t norm based addition of fuzzy intervals abstract the aim of this paper is to provide new results regarding the effective practical computation of t norm based additions of lr fuzzy intervals

robust partial pole assignment problem for high order control systems in this paper we consider the partial pole assignment problem ppap for high order control systems it is shown that solving the ppap is essentially solving a pole assignment for a linear system of a much lower order and the robust ppap is then concerning the robust pole assignment problem for this linear system based on this theory a rather simple algorithm for solving the robust ppap is proposed and numerical examples show that this algorithm does lead to comparable results with earlier algorithms but at much lower computational cost

perturbation of eigenvalues for periodic matrix pairs via the bauer fike theorems abstract in earlier papers the bauer fike technique was applied to the ordinary eigenvalue problem a x x the generalized eigenvalue problem a x b x and the matrix polynomial eigenvalue problem k 0 m k a k x 0 general multiple eigenvalues were dealt with and condition numbers were obtained for individual as well as clusters of eigenvalues in this paper we shall generalize the technique to the eigenvalue problem for regular periodic matrix pairs perturbation to eigenvalues simple or multiple finite or infinite will be considered for perturbations of any size for small perturbations clusters of eigenvalues will be considered

multi linear measure theory and multiple stochastic integration stochastic integration in a lebesgue stieltjes sense is developed in a general context of multi linear measure theory based on the fundamental grothendieck inequality and factorization theorem

partial eigenstructure assignment for undamped vibration systems using acceleration and displacement feedback abstract a new method for partial eigenstructure assignment using acceleration and displacement feedback for undamped vibration systems is presented in this paper firstly a necessary and sufficient condition is proposed for the incremental mass and stiffness matrices that modify some eigenpairs while keeping other eigenpairs unchanged secondly based on this condition an algorithm for determining the required control gain matrices of acceleration and displacement feedback which assign the desired eigenstructure is developed this algorithm is easy to implement and works directly on the second order system model more importantly the algorithm allows the control matrix to be specified beforehand and also leads naturally to a small norm solution of the feedback gain matrices finally some numerical examples are given to demonstrate the effectiveness and accuracy of the proposed algorithm

on the inverse eigenvalue problem for t alternating and t palindromic matrix polynomials abstract the inverse eigenvalue problem for t alternating matrix polynomials over arbitrary algebraically closed fields of characteristic different from two is considered the main result shows that the necessary conditions obtained in 9 for a matrix polynomial to be the smith form of a t alternating matrix polynomial are under mild conditions also sufficient to be the smith form of a t alternating matrix polynomial with invertible leading coefficient which is additionally in anti triangular form in particular this result implies that any t alternating matrix polynomial with invertible leading coefficient is equivalent to a t alternating matrix polynomial in anti triangular form that has the same finite and infinite elementary divisors as the original matrix polynomial finally the inverse eigenvalue problem for t palindromic matrix polynomials is considered excluding the case that both 1 and 1 are eigenvalues

closed form solutions to the nonhomogeneous yakubovich transpose matrix equation abstract the nonhomogeneous yakubovich transpose matrix equation x a x t b c y r which contains the well known kalman yakubovich transpose matrix equation and general discrete lyapunov transpose matrix equation as special cases has many important applications in control system theory this study presents two methods to obtain the closed form solutions of the nonhomogeneous yakubovich transpose matrix equation moreover the equivalent forms of the solutions are provided and one of the solutions is established with the controllability matrix the observability matrix and symmetric operator matrix

technical communique complete parametric approach for eigenstructure assignment in a class of second order linear systems this note deals with eigenstructure assignment in the second order linear system email protected email protected cq bu using the proportional plus derivative feedback controller u k 0q k email protected under the controllability condition of the matrix pair ab very simple general and complete parametric expressions in direct closed forms for both the closed loop eigenvector matrix and the feedback gains are established in terms of the closed loop eigenvalues and a group of parameter vectors the main computations are two sets of elementary matrix transformations which can be replaced by a series of singular value decompositions when the closed loop eigenvalues are chosen a priori the approach utilizes directly the original system data a b and c and involves manipulations on only n dimensional matrices an example illustrates the effect of the proposed approach

robust partial quadratic eigenvalue assignment with time delay using the receptance and the system matrices abstract in this paper we consider the robust partial quadratic eigenvalue assignment problem in vibration by active feedback control based on the receptance measurements and the system matrices we propose an optimization method for the robust and minimum norm partial quadratic eigenvalue assignment problem we provide a new cost function and the closed loop eigenvalue sensitivity and the feedback norms can be minimized simultaneously our method is also extended to the case of time delay between measurements of state and actuation of control numerical tests demonstrate the effectiveness of our method

linear and numerical linear algebra in control theory some research problems abstract this paper presents an informal survey of theoretical and computational aspects of three linear algebra problems arising in control theory namely the sylvester observer matrix equation the matrix eigenvalue assignment problem and the stability and stabilization of large second order systems difficulties are highlighted recent developments are mentioned some research problems in these areas which should be of interest to both linear algebraists and control theorists are described

parametric eigenstructure assignment in second order descriptor linear systems this note considers eigenstructure assignment in second order descriptor linear systems via proportional plus derivative feedback it is shown that the problem is closely related with a type of so called second order sylvester matrix equations through establishing two general parametric solutions to this type of matrix equations two complete parametric methods for the proposed eigenstructure assignment problem are presented both methods give simple complete parametric expressions for the feedback gains and the closed loop eigenvector matrices the first one mainly depends on a series of singular value decompositions and is thus numerically simple and reliable the second one utilizes the right factorization of the system and allows the closed loop eigenvalues to be set undetermined and sought via certain optimization procedures an example shows the effect of the proposed approaches

orthogonality and partial pole assignment for the symmetric definite quadratic pencil abstract the eigenvectors of a symmetric matrix can be chosen to form an orthogonal set with respect to the identity and to the matrix itself similarly the eigenvectors of a symmetric definite linear pencil can be chosen to be orthogonal with respect to the pair this paper presents the three sets of matrix weights with respect to which the eigenvectors of the symmetric definite quadratic pencil are orthogonal one of these is used to derive an explicit solution of the partial pole assignment problem by state feedback control for a control system modeled by a system of second order differential equations the solution may be of particular interest in the stabilization and control of flexible large space structures where only a small part of the spectrum is to be reassigned and the rest of the spectrum is required to remain unchanged

approximate pole assignment a novel approach and some new algorithms for the pole assignment problem of a controllable time invariant linear multivariable system with linear state or output feedback are presented the main theme of the approach and the algorithms is to satisfy some constraints in the problem approximately various rank 1 update algorithms can then be derived depending on different extents to which the constraints are approximated functionals have to be minimized when eigenvectors of the closed loop system are chosen a perturbation analysis on the effect of the approximation and several numerical examples will be presented

solution to the second order sylvester matrix equation mvf sup 2 dvf kv bw this note provides a complete general parametric solution v w to the generalized second order sylvester matrix equation mvf sup 2 dvf kv bw with f being an arbitrary square matrix the primary feature of this solution is that the matrix f does not need to be in any canonical form or may be even unknown a priori the results provide great convenience to the computation and analysis of the solutions to this class of equations and can perform important functions in many analysis and design problems involving second order dynamical systems

orthogonal basis selection method for robust partial eigenvalue assignment problem in second order control systems in this paper we study the robust partial eigenvalue assignment problem using state feedback control in second order control systems which means that the feedback control matrices not only assign specific eigenvalues to the second order closed loop system but also that the system is robust or insensitive to perturbations in the coefficient matrices some measures of robustness of the closed loop system are discussed and a numerical method is proposed such that it aims to minimize one measure of the conditioning of the closed loop system numerical examples show that the method is convergent and often leads to better conditioned closed loop system

parametric control to a type of quasi linear second order systems via output feedback abstractthis paper considers the design of output feedback control for a type of quasi linear second order systems with the time varying coefficient matrices containing the state variables and a time varying parameter vector based on the solution to a type of second order generalised sylvester matrix equations general complete parameterisation of a quasi linear output feedback controller is established with respect to the state variables the time varying parameter vector the constant closed loop system and another two groups of arbitrary parameters and also for the left and right closed loop eigenvectors matrices with the proposed parametric output feedback control the closed loop system can be transformed into a constant linear system with desired eigenstructure finally simulation results are provided to illustrate the convenience and effectiveness of application in the general spacecraft rendezvous problem

projection and deflation method for partial pole assignment in linear state feedback two projection methods are proposed for partial pole placement in linear control systems these methods are of interest when the system is very large and only a few of its poles must be assigned the first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace the second method can be regarded as a variant of the weilandt deflation technique used in eigenvalue methods

neurodynamics based robust pole assignment for high order descriptor systems in this paper a neurodynamic optimization approach is proposed for synthesizing high order descriptor linear systems with state feedback control via robust pole assignment with a new robustness measure serving as the objective function the robust eigenstructure assignment problem is formulated as a pseudoconvex optimization problem a neurodynamic optimization approach is applied and shown to be capable of maximizing the robust stability margin for high order singular systems with guaranteed optimality and exact pole assignment two numerical examples and vehicle vibration control application are discussed to substantiate the efficacy of the proposed approach

feedback stabilization of a second order system a nonmodal approach a novel approach for feedback stabilization of a second order model is proposed specifically two nonmodal algorithms are described and it is shown mathematically that under some mild assumptions on the damping matrix the feedback matrix obtained by each algorithm indeed stabilizes a closed loop system the first algorithm requires the solution of a symmetric positive definite linear system and the inversion of a small matrix a remarkable feature of this algorithm is that it does not require knowledge of the stiffness and damping for implementation which makes it very feasible for practical application the second algorithm requires the solution of a small linear least squares problem and an estimate of the stability index which can be obtained just by computing the extremal eigenvalues of the data matrices which are symmetric for almost all practical applications these minimal computational requirements make the proposed algorithms suitable for practical implementations even for large and sparse systems using the state of the art techniques of matrix computations this is in sharp contrast with the traditional modal approach ordinarily used by practicing engineers which requires the solution of a quadratic eigenvalue problem or equivalently the solution of a 2n x 2n generalized eigenvalue problem and therefore may not be practical for very large and sparse problems besides the proposed algorithms the paper also contains some mathematical results on the bounds of the eigenvalues of a second order pencil which may be useful for investigating stability of second order systems and are of independent interest

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

least squares symmetric and skew symmetric solutions of the generalized sylvester matrix equation σi 1 s a i x b i σj 1 t c j y d j e the generalized sylvester matrix equation i 1 s a i x b i j 1 t c j y d j e with unknown matrices x and y is encountered in many system and control applications in this paper a direct method is established to solve the least squares symmetric and skew symmetric solutions of the equation by using the kronecker product and the generalized inverses and the expression of the solution set s are provided moreover an optimal approximation between a given matrix pair and the affine subspace s is discussed and an explicit formula for the unique optimal approximation solution is presented finally two numerical examples are given which demonstrate that the introduced algorithm is quite efficient

numerically robust pole assignment for second order systems we propose two new methods for solution of the eigenvalue assignment problem associated with the second order control system global hsize 30pc specifically the methods construct feedback matrices f 1 and f 2 such that the closed loop quadratic pencil has a desired set of eigenvalues and the associated eigenvectors are well conditioned method 1 is a modification of the singular value decomposition based method proposed by juang and maghami which is a second order adaptation of the well known robust eigenvalue assignment method by kautsky et al for first order systems method 2 is an extension of the recent non modal approach of datta and rincon for feedback stabilization of second order systems robustness to numerical round off errors is achieved by minimizing the condition numbers of the eigenvectors of the closed loop second order pencil control robustness to large plant uncertainty will not be explicitly considered in this paper numerical results for both the two methods are favourable a compara

arnoldi methods for large sylvester like observer matrix equations and an associated algorithm for partial spectrum assignment abstract we propose an arnoldi based numerical method for solving a sylvester type equation arising in the construction of the luenberger observer given an n n matrix a and an n m matrix g the method simultaneously constructs an m m hessenberg matrix h with a preassigned spectrum and an n m orthonormal matrix x such that ax xh g we consider the case when a is large and sparse so that the standard techniques such as the well known hessenberg schur method for solving a sylvester equation cannot be easily applied as a byproduct we propose an algorithm for the partial pole assignment problem for large matrices

an iterative updating method for damped structural systems using symmetric eigenstructure assignment an iterative method for updating finite element models with measured modal results using a symmetric eigenstructure assignment technique is developed by the method the updated symmetric damping and stiffness matrices can be obtained within finite iteration steps in the absence of roundoff errors by choosing a special kind of initial matrices and the measured data are embedded in the updated model the numerical results show that the proposed method is reliable and attractive

a solution of the affine quadratic inverse eigenvalue problem abstract the quadratic inverse eigenvalue problem qiep is to find the three matrices m c and k given a set of numbers closed under complex conjugations such that these numbers become the eigenvalues of the quadratic pencil p 2 m c k the affine inverse quadratic eigenvalue problem aqiep is the qiep with an additional constraint that the coefficient matrices belong to an affine family that is these matrices are linear combinations of substructured matrices an affine family of matrices very often arise in vibration engineering modeling and analysis research on qiep and aqiep are still at developing stage in this paper we propose three methods and the associated mathematical theories for solving aqiep a newton method an alternating projections method and a hybrid method combining the two validity of these methods are illustrated with results on numerical experiments on a spring mass problem and comparisons are made with these three methods amongst themselves and with another newton method developed by elhay and ram 2002 12 the results of our experiments show that the hybrid method takes much smaller number of iterations and converges faster than any of these methods

robust partial eigenvalue assignment problem for the second order system in this paper we study the partial eigenvalue assignment problem for the second order system where only a small part of eigenvalues of the open loop system is to be reassigned and the rest are required to remain unchanged it is desirable that the feedback controller not only assigns specific eigenvalues to the second order closed loop system but also that the system is robust or insensitive to perturbations we propose a numerical method such that the condition number of the matrix of the eigenvectors of the closed loop system is minimized in the method we only need the knowledge of the eigenvalues to be altered and the corresponding eigenvectors while we do not need the knowledge of the eigenstructures that are required to remain unchanged and are often unknown numerical examples show that the present method often leads to better conditioned closed loop system

pole assignment in vibratory systems by multi input control the problem of reassigning some poles of a vibratory system while keeping the other poles unchanged is considered the problem may be solved uniquely by single input state feedback control a family of solutions to the partial pole assignment problem may be obtained by applying multi input control forces an algorithm for determining a multi input control which is small in some sense is presented the non iterative algorithm proposed defines a closed form solution to the partial pole assignment problem in its natural second order form and no first order realization is used the reduction in the control effort achieved by the proposed method is demonstrated by numerical examples