though the plant does not have a coprime factorization

robustness analysis of uncertain linear singular systems with output feedback control the robustness analysis for a linear singular system with uncertain parameters and static output feedback control is considered the problem is transformed into a robust nonsingularity problem based on the linear fractional transformation lft approach the robustness bounds to preserve regularity impulse immunity and stability are found in terms of the structured singular value spl mu with respect to parametric uncertainties the lft approach provides a unified framework for robustness analysis of both uncertain linear continuous discrete time singular systems

optimal tradeoff between instantaneous and delayed neighbor information in consensus algorithms we consider a distributed consensus problem over a network where at each time instant every node receives two pieces of information from disjoint neighboring sets a weighted average of current st

a convex characterization of multidimensional linear systems subject to sqi constraints this technical note proposes a convex characterization of the set of all stable closed loop linear systems that are obtained from a given plant which may be multidimensional by interconnecting it in feedback with controllers that satisfy a certain pre selected constraint we take an approach that is particularly useful when a doubly coprime factorization of the plant is difficult to obtain and a stable stabilizing controller may not exist the plant is not strongly stabilizable or when one may be difficult to find most related work requires one of these we adopt the so called coordinate free approach which unlike youla s parametrization does not rely on a doubly coprime factorization of the plant we show that if constraints which satisfy a condition called strong quadratic invariance sqi are imposed on the controllers then the set of all stable closed loop multidimensional linear systems has a convex representation and norm optimal control problems can be cast in convex form although the sqi condition is in general slightly stronger than quadratic invariance qi which was developed in related work they are equivalent for common classes of problems arising in decentralized control

stability and stabilization of multidimensional input output systems in this paper we discuss stability and stabilization of continuous and discrete multidimensional input output io behaviors of dimension r which are described by linear systems of complex partial differential resp difference equations with constant coefficients where the signals are taken from various function spaces in particular from those of polynomial exponential functions stability is defined with respect to a disjoint decomposition of the r dimensional complex space into a stable and an unstable region with the standard stable region in the one dimensional continuous case being the set of complex numbers with negative real part a rational function is called stable if it has no poles in the unstable region an io behavior is called stable if the characteristic variety of its autonomous part has no points in the unstable region this is equivalent to the stability of its transfer matrix and an additional condition the system is called stabilizable if there is a compensator io system such that the output feedback system is well posed and stable we characterize stability and stabilizability and construct all stabilizing compensators of a stabilizable io system parametrization the theorems and proofs are new but essentially inspired and influenced by and related to the stabilization theorems concerning multidimensional io maps as developed for instance by bose guiver shankar sule xu lin ying zerz and quadrat and of course the seminal papers of vidyasagar youla and others in the one dimensional case in contrast to the existing literature the theorems and proofs of this paper do not need or employ the so called fractional representation approach i e various matrix fraction descriptions of the transfer matrix thus avoiding the often lengthy matrix computations and seeming to be of interest even for one dimensional systems at least to the author an important mathematical tool new in systems theory is gabriel s localization theory which only in the case of ideal convex shankar sule unstable regions coincides with the usual one algorithmic tests for stability stabilizability and ideal convexity and the algorithmic construction of stabilizing compensators are addressed but still encounter many difficulties see in particular the open problems listed by xu e

the admm algorithm for distributed quadratic problems parameter selection and constraint preconditioning this paper presents optimal parameter selection and preconditioning of the alternating direction method of multipliers admm algorithm for a class of distributed quadratic problems which can be formulated as equality constrained quadratic programming problems the parameter selection focuses on the admm step size and relaxation parameter while the preconditioning corresponds to selecting the edge weights of the underlying communication graph we optimize these parameters to yield the smallest convergence factor of the iterates explicit expressions are derived for the step size and relaxation parameter as well as for the corresponding convergence factor numerical simulations justify our results and highlight the benefits of optimal parameter selection and preconditioning for the admm algorithm

a generalization of serre s conjecture and some related issues abstract several topics concerned with multivariate polynomial matrices like unimodular matrix completion matrix determinantal or primitive factorization matrix greatest common factor existence and subsequent extraction along with relevant primeness and coprimeness issues are related to a conjecture which may be viewed as a type of generalization of the original serre problem conjecture solved nonconstructively in 1976 and constructively more recently this generalized serre conjecture is proved to be equivalent to several other unsettled conjectures and therfore all these conjectures constitute a complete set in the sense that solution to any one also solves all the remaining

the stabilization problem for discrete time varying linear systems in this paper we consider the strong stabilization problem for a time varying linear system which admits a coprime factorization we also study the simultaneous and robust stabilization problems for this class of systems

on the difference equation xn 1 xn 1 1 xnxn 1 in this paper we investigate the solutions of the difference equation x n 1 x n 1 1 x nx n 1 n 0 1 2 where x 1 and x 0 are the real numbers such that x 1x 0 1

on the positive solutions of the difference equation xn 1 xn 11 axnxn 1 the positive solutions of the difference equation x n 1 x n 11 ax nx n 1 n 0 1 2 are investigated where x 1 x 0 and a are the nonnegative real numbers

consensus algorithms with state dependent weights we provide an analysis of a distributed consensus type algorithm with weights dependent only on the received data our approach does not require any global knowledge of the network which distinguishes our approach from most other contributions in general the weights may be further modified by any function this in turn may model various network behaviors e g link failures and time varying networks we provide general convergence conditions prove several important properties derive steady states for such locally derived weights as well as analyze the convergence rate of the algorithm applications of such weight model include distributed algorithms which do not require exact average and have no global information about the network topology