face counting on an acyclic birkhoff polytope in this paper we present some algorithms allowing an exhaustive account on the number of edges and faces of the acyclic birkhoff polytope

transcendental and interpolation methods in simultaneous stabilization and simultaneous partial pole placement problems in this paper we investigate the existence of a compensator which simultaneously renders a given r tuple of multiinput multioutput p times m linear dynamical systems internally stable in particular we parametrize a set of simultaneously stabilizable r tuples of plants and show that provided r leqq max m p the above set is semialgebraic and dense in the space sigma of r tuples of plants furthermore we also consider an extension of the classical pole placement and stabilization problems and investigate the simultaneous partial pole placement problem consequently we consider a suitable topology in and obtain a necessary condition and a sufficient condition for the generic partial pole placement problem surprisingly enough the problem of simultaneously stabilizing a triplet of m times m plants chosen generically is shown equivalent to the problem of partially pole placing a single m times m plant by a stable minimum phase compensator on the other hand the problem of simultaneous

on lattices with a smallest set of aggregation functions given a bounded lattice l with bounds 0 and 1 it is well known that the set pol 0 1 l of all 0 1 preserving polynomials of l forms a natural subclass of the set c l of aggregation functions on l the main aim of this paper is to characterize all finite lattices l for which these two classes coincide i e when the set c l is as small as possible these lattices are shown to be completely determined by their tolerances also several sufficient purely lattice theoretical conditions are presented in particular all simple relatively complemented lattices or simple lattices for which the join meet of atoms coatoms is 1 0 are of this kind

fractional perfect b matching polytopes i general theory the fractional perfect b matching polytope of an undirected graph g is the polytope of all assignments of nonnegative real numbers to the edges of g such that the sum of the numbers over all edges incident to any vertex v is a prescribed nonnegative number b v general theorems which provide conditions for nonemptiness give a formula for the dimension and characterize the vertices edges and face lattices of such polytopes are obtained many of these results are expressed in terms of certain spanning subgraphs of g which are associated with subsets or elements of the polytope for example it is shown that an element u of the fractional perfect b matching polytope of g is a vertex of the polytope if and only if each component of the graph of u either is acyclic or else contains exactly one cycle with that cycle having odd length where the graph of u is defined to be the spanning subgraph of g whose edges are those at which u is positive

simultaneous stabilization of single input single output discrete time systems the problem of finding one compensator which simultaneously stabilizes a family of single input single output siso discrete time plants is considered the family of plants is described by the transfer functions pz q q in q which are generated via a z transformation a number of assumptions describing the set of allowable plants are then given these assumptions include some regularity conditions on the plants and a minimum phase requirement the satisfaction of these assumptions guarantees the existence of a strictly proper stable compensator c z for simultaneous stabilization an iterative computation method is provided for control design

simultaneous identification of linear systems a heuristic approach abstract the problem of simultaneous system identification is posed and an efficient algorithm for its solution is formulated our algorithm is a blend of an a search together with simulated annealing the proposed algorithm returns the optimal solution while the number of required operations is usually much smaller than any other brute force algorithm

simultaneous stabilization using stable system inversion abstract this paper investigates the use of stable system inversion to design controllers for the simultaneous stabilization of multi input multi output systems a parametrization of all simultaneously stabilizing controllers for systems admitting a stable inverse is developed the controller is shown to have the structure of a generalized observer for strictly proper systems an intermediate step of the design requires solving a sequence of strong stabilization subproblems for systems with components having identical stable minimum phase transfer functions the design requires only a single model of the component in the controller in systems where a stable inverse fails to exist an interpolation scheme is proposed to develop a stabilizing controller

simultaneous partial pole placement a new approach to multimode system design simultaneous partial pole placement of a family of single input single output plants is proposed as a generalization of the classical pole placement and stabilization problems this problem finds application in the design of a compensator for a family of linear dynamical systems in this note we show that the proposed problem is equivalent to a new class of transcendental problem using stable minimum phase rational functions with real coefficients a necessary condition for the solvability of the associated transcendental problem is obtained finally a counterexample to the following conjecture is obtained pairs of simultaneously stabilizable plants of bounded mcmillan degree have simultaneously stabilizing compensators of bounded mcmillan degree

stabilization of a linear plant via a stable compensator having no real unstable zeros abstract this paper studies the following problem under what conditions can a linear plant be stabilized by a stable compensator having no real zeros in the closed right half plane solving this problem is an important step towards to solving the problems of stabilization of linear systems via stable minimum phase compensation and simultaneous stabilization of n n 2 plants in the paper necessary and sufficient conditions are derived these conditions are completely general and therefore encompass unstable nonminimum phase plants as well it is shown that the stabilizability solely depends on the locations of real zeros and real poles of a given plant for a plant satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is also provided and illustrated via an example

eigenvalues of tridiagonal pseudo toeplitz matrices abstract in this article we determine the eigenvalues of sequences of tridiagonal matrices that contain a toeplitz matrix in the upper left block

some remarks about acyclic and tridiagonal birkhoff polytopes abstract for a given tree t we consider the facial structure of the acyclic birkhoff polytope t we also determine the f vector of the polytope n t consisting of all tridiagonal doubly stochastic matrices of order n finally we count the number of combinatorially distinct faces of n t in each dimension

on the decomposability of aggregation functions on direct products of posets abstract based on results concerning equivalences on direct products of sets a representation of aggregation functions acting on products of ordered structures by means of aggregation functions acting component wise is obtained and discussed in particular t norms and t conorms on direct products of bounded lattices are considered generalizing some earlier results of de baets and mesiar

alternating sign matrices related 0 1 matrices and the smith normal form abstract we investigate the smith normal form snf of alternating sign matrices asms and related matrices of 0 s and 1 s 0 1 matrices we identify certain classes of asms and 0 1 matrices whose snfs are 0 1 matrices we relate some of our work to various ranks in particular the 0 1 rank of a 0 1 matrix that is the bipartite partition number of a bipartite graph

the skeleton of acyclic birkhoff polytopes abstract for a fixed tree t with n vertices the corresponding acyclic birkhoff polytope n t consists of doubly stochastic matrices having support in positions specified by t this is a face of the birkhoff polytope n which consists of all n n doubly stochastic matrices the skeleton of n t is the graph where vertices and edges correspond to those of n t and we investigate some properties of this graph in particular we characterize adjacency of pairs of vertices compute the minimum degree of a vertex and show some properties of the maximum degree of a vertex in the skeleton we also determine the maximum degree for certain classes of trees including paths stars and caterpillars

l rays of permutation matrices and doubly stochastic matrices abstract let m n be the space of real n n matrices we investigate a linear transformation m n r n called an l ray motivated by x ray which is defined in terms of sums of the entries in the blocks of a certain l shaped partition of the positions of a matrix a m n we find descriptions of the image of the classes of permutation matrices and doubly stochastic matrices under this map and show connections to majorization theory

spanning tree invariants loop systems and doubly stochastic matrices abstract the spanning tree invariant of lind and tuncel 12 is observed in the context of loop systems of markov chains for n 1 2 3 the spanning tree invariants of the loop systems of a markov chain determined by an irreducible stochastic n n matrix p coincide if and only if p is doubly stochastic and in this case the common value of the spanning tree invariants of the loop systems is n

sufficient conditions for generic simultaneous pole assignment and stabilization of linear mimo dynamical systems it has been shown that a generic r tuple of m input p output dynamical systems is simultaneously stabilizable pole assignable if r m p and the mcmillian degrees of the systems are not too different this result improves the currently known upper bound r spl les max m p on the number of plants in the case r spl les max m p an upper bound on the degree of the simultaneous pole assigning compensator has also been derived which improves the bound obtained by ghosh and byrnes 1983

on minimal degree simultaneous pole assignment problems in this paper we show that a generic r tuple of m input p output linear systems is simultaneously pole assignable if r m p and the mcmillan degrees of the systems are not too different we also obtain upper bounds for the degrees of the compensators which simultaneously assign the characteristic polynomials of the r tuple of closed loop systems the upper bounds are obtained for each of the two cases r max m p and max m p r m p 2002 elsevier science inc all rights reserved

on linear preservers of g tridiagonal majorization on rn abstract for vectors x y r n it is said that x is g tridiagonal majorized by y written as x g t y if there exists a tridiagonal g doubly stochastic matrix d such that x d y in this paper we continue the previous work armandnejad and gashool 2012 3 and give a complete characterization of linear operators preserving g t on r n

on generating of idempotent aggregation functions on finite lattices abstract in a recent paper 9 we proposed the study of aggregation functions on lattices via clone theory approach observing that aggregation functions on lattices just correspond to 0 1 monotone clones as the main result of 9 we have shown that all aggregation functions on a finite lattice l can be obtained as usual composition of lattice operations and certain unary and binary aggregation functions the aim of this paper is to present a generating set for the class of intermediate or equivalently idempotent aggregation functions this set consists of lattice operations and certain ternary idempotent aggregation functions

inequalities for the spectra of symmetric doubly stochastic matrices we prove majorization relations for symmetric doubly stochastic matrices whose nonzero off diagonal entries lie in an edge transitive graph these results are then used to solve the fastest mixing markov chain problem on edge transitive graphs

tridiagonal doubly stochastic matrices abstract we study the facial structure of the polytope t n in r n n consisting of the tridiagonal doubly stochastic matrices of order n we also discuss some subclasses of t n with focus on spectral properties and rank formulas finally we discuss a connection to majorization

an estimate for the nonstochastic eigenvalues of doubly stochastic matrices abstract we introduce a new measure of irreducibility of a doubly stochastic matrix and find the best estimate from below for the distance of nonstochastic eigenvalues from one the estimate is used to obtain a cheeger type inequality for the second laplacian eigenvalue of a weighted graph

the diameter of the acyclic birkhoff polytope abstract in this work we give an interpretation of vertices and edges of the acyclic birkhoff polytope t n n t where t is a tree with n vertices in terms of graph theory we generalize a recent result relatively to the diameter of the graph g t n

generators of aggregation functions and fuzzy connectives we show that the class of all aggregation functions on 0 1 can be generated as a composition of infinitary sup operation bigvee acting on sets with cardinality not exceeding mathfrak c b medians mathsf med b b in 0 1 and unary aggregation functions 1 0 1 and 1 a 1 a in 0 1 moreover we show that we cannot relax the cardinality of argument sets for suprema to be countable thus showing a kind of minimality of the introduced generating set as a by product generating sets for fuzzy connectives such as fuzzy unions fuzzy intersections and fuzzy implications are obtained too

a sufficient condition for simultaneous stabilization the condition under which it is possible to find a single controller that stabilizes k single input single output linear time invariant systems p sub i s i 1 k is investigated the concept of avoidance in the complex plane is introduced and used to derive a sufficient condition for k systems to be simultaneously stabilizable a method for constructing a simultaneous stabilizing controller is also provided and is illustrated by an example

an approach to simultaneous system design i semialgebraic geometric methods this paper introduces semialgebraic parameterization as an approach to analyze simultaneous stabilization and pole placement problems rational families of plants of a given mcmillan degree that are simultaneously stabilizable by a fixed family of compensators are parameterized for a discrete family of plants the parameterization problem reduces to the simultaneous stabilization or the pole placement problem of a r tuple of multi input multi output plants by a nonswitching compensator it is shown that by removing a semialgebraic subset of a proper algebraic set the space of plants can be decomposed into components that are either simultaneously stabilizable or simultaneously unstabilizable under special cases explicit parameterization of the semialgebraic set is obtained finally a necessary condition for the simultaneous stabilization of single input or single output plants is obtained

the solution of a transcendental problem and its applications in simultaneous stabilization problems a complete solution for a special transcendental problem in system theory is given one of the interpretations of this transcendental problem is the following simultaneous stabilization problem under what conditions can two linear plants be simultaneously stabilized by a single compensator having no real poles in the closed right half of the complex plane these conditions are completely general and therefore encompass unstable non minimum phase plants as well it is shown that the simultaneous stabilizability of two given plants via such a restricted compensator depends solely on the locations of the real zeros of the two plants and their difference plant in the closed right half of the complex plane for two plants satisfying the stabilizability conditions a computational design procedure for constructing a desired compensator is provided and illustrated a computationally checkable necessary condition for simultaneous stabilization of three plants is also given

on the clone of aggregation functions on bounded lattices the main aim of this paper is to study aggregation functions on lattices via clone theory approach observing that the aggregation functions on lattices just correspond to 0 1 monotone clones as the main result we show that for any finite n element lattice l there is a set of at most 2 n 2 aggregation functions on l from which the respective clone is generated namely the set of generating aggregation functions consists only of at most n unary functions at most n binary functions and lattice operations and all aggregation functions of l are composed of them by usual term composition moreover our approach works also for infinite lattices such as mostly considered bounded real intervals a b where in contrast to finite case infinite suprema or equivalently a kind of limit process have to be considered

the median and its extensions we review various representations of the median and related aggregation functions an advantage of the median is that it discards extreme values of the inputs and hence exhibits a better central tendency than the arithmetic mean however the value of the median depends on only one or two central inputs our aim is to design median like aggregation functions whose value depends on several central inputs such functions will preserve the stability of the median against extreme values but will take more inputs into account a method based on graduation curves is presented

faces of faces of the tridiagonal birkhoff polytope abstract the tridiagonal birkhoff polytope n t is the set of real square matrices with nonnegative entries and all rows and columns sums equal to 1 that are tridiagonal this polytope arises in many problems of enumerative combinatorics statistics combinatorial optimization etc in this paper for a given a p face of n t we determine the number of faces of lower dimension that are contained in it and we discuss its nature in fact a 2 face of n t is a triangle or a quadrilateral and the cells can only be tetrahedrons pentahedrons or hexahedrons