on the multifractal nature of fully developed turbulence and chaotic systems it is generally argued that the energy dissipation of three dimensional turbulent flow is concentrated on a set with non integer hausdorff dimension recently in order to explain experimental data it has been proposed that this set does not possess a global dilatation invariance it can be considered to be a multifractal set the authors review the concept of multifractal sets in both turbulent flows and dynamical systems using a generalisation of the beta model

lacunarity and multifractal analysis of the large dla mass distribution abstract we show the methodology used to analyze fractal and mass multifractal properties of very large diffusion limited aggregation dla clusters with a maximum of 10 9 particles for 2d aggregates and 10 8 particles for 3d clusters to support our main result the scaling behavior obtained by our experimental results corresponds to the expected performance of monofractal objects in order to estimate lacunarity measures for large dla clusters we develop a variant of the gliding box algorithm which reduces the computer time needed to obtain experimental results we show how our mass multifractal data have a tendency to present monofractal behavior for the mass distribution of the cases presented in this paper in the limit of very large clusters lacunarity analysis shows provided we study small clusters mass distributions data which might be interpreted as two different values of fractal dimensions while the cluster grows however this effect tends to vanish when the cluster size increases further in such a way that monofractality is achieved the outcomes of this paper lead us to conclude that the previously reported mass multifractality behavior vicsek et al 1990 13 detected for dla clusters is a consequence of finite size effects and floating point precision limitations and not an intrinsic feature of the phenomena since the scaling behavior of our dla clusters space corresponds to monofractal objects being this situation remarkably noticeable in the limit of very large clusters

recurrent neural network for computing the drazin inverse this paper presents a recurrent neural network rnn for computing the drazin inverse of a real matrix in real time this recurrent neural network rnn is composed of n independent parts subnetworks where n is the order of the input matrix these subnetworks can operate concurrently so parallel and distributed processing can be achieved in this way the computational advantages over the existing sequential algorithms can be attained in real time applications the rnn defined in this paper is convenient for an implementation in an electronic circuit the number of neurons in the neural network is the same as the number of elements in the output matrix which represents the drazin inverse the difference between the proposed rnn and the existing ones for the drazin inverse computation lies in their network architecture and dynamics the conditions that ensure the stability of the defined rnn as well as its convergence toward the drazin inverse are considered in addition illustrative examples and examples of application to the practical engineering problems are discussed to show the efficacy of the proposed neural network

multifractal decompositions of moran fractals we present a rigorous construction and generalization of the multifractal decomposition for moran fractals with infinite product measure the generalization is specified by a system of nonnegative weights in the partition sum all the usual smooth properties of the f theory are recovered for the case that the weights are equal to unity the generalized spectrum f w is invariant to a group of gauge transformations of the weights and in addition need no longer be concave in case the fractal is a cantor set generated by an iterated function system of similarities is the pointwise dimension of the measure we discuss properties of some examples

neural network approach to computing matrix inversion a neural network for matrix inversion is proposed we show both analytically and by simulations that this network is guaranteed to be stable and to provide results arbitrarily close to the accurate inversion of a matrix within an elapsed time of only a few characteristic time constants of the network the parameters such as the interconnection strengths of this network can be obtained from the known matrix without any computations

recurrent neural networks for computing pseudoinverses of rank deficient matrices three recurrent neural networks are presented for computing the pseudoinverses of rank deficient matrices the first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of moore penrose inversion under the condition of zero initial states the second recurrent neural network consists of an array of neurons corresponding to a pseudoinverse matrix with decaying self connections and constant connections in each row or column the third recurrent neural network consists of two layers of neuron arrays corresponding respectively to a pseudoinverse matrix and a lagrangian matrix with constant connections all three recurrent neural networks are also composed of a number of independent subnetworks corresponding to the rows or columns of a pseudoinverse the proposed recurrent neural networks are shown to be capable of computing the pseudoinverses of rank deficient matrices

a recurrent neural network for solving sylvester equation with time varying coefficients presents a recurrent neural network for solving the sylvester equation with time varying coefficient matrices the recurrent neural network with implicit dynamics is deliberately developed in the way that its trajectory is guaranteed to converge exponentially to the time varying solution of a given sylvester equation theoretical results of convergence and sensitivity analysis are presented to show the desirable properties of the recurrent neural network simulation results of time varying matrix inversion and online nonlinear output regulation via pole assignment for the ball and beam system and the inverted pendulum on a cart system are also included to demonstrate the effectiveness and performance of the proposed neural network

minimizing the condition number of a gram matrix the condition number of a gram matrix defined by a polynomial basis and a set of points is often used to measure the sensitivity of the least squares polynomial approximation given a polynomial basis we consider the problem of finding a set of points and or weights which minimizes the condition number of the gram matrix the objective function f in the minimization problem is nonconvex and nonsmooth we present an expression of the clarke generalized gradient of f and show that f is clarke regular and strongly semismooth moreover we develop a globally convergent smoothing method to solve the minimization problem by using the exponential smoothing function to illustrate applications of minimizing the condition number we report numerical results for the gram matrix defined by the weighted vandermonde like matrix for least squares approximation on an interval and for the gram matrix defined by an orthonormal set of real spherical harmonics for least squares approximation on the sphere

a one layer recurrent neural network for pseudoconvex optimization subject to linear equality constraints in this paper a one layer recurrent neural network is presented for solving pseudoconvex optimization problems subject to linear equality constraints the global convergence of the neural network can be guaranteed even though the objective function is pseudoconvex the finite time state convergence to the feasible region defined by the equality constraints is also proved in addition global exponential convergence is proved when the objective function is strongly pseudoconvex on the feasible region simulation results on illustrative examples and application on chemical process data reconciliation are provided to demonstrate the effectiveness and characteristics of the neural network

recurrent neural network approach based on the integral representation of the drazin inverse in this letter we present the dynamical equation and corresponding artificial recurrent neural network for computing the drazin inverse for arbitrary square real matrix without any restriction on its eigenvalues conditions that ensure the stability of the defined recurrent neural network as well as its convergence toward the drazin inverse are considered several illustrative examples present the results of computer simulations

the global statistics of return times return time dimensions versus generalized measure dimensions we investigate return times in dynamical systems i e the time required by a trajectory to complete a return journey to a neighborhood of the initial position in particular we study the relations holding between the scaling exponents of phase space moments of return times in balls of diminishing radius on the one side and the generalized dimensions of invariant measures on the other because of a heuristic use of kac theorem the former have been used in place of the latter in numerical and experimental investigations to mark the distinction we call them return time dimensions we derive a full set of inequalities linking generalized dimensions of invariant measures and return time dimensions we comment on their optimality with the aid of two maps due to von neumann kakutani and to gaspard wang we conjecture a formula for the return time dimensions in a typical system we only assume that the dynamical system under investigation is ergodic and that motion takes place in a compact finite dimensional space

an algorithm for robust pole assignment via polynomial approach a computational method for designing controllers which attempt to place the roots of the characteristic polynomial of an uncertain system inside some prescribed regions is presented the analysis is based on transfer functions of characteristic polynomials and the problem is formulated as one of semi infinite programming an example of an application is given to illustrate this approach

how much resolution is enough influence of downscaling the pixel resolution of digital images on the generalised dimensions fractals are very often illustrated by digital images this is a consequence of the widespread availability of electronic and computational equipment these images are always limited by their pixel resolution subsequently the determination of dimensions for such images is restricted practically because for their calculation the range of scales is not infinite downscaling the pixel resolution of images to get images with reduced resolution worsens the achievable absolute computational results but surprisingly the changes in these values and especially the changes of the courses of the calculated generalised dimensions give very promising results this is due to the qualitative nature of these changes with respect to pixel downscaling this opens the possibility of determining the quality of the estimation of the fractal dimensions of any image with any particular pixel resolution furthermore the pattern of changes itself caused by downscaling is different between the individual fractals several geometrical fractals sierpinski gasket a fern a menger gasket and a modified menger gasket with circles as well as an example of a measured fractal the digital images of cancer invasion studies in vitro were investigated to study the influence of downscaling the pixel resolution of digital images on the estimation of fractal dimensions

complex neural network models for time varying drazin inverse two complex zhang neural network znn models for computing the drazin inverse of arbitrary time varying complex square matrix are presented the design of these neural networks is based on corresponding matrix valued error functions arising from the limit representations of the drazin inverse two types of activation functions appropriate for handling complex matrices are exploited to develop each of these networks theoretical results of convergence analysis are presented to show the desirable properties of the proposed complex valued znn models numerical results further demonstrate the effectiveness of the proposed models

on modular homology in the boolean algebra iii abstract let be a set ra ring of characteristicp 0 and denote bymkther module withk element subsets of as basis theset inclusion map mk mk 1is the homomorphism which associates to ak element subset the sum 1 2 kof all its k 1 element subsets i in this paper we study the chain formula arising from we introduce the notion ofp exactness for a sequence if is infinite we show that isp exact for all prime characteristicsp 0 this result can be extended to various submodules and quotient modules and we give general constructions arising from permutation groups with a finitary section two particular applications are the following the orbit module sequence of such a permutation group on isp exact for every primep and we give a formula for thep rank of the orbit inclusion matrix if the group has finitely many orbits onk element subsets

recurrent neural networks for computing weighted moore penrose inverse1this project is supported by the national nature science foundation of china doctoral point foundation of china and youth science foundation of universities in shanghai of china 1 three recurrent neural networks are presented for computing the weighted moore penrose inverse of rank deficient matrices the first recurrent neural network has the dynamical equation similar to the one proposed earlier for matrix inversion and is capable of weighted moore penrose inverse under the condition of zero initial states the second recurrent neural network consists of an array of neurons corresponding to a weighted moore penrose inverse matrix with decaying self connections and constant connections in each row or column the third recurrent neural network consists of two layers of neuron arrays corresponding respectively to a weighted moore penrose inverse and a lagrangian matrix with constant connections

numerical estimates of the generalized dimensions of the henon attractor for negative q the usual fixed size box counting algorithms are inefficient for computing generalized fractal dimensions in the range of q 0 in this letter we describe a new numerical algorithm specifically devised to estimate generalized dimensions for large negative q providing evidence of its better performance we compute the complete spectrum of the henon attractor and interpret our results in terms of a phase transition between different multiplicative laws

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

a one layer projection neural network for nonsmooth optimization subject to linear equalities and bound constraints this paper presents a one layer projection neural network for solving nonsmooth optimization problems with generalized convex objective functions and subject to linear equalities and bound constraints the proposed neural network is designed based on two projection operators linear equality constraints and bound constraints the objective function in the optimization problem can be any nonsmooth function which is not restricted to be convex but is required to be convex pseudoconvex on a set defined by the constraints compared with existing recurrent neural networks for nonsmooth optimization the proposed model does not have any design parameter which is more convenient for design and implementation it is proved that the output variables of the proposed neural network are globally convergent to the optimal solutions provided that the objective function is at least pseudoconvex simulation results of numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network

frequency estimation by principal component ar spectral estimation method without eigendecomposition an eigenvalue filtering method is proposed that applies a transformation to an autocorrelation matrix which has the effect of truncating the undesired eigenvalues so that the corresponding matrix function closely approximates the pseudoinverse it is shown using a computer simulation that compared to the forward backward method the proposed method enhances the threshold in snr by about 6 8 db further improvement is obtained by a simple subset selection method and a second eigenvalue filtering iteration

real time computation of the eigenvectors of a class of positive definite matrices this paper proposes an analog circuit approach to computing in real time the eigenvectors corresponding to all the eigenvalues of a class of positive definite matrices we show analytically and by simulations that the proposed circuit can provide the desired eigenvectors with arbitrarily small error during an elapsed time of only a few characteristic time constants of the circuit

pole assignment via sylvester s equation it is shown that the pole assignment problem can be reduced to solving the linear matrix equations ax xa bg fx g successively for x and then f for almost any choice of g the result is a new pole assignment procedure and proof of the pole assignment theorem that should play an important role in both theoretical and practical applications

optimizing condition numbers in this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite n times n matrices we show that the condition number is a clarke regular strongly pseudoconvex function we prove that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program this asymptotic analysis provides a valuable tool for designing an implementable algorithm for solving the problem of minimizing condition numbers

robustness in partial pole placement the robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined the projection procedure gives a reduced order pole assignment problem it is shown that the sensitivities of the assigned poles in the complete closed loop system are bounded in terms of the sensitivities of the assigned reduced order poles and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open loop poles if the assigned poles are well separated from the unaltered poles these bounds are expected to be tight the projection procedure is described in 3 and techniques for finding robust or insensitive solutions to the reduced order problem are given in 1 2

sizing and least change secant methods oren and luenberger introduced in 1974 a strategy for replacing hessian approximations by their scalar multiples and then performing quasi newton updates generally least change secant updates such as the bfgs or dfp updates oren and luenberger management sci 20 1974 pp 845 862 in this paper the function omega a left frac operatorname trace a n operatorname det a 1 n right is shown to be a measure of change with a direct connection to the oren luenberger strategy this measure is interesting because it is related to the ell 2 condition number but it takes all the eigenvalues of a into account rather than just the extremes if the class of possible updates is restricted to the broyden class i e scalar premultiples are not allowed then the optimal update depends on the dimension of the problem it may or may not be in the convex class but it becomes the bfgs update as the dimension increases this seems to be yet another explanation for why

two representations in multifractal analysis two representations in multifractal analysis the so called q and tau representations are discussed theoretically and computed practically complementary to the standard q representation the so called tau representation is especially suited to resolving the most rarified subsets of the distributed measure moreover these two representations are especially adapted respectively to the well known fixed size and fixed mass box counting algorithms both strategies are first applied to iteratively constructed mathematical measures once tested in this way we use them to analyse the mass distribution and the growth probability distribution of an experimental electrodeposited pattern

uniform partitions and a dimensions spectrum for lacunar measures a multifractal analysis has been proposed to investigate complex systems which exhibit a nonuniform local structure multifractal measures are normalized mass distributions inhomogeneous at every scale to every point p is associated the exponent of the power law r describing the asymptotic behaviour as r 0 of the mass of a sphere of radius r and centre p the measure properties are specified by the dimension spectrum f of the set of points p with the same scaling exponent this spectrum is nontrivial even when the mass distribution has no holes measure with euclidean support and the box counting dimension is an integer in this case it can be evaluated by considering a sequence of uniform grids whose spacing decreases as 2 n known as uniform partitions we consider here a family of iterated function system fractal measures with support on the unit square with random defects specified by three parameters a scale a probability p and an attenuation factor given a partition with a diameter less than any cell is chosen with probability p and its mass is multiplied by the corresponding pre measure is obtained after normalization in all the examples examined the f spectrum appears to widen monotonically as decreases this result suggests the possibility of using the method to detect the presence of defects in sponge like structures such as cancellous bone sponge like by analysing their radiographs since the grey intensity is related to the mass density of the structure a widening of the f spectrum is indeed observed in osteoporotic bone radiographs compared to normal bone radiographs this may be attributed to the rarefaction of the cancellous bone

two finite time convergent zhang neural network models for time varying complex matrix drazin inverse abstract this paper concerns the computation of the drazin inverse of a complex time varying matrix based on two zhang functions constructed from two limit representations of the drazin inverse we present two complex zhang neural network znn models with the li activation function for computing the drazin inverse of a complex time varying square matrix we prove that our znn models globally converge in finite time in addition upper bounds of the convergence time are derived analytically via the lyapunov theory our simulation results verify the theoretical analysis and demonstrate the superiority of our znn models over the gradient based gnn models

recurrent neural network for computing the w weighted drazin inverse abstract two gradient based recurrent neural networks rnns for computing the w weighted drazin inverse of a real rectangular matrix are proposed and considered usage of the first rnn is limited by a specific constraint on the spectrum of a certain matrix the second rnn is usable without restrictions the stability of the recurrent neural networks as well as their convergence are considered numerical examples are given to show the efficiency of the proposed neural networks

multifractal analysis of river networks sandbox approach 1 two fixed size algorithms were used to investigate natural river networks the box counting method and the sandbox method the first produces good results for nonnegative moment orders q but suffers from border effects the second solves border problems and is particularly adapted to negative moment orders for the reconstruction of the right side of the multifractal spectrum f in the box counting applications the influence of the mesh number was investigated in the range 20 to 100 for moment orders from 0 to 10 showing that the error in the assessment of the generalized fractal dimensions is not greater than 3 the sandbox method was applied to the river networks for the first time and the theoretical expression of the information entropy was derived results were obtained also for negative moment orders showing that the analyzed river networks are multifractal and non plane filling structures the sandbox method avoids border effects as verified through an application to a square portion extracted from a river network result analysis suggests a dependence of the f spectra from the lithologic characteristics of the source rocks

recurrent neural networks for solving linear matrix equations abstract recurrent neural networks for solving linear matrix equations are proposed the proposed recurrent neural networks consist of two bidirectionally connected layers and each layer consists of an array of neurons the proposed recurrent neural networks are shown to be asymptotically stable in the large and capable of computing inverse matrices and solving lyapunov matrix equations the operating characteristics of the proposed recurrent neural networks are demonstrated via several illustrative examples

approaches to robust pole assignment abstract robust pole assignment is a non linear optimization problem in many variables we describe numerical methods for determining robust or well conditioned so lutions to the problem of pole assignment by state feedback the solutions are chosen to minimize various objective functions based on the condition number of the eigenvector matrix careful choice of parametrization and objective function avoids singularities and artificial variable constraints explicit formulae for the gradient and hessian permit rigorous stopping criteria and rapid local convergence several computational examples are included

pole assignment with optimal spectral conditioning this paper presents a novel method for pole assignment with robustness measured in terms of the spectral condition number of the closed loop eigenvector matrix it is established that the spectral condition number can be minimized asymptotically via a sequence of unconstrained minimizations on some auxiliary objective functions moreover the sequence of minimizers converges to a minimizer of the spectral condition number a numerical algorithm with analytical formulas of the gradient of the auxiliary objective functions is provided the efficiency and effectiveness of the approach is demonstrated via an example

robust pole assignment for synthesizing feedback control systems using recurrent neural networks this paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback the problem is formulated as a pseudoconvex optimization problem with robustness measure i e the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment two coupled recurrent neural networks are applied for solving the formulated problem in real time in contrast to existing approaches the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority

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

analog approach for the eigen decomposition of positive definite matrices abstract this paper proposes an analog approach for performing the eigen decomposition of positive definite matrices we show analytically and by simulations that the proposed circuit is guaranteed to converge to the desired eigenvectors and eigenvalues of positive definite matrices

robust pole assignment abstract this paper presents new theorems on the theory of interval matrix inequalities and the theory of polynomials with interval roots and applies them to the problem of robust pole placement we formulate optimization problems and derive convergent iterative algorithms which allow the designer to find controllers that place closed loop poles within desired intervals for plants with unknown but bounded parameter uncertainties the algorithms are computationally reasonable and provide a useful addition to currently existing control cad tools

generalized dimensions large deviations and the distribution of rare events abstract generalized dimensions of multifractal measures are usually seen as static objects related to the scaling properties of suitable partition functions or moments of measures of cells when these measures are invariant for the flow of a chaotic dynamical system generalized dimensions take on a dynamical meaning as they provide the rate function for the large deviations of the first hitting time which is the average time required to connect any two different regions in phase space we prove this result rigorously under a set of stringent assumptions as a consequence the statistics of hitting times provides new algorithms for the computation of the spectrum of generalized dimensions numerical examples presented along with the theory suggest that the validity of this technique reaches far beyond the range covered by the theorem we state our result within the framework of extreme value theory this approach reveals that hitting times are also linked to dynamical indicators such as stability of the motion and local dimensions of the invariant measure this suggests that one can use local dynamical indicators from finite time series to gather information on the multifractal spectrum of generalized dimension we show an application of this technique to experimental data from climate dynamics

a schur method for pole assignment in this paper a new numerical algorithm for pole assignment of linear time invariant systems is presented the proposed algorithm uses reliable numerical techniques based on the schur form of the state matrix and on the use of orthogonal transformations only the bad eigenvalues of the system are modified by a sequential pole shifting procedure and the resulted gains in the feedback matrix are minimized

neural network for computing pseudoinverses and outer inverses of complex valued matrices we propose two continuous time neural networks for computing generalized inverses of complex valued matrices with rank deficient cases the first of them is applicable in the pseudoinverse computation and the second one is applicable in construction of outer inverses the proposed continuous time neural networks have a low complexity of implementation and they are proved to be globally convergent without any condition compared with the existing algorithms for computing the pseudoinverse and outer inverses of matrices the global convergence of the proposed continuous time neural networks is analyzed in the complex domain effectiveness of the proposed continuous time neural networks is evaluated numerically via examples

robust exact pole placement via an lmi based algorithm this technical note deals with the robust exact pole placement problem pole placement algorithms that guarantee a small variation of the assigned poles against possible perturbations the solution to this problem is related to the solvability of a sylvester like equation thus the main issue is to compute a well conditioned solution to this equation also the best candidate solution must possess the minimal condition number to reduce sensitivity to perturbation this problem is cast as a global optimization under linear matrix inequality constraints for which a numerical convergent algorithm is provided and compared with the most attractive methods in the literature

scaling laws for invariant measures on hyperbolic and nonhyperbolic atractors the analysis of dynamical systems in terms of spectra of singularities is extended to higher dimensions and to nonhyperbolic systems prominent roles in our approach are played by the generalized partial dimensions of the invariant measure and by the distribution of effective liapunov exponents for hyperbolic attractors the latter determines the metric entropies and provides one constraint on the partial dimensions for nonhyperbolic attractors there are important modifications we discuss them for the examples of the logistic and henon map we show in particular that the generalized dimensions have singularities with noncontinuous derivative similar to first order phase transitions in statistical mechanics

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 improved multifractal formalism and self similar measures abstract to characterize the geometry of a measure its generalized dimensions dq have been introduced recently the mathematically precise definition given by falconer fractal geometry 1990 turns out to be unsatisfactory for reasons of convergence as well as of undesired sensitivity to the particular choice of coordinates in the negative q range a new definition is introduced which is also based on box counting but which carries relevant information about for negative q also in particular the legendre connection between generalized dimensions and the multifractal spectrum is established using large deviations and rigorous proofs are provided for the implicit formula giving the generalized dimensions of selfsimilar measures which was until now known only for positive q

brief a gradient flow approach to on line robust pole assignment for synthesizing output feedback control systems pole assignment is a basic design method for synthesis of feedback control systems in this paper a gradient flow approach is presented for robust pole assignment in synthesizing output feedback control systems the proposed approach is shown to be capable of synthesizing linear output feedback control systems via on line robust pole assignment convergence of the gradient flow can be guaranteed moreover with appropriate design parameters the gradient flow converges exponentially to an optimal solution to the robust pole assignment problem and the closed loop control system based on the gradient flow is globally exponentially stable these desired properties make it possible to apply the proposed approach to slowly time varying linear control systems simulation results are shown to demonstrate the effectiveness and advantages of the proposed approach

robust pole assignment in systems subject to structured perturbations the problem of robust pole assignment by feedback in a linear multivariable time invariant system which is subject to structured perturbations is investigated a measure of robustness or sensitivity of the poles to a given class of perturbations is derived and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure