pole placement by parametric output feedback abstract this note presents a new analytical solution to the problem of pole placement via constant output feedback under the condition m p n where n m and p are the number of states inputs and outputs respectively the approach is based upon parametric eigenstructure assignment of linear time invariant multivariable systems in combination with a special explicit formulation of the pole assignment equations thus the resulting analytical solution explicitly offers all remaining m p n degrees of freedom beyond eigenvalue assignment which can be used for additional design goals such as response shaping minimizing the norm of the feedback matrix and robust control respectively

structured squaring down and zero assignment the problem of zero assignment by squaring down is considered for a system of p inputs n outputs and n states m p where not all outputs are free variables for design we consider the case where a k subset of outputs is preserved in the new output set and the rest are recombined to produce a total new set of p outputs new invariants for the problem are introduced which include a new class of fixed zeros and the methodology of the global linearization developed originally for the output feedback pole assignment problem is applied to this restricted form of the squaring down problem it is shown that the problem can be solved generically if p k m p where k k p is the number of fixed outputs and is a system and compensation scheme invariant which is defined as the restricted forney degree

assigning frequencies via determinantal equations new counterexamples and invariants the problem of arbitrary pole zero assignment by fixed structure compensators has been addressed so far in terms of either necessary or sufficient conditions the strongest existing condition is based on the rank of the differential of a related map on a degenerate controller and holds true generically when the degrees of freedom of the compensator exceed the number of frequencies to be assigned mp n for the output feedback problem the complete nongeneric solvability of the problem is still open even when complex controllers are considered a simple necessary solvability condition is that the linear map appearing as a factor of the main determinantal map defining the assignment problem is onto here we examine the special problem of assignment of matrix pencil zeros via diagonal perturbations and we present a new necessary and sufficient condition for complex solvability in terms of a new invariant involving the minors of this linear map based on this result we demonstrate that for the important case where the degrees of freedom of the controller are equal to the number of frequencies to be assigned the surjectivity of this linear map although it is necessary it is not sufficient for the solvability of the problem

grassmannian central projection and output feedback pole assignment of linear systems a sufficient rank condition for arbitrary pole assignability by static output feedback of m input p output linear systems of mcmillan degree n mp is given this condition is easy to check and is satisfied by the generic system an effective computational method to compute the feedback laws assigning any self conjugate set of closed loop poles is also given

pole placement by static output feedback for generic linear systems we consider linear systems with m inputs p outputs and mcmillan degree n such that n mp if both m and p are even we show that there is a nonempty open in the usual topology subset u of such systems where the real pole placement map is not surjective it follows that for each system in u there exists an open set of pole configurations symmetric with respect to the real line which cannot be assigned by any real static output feedback

exact analysis of dodgson elections lewis carroll s 1876 voting system is complete for parallel access to np in 1876 lewis carroll proposed a voting system in which the winner is the candidate who with the fewest changes in voters preferences becomes a condorcet winner a candidate who beats all other candidates in pairwise majority rule elections bartholdi tovey and trick provided a lower bound np hardness on the computational complexity of determining the election winner in carroll s system we provide a stronger lower bound and an upper bound that matches our lower bound in particular determining the winner in carroll s system is complete for parallel access to np that is it is complete for theta 2 p for which it becomes the most natural complete problem known it follows that determining the winner in carroll s elections is not np complete unless the polynomial hierarchy collapses

on two generalized inverse eigenvalue problems for hessenberg upper triangular pencils and their application to the study of gmres convergence abstract we discuss two generalized inverse eigenvalue problems the first one for a given unreduced upper hessenberg matrix h find a nonsingular upper triangular matrix t such that all the pencils h k t k have prescribed eigenvalues where h k and t k are the leading k k principal submatrices of h and t respectively the second one for a given unitary unreduced upper hessenberg matrix q find a nonsingular upper triangular matrix t such that all the pencils t k q k have prescribed eigenvalues where t k is the leading k k principal submatrix of t and q k is the conjugate transpose of the leading k k principal submatrix of q we present the necessary and sufficient conditions for the solvability of the two problems our results lead to an alternative proof for the statement that any admissible ritz value set or admissible harmonic ritz value set is possible for the prescribed gmres residual norms here the term admissible means there are some restrictions on the sets if gmres stagnates at some iterations

complex scaling circle criteria for lure systems abstractthis study reports alternative frequency domain interpretation and implementation of the circle criteria for absolute stability in lure systems by means of complex scaling and the argument principle by lure system a feedback configuration with a nominal lti model subject to sector nonlinearities is meant as usual firstly the complex scaling stability criterion is proved for asymptotic stability in lti feedback connections which dispenses open loop poles and contour locus pre orientation and possesses bounded loci without prior frequency sweeping secondly a novel frequency domain interpretation for positive realness of transfer functions is developed and employed for claiming the complex scaling circle criteria which accommodate various sector nonlinearities with unified conditions the new circle criteria are conformable in both multivariable and scalar cases implementable graphically and tractable numerically besides being a frequency complex domain analytical technique thirdly the re

sobolev spaces with variable exponents on complete manifolds we study variable exponent function spaces on complete non compact riemannian manifolds using classic assumptions on the geometry continuous embeddings between sobolev and holder function spaces are obtained we prove compact embeddings of h invariant sobolev spaces where h is a compact lie subgroup of the group of isometries of the manifold as an application we prove the existence of non trivial solutions to non homogeneous q x laplace equations

the complexity of manipulative attacks in nearly single peaked electorates many electoral control and manipulation problems which we will refer to in general as manipulative actions problems are np hard in the general case it has recently been noted that many of these problems fall into polynomial time if the electorate is single peaked i e is polarized along some axis issue however real world electorates are not truly single peaked there are usually some mavericks and so real world electorates tend merely to be nearly single peaked this paper studies the complexity of manipulative action algorithms for elections over nearly single peaked electorates we do this for many notions of nearness and for a broad range of election systems we provide instances where even one maverick jumps the manipulative action complexity up to np hardness but we also provide many instances where some number of mavericks can be tolerated without increasing the manipulative action complexity

when are elections with few candidates hard to manipulate in multiagent settings where the agents have different preferences preference aggregation is a central issue voting is a general method for preference aggregation but seminal results have shown that all general voting protocols are manipulable one could try to avoid manipulation by using protocols where determining a beneficial manipulation is hard especially among computational agents it is reasonable to measure this hardness by computational complexity some earlier work has been done in this area but it was assumed that the number of voters and candidates is unbounded such hardness results lose relevance when the number of candidates is small because manipulation algorithms that are exponential only in the number of candidates and only slightly so might be available we give such an algorithm for an individual agent to manipulate the single transferable vote stv protocol which has been shown hard to manipulate in the above sense this motivates the core of this article which derives hardness results for realistic elections where the number of candidates is a small constant but the number of voters can be large the main manipulation question we study is that of coalitional manipulation by weighted voters we show that for simpler manipulation problems manipulation cannot be hard with few candidates we study both constructive manipulation making a given candidate win and destructive manipulation making a given candidate not win we characterize the exact number of candidates for which manipulation becomes hard for the plurality borda stv copeland maximin veto plurality with runoff regular cup and randomized cup protocols we also show that hardness of manipulation in this setting implies hardness of manipulation by an individual in unweighted settings when there is uncertainty about the others votes but not vice versa to our knowledge these are the first results on the hardness of manipulation when there is uncertainty about the others votes

mixed integer programming with convex concave constraints fixed parameter tractability and applications to multicovering and voting abstract a classic result of lenstra math oper res 1983 says that an integer linear program can be solved in fixed parameter tractable fpt time for the parameterization by the number of variables we extend this result by incorporating piecewise linear convex or concave functions to our mixed integer programs this general technique allows us to analyze the parameterized complexity of a number of classic np hard computational problems in particular we prove that weighted set multicover is in fpt when parameterized by the number of elements to cover and that there exists an fpt time approximation scheme for multiset multicover for the same parameter this is our most technical result further we use our general technique to prove that a number of problems from computational social choice e g problems related to bribery and control in elections are in fpt when parameterized by the number of candidates for bribery this resolves a nearly 10 year old family of open problems and for weighted electoral control of approval voting this improves some previously known xp memberships to fpt memberships

existence and multiplicity results for a new p x kirchhoff problem abstract in this work we study the existence and multiplicity results for the following nonlocal p x kirchhoff problem 0 1 a b 1 p x u p x d x d i v u p x 2 u u p x 2 u g x u in u 0 on where a b 0 are constants r n is a bounded smooth domain p c with n p x 1 is a real parameter and g is a continuous function the analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties

quadratically parameterized root locus analysis classical affine root locus applies to controllers that are linear in a parameter k and yield affinely parameterized closed loop denominator polynomials this paper presents root locus rules for controllers that are rational in k and yield quadratically parameterized closed loop denominator polynomials we show that the quadratic root locus has several advantages relative to the classical affine root locus specifically the quadratic root locus is high parameter stabilizing for minimum phase systems that are relative degree 1 2 or 3 moreover the quadratic root locus admits a wider variety of asymptote angles which provides more controller design flexibility the quadratic root locus is illustrated on several examples that are difficult to handle using affine root locus such as high parameter stabilization of the triple integrator

output feedback and generic stabilizability we consider questions of pole placement and stabilization for generic linear systems with prescribed state input and output dimensions where the controller must be implemented by linear memoryless output feedback we present a criterion in terms of a special pole placement property for generic stabilizability and apply this to describe constraints on the dimensions which are consistent with generic stabilizability we also discuss the rationality and solvability by radicals of stabilizing or pole positioning gains and we describe how decision algebra can theoretically handle existence questions for generic systems

variable exponent linear growth functionals in image restoration we study a functional with variable exponent 1 leq p x leq 2 which provides a model for image denoising enhancement and restoration the diffusion resulting from the proposed model is a combination of total variation tv based regularization and gaussian smoothing the existence uniqueness and long time behavior of the proposed model are established experimental results illustrate the effectiveness of the model in image restoration

grassmann invariants almost zeros and the determinantal zero pole assignment problems of linear multivariable systems the strucxpects of the rationxr spaces x c x fwhere x c is the columxof the transfer function matrix g s and x f is the space associated with right matrix fracxcriptions of g s are investigated for x f gcanonixqb s grassmgesentax g x c and g x f arxd and are shown xmplete basis free invariants for x c and x f respectively the almost zeros az and almost decoupling zeros adz of g s gdefinex local minima of a normgn defix g x c and g x f respectively the computation and certain aspects of the distribution in the complex plane of azs and adzs are examined the role of azs and adzs in the determinantal zero and pole assignment problems respectively is examined next two important families of systems are defined the strongly zero non assignable szna and the strongly pole non assignable spna systems for szna and spna systems minimal radius discs dem e z r em e z and dem f zb centred at an az and adz respectively are defined it is shown that dem e r em e z contains at least one zer

the mcmillan and newton polygons of a feedback system and the construction of root loci abstract the local behaviour of root loci around zeros and poles is investigated this is done by relating the newton diagrams which arise in the local analysis to the mcmillan structure of the open loop system by means of what we shall call the mcmillan polygon this geometric construct serves to clarify the precise relationship between the mcmillan structure the principal structure and the branching patterns of the root loci in addition several rules are obtained which are useful in the construction of the root loci of multivariable control systems

the pole placement problem via pi feedback controllers in this paper we study the pole placement problem using generalized pi controllers of a fixed lag k as compensators we derive a new strong sufficiency condition which guarantees the arbitrary pole assignability of a given system having m inputs p outputs and mcmillan degree n this sufficiency condition misses the theoretical best possible necessary condition by one degree of freedom the proof of the main result can be used to derive a numerical procedure this numerical procedure is however very sensitive in the parameters and further research is required to investigate the conditions under which sensitivity occurs and whether the solution can be made more robust in this regard

behavioral analysis of anisotropic diffusion in image processing in this paper we analyze the behavior of the anisotropic diffusion model of perona and malik 1990 the main idea is to express the anisotropic diffusion equation as coming from a certain optimization problem so its behavior can be analyzed based on the shape of the corresponding energy surface we show that anisotropic diffusion is the steepest descent method for solving an energy minimization problem it is demonstrated that an anisotropic diffusion is well posed when there exists a unique global minimum for the energy functional and that the ill posedness of a certain anisotropic diffusion is caused by the fact that its energy functional has an infinite number of global minima that are dense in the image space we give a sufficient condition for an anisotropic diffusion to be well posed and a sufficient and necessary condition for it to be ill posed due to the dense global minima the mechanism of smoothing and edge enhancement of anisotropic diffusion is illustrated through a particular orthogonal decomposition of the diffusion operator into two parts one that diffuses tangentially to the edges and therefore acts as an anisotropic smoothing operator and the other that flows normally to the edges and thus acts as an enhancement operator

matrices with prescribed eigenvalues and principal submatrices abstract we give a necessary and sufficient condition for the existence of a square matrix with prescribed eigenvalues and prescribed complementary principal blocks

generic eigenvalue assignment by memoryless real output feedback by extensive use of methods from algebraic geometry x wang proved that arbitrary pole placement by static output feedback is generically possible for strictly proper plants with n states m inputs and p outputs if n mp here we show the same result using no more of algebraic geometry than the definition of genericity

complexity of and algorithms for the manipulation of borda nanson s and baldwin s voting rules we investigate manipulation of the borda voting rule as well as two elimination style voting rules nanson s and baldwin s voting rules which are based on borda voting we argue that these rules have a number of desirable computational properties for unweighted borda voting we prove that it is np hard for a coalition of two manipulators to compute a manipulation this resolves a long standing open problem in the computational complexity of manipulating common voting rules we prove that manipulation of baldwin s and nanson s rules is computationally more difficult than manipulation of borda as it is np hard for a single manipulator to compute a manipulation in addition for baldwin s and nanson s rules with weighted votes we prove that it is np hard for a coalition of manipulators to compute a manipulation with a small number of candidates because of these np hardness results we compute manipulations using heuristic algorithms that attempt to minimise the number of manipulators we propose several new heuristic methods experiments show that these methods significantly outperform the previously best known heuristic method for the borda rule our results suggest that whilst computing a manipulation of the borda rule is np hard computational complexity may provide only a weak barrier against manipulation in practice in contrast to the borda rule our experiments with baldwin s and nanson s rules demonstrate that both of them are often more difficult to manipulate in practice these results suggest that elimination style voting rules deserve further study

on time adaptive critical variable exponent vectorial diffusion flows and their applications in image processing i analysis abstract variable exponent spaces have found interesting applications in real world problems in imaging models the variable exponent can approach the critical value 1 and this poses unique challenges in proving existence of solutions for the corresponding pdes in this work we develop some new functional framework to study time dependent parabolic variable exponent flows specifically we consider bounded vectorial partial variation b v p v space and its variable exponent counterpart we then prove the existence of weak solutions to the critical vectorial p t x laplacian flow in the variable exponent b v p v space for time independent critical vectorial p x laplacian flow we obtain a unique semigroup solution our results are in particular valid in the scalar case and solve a long standing open problem

a quantitative version of the gibbard satterthwaite theorem for three alternatives the gibbard satterthwaite theorem states that every nondictatorial election rule among at least three alternatives can be strategically manipulated we prove a quantitative version of the gibbard satterthwaite theorem a random manipulation by a single random voter will succeed with a nonnegligible probability for any election rule among three alternatives that is far from being a dictatorship and from having only two alternatives in its range

multivariable singularly perturbed feedback systems with time delay multivariable singularly perturbed systems with both small and large time delays in the feedback loop are considered conditions for stability of the full order closed loop system are given in terms of properties of the slow and fast subsystems

periodically varying compensation of time invariant systems linear time invariant discrete time scalar systems under periodically varying output feedback and the associated problems of stabilization and arbitrary eigenvalue assignment are investigated the general form of the characteristic polynomial of the closed loop periodically varying system is obtained and some detailed results are provided for the second order case interesting research questions are pointed out

existence of solutions for systems arising in electromagnetism abstract in this paper we study the following p x curl systems u p x 2 u a x u p x 2 u f x u g x u u 0 in u p x 2 u n 0 u n 0 on where r 3 is a bounded simply connected domain with a c 1 1 boundary denoted by p 1 is a continuous function a l f g r 3 r 3 are caratheodory functions and are two parameters using variational arguments based on fountain theorem and dual fountain theorem we establish some existence and non existence results for solutions of this problem our main results generalize the results of xiang et al 2017 41 bahrouni and repovs 2018 9 and ge and lu 2019 22

identification and estimation of dynamic errors in variables models abstract we consider here the factor analysis approach to the analysis of linear dynamic errors in variables models identification of the most general models and the question of nonuniqueness are discussed we show how these models are generalizations of the total least squares model and how the grassmann manifold provides a natural setting for their analysis under certain assumptions we analyze the problem of maximum likelihood estimation and indicate how this involves maximization of a functional on a grassmann manifold

harnack s inequality and the strong p laplacian abstract we study solutions of the strong p laplace equation we show that in contrast to p laplace solutions these solutions satisfy the ordinary scale invariant harnack inequality as consequences we derive the strong maximum principle and global integrability of solutions

parameterized computational complexity of control problems in voting systems voting systems are common tools in a variety of areas this paper studies parameterized computational complexity of control of plurality condorcet and approval voting systems respectively the types of controls considered include adding or deleting candidates or voters under constructive or destructive setting we obtain the following results 1 constructive control by adding candidates in plurality voting is w 2 hard with respect to the parameter number of added candidates 2 destructive control by adding candidates in plurality voting is w 2 hard with respect to the parameter number of added candidates 3 constructive control by adding voters in condorcet voting is w 1 hard with respect to the parameter number of added voters 4 constructive control by deleting voters in condorcet voting is w 1 hard with respect to the parameter number of deleted voters 5 constructive control by adding voters in approval voting is w 1 hard with respect to the parameter number of added voters and 6 constructive control by deleting voters in approval voting is w 2 hard with respect to the parameter number of deleted voters

on decentralized dynamic pole placement and feedback stabilization in this paper we study the feedback control problem using an r channel decentralized dynamic feedback control scheme we will develop the theory in the behavioral framework using this framework we introduce an algebraic parameterization of the space of all possible feedback compensators having a bounded mcmillan degree and we show that this parameterization has the structure of an algebraic variety we define the pole placement map for this problem and we give exact conditions when this map is onto and almost onto finally we provide new necessary and sufficient conditions which guarantee that the set of stabilizable plants is a generic set

a nyquist type stability test for multivariable distributed systems a multivariable nyquist criterion is given that applies to a wide class of open loop transfer matrices including some that are improper or have infinitely many poles in the right half plane application of the test to specific examples requires only elementary knowledge of complex variable theory the actual test requires operations similar to those used in the standard nyquist test the simplicity of the frequency domain description of the class t analyticity and polynomial boundedness makes it relatively easy to verify if the test is applicable to a given transfer matrix

exact algorithms for weighted and unweighted borda manipulation problems we derive exact combinatorial algorithms for both weighed and unweighted borda manipulation problems we derive an fpt algorithm for the unweighted borda manipulation problem with respect to the number of candidates we prove that borda manipulation with two manipulators is polynomial time solvable in single peaked elections we propose o m 2 m t 1 time and o t m 1 t t 1 m time algorithms for the weighted and the unweighted borda manipulation problems respectively where t is the number of manipulators and m is the number of candidates in particular for t 2 our algorithm for the unweighted case runs in o 3 m time affirmatively resolving one open problem posed by betzler et al 2 as a byproduct of our results we show that the unweighted borda manipulation problem admits an algorithm with running time o 2 9 m 2 log m based on an integer linear programming technique finally we prove that the unweighted borda manipulation problem is polynomial time solvable in single peaked elections in contrast to the np hardness in the general case

on the evaluation of election outcomes under uncertainty we investigate the extent to which it is possible to compute the probability of a particular candidate winning an election given imperfect information about the preferences of the electorate we assume that for each voter we have a probability distribution over a set of preference orderings thus for each voter we have a number of possible preference orderings we do not know which of these orderings actually represents the preferences of the voter but for each ordering we know the probability that it does for the case where the number of candidates is a constant we are able to give a polynomial time algorithm to compute the probability that a given candidate will win we present experimental results obtained with an implementation of the algorithm illustrating how the email protected s performance in practice is better than its predicted theoretical bound however when the number of candidates is not bounded we prove that the problem becomes p hard for the plurality k approval borda copeland and bucklin voting rules we further show that even evaluating if a candidate has any chance of winning is np complete for the plurality voting rule in the case where voters may have different weights with unweighted voters we give a polynomial algorithm for plurality and show that the problem is hard for many other voting rules finally we give a monte carlo approximation algorithm for computing the probability of a candidate winning in any settings with an error that is as small as desired

decentralized feedback pole placement of linear systems a projective product spaces model is used to analyse decentralized systems the degree of the pole placement map is computed the conditions under which the degree is odd are also given twin lift systems are studied it is proved that the poles of a twin lift system can be assigned to any values by local static and local dynamic feedback laws if and only if the system is jointly controllable communicated by professor a isidori

the learnability of voting rules scoring rules and voting trees are two broad and concisely representable classes of voting rules scoring rules award points to alternatives according to their position in the preferences of the voters while voting trees are iterative procedures that select an alternative based on pairwise comparisons in this paper we investigate the pac learnability of these classes of rules we demonstrate that the class of scoring rules as functions from preferences into alternatives is efficiently learnable in the pac model with respect to voting trees while in general a learning algorithm would require an exponential number of samples we show that if the number of leaves is polynomial in the size of the set of alternatives then a polynomial training set suffices we apply these results in an emerging theory automated design of voting rules by learning

on the solvability of polynomial systems arising in control we consider a compactification of a general system of polynomial equations in weighted projective space and give some sufficient conditions about the solvability of a polynomial system over c and r we also prove that for generic linear subspaces the inverse eigenvalue problem with perturbations in the linear subspace always has n solutions

existence of solutions for p x laplacian dirichlet problem this paper presents several sufficient conditions for the existence of solutions for the dirichlet problem of p x laplacian div u p x 2 u f x u x u 0 x especially an existence criterion for infinite many pairs of solutions for the problem is obtained the discussion is based on the theory of the spaces lp x and w01 p x

decentralized pole assignment and product grassmannians the pole assignment problems of linear systems by decentralized static output feedback are considered in this paper a compactification of decentralized static feedback space product grassmannians is introduced in this paper its degree under plucker segre embedding is computed sufficient conditions for arbitrary and almost arbitrary pole assignability are given it is also proved that the generic m times p system of mcmillan degree n has arbitrary pole assignability by r channel decentralized static output with m i inputs and p i outputs on the i th channel if sum i 1 r m ip i geq n when the degree of the product grassmannians is odd or if sum i 1 r m ip i n and the local channels have either the same numbers of inputs or the same numbers of outputs when the degree of the product grassmannians is even

necessary and sufficient conditions for zero assignment by constant squaring down the problem of zero assignment by constant squaring down czap is studied for minimal systems described by a transfer function g s rm l s m l using tools from exterior algebra and algebraic geometry conditions for its solvability are given in terms of the numbers m l the forney dynamical order and the rank of the plucker matrix p for the cases l 1 or l m 1 it is shown that g s is completely zero assignable cza if and only if 1 for the cases l 1 m 1 it is proved that g s is cza or generically zero assignable gza under a complex squaring down if and only if l m l 1 and 1 the latter conditions also provide necessary conditions for the existence of a real solution for a generic g s sufficient conditions for solvability of czap by a real squaring down are that l m l 1 and that the number g a0 al 1 1 a0 al 1 i j ai aj is odd for some set a0 al 1 satisfying 1 l 1i 0ai l l 1 2 and 0 a0 a1 al 1 m 1 apart from the existence results the present approach also allows the computation of the solutions whenever they exist finally it is proved that the only fixed zeros of czap are the zeros of g s and a procedure for computing the solutions of czap whenever such solutions exist based on an optimization problem is given

output feedback pole assignment for transfer functions with symmetries this paper studies the problem of pole assignment for symmetric and hamiltonian transfer functions a necessary and sufficient condition for pole assignment by complex symmetric output feedback transformations is given moreover in the case where the mcmillan degree coincides with the number of parameters appearing in the symmetric feedback transformations we derive an explicit combinatorial formula for the number of pole assigning symmetric feedback gains the proof uses intersection theory in projective space as well as a formula for the degree of the complex lagrangian grassmann manifold

output feedback eigenstructure assignment using a new reduced orthogonality condition this paper presents a new method of output feedback eigenstructure assignment a new reduced orthogonality condition is derived which is less restrictive on the design degrees of freedom than others in the literature from this a novel general formulation for the gain matrix is admitted which utilizes a two stage design process in the first stage a subset of desired eigenvectors is assigned either left or right in the second stage a dual set is assigned which adheres to the necessary and sufficient conditions for output feedback eigenstructure assignment proved earlier in the paper a numerical example is presented to illustrate the whole procedure

global asymptotic linearisation of the pole placement map a closed form solution for the constant output feedback problem abstract the problem of pole assignment by constant output feedback controllers is studied for minimal systems described by a proper transfer function matrix g s r m p s with mcmillan degree n a new method is presented based on asymptotic linearisation around a degenerate point of the pole placement map related to the problem the essence of the present approach is to reduce the multilinear nature of the problem to one of solving a linear set of equations and this is achieved without losing any of the degrees of freedom in the controller the solution is given in closed form in terms of a one parameter family of static feedback compensators for which the closed loop poles approach the required ones as 0 conditions for the generic as well as exact solvability of the arbitrary pole placement problem are given in terms of the numbers m p n and the rank of a new system invariant the d restricted plucker matrix it is shown that the method works generically when mp n which along with the boundary case mp n is the best possible condition as far as the number of states of the open loop system is concerned for achieving arbitrary pole placement via constant output feedback

variable exponent functionals in image restoration abstract we study a functional with variable exponent 1 p x 2 which provides a model for image denoising and restoration here p x is defined by the gradient information in the observed image the diffusion derived from the proposed model is between total variation based regularization and gaussian smoothing the diffusion speed of the corresponding heat equation is tuned by the variable exponent p x the minimization problem and its associated flow in a weakened formulation are discussed the existence uniqueness stability and long time behavior of the proposed model are established in the variable exponent functional space w 1 p x experimental results illustrate the effectiveness of the model in image restoration

matrices with prescribed rows and invariant factors abstract in this paper we solve the problem of the existence of an n n matrix over an arbitrary field when its invariant polynomials and either some rows or columns are prescribed the solution is given in terms of invariant factor inequalities and of majorization inequalities involving controllability indices and the degrees of the invariant polynomials

spectrally arbitrary patterns abstract an n n sign pattern matrix s is an inertially arbitrary pattern iap if each nonnegative triple n 1 n 2 n 3 with n 1 n 2 n 3 n is the inertia of a matrix with sign pattern s analogously s is a spectrally arbitrary pattern sap if for any given real monic polynomial r x of order n there is a matrix with sign pattern s and characteristic polynomial r x focusing on tree sign patterns consider the n n tridiagonal sign pattern t n with each superdiagonal entry positive each subdiagonal entry negative the 1 1 entry negative the n n entry positive and every other entry zero it is conjectured that t n is an iap by constructing matrices a n with pattern t n it is proved that t n allows any inertia with n 3 0 1 2 n 1 n for all n 2 this leads to a proof of the conjecture for n 5 the truth of the conjecture is extended to n 7 by showing the stronger result that t n is a sap the proof of this latter statement involves finding a matrix a n with pattern t n that is nilpotent further questions about patterns that are saps and iaps are considered

a pole placement design approach for systems with multiple operating conditions the author proposes design procedures based on state space pole placement techniques for systems with multiple operating conditions this is the so called simultaneous pole placement problem first the full state feedback problem is studied in which a nonlinear local pole placement solution is proposed the design condition is formulated in terms of the rank condition of a multimode controllability matrix then the output feedback problem is approached using a multimodel controller design which is an extension of the observer design to multimode systems the design is decomposed into separated global pole placement subproblems and a local pole placement subproblem for a system with some operating conditions having modes on the j omega axis but no modes at the origin in the open right half of the complex plane stabilizability and detectability conditions for the design of an asymptotically stabilizing control are established without any restriction on the number of inputs or outputs relations of this approach to other simultaneous control design approaches are pointed out

special loop connections of linear systems in this paper we completely determine the possible eigenvalues of a matrix of a system obtained as a result of special loop connections of arbitrary many linear systems

control of condorcet voting complexity and a relation algebraic approach abstract we study the constructive variant of the control problem for condorcet voting where control is done by deleting voters we prove that this problem remains np hard if instead of condorcet winners the alternatives in the uncovered set win furthermore we present a relation algebraic model of condorcet voting and relation algebraic specifications of the dominance relation and the solutions of the control problem all our relation algebraic specifications immediately can be translated into the programming language of the obdd based computer system relview our approach is very flexible and especially appropriate for prototyping and experimentation and as such very instructive for educational purposes it can easily be applied to other voting rules and control problems

multivariable nyquist criteria root loci and pole placement a geometric viewpoint classical control theory is concerned with the topics in our title in the context of single input single output systems there is now a large and growing literature on the extension of these ideas to the multiinput multioutput case this development has posed certain difficulties some due to the intrinsic nature of the problem and some we would argue due to an inadequate reflection on what the multivariable problem calls for in this paper we describe what seems to us to be the natural multivariable analogs of these concepts from classical control theory a rather satisfactory generalization of the nyquist criterion will be described and a clear analog of the asymptotic properties of the root locus will be obtained in the multiparameter case however an example is given which illustrates the quite surprising fact that the root locus map is not always continuous at infinite gains this calls for a new ingredient a compactification of the space of gains and perhaps the most interesting new feature in this circle of ideas comes in the area of pole placement this problem is difficult in the multivariable case but by establishing a correspondence with a classical set of problems in geometry we are able to understand its main aspects and to derive results on pole placement by output feedback over the real field

double phase image restoration abstract in this paper we explore the potential of the double phase functional in an image processing context to this end we study minimizers of the double phase energy for functions with bounded variation and show that this energy can be obtained by convergence or relaxation of regularized functionals a central tool is a capped fractional maximal function of the derivative of bv functions

pole placement and matrix extension problems a common point of view this paper studies a general inverse eigenvalue problem which generalizes many well studied pole placement and matrix extension problems it is shown that the problem corresponds geometrically to a so called central projection from some projective variety the degree of this variety represents the number of solutions the inverse problem has in the critical dimension we are able to compute this degree in many instances and we provide upper bounds in the general situation

parameterized computational complexity of dodgson and young elections abstract we show that the two np complete problems of dodgson score and young score have differing computational complexities when the winner is close to being a condorcet winner on the one hand we present an efficient fixed parameter algorithm for determining a condorcet winner in dodgson elections by a minimum number of switches in the votes on the other hand we prove that the corresponding problem for young elections where one has to delete votes instead of performing switches is w 2 complete in addition we study dodgson elections that allow ties between the candidates and give fixed parameter tractability as well as w 2 completeness results depending on the cost model for switching ties

a variable exponent nonlocal p x laplacian equation for image restoration abstract in this paper we focus on the mathematical and numerical study of a variable exponent nonlocal p x laplacian equation for image denoising based on the semigroup theory we prove the existence and uniqueness of solution for the proposed model to illustrate the efficiency and effectiveness of our model we provide the denoising experimental results as well we compare it with some existing models in the literature

almost everything you need to know about relatively compact sets in variable lebesgue spaces abstract we study relatively compact sets in variable lebesgue spaces the full characterization of such sets is given in the case of variable lebesgue space on metric measure spaces the paper contains a detailed discussion of relatively compact sets in variable lebesgue space on the euclidean space moreover some applications of the theorems are given

on output feedback via grassmannians the output feedback pole placement map chi has been studied by using the central projection model necessary and sufficient conditions for chi being dominant are given 2 times 2 systems of mcmillan degree 4 and 2 times 3 systems of mcmillan degree 6 are studied intensively

ranking chain sum orders ranking information is an important topic in information sciences internet searching voting systems and sports in the full information approach a ranking is a total order of the candidates we compare two rankings by pairwise comparisons under the nearest neighbor kendall tau distance and study the distance and rank aggregation problems in many settings the information is incomplete and a ranking is given by a partial order a bucket order is obtained if a ranking allows ties and treats tied candidates as equivalent then the distance and rank aggregation problems can be solved efficiently in almost linear time a chain sum order is complementary to a bucket order and consists of a set of disjoint total orders its width and height is the number and the maximum size of the total orders respectively we show that the distance and rank aggregation problems of a total order and a chain sum order of bounded width or of height at most two can be solved in polynomial time and are np complete for a total and a chain sum order of height at least 12 both problems remain np complete for a total and a heap order which is the partial order obtained from a single elimination tournament in sports however the problems are fixed parameter tractable with respect to the distance and the ulam distance but are fixed parameter intractable with respect to the order dimension

cascade equivalence of linear systems abstract this paper concerns the characterization of a linear system with respect to output feedback as well as to slightly more general transformations called cascade transformations with a transfer function t s we associate a finite tuplee of numbers that is invariant under cascade transformation

on the linear static output feedback problem the annihilating polynomial approach abstract one of the fundamental open problems in control theory is that of the stabilization of a linear time invariant dynamical system through static output feedback we are given a linear dynamical system defined through w a w b u y c w the problem is to find if it exists a feedback u k y such that the matrix a b k c has all its eigenvalues in the complex left half plane and if such a feedback does not exist to prove that it does not substantial progress has not been made on the computational aspect of the solution to this problem in this paper we consider instead which annihilating polynomials can a matrix of the form a b k c possess we give a simple solution to this problem when the system has either a single input or a single output for the multi input multi output case we use these ideas to characterize the annihilating polynomials when k has rank one and suggest possible computational solutions for general k we also present some numerical evidence for the plausibility of this approach for the general case as well as for the problem of shifting the eigenvalues of the system

zero assignment of matrix pencils by additive structured transformations abstract matrix pencil models are natural descriptions of linear networks and systems changing the values of elements of networks that is redesigning them implies changes in the zero structure of the associated pencil and this is achieved by structured additive transformations the paper examines the problem of zero assignment of regular matrix pencils by a special type of structured additive transformations for a certain family of network redesign problems the additive perturbations may be described as diagonal perturbations and such modifications are considered here this problem has certain common features with the pole assignment of linear systems by structured static compensators and thus the new powerful methodology of global linearization j leventides n karcanias sufficient conditions for arbitrary pole assignment by constant decentralised output feedback mathematics of control for signals and systems 8 1995 222 240 j leventides n karcanias global asymptotic linearisation of the pole placement map a closed form solution for the constant output feedback problem automatica 31 1995 1303 1309 can be used for regular pencils with infinite zeros families of structured degenerate additive transformations are defined and parameterized and this lead to the derivation of conditions for zero structure assignment as well as methodology for computing such solutions the case of regular pencils with no infinite zeros is also considered and conditions of zero assignment are developed the results here provide the means for studying problems of linear network redesign by modification of the non dynamic elements

holder regularity for the gradients of solutions of the strong p x laplacian abstract under some assumptions on the continuous function p x 1 we obtain the local c 1 regularity of solutions of the strong p x laplacian div u p x 2 u u p x 2 log u u p 0 by using the integral estimates in campanato spaces

on pole placement via eigenstructure assignment approach this note comes back to the hard problem of pole placement by static output feedback let a triplet of matrices a b c be given with n state variables m inputs and p ouputs find a matrix k such that the spectrum of a bkc equals a specified set when mp m p a simple noniterative technique based upon the notion of eigenstructure that in most cases assigns m p roots is proposed it therefore enables the designer to assign the whole of the desired spectrum when m p n mp

matrices with prescribed characteristic polynomial and principal blocks ii abstract in this paper we present some new sufficient conditions for the existence of a square matrix with prescribed characteristic polynomial and two complementary principal submatrices

exact pole assignment with regularity by output feedback in descriptor systems part 2 in this paper the first of two we examine the problem of modal control of linear time invariant multivariable descriptor systems in particular for systems satisfying a certain inequality we will give necessary and sufficient conditions for the existence of an output feedback matrix possibly complex which exactly assigns an arbitrary set of r the number of independent semi state variables of the system distinct complex numbers to a generalized eigenspectrum of the closed loop system while ensuring that the resulting system has a unique smooth solution for each admissible initial condition furthermore it is shown that if the set of proposed poles contains only real elements the assignment can be carried out using real feedback next we present conditions that are necessary and sufficient for pole assignability by real feedback of a self conjugate set of complex numbers provided that the system satisfies a further inequality

a sufficient condition for arbitrary eigenvalue assignment in linear descriptor systems by output feedback the problem of eigenvalue assignment in the linear descriptor system e mathdotx ax bu y cx via output feedback is considered it is shown that mp rank e m and p are respectively the numbers of inputs and outputs of the system is a sufficient condition for generic real output feedback eigenvalue assignability the result is the best possible for general m p rank e in general the assignment is achieved not in an exact sense but in arbitrarily small neighborhoods around a given set of eigenvalues

rational functions with real critical points and the b and m shapiro conjecture in real enumerative geometry suppose that 2d 2 tangent lines to the rational normal curve z 1 z z d in d dimensional complex projective space are given it was known that the number of codimension 2 subspaces intersecting all these lines is always finite for a generic configuration it is equal to the d th catalan number we prove that for real tangent lines all these codimension 2 subspaces are also real thus confirming a special case of a general conjecture of b and m shapiro this is equivalent to the following result if all critical points of a rational function lie on a circle in the riemann sphere for example on the real line then the function maps this circle into a circle

parameterized complexity of candidate control in elections and related digraph problems there are different ways for an external agent to influence the outcome of an election we concentrate on control by adding or deleting candidates our main focus is to investigate the parameterized complexity of various control problems for different voting systems to this end we introduce natural digraph problems that may be of independent interest they help in determining the parameterized complexity of control for different voting systems including llull copeland and plurality voting devising several parameterized reductions we provide an overview of the parameterized complexity of the digraph and control problems with respect to natural parameters such as adding deleting only a bounded number of candidates or having only few voters

eigenvalue assignment by static output feedback on a new solvability condition and the computation of low gain feedback matrices in this article the static output feedback problem for linear time invariant systems is considered for arbitrary assignability of the roots of the characteristic polynomial by static output feedback a new necessary and sufficient condition is derived although the proof is based on simple analysis the known sufficient conditions derived by techniques of algebraic geometry are directly covered furthermore an algorithm for the calculation of feedback matrices assigning a desired set of eigenvalues is proposed this algorithm does not require the desired eigenvalues to be distinct and it explicitly exploits the available degrees of freedom for reducing the feedback gain the presented approach is illustrated on computational examples

algorithms for the coalitional manipulation problem we investigate the problem of coalitional manipulation in elections which is known to be hard in a variety of voting rules we put forward efficient algorithms for the problem in borda maximin and plurality with runoff and analyze their windows of error specifically given an instance on which an algorithm fails we bound the additional power the manipulators need in order to succeed we finally discuss the implications of our results with respect to the popular approach of employing computational hardness to preclude manipulation

sobolev spaces with variable exponents on riemannian manifolds abstract in this article we study variable exponent sobolev spaces on riemannian manifolds the spaces are examined in the case of compact manifolds continuous and compact embeddings are discussed the paper contains an example of the application of the theory to elliptic equations on compact manifolds

multiscale tikhonov total variation image restoration using spatially varying edge coherence exponent edge preserving regularization using partial differential equation pde based methods although extensively studied and widely used for image restoration still have limitations in adapting to local structures we propose a spatially adaptive multiscale variable exponent based anisotropic variational pde method that overcomes current shortcomings such as over smoothing and staircasing artifacts while still retaining and enhancing edge structures across scale our innovative model automatically balances between tikhonov and total variation tv regularization effects using scene content information by incorporating a spatially varying edge coherence exponent map constructed using the eigenvalues of the filtered structure tensor the multiscale exponent model we develop leads to a novel restoration method that preserves edges better and provides selective denoising without generating artifacts for both additive and multiplicative noise models mathematical analysis of our proposed method in variable exponent space establishes the existence of a minimizer and its properties the discretization method we use satisfies the maximum minimum principle which guarantees that artificial edge regions are not created extensive experimental results using synthetic and natural images indicate that the proposed multiscale tikhonov tv mttv and dynamical mttv methods perform better than many contemporary denoising algorithms in terms of several metrics including signal to noise ratio improvement and structure preservation promising extensions to handle multiplicative noise models and multichannel imagery are also discussed