systems over a principal ideal domain a polynomial model approach the polynomial model approach to linear dynamical systems over a field was developed principally by p a fuhrmann starting in 1976 j franklin inst 305 1976 pp 521 540 in this paper an analogous approach is proposed for systems over a principal ideal domain when the concept of extended linear i o map is introduced fractional representations of transfer function matrices arise naturally in this theoretical framework a correspondence between fractional representations of the transfer function matrix of a given i o map and its reachable or observable realizations is established the mcmillan degree of a linear i o map is proved to be equal to the degree of the determinant of the matrix appearing as denominator in a coprime fractional representation of the associated transfer function matrix

social balance as a satisfiability problem of computer science reduction of frustration was the driving force in an approach to social balance as it was recently considered by antal t antal p l krapivsky and s redner phys rev e 72 036121 2005 we generalize their triad dynamics to k cycle dynamics for arbitrary integer k we derive the phase structure determine the stationary solutions and calculate the time it takes to reach a frozen state the main difference in the phase structure as a function of k is related to k being even or odd as a second generalization we dilute the all to all coupling as considered by antal to a random network with connection probability w 1 interestingly this model can be mapped to a satisfiability problem of computer science the phase of social balance in our original interpretation then becomes the phase of satisfaction of all logical clauses in the satisfiability problem in common to the cases we study the ideal solution without any frustration always exists but the question actually is as to whether this solution can be found by means of a local stochastic algorithm within a finite time the answer depends on the choice of parameters after establishing the mapping between the two classes of models we generalize the social balance problem to a diluted network topology for which the satisfiability problem is usually studied on the other hand in connection with the satisfiability problem we generalize the random local algorithm to a p random local algorithm including a parameter p that corresponds to the propensity parameter in the social balance problem the qualitative effect of the inclusion of this parameter is a bias towards the optimal solution and a reduction of the needed simulation time

regular paper model matching for linear systems with delays and 2d systems model matching problem for linear systems with delays is considered via a transfer matrix approach we deal with a general class of neutral delay differential systems which is equivalent to 2d systems from a realizability point of view the solution of the problem is based on the decomposition of the ring of the causal rational functions which is not a principal ideal domain as the intersection of two suitable principal ideal domains

on feedback invariance properties for systems over a principal ideal domain simple necessary and sufficient conditions for the solvability of many control problems for linear systems over a field are based on the equivalence between the a b invariance property and the a bf invariance or feedback invariance property for systems over a ring this equivalence is no longer true and many results of the geometric control theory cannot be extended we present new algorithmically checkable characterizations of the a bf invariance property for systems defined over a principal ideal domain and a new solvability condition for the disturbance rejection problem

model matching with strong stability in switched linear systems abstract this work deals with model matching by output dynamic feedback in switched linear systems the plant and the model are assumed to be subject to different switching signals a necessary and sufficient condition for achieving model matching with asymptotic stability of both the closed loop compensated system and the compensator for a sufficiently large dwell time is proven such condition is obtained by specializing the structural condition with a suitable redefinition of the robust controlled invariant subspace involved capable of capturing not only the structural aspect of the problem but also the stability aspects the effect of the combined action of nonzero initial states and nonzero inputs is dealt with the solution to a more demanding problem formulation where the dwell time is assumed to be fixed and given is also discussed

necessary and sufficient conditions for asymptotic model matching of switching linear systems this paper investigates the problem of designing a feedback controller to force the response of a given plant to match asymptotically that of a prescribed model in case both the plant and the model are switching linear systems matching has to be achieved with stability of the feedback loop for any initial conditions of the plant the model and the controller in case it is dynamic and for any choice of the switching law solvability of the problem is characterized in terms of necessary and sufficient conditions that in part refer to the geometric structure of the difference system which compares the output of the model and of the plant stability is considered both for slow switching and for arbitrary switching proofs of the solvability conditions provide viable procedures for synthesizing the static or dynamic controllers that achieve the matching respectively when the state of the model is measurable and when it is not weaker sufficient conditions that can be practically checked by simple algorithmic procedures are provided both in the general situation and under slightly restrictive hypotheses

some extremal bounds for subclasses of univalent functions in this paper we obtain the sharp lower bound for ref z z u for functions f that are k uniformly convex in the unit disk u next we consider the problem of finding the minimum of ref z for functions f that are k uniformly convex in the disk of radius r corresponding results for the class of starlike functions related to the class of k uniformly convex functions are presented

detectability of linear systems over a principal ideal domain with unknown inputs abstract observability and detectability conditions are obtained for a sort of linear time invariant systems affected by unknown inputs it is assumed that the system can be described using matrices whose elements are within a principal ideal domain pid it is shown that under suitable hypothesis the obtained conditions are necessary and sufficient the analysis is carried out by making use of the smith normal form of matrices over a pid the obtained conditions are a generalization of known conditions for particular sorts of systems which are included in those considered here

infinite structure and exact model matching problem a geometric approach we first generalize to a b c d quadruples the geometric characterization of the infinite zero structure we then give a new geometric proof for a solvability condition of the exact model matching problem expressed in terms of this concept and previously established in the polynomial context by morse verghese and pernebo this emphasizes the approach independent character of the infinite zero structure

controller design for delay systems via eigenvalue assignment on a new result in the distribution of quasi polynomial roots this paper considers the eigenvalue distribution of a linear time invariant lti system with time delays and its application to some controllers design for a delay plant via eigenvalue assignment first a new result on the root distribution for a class of quasi polynomials is developed based on the extension of the hermite biehler theorem then such result is applied to proportional integral pi controller parameter design for a first order plant with time delay through pole placement the complete region of pi gains can be obtained so that the rightmost eigenvalues in the infinite eigenspectrum of the closed loop system with delay plant are assigned to desired positions in the complex plane furthermore on the basis of the previous result this paper also extended the pi control to the proportional integral derivative pid control it is worth pointing out that this work aims to improve the performance of the closed loop system on the premise of guaranteeing the stability

dynamics of social balance on networks we study the evolution of social networks that contain both friendly and unfriendly pairwise links between individual nodes the network is endowed with dynamics in which the sense of a link in an imbalanced triad a triangular loop with one or three unfriendly links is reversed to make the triad balanced with this dynamics an infinite network undergoes a dynamic phase transition from a steady state to paradise all links are friendly as the propensity p for friendly links in an update event passes through 1 2 a finite network always falls into a socially balanced absorbing state where no imbalanced triads remain if the additional constraint that the number of imbalanced triads in the network not increase in an update is imposed then the network quickly reaches a balanced final state i introduction in this work we investigate the role of friends and enemies on the evolution of social networks we represent individuals as nodes in a graph and a relationship between individuals as a link that joins the corresponding nodes to quantify a relationship we assign the binary variable sij 1 to link ij with sij 1 if nodes i and j are friends and sij 1 ifi and j are enemies fig 1 a basic characterization of relationships between mutual acquaintances is the notion of social balance 1 2 the triad ijk is defined as balanced if the sign of the product of the links in the triad sijsjkski equals 1 while the triad is imbalanced otherwise we define a triad to be of type k if it contains k negative links thus 0 and 2 are balanced while 1 and 3 are imbalanced a balanced triad therefore fulfills the adage that i a friend of my friend is my friend ii an enemy of my friend

paper implicit and explicit lqg self tuning controllers the design of optimal controllers for use in self tuning systems is considered linear quadratic gaussian lqg controllers are widely used elsewhere but have not until recently been applied in self tuning systems except in minimum output variance forms the lqg controllers offer a guarantee of stability when the plant parameters are known which is particularly useful for nonminimum phase systems the explicit lqg self tuning controllers introduced in the following are relatively simple to implement the first version of an implicit lqg self tuning controller is also introduced the magnitude of the transport delay terms need not be known a priori and integral action may be introduced easily if required the desired closed loop poles of the system can be prespecified

conic regions and k uniform convexity abstract let k c denote a domain such that 1 k and k is a conic section with eccentricity equal to 1 k in this paper authors introduce the class of k uniformly convex functions k ucv with the property that the values of the expression 1 zf z f z lie inside the domain k necessary and sufficient conditions for membership in k ucv as well as sharp growth and distortion theorems for k uniformly convex functions are given the obtained results generalize the concept of uniform convexity due to a w goodman ann polon math 56 1991 87 92

feedback realization of nonsingular precompensators for linear systems with delays the problem of realization of dynamic precompensators for linear systems with delays by static or dynamic state feedback and static output feedback is considered necessary and sufficient conditions for the solutions are given

on certain problem in the class of k starlike functions in this paper we consider the classes of k uniformly convex and k starlike functions defined in kanas and wisniowska 1999 2000 1 2 which generalize the class of uniformly convex functions introduced by goodman 1991 3 we discuss the real part of f z z when f is k starlike we find the minimum of ref z z improving the results obtained recently in wisniowska wajnryb 2009 11

fraction representations of non linear systems a simplified approach abstract a non linear system has a right fraction representation if it can be represented as pq 1 where p and q are stable systems and it has a left fraction representation if it can be represented as g 1 t where g and t are stable systems we develop here a theory of right and of left fraction representations for discrete time non linear systems with bounded input sequences we indicate the connection between fraction representations and the stabilization problem for non linear systems

algebraic design of anisochronic controllers for time delay systems the prime objective of the paper is to overcome the conventional restriction to the field of rational functions as far as the algebraic design of control systems is concerned by adopting the affine parameterization approach from algebraic control synthesis for the controllers given as the so called rq meromorphic functions an algebraic solution to time delay system control design is opened where neither an introduction of 2d transfer functions nor the assumption of commensurate delays is needed the proposed design results in controllers combining both the integrators and delayers due to this property referred to as anisochronic

diophantine equations in control a survey abstract this survey is also a tutorial whose aim is to explain the role of diophantine equations in the synthesis of feedback control systems these are linear equations in a ring and result from a fractional representation of the systems involved the cornerstone of the exposition is a simple parametrization of all stabilizing controllers for a given plant one can then choose in principle the best controllers for various applications these ideas evolved from early attempts to use polynomial equations in the design of discrete time linear systems by now they have been extended to continuous time infinite dimensional time varying and non linear systems

the disturbance decoupling problem for systems over a ring up to now the use of geometric methods in the study of disturbance decoupling problems ddps for systems over a ring has provided only necessary conditions for the existence of solutions in this paper we study such problems considering separately the case in which only static feedback solutions are allowed and the one in which dynamic feedback solutions are admitted in the first case we give a complete geometric characterization of the solvability conditions of such problems for injective systems with coefficients in a commutative ring practical procedures for testing the solvability conditions and for constructing solutions if any exist are given in the case of systems with coefficients in a principal ideal domain pid in the second case we give a complete geometric characterization of the solvability conditions for systems with coefficients in a pid

robust control of delay systems a sliding mode control design via lmi this paper considers the sliding mode control of uncertain systems with single or multiple constant or time varying state delays submitted to additive perturbations the sliding surface is designed so to maximize the calculable set of admissible delays the conditions for the existence of the sliding regime are studied by using lyapunov krasovskii functionals and lyapunov razumikhin functions lmis are used for the optimization procedure two examples illustrate the proposed method

decoupling without prediction of linear systems with delays a structural approach we exhibit using a new structural approach specific for linear systems with delays a necessary and sufficient condition for static row by row decoupling without prediction moreover the decoupling problem is analyzed through two different concepts the total one without any time assumption and the partial one in a temporal mean which can be considered if the total one has no solution

universality class of triad dynamics on a triangular lattice we consider triad dynamics as it was recently considered by antal et al phys rev e 72 036121 2005 as an approach to social balance here we generalize the topology from all to all to the regular one of a two dimensional triangular lattice the driving force in this dynamics is the reduction of frustrated triads in order to reach a balanced state the dynamics is parametrized by a so called propensity parameter p that determines the tendency of negative links to become positive as a function of p we find a phase transition between different kinds of absorbing states the phases differ by the existence of an infinitely connected percolated cluster of negative links that forms whenever p ensuremath leqslant p c moreover for p ensuremath leqslant p c the time to reach the absorbing state grows powerlike with the system size l while it increases logarithmically with l for pg p c from a finite size scaling analysis we numerically determine the static critical exponents ensuremath beta and ensuremath nu ensuremath perp together with ensuremath gamma ensuremath tau ensuremath sigma and the dynamical critical exponents ensuremath nu ensuremath vert and ensuremath delta the exponents satisfy the hyperscaling relations we also determine the fractal dimension d f that satisfies a hyperscaling relation as well the transition of triad dynamics between different absorbing states belongs to a universality class with different critical exponents we generalize the triad dynamics to four cycle dynamics on a square lattice in this case again there is a transition between different absorbing states going along with the formation of an infinite cluster of negative links but the usual scaling and hyperscaling relations are violated

frequency domain synthesis of hereditary control systems via anisochronic state space a method of control feedback design for systems with hereditary properties is presented which is based on the concept of anisochronic state space a new kind of state feedback control is proposed using as state variables the system accumulation attributes only while the other delay dynamics are represented by functional terms assigning the control parameters is approached as a placement of characteristic function zeros however owing to the infinite set of these zeros in the hereditary system only the dominant zeros are placed for this purpose a new technique applying the conformal mapping of transcendental characteristic function of the hereditary system has been developed