new solution method of linear static output feedback design problem for linear control systems abstract a new method of construction of the linear static output feedback for linear control systems is offered the essence of this method consists in construction of an initial approximation of the feedback matrix such that a numerical sequence which generated by arbitrary iterative method and beginning from this initial approximation converges to an exact solution of the feedback design problem examples are given

eigenvalue assignment by minimal state feedback gain in lti multivariable systems in this article an improved method for eigenvalue assignment via state feedback in the linear time invariant multivariable systems is proposed this method is based on elementary similarity operations and involves mainly utilisation of vector companion forms and thus is very simple and easy to implement on a digital computer in addition to the controllable systems the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs moreover two types of state feedback gain matrices can be achieved by this method 1 the numerical one which is unique and 2 the parametric one in which its parameters are determined in order to achieve a gain matrix with minimum frobenius norm the numerical examples are presented to demonstrate the advantages of the proposed method

parametric output feedback controller design abstract a parameterization of fixed gain output feedback controllers which will assign a complete set of distinct eigenvalues to a given state space system is presented the main result is a compact parametric expression for the output feedback controller gain matrix explicitly characterized by two sets of free parameters the set of n closed loop system eigenvalues and a set of mr n design parameters for n state r input m output systems the free design parameters are determined by a sequential design procedure which automatically satisfies the basic orthogonality constraints on the left and right closed loop eigenvectors under the condition m r n the principal benefits of the explicit characterization of a parametric class of output feedback controllers lie in the ability to directly accommodate various different design criteria an illustration of the parametric output feedback design procedure is given by way of approximating the optimal full state regulator response of a fifth order pilot plant evaporator model

pole assignment by output feedback using cylindrical algebraic decomposition recently a new polynomial method for pole assignment by static output feedback has been developed in this paper we show how this method can be generalized to partial pole clustering some poles are exactly assigned the others being clustered in a specified region of the complex plane a constructive and systematic algorithm for the numerical resolution of both problems the collins cylindrical algebraic decomposition algorithm is presented and applied to an illustrative example

the continuous adjoint method for the design of hydraulic turbomachines abstract this article presents the development and application of the continuous adjoint method for designing optimizing the shape of hydraulic turbomachines the reynolds averaged flow equations are solved in the rotating reference frame and the terms arising from the differentiation of the coriolis and centripetal forces are taken into account in the formulation of the adjoint equations the objective functions presented in this article can be used for achieving a the optimal collaboration of the runner impeller with the draft tube by controlling the meridional and circumferential velocity profiles at the exit of the runner b the operation at the desired hydraulic head and or c the cavitation suppression all of them are used to improve an existing francis runner it is important to note that the objective function related to cavitation is by definition non differentiable and a way to effectively handle it is proposed the continuous adjoint method is presented in its most general form and could readily be adapted to other objective functions in the field of hydraulic turbomachines

pole assignment of strictly proper and proper linear systems by constant output feedback a new unifying approach for the study of pole assignment by constant output feedback cpap for strictly proper and proper linear systems is presented the multilinear nature of cpap is reduced to a linear problem and to the standard multilinear problem of decomposability of multivectors the solvability of cpap thus becomes a problem of finding real intersections of a linear variety with the grassmann variety of a projective space an alternative proof to the ml n m i n are the numbers of outputs inputs states necessary and sufficient condition for generic pole assignability of strictly proper systems by complex output feedback is given the above result is extended to the ml n 1 condition for the case of proper systems stronger necessary conditions for generic pole assignment by a real output feedback are obtained by using the recently introduced invariant the plucker matrix pn such conditions are that pn must have full rank and ml n strictly proper case or ml n 1 proper case it is sh

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

on linear solutions of the output feedback pole assignment problem a new linear method for solving the output feedback pole assignment problem of linear systems is introduced and new sufficient conditions are obtained

constant solutions of polynomial equations abstract a necessary and sufficient condition is given for the equation ax by c in polynomial matrices to have a constant solution pair x y and also for x to be non singular a sufficient condition is then established under which the equation with a and b fixed has a constant solution for each c from a given class applications to the construction of static state feedback or static output injection in linear systems are discussed

a necessary condition for pole assignment by constant output feedback in this paper we shall investigate the pole assignment problem by constant output feedback using transfer function techniques in particular a necessary condition is given for the existence of constant output feedback which assigns the eigenvalues of closed loop system to any desired positions

exact pole assignment by output feedback part 1 abstract we shall prove that exact assignment of distinct poles using output feedback is possible in any controllable and observable linear time invariant multivariable system in which the number of inputs plus the number of outputs exceeds the number of states except in clearly identified circumstances furthermore we give a construction for the entire class of pathological cases the main part of our argument is concerned with the assigning of complex conjugate eigenvalues by means of a real feedback matrix indeed we begin by giving a simple algorithm which is effective over any field although this problem has been discussed by numerous authors in the past they have usually presented only generic results we examine the complete class of systems satisfying the hypotheses mentioned

multistage parametric eigenstructure assignment by output feedback control this paper develops an efficient multistage parametric approach for eigenstructure assignment in linear multivariable systems by output feedback control the sets of closed loop eigenvalues and associated eigenvectors are suitably divided into subsets and the entire eigenstructure is constructed by parts in two or more consecutive stages this allows the subsets of right and left eigenvectors to be assigned in separate stages and thus the computational algorithm is relaxed from the orthogonality conditions the number of effective free parameters beyond eigenvalue assignment is determined and the notion of redistributing these parameters among the assignable right and left eigenvectors is introduced numerical examples are included to demonstrate the design procedure

output feedback eigenstructure assignment using two sylvester equations the eigenstructure assignment problem with output feedback is studied for systems satisfying the condition p m n the main tool used is the concept of c a b invariance and two coupled sylvester equations the solution of which leads to the computation of an output stabilizing feedback a computationally efficient algorithm for the solution of these two coupled equations which leads to the computation of a desired output feedback is presented

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

optimal path in two and three dimensions we apply the dijkstra algorithm to generate optimal paths between two given sites on a lattice representing a disordered energy landscape we study the geometrical and energetic scaling properties of the optimal path where the energies are taken from a uniform distribution our numerical results for both two and three dimensions suggest that the optimal path for random uniformly distributed energies is in the same universality class as the directed polymers we present physical realizations of polymers in a disordered energy landscape for which this result is relevant s1063 651x9808212 9

eigenstructure assignment by output feedback and residue analysis this note deals with the use of feedback to approximate the closed loop eigenstructure of a system to a prescribed set of values a new method is proposed to reduce the controller complexity based on eigenvalue sensitivity concepts a flight control example is presented as an application

output feedback pole assignment procedure a new algorithm based on pole assignment considerations for linear time invariant m input p output systems by means of static output feedback is presented for the case in which the number of inputs m and the number of outputs p are less than the order of the system n this algorithm determines the output feedback matrix required to assign max p m 1 poles and simultaneously calculates the coefficients of the residual polynomial the roots of which are the remaining unassigned poles the root locus method is used to find an appropriate feedback gain to provide acceptable locations for the unassigned poles some numerical examples are provided to illustrate this method

solutions of the equation av bw vf and their application to eigenstructure assignment in linear systems two new simple complete analytical and restriction free solutions with complete and explicit freedom of the matrix equation av bw vf are proposed here ab is known and is controllable and f is in the jordan form with arbitrary given eigenvalues based on the proposed solutions of this matrix equation a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed and two new algorithms are presented the proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective

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

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

numerical algorithms for eigenvalue assignment by constant and dynamic output feedback algorithms are proposed for eigenvalue assignment eva by constant as well as dynamic output feedback the main algorithm is developed for single input multioutput systems and the results are then extended to multiinput multioutput systems in computing the feedback use is made of the fact that the closed loop eigenvalues can almost always be assigned arbitrarily close to the desired locations in the complex plane provided the system satisfies the condition m p n where m p and n are respectively the number of inputs outputs and states of the system the eva problem has been treated as a converse of the algebraic eigenvalue problem the proposed algorithms are based on the implicitly shifted qr algorithm for solving the algebraic eigenvalue problem the performance of the algorithms is illustrated by several numerical examples

exact pole assignment by output feedback part 3 abstract this part concludes a series of three papers concerning controllable and observable linear time invariant multivariable control systems in which the number of outputs plus the number of inputs exceeds the number of states following from the second paper fletcher 1987 it remains to consider the assignment by real output feedback of a set of distinct eigenvalues consisting of a mixture of real numbers and complex conjugate pairs of non real numbers we examine the possibility that in the algorithm described in the first paper fletcher and magni 1987 all the real eigenvalues can be assigned before any of the complex conjugate pairs if this is possible then the argument of fletcher 1987 can be used to complete the assignment it is only from the failure of this possibility that the pathological cases detailed in the first paper can arise

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

on eigenstructure assignment by gain output feedback in this paper the eigenstructure assignment of linear multivariable control systems is studied from a geometric point of view for the class of systems in which the number of outputs plus the number of inputs exceeds the number of states genericity properties relative to this problem are derived it is shown without any assumption on the genericity of the system that the pole assignment can be carried out by choosing some closed loop eigenvectors almost freely the crucial point is that all the expected degrees of freedom in pole assignment are so described without redundancy which fully justifies the practical interest of such techniques despite the technicality required for the derivation of intermediate results the main result which is an eigenstructure assignment algorithm is very easy to implement because it is only based on the computation of certain sums and intersections of characteristic subspaces furthermore it is shown how the basic tools developed here can be used to tackle the prob

solvability controllability and observability of continuous descriptor systems in this paper we investigate the properties of the continuous descriptor system e dot x t ax t bu t 0 leqt leqb where e a and b are complex and possibly singular matrices and u t is a complex function differentiable sufficiently many times the traditional approach to such systems is to separate the state equations from the algebraic equations however such algorithms usually destroy the natural physically based sparsity and structure of the original system therefore we consider descriptor systems in their original form such systems possess numerous properties not shared by the well known state variable systems first we relate classical theories of matrix pencils to the solvability of descriptor systems then we extend the concepts of reachability controllability and observability of state variable systems to descriptor systems and describe the set of reachable states for descriptor systems

mean field behavior of the negative weight percolation model on random regular graphs we investigate both analytically and numerically the ensemble of minimum weight loops in the negative weight percolation model on random graphs with fixed connectivity and bimodal weight distribution this allows us to study the mean field behavior of this model the analytical study is based on a conjectured equivalence with the problem of self avoiding walks in a random medium the numerical study is based on a mapping to a standard minimum weight matching problem for which fast algorithms exist both approaches yield results that are in agreement on the location of the phase transition on the value of critical exponents and on the absence of any sizable indications of a glass phase by these results the previously conjectured upper critical dimension of d u 6 is confirmed

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

a geometric framework for pole assignment algorithms the problem of pole assignment by gain output feedback or by low order dynamical compensator is considered from a geometric point of view this makes it possible to unify in a general framework most of the existing pole assignment methods formulated in a state space context such as the minimal order observers the brasch pearson compensator and the methods proposed by h kimura and to simplify their presentation moreover new pole assignment algorithms may be derived from this general formulation

discrete adjoint based approach for optimization problems on three dimensional unstructured meshes a comprehensive strategy for developing and implementing discrete adjoint methods for aerodynamic shape optimization problems is presented by linearizing each procedure in the entire optimization problem transposing each linearization and reversing the sequential order of operations the adjoint of the complete optimization problem including flow equations and mesh motion equations is constructed in a modular and verifiable fashion this construction is also shown to produce minimal memory overheads and retain the same convergence characteristics of the original analysis problem in the sensitivity analysis these techniques are implemented in a three dimensional unstructured multigrid navierstokes solver and demonstrated on a transonic drag reduction problem for a wing body configuration

polynomial combinatorial optimization methods for analysing the ground states of disordered systems we discuss the application of polynomial combinatorial optimization algorithms to extract the universal zero temperature properties of various disordered systems dijkstras algorithm is used for models of non directed elastic lines on general regular graphs with isotropically correlated random potentials the successive shortest path algorithm for minimum costflow problems is applied for the study of ground state properties and the entanglement of many elastic lines in a disordered environment and the disorder induced loop percolation transition in a vortex glass model the preflow push algorithm for minimum cut maximum flow problems is used for the investigation of a roughening transition occurring in a model for elastic manifolds in a periodic potential in the presence of point disorder

families of fixed degree graphs for processor interconnection a construction is presented which given a fixed undirected graph of low degree and small average path length yields an infinite sequence of low diameter graphs of increasing order and fixed degree as examples of the construction infinite sequences of low diameter graphs are presented with degrees in the range 3 to 30 expressed as a function of the order of the graphs the degree 3 sequence has diameter bounded above by 1 4722 log2 n o 1 and the degree 4 sequence by 0 9083 log 2 n o 1

static output feedback pole placement via a trust region approach this technical note presents two closely related algorithms for the problem of pole placement via static output feedback the algorithms are based on two different trust region methods and utilize the derivatives of the closed loop poles extensive numerical experiments show the effectiveness of the algorithms in practice though convergence to a solution is not guaranteed for either algorithm while desired poles must be distinct strategies for dealing with repeated poles are also presented

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

quadratic characterization and use of output stabilizable subspaces this note treats the problem of stabilization of linear systems by static output feedback using the concept of c a b invariant subspaces the work provides a new characterization of output stabilizable c a b invariant subspaces through two coupled quadratic stabilization conditions an equivalence is shown between the existence of a solution to this set of conditions and the possibility to stabilize the system by static output feedback an algorithm is provided and numerical examples are reported to illustrate the approach

upper critical dimension of the negative weight percolation problem by means of numerical simulations we investigate the geometric properties of loops on hypercubic lattice graphs in dimensions d 2 through 7 where edge weights are drawn from a distribution that allows for positive and negative weights we are interested in the appearance of system spanning loops of total negative weight the resulting negative weight percolation nwp problem is fundamentally different from conventional percolation as we have seen in previous studies of this model for the two dimensional case here we characterize the transition for hypercubic systems where the aim of the present study is to get a grip on the upper critical dimension d u of the nwp problem for the numerical simulations we employ a mapping of the nwp model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms we characterize the loops via observables similar to those in percolation theory and perform finite size scaling analyses e g three dimensional hypercubic systems with side length up to l 56 sites in order to estimate the critical properties of the nwp phenomenon we find our numerical results consistent with an upper critical dimension d u 6 for the nwp problem

a new approach to eigenstructure assignment by output feedback the eigenstructure assignment problem for a linear time invariant multi input multi output system using output feedback is considered a new approach is developed which identifies the eigenspaces for the desired set of all the closed loop eigenvalues for the assignment of this desired set necessary and sufficient conditions are established these conditions contain two coupled sylvester matrix equations one of which is proven to be a reduced order square sylvester matrix equation this results in an efficient analytical procedure numerically superior to known techniques for the determination of the output feedback gain matrix

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

analysis and synthesis of robust control systems via parameter dependent lyapunov functions in this paper the problem of robust stability of systems subject to parametric uncertainties is considered sufficient conditions for the existence of parameter dependent lyapunov functions are given in terms of a criterion which is reminiscent of but less conservative than popov s stability criterion an equivalent frequency domain criterion is demonstrated the relative sharpness of the proposed test and existing stability criteria is then discussed the use of parameter dependent lyapunov functions for robust controller synthesis is then considered it is shown that the search for robustly stabilizing controllers may be limited to controllers with the same order as the original plant a possible synthesis procedure and a numerical example are then discussed

a bilinear formulation for the output feedback problem in linear systems this note ties together a geometric theory and previous algebraic results for the closed loop eigenstructure assignment by output feedback in multivariable systems necessary and sufficient conditions for the closed loop stabilization eigenstructure assignment are presented in terms of a bilinear sylvester equation the solutions of which completely characterize the closed loop eigenstructure problem with output feedback some preliminary results for the solution of this bilinear equation are presented

unsteady aerostructure coupled adjoint method for flutter suppression an unsteady aerostructure coupled adjoint method is presented for computing shape sensitivities of unsteady flows with fluid structure interactions the nominal flow solver is an unsteady euler solver based on a stationary cartesian grid using transpiration boundary conditions with hilbert transformation a novel damping related cost function is defined for which the shape sensitivity can be computed by the new unsteady aerostructure coupled adjoint method the capability of the new method is demonstrated by a successful airfoil shape optimization for flutter suppression

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

discrete adjoint approach for nonlinear unsteady aeroelastic design optimization presented is a discrete adjoint approach for computing nonlinear unsteady aeroelastic geometric design sensitivities which can subsequently be used for nonlinear unsteady aeroelastic geometric des

feedback and pole placement in descriptor variable systems the effects and uses of applying linear feedback to continuous time descriptor systems are studied structural changes resulting from feeding back the slow and fast parts of the trajectory separately are characterized it is shown that under certain conditions related to controllability the poles of the slow subsystem may be shifted arbitrarily and the impulsive behaviour of the fast subsystem may be eliminated

eigenvalue generalized eigenvector assignment by output feedback this note generalizes the previous results of the closed loop eigenstructure assignment via output feedback in linear multivariable systems necessary and sufficient conditions for the closed loop eigenstructure assignment by output feedback are presented some known results on entire eigenstructure assignment are deduced from this result

some remarks on real and complex output feedback we provide some new necessary and sufficient conditions which guarantee arbitrary pole placement of a particular linear system over the complex numbers we exhibit a nontrivial real linear system which is not controllable by real static output feedback and discuss a conjecture from algebraic geometry concerning the existence of real linear systems for which all static feedback laws are real

some results on the genericity of the pole placement problem abstract in this note the pole placement problem for a linear mimo systems with p outputs and m inputs is studied from the algebraic point of view a formulation is proposed that allows to analyze both theoretical and numerical aspects of the case min m p 2 with more sharpness moreover here it is shown that arbitrary pole placement by static output feedback of unitary rank is generically not possible even if m p n holds true

biased and greedy random walks on two dimensional lattices with quenched randomness the greedy ant within a disordered environment the main characteristics of biased greedy random walks bgrws on two dimensional lattices with real valued quenched disorder on the lattice edges are studied here the disorder allows for negative edge weights in previous studies considering the negative weight percolation nwp problem this was shown to change the universality class of the existing static percolation transition in the presented study four different types of bgrws and an algorithm based on the ant colony optimization heuristic were considered regarding the bgrws the precise configurations of the lattice walks constructed during the numerical simulations were influenced by two parameters a disorder parameter ensuremath rho that controls the amount of negative edge weights on the lattice and a bias strength b that governs the drift of the walkers along a certain lattice direction the random walks are greedy in the sense that the local optimal choice of the walker is to preferentially traverse edges with a negative weight associated with a net gain of energy for the walker here the pivotal observable is the probability that after termination a lattice walk exhibits a total negative weight which is here considered as percolating the behavior of this observable as function of ensuremath rho for different bias strengths b is put under scrutiny upon tuning ensuremath rho the probability to find such a feasible lattice walk increases from zero to 1 this is the key feature of the percolation transition in the nwp model here we address the question how well the transition point ensuremath rho mathrm c resulting from numerically exact and static simulations in terms of the nwp model can be resolved using simple dynamic algorithms that have only local information available one of the basic questions in the physics of glassy systems

recursive sampling of random walks self avoiding walks in disordered media the author presents a new algorithm for simulating random walks which is simple versatile and efficient it uses recursive function calls and can be used to obtain unbiased samples with any given length distribution this makes it particularly useful in disordered geometries where the effective connectivity constant is not known a priori when applying it to self avoiding random walks on two dimensional media with quenched randomness he finds evidence for at least two new renormalization group fixed points

new results in pole assignment by real output feedback this paper considers the problem of tuning natural frequencies of a linear system by a memoryless controller using algebro geometric methods it is shown how it is possible to improve current sufficiency conditions the main result is an exact combinatorial characterization of the nilpotency index of the bmod 2 cohomology ring of the real grassmannian using this characterization new sufficiency results for generic pole assignment for the linear system with m inputs p outputs and mcmillan degree n are given among other results it is shown that 2 25 cdot max m p min m p 3 geq n is a sufficient condition for generic real pole placement provided min m p geq 4

fundamental theorem of state feedback for singular systems abstract the limits of state feedback in altering the dynamics of singular systems are studied a necessary and sufficient condition is given for a list of polynomials to be invariant polynomials of a proper system obtained by state feedback from the singular system the condition consists of inequalities which involve the controllability indices of the singular system and the degrees of the invariant polynomials the development is based on the properties of polynomial matrices a procedure is given for the calculation of a feedback gain which achieves the desired dynamics

pole placement via static output feedback is np hard this note proves that the problem of pole placement via static output feedback for linear time invariant systems is np hard

eigenstructure assignment in descriptor systems coordinate free conditions are given for pole assignment by feedback in linear descriptor singular systems which guarantee closed loop regularity these conditions are shown to be both necessary and sufficient for assignment of the maximum possible number of finite poles transformation to special coordinates are not used and the results provide a robust algorithm for the computation of the required feedback

directed negative weight percolation we consider the negative weight percolation model on directed graphs in particular we study the model on a two dimensional weighted periodic centered square lattice bond weights are taken from a distribution that allows for both positive and negative values for a given realization of the disorder a minimally weighted directed loop and path configuration is determined by performing a nontrivial transformation of the original lattice into a minimum weight perfect matching problem for this problem fast polynomial time algorithms are available thus we could study large systems with high accuracy depending on the fraction of negatively and positively weighted bonds on the lattice a continuous phase transition is identified and its characterizing critical exponents are estimated by means of a finite size scaling analysis we observe a strong change of the universality class with respect to standard directed percolation as well as with respect to undirected negative weight percolation furthermore the relation to directed polymers in random media is illustrated

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

decoupling of square singular systems via proportional state feedback necessary and sufficient conditions for the decoupling of a solvable square singular system ex t ax t bu t with output y t dx t through an admissible control law of the form u t kx t hr t where h is a square nonsingular matrix it has been shown that for a given singular system that satisfies these conditions a propagational state feedback exists for which the system s transfer function is a diagonal nonsingular and proper rational matrix the proofs of the main results are constructive and provide a procedure for computing an appropriate proportional state feedback

stabilizability of multivariable systems and the ljusternik snirel mann category of real grassmannians abstract in this paper a numeric criterion k m p n is given for stabilizability by constant gain output feedback of the generic linear multivariable system with m inputs n states and p outputs this criterion is defined in terms of a topological invariant of the space of gains both finite and infinite arising from an interpretation of the problem of stabilizability as a problem concerning open covers of this space this invariant originally considered by ljusternik and snirel mann in the calculus of variations can be estimated from below by using a theorem of eilenberg together with the methods of the schubert calculus thus leading to some very explicit corollaries concerning generic stabilizability as far as i am aware these corollaries cannot be derived from existing results concerning pole assignability after passing to a problem on coverings of the compactified gain space the main technical problem which remains in a high gain stability analysis stated here as a high gain lemma which appears to be of independent interest that is the topological argument implies that the closed loop system is stable for some gain possibly infinite if the root locus map were defined and continuous at all infinite gains then the conclusion that the system is stabilizable by finite gain could be deduced from a simple continuity argument however it is known that if mp n then the root locus map has points of discontinuity at infinity and since mp n is now known to be necessary for generic stabilizability in most cases of interest one requires a far more subtle argument than one would give for example in the scalar case

a general formula for eigenvalue assignment by static output feedback with application to robust design in this note generalizing an idea of a previous paper we derive a new expression of the characteristic polynomial of a linear system subject to static output feedback from this expression an explicit form of the assignment equations in the unknown elements of the feedback matrix is obtained the equations are completely general and seem much simpler than many others proposed until now in special cases a closed or almost a closed form solution is obtained the assignment equations are then used within an algorithm for global optimization to solve the problem of exactly assigning the eigenvalues of the nominal plant while maximizing the norm of perturbation matrices for which the perturbed eigenvalues remain in specified regions of the complex plane

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

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

critical properties of loop percolation models with optimization constraints we study loop percolation models in two and in three space dimensions in which configurations of occupied bonds are forced to form a closed loop we show that the uncorrelated occupation of elementary plaquettes of the square and the simple cubic lattice by elementary loops leads to a percolation transition that is in the same universality class as the conventional percolation in contrast to this an optimization constraint for the loop configurations which then have to minimize a particular generic energy function leads to a percolation transition that constitutes a universality class for which we report the critical exponents implication for the physics of solid on solid and vortex glass models are discussed

eigenvalue placement for generalized linear systems this paper deals with some aspects of eigenvalue placement by state feedback for generalized linear systems described by e ax bu where e is a singular map it is shown that controllability of the infinite eigenvalues of the pencil se a is equivalent to the existence of a state feedback map which assigns those eigenvalues to pre specified complex numbers a procedure for the assignment of all eigenvalues to distinct complex numbers is also discussed

perturbation theory of output feedback pole assignment perturbation theory for output feedback eigenstructure assignment is considered the analysis is based on general conditions for eigenstructure assignment together with the well known perturbation theory for the pseudo inverse of a matrix this enables us to present a variety of sensitivity analyses for this problem and to indicate some precautions when choosing eigenvectors in the pole assignment problem

feedback canonical form for singular systems controllability and impulse controllability indices for singular systems are defined via the concept of minimal indices for modules over polynomial rings these indices are invariant under the transformations of restricted system equivalence and feedback equivalence they yield a characterization of controllability and impulse controllability of singular systems analogous to the state space situation and form a complete list of invariants for impulse controllable systems under feedback equivalence a feedback canonical form described by these invariants is constructed explicitly

eigenstructure perturbation analysis in disjointed domains for linear uncertain systems sufficient bounds are presented on the norm bounded uncertainties for the perturbed eigenvalues to remain in a set of disjointed neighbourhoods of the nominal eigenvalues for such perturbed eigenvalues bounds on the corresponding eigenvector perturbations are also presented the study is used to analyse design methodologies based on eigenstructure assignment with parameter variations in a conrollable pair the left and right eigenvector perturbation analysis carried out in this paper is useful in the time response analysis of linear uncertain systems

exact ground states of large two dimensional planar ising spin glasses studying spin glass physics through analyzing their ground state properties has a long history although there exist polynomial time algorithms for the two dimensional planar case where the problem of finding ground states is transformed to a minimum weight perfect matching problem the reachable system sizes have been limited both by the needed cpu time and by memory requirements in this work we present an algorithm for the calculation of exact ground states for two dimensional ising spin glasses with free boundary conditions in at least one direction the algorithmic foundations of the method date back to the work of kasteleyn from the 1960s for computing the complete partition function of the ising model using kasteleyn cities we calculate exact ground states for huge two dimensional planar ising spin glass lattices up to 3000 2 spins within reasonable time according to our knowledge these are the largest sizes currently available kasteleyn cities were recently also used by thomas and middleton in the context of extended ground states on the torus moreover they show that the method can also be used for computing ground states of planar graphs furthermore we point out that the correctness of heuristically computed ground states can easily be verified finally we evaluate the solution quality of heuristic variants of the l bieche et al approach

exact pole assignment using direct or dynamic output feedback this note addresses the problem of the assignability of the eigenvalues of the matrix a bpc by choice of the matrix p this mathematical problem corresponds to pole assignment in the direct output feedback control problem and by proper changes of variables it also represents the pole assignment problem with dynamic feedback controllers the key to our solution is the introduction of the new concept of local complete assignability which in loose terms is the arbitrary perturbability of the eigenvalues of a bpc by perturbations of p if n x is the order of the system we show that if a bp 0 c has distinct eigenvalues a necessary and sufficient condition for local complete assignability at p 0 is that the matrices c a bp 0 c i 1 b be linearly independent for 1 leq i leq n x in special cases this condition reduces to known criteria for controllability and observability although these latter properties are necessary conditions for assignability we also address the question of the assignability of uncontrollable or unobservable systems both by direct output feedback and dynamic compensation the main result of this note yields an algorithm that assigns the closed loop poles to arbitrarily chosen values in the direct and in the dynamic output feedback control problems

optimal paths in strong and weak disorder a unified approach we present a unified scaling theory for the optimal path connecting opposite edges of a disordered lattice of size l each bond of the lattice is assigned a cost expar where r is a uniformly distributed random variable and a is disorder strength the optimal path minimizes the sum of the costs of the bonds along the path we argue that for la where is the correlation exponent of percolation the path becomes equivalent to a directed polymer on an effective lattice consisting of blobs of size a it is self affined and characterized by the roughness exponent of directed polymers for la or on the length scales below the blob size the path behaves as an optimal path in the strong disorder limit it has a self similar fractal shape with fractal dimension dopt we derived the scaling relations for the length of the path its transversal displacement the average cost and its fluctuation we test our scaling theoretical predictions by numerical simulations on a square lattice

a new sufficient condition for arbitrary pole placement by real constant output feedback abstract a new sufficient condition for generic pole assignment is given based on the height of the first whitney class of a certain grassmannian this result contains the condition m p 1 n and is stronger than lscat p m n this test is equivalent to the factorial test in 7 but it has the advantage that it is testable for most of the cases

adjoint based sensitivity formulation for fully coupled unsteady aeroelasticity problems a method to compute sensitivities for use in gradient based shape optimization applied to unsteady aeroelasticity problems is presented the method takes into account the coupling between all three fundamental aspects of computational aeroelasticity namely unsteady flow equations time varying structural response to aerodynamic loads and dynamic meshes that accommodate geometric deformations the devised method provides discretely exact sensitivities of time integrated and non time integrated objective functions with respect to design variables that control the shape of geometry the algorithm is formulated in a general manner and can be readily extended to coupled multidisciplinary problems involving any number of disciplines the algorithm is applied to a simple two dimensional flutter model to demonstrate the proof of concept

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

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

directed polymers in a random medium abstract the problem of a polymer in a random medium can be formulated as follows consider a regular lattice with on each bond ij a random energy ij the energy e w of a self avoiding walk w on this lattice is the sum of the energies of all the bonds visited by the walk then the problem is to compute the partition function z w exp e w t several recent results will be presented 1 the mean field version of this problem can be solved exactly and one observes a low temperature phase similar to the spin glass phase 2 for finite dimensional lattices one can derive bounds on the transition temperature in high enough dimension 3 for hierarchical lattices the problem can be reduced to finding stable laws when one combines random variables in a non linear way for example z z 1 z 2 z 3 z 4

a generalized state space for singular systems systems of the form e dot x ax bu y cx with e singular are studied of particular interest are the impulsive modes that may appear in the free response of such systems when arbitrary initial conditions are permitted modes that are associated with natural system frequencies at infinity a generalized definition of system order that incorporates these impulsive degrees of freedom is proposed and concepts of controllability and observability are defined for the impulsive modes allowable equivalence transformations of such singular systems are specified the present framework is shown to overcome several difficulties inherent in other treatments of singular systems and to extend in a natural and satisfying way many results previously known only for regular state space systems

some necessary and sufficient conditions for eigenstructure assignment abstract some necessary and sufficient conditions for closed loop eigenstructure assignment by output feedback in time invariant linear multivariable control systems are presented a simple condition on a square matrix necessary and sufficient for it to be the closed loop plant matrix of a given system with some output feedback is the basis of the paper some known results on entire eigenstructure assignment are deduced from this the concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors

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

phase transitions in diluted negative weight percolation models we investigate the geometric properties of loops on two dimensional lattice graphs where edge weights are drawn from a distribution that allows for positive and negative weights we are interested in the appearance of spanning loops of total negative weight the resulting percolation problem is fundamentally different from conventional percolation as we have seen in a previous study of this model for the undiluted case here we investigate how the percolation transition is affected by additional dilution we consider two types of dilution either a certain fraction of edges exhibits zero weight or a fraction of edges is even absent we study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms we perform a finite size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary we find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change in the universality class

discrete adjoint approach for modeling unsteady aerodynamic design sensitivities a discrete adjoint approach is presented for computing steady and unsteady aerodynamic design sensitivities for compressible viscous flows about airfoil configurations the nominal flow solver method is based on a harmonic balance solution technique which is capable of modeling both steady and nonlinear periodic unsteady flows the computer code for the discrete adjoint solver which is derived from the nominal harmonic balance solver has been generated with the aid of the advanced automatic differentiation software tool known as taf transformation of algorithms in fortran