where is the nearest non regular pencil abstract this is a first step toward the goal of finding a way to calculate a smallest norm deregularizing perturbation of a given square matrix pencil minimal de regularizing perturbations have geometric characterizations that include a variable projection linear least squares problem and a minimax characterization reminiscent of the courant fischer theorem the characterizations lead to new computationally attractive upper and lower bounds we give a brief survey and illustrate strengths and weaknesses of several upper and lower bounds some of which are well known and some of which are new the ultimate goal remains elusive

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

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

robust impulse control of uncertain singular systems by decentralized output feedback this correspondence considers a problem of robust impulse control of uncertain singular systems by decentralized output feedback it derives a perturbation upper bound that ensures the existence of decentralized output feedback control law such that the closed loop system remains both regularity and impulse free for any allowable perturbations algebraic sufficient conditions are also presented that guarantee the existence of so called decentralized robust impulse controllers

robust control for linear systems with structured state space uncertainty abstract a recent sufficient condition for the stability robustness of linear systems with time varying norm bounded state space uncertainty is extended to include the structure of the uncertainty our new result requires that the nominal eigenvalues lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainty and the nominal closed loop eigenvector matrix therefore this robustness result is especially well suited to the design of control systems using eigenstructure assignment when the uncertainty is time invariant our norm is also an upper bound on the incremental eigenvalue perturbations we also consider the use of perron weightings to reduce conservatism and the extension of the results to discrete time systems

an algorithm for pole assignment in high order multivariable systems an efficient computational method is presented for solving the problem of pole assignment by state feedback in linear multivariable systems with large dimensions a given multiinput system is first transformed to an upper block hessenberg form by means of orthogonal state coordinate transformations the state feedback problem is then reformulated in terms of the sylvester equation the transformed system matrices along with certain assumed block forms for unknown matrices enable the sylvester equation to be decomposed and solved effectively a distinct point of the proposed algorithm is that the solution procedure can be tailored to parallel implementation and is therefore fast computational aspects of the algorithm are discussed and numerical examples are provided

a closed form solution to the discrete time kalman filter and its applications abstract this paper presents a closed form solution to the discrete time kalman filter and its applications we first represent the kalman filter in terms of model parameters without using the riccati equation and requiring any artificial conditions such as invertibility of a system matrix and no system noises replacing the initial time with the fixed lag time to achieve the finite memory with respect to inputs and outputs and choosing the proper initial covariances on the recent finite horizon we easily obtain the minimum variance finite memory filter and then propose its iterative computation algorithm as another application a closed form solution to the difference riccati equation on the finite horizon is utilized to obtain a stabilizing gain matrix of a luenberger type filter as in ackermann s formula

an implementation of karmarkar s algorithm for linear programming this paper describes the implementation of power series dual affine scaling variants of karmarkar s algorithm for linear programming based on a continuous version of karmarkar s algorithm two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested linear programs are expressed in an inequality form which allows for the inexact computation of the algorithm s direction of improvement resulting in a significant computational advantage implementation issues particular to this family of algorithms such as treatment of dense columns are discussed the code is tested on several standard linear programming problems and compares favorably with the simplex codeminos 4 0

brief paper the open loop linear quadratic differential game for index one descriptor systems in this paper we consider the linear quadratic differential game for descriptor systems that have index one we derive both necessary and sufficient conditions for existence of an open loop nash equilibrium

stability robustness of almost linear state equations sufficient conditions for stability robustness of finite dimensional autonomous systems are discussed the system comprises a stable linear nominal part and different types of unstructured norm bounded perturbations quantitative sufficient conditions for stability robustness are introduced for the case in which the perturbations are almost linear in the sense that both the size and the derivative of the perturbations are bounded these conditions describe a tradeoff between the size of the perturbations and their distance from linearity the arbitrary nonlinear case and a special linear case are shown to be limiting cases of the almost linear type as an illustration the same quantitative sufficient conditions for stability are applied to a system with slowly varying linear perturbations

loose eigenstructure assignment via rank one lmi approach with application to transient response shaping in h control this article proposes a new regional eigenstructure assignment via rank one lmi approach a gain parameter condition for the regional eigenvalue eigenstructure assignment is newly derived this assignment condition is easily combined with h design by means of enhanced lmi characterisation in the present approach the desired assignment of closed loop eigenvalues i e poles are not previously fixed but constrained into individual assignment regions to bring us more design freedom than classical exact assignment the regional assignment discussed in this article never falls into an ordinary lmi root clustering because the union of assignment regions is disjoint in general each closed loop eigenvector is also constrained into individual alignment cone to show the practical use of the extra design freedom brought by regional assignment a transient response shaping in h design is also discussed a useful design algorithm based on linearisation algorithm is proposed

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

a robust periodic pole assignment algorithm in this note a robust periodic pole assignment algorithm is proposed for linear time invariant discrete time systems the condition numbers of the eigenvector matrices of the closed loop system are assumed as a robustness measure and a periodic state feedback law is deduced by the minimization of the condition numbers associated to the eigenvectors of the monodromy matrix of the closed loop system the proposed periodic pole assignment algorithm has been tested on a number of examples giving satisfactory results

new approach to robust observer design this paper shows that based on the recent development of observer design solution an observer pole selection method can be formulated to minimize the observer gain to the system input it is proved that this method is a deterministic approach to the recovery of the loop transfer function and robustness of direct state feedback systems

a new approach for computing the state feedback gains of multivariable systems this note presents some new results in linear systems first the relationship between the polynomial matrix description and the state space representation of multivariable systems is clarified then we show that once such a relationship is determined the coprime matrix fraction description can be easily computed and we can further develop a closed form formula to solve the pole assignment problem of multivariable systems such formula can be thought of as an extension of the ackermann s formula for mimo systems thus this note potentially gives us a clearer insight into linear systems from the theoretical viewpoint

deflation in eigenvalue assignment of descriptor systems using state feedback it is shown how deflation by unitary equivalence transformations can be used to solve the eigenvalue assignment problem for descriptor systems using state feedback the system is first transformed to a form that reveals its controllability the uncontrollable part of the system if any is then discarded and the assignments are continued with the completely controllable part of the system to give insight into the approach a mathematical method for the solution is derived without considering numerical issues using the idea of deflation it is shown how this method can be modified to derive a numerically efficient algorithm the numerical stability of the algorithm is proved and a numerical example is presented

inverse eigenvalue problems a collection of inverse eigenvalue problems are identified and classified according to their characteristics current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper this exposition also reveals many open questions that deserve further study an extensive bibliography of pertinent literature is attached

schur method for robust pole assignment of descriptor systems via proportional plus derivative state feedback the pole assignment problem for descriptor systems is a classical inverse algebraic eigenvalue problem which has attracted attention for decades in this paper we propose a direct method to solve

on the stability radius of a generalized state space system the concept of distance to instability of a system matrix is generalized to system pencils which arise in descriptor semistate systems difficulties arise in the case of singular systems because the pencil can be made unstable by an infinitesimal perturbation it is necessary to measure the distance subject to restricted or structured perturbations in this paper a suitable measure for the stability radius of a generalized state space system is defined and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one for systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles

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

a boundedness criterion for generalized calderon zygmund operators in 1965 a p calderon showed the l2 boundedness of the so called first calderon commutator this is one of the first examples of a non convolution operator associated to a kernel which satisfies certain size and smoothness properties comparable to those of the kernel of the hilbert transform these properties together with the l2 boundedness imply the lp boundedness for all p s in 1 oo many operators in analysis such as certain classes of pseudo differential operators and the cauchy integral operator on a curve are associated with kernels having these properties for these operators one of the major questions is if they are bounded on l2 we are going to give necessary and sufficient conditions for such an operator to be bounded on l2 they are essentially that the images of the function 1 under the actions of the operator and its adjoint both lie in bmo in the case of the aforementioned first commutator this can be checked by an integration by parts in the first section we present some basic notions and state the theorem which is proved in sections 2 and 3 in section 4 we show how to recover some classical results in sections 5 and 6 we construct a functional calculus for small perturbations of a and in section 7 we show a connection between the theory of calderon zygmund operators and kato s conjecture it is a pleasure to express our thanks to r r coifman and y meyer for suggesting many elegant simplifications in our proofs and most of the applications we also wish to thank stephen semmes for several pertinent remarks

algebraic characterization of controllability subspaces in the current base and its practical computation from the concepts of input chain and controllability chain introduced by heymann and in view of the generalized eigenvector assignment a new algebraic characterization of controllability subspaces css is developed compared with the previous ones based on matrix pencil theory it presents both the advantages of being stated in the current base and of being derived without resorting to use of canonical forms a practical algebraic algorithm is provided in order to compute the controllable structure of a given pair a b this approach is then applied to characterize css contained in a given subspace and span css via eigenvector assignment

on implementing mehrotra s predictor corrector interior point method for linear programming mehrotra tech report 90 03 department of industrial engineering and management sciences northwestern university evanston il 1990 recently described a predictor corrector variant of the primal dual interior point algorithm for linear programming this paper describes a full implementation of this algorithm with extensions for solving problems with free variables and problems with bounds on primal variables computational results on the netlib test set are given to show that this new method almost always improves the performance of the primal dual algorithm and that the improvement increases dramatically as the size and complexity of the problem increases a numerical instability in using schur complements to remove dense columns is identified and a numerical remedy is given

least squares pole assignment by memoryless output feedback in this paper a pole assignment problem for a linear time invariant control system by memoryless output feedback is posed as a least squares optimisation problem and analysed the cost functions are appropriately modified so as to obtain convergence of the corresponding gradient flow and existence of the global minimum this approach is also extended to accommodate the output pole assignment problem with insensitivity against disturbances in system parameters the relation between the modified cost functions and the original pole assignment problem is revealed the proposed approach is compared with other existing approaches and illustrated by numerical results

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

output deadbeat control discrete time multivariate systems an algorithm is presented to compute output deadbeat controls for linear multivariable systems the algorithm based on quadratic optimization with no cost on control cheap control is numerically stable and covers the most general cases the resulting controls are internally stable and are shown to drive the outputs of the system to zero in minimum time using state feedback the central part of the algorithm is the construction of the nonunique state cost matrix two alternatives are presented having different complexities and resulting in solutions having different properties

a new robust stability measure for state feedback systems abstract this brief paper proposes the use of sensitivities of each individual system pole to measure robust stability of state feedback systems compared with the existing measures of this kind m 1 and m 2 this measure is much easier to work with than m 1 while at least as accurate and is definitely more accurate than m 2 the upper and lower bounds of this measure are also derived and proved to be the same as those of m 1 this measure can be maximized numerically using existing explicit and systematic procedures some analytical guidelines which relate explicitly and directly the state feedback system s individual pole selection performance and decoupling to this new measure are also available and presented

the open loop discounted linear quadratic differential game for regular higher order index descriptor systems in this article we consider the discounted linear quadratic differential game for descriptor systems that have an index larger than one we derive both necessary and sufficient conditions for existence of an open loop nash oln equilibrium in a small macro economic stabilisation game we illustrate that the corresponding optimal response is generically cyclic

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

classes of weights related to schrodinger operators abstract in this work we obtain boundedness on weighted lebesgue spaces on r d of the semi group maximal function riesz transforms fractional integrals and g function associated to the schrodinger operator v where v satisfies a reverse holder inequality with exponent greater than d 2 we consider new classes of weights that locally behave as muckenhoupt s weights and actually include them the notion of locality is defined by means of the critical radius function of the potential v given in shen 1995 8

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

destabilizing effects of small time delays on feedback controlled descriptor systems abstract in the last 15 years the problem of stabilizability and stabilization of descriptor systems have received considerable attention in this paper it is shown that if a descriptor system e x ax bu exhibits impulsive behavior then the stability of the closed loop system is extremely sensitive to small delays more precisely if f is the feedback which leads to a stable and impulsive free closed loop system then there exist numbers ej 0 and sj c with limj ej 0 and limj re sj and such that the delayed closed loop system obtained by applying the feedback u t fx t ej has a pole at sj moreover if the open loop system does not have impulsive behavior the same phenomenon occurs provided that the spectral radius of the matrix lim s f se a 1b is greater than 1 if this spectral radius is smaller than 1 it is shown that the closed loop stability is robust with respect to small delays

effects of using observers on stabilization of uncertain linear systems the effects of observers on robust linear feedback controllers are studied sufficient conditions are obtained that guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback the effects of the resulting high gain observers on the disturbance rejection bounds are also studied it is shown that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection however if there is only additive plant disturbance and no measurement disturbance this degradation can be prevented

a unified closed loop stability measure for finite precision digital controller realizations implemented in different representation schemes a computationally tractable unified finite word length closed loop stability measure is derived which is applicable to fixed point floating point and block floating point representation schemes both the dynamic range and precision of an arithmetic scheme are considered in this new unified measure for each arithmetic scheme the optimal controller realization problem is defined and a numerical optimization approach is adopted to solve it numerical examples are used to illustrate the design procedure and to compare the optimal controller realizations in different representation schemes

maximal stability robustness for state equations a measure for stability robustness of a linear time invariant finite dimensional system state equations is introduced an upper bound for the measure is derived using the characteristic values of the system it is shown that the set of optimal systems namely systems for which the stability robustness measure attains the bound contains the normal set which has been considered as the set of optimal robustness

an algorithm for pole assignment of time invariant linear systems an algorithm is suggested for the computation of a linear state feedback for a single input system such that the resultant closed loop system has specified eigenvalues the algorithm is more efficient than many comparable techniques and has some desirable numerical properties it is closely related to the qr algorithm for the eigenproblem and extends to descriptor systems

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

an algorithm for the multiinput eigenvalue assignment problem a very simple and inexpensive algorithm is presented for pole placement in the multiinput case the algorithm consists of orthogonal reduction to a block hessenberg form and a simple linear recursion it yields a matrix f such that a bf has any specified set of eigenvalues whenever the system is controllable it is extremely easy to program on a computer the algorithm is not a robust pole placement algorithm but appears to give comparable results in most well conditioned cases at a fraction of the cost it is a direct noniterative algorithm and no eigenvalues or singular values are computed the algorithm does not need any complex arithmetic even when complex conjugate eigenvalues need to be assigned

robust pole assignment in singular control systems abstract necessary conditions are given for the problem of pole assignment by state feedback in singular linear systems descriptor systems to have a solution which is regular and nondefective for a robust solution such that the assigned closed loop poles are insensitive to perturbations in the system data the same conditions must hold it can be shown that these conditions are also sufficient for the existence of a feedback which assigns the maximum possible number of finite poles with regularity these results provide the basis of a procedure for constructing closed loop semistate systems with given poles guaranteed regularity and maximum robustness

eigenvalue assignment in a single input linear system a procedure for eigenvalue assignment in a single input linear system in hessenberg form is described the procedure uses real arithmetic throughout and includes a facility for estimating the robustness of the assigned eigenvalues the assigned eigenvalues may be real or complex simple or multiple

postponing the choice of the barrier parameter in mehrotra type predictor corrector algorithms abstract recently salahi et al have considered a variant of mehrotra s celebrated predictor corrector algorithm by a numerical example they showed that this variant might make very small steps in order to keep the iterate in a certain neighborhood of the central path that itself implies the inefficiency of the algorithm this observation motivated them to incorporate a safeguard in their algorithmic scheme that gives a lower bound for the step size at each iteration and thus imply polynomial iteration complexity in this paper we propose a different approach that enables us to have control on the iterates our new approach is based on postponing the choice of the barrier parameter and it does not require any safeguard strategy to do so first we fix a step size in the corrector step then by solving a one dimensional optimization problem we calculate the barrier parameter finally using the calculated barrier parameter we make the next step it is proved for the feasible case that our new algorithm stops after at most o n 2 log n iterations without any safeguard strategy we further modified the proposed algorithm by slightly changing the newton system in the corrector step this variant enjoys an even better worst case iteration complexity bound i e o n log n superlinear convergence of both algorithms are established finally our numerical results demonstrate that a theoretically rigorous ipm may have the same or better computational efficiency than the ones enhanced by aggressive heuristics

an algorithm for the assignment of system zeros abstract this paper presents an algorithm for assigning the locations and number of zeros to a linear system through synthesis of the system input and output space couplings the approach imposes no restrictions on the state space model can assign both real and complex zeros using only real arithmetic and is computationally efficient numerical properties of the algorithm are discussed and examples are given to illustrate its performance

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

a self correcting version of karmarkar s algorithm a relaxed version of karmarkar s algorithm is developed that does not require the direction of movement to be in the null space of the constraint matrix the algorithm is proved to have the same rate of convergence as karmarkar s algorithm conditions are also given guaranteeing that the approach suggested by karmarkar for transforming an inequality form linear program into the form required by his algorithm is well defined

sensitivity properties of multirate feedback control systems based on eigenstructure assignment some sampled data systems e g fly by wire control schemes have a necessarily multirate structure various input and or outputs sampled at different rates when considering a multirate system which has parameter uncertainty it is important to examine ways in which the full freedom of the multivariable design can be utilized to minimize the sensitivity to parameter variations given the accompanying problems induced by intersample ripple disturbance this note examines the design capabilities of a class of multirate systems with multiple input and fixed state sampling rates mifs based on eigenstructure assignment although the use of eigenstructure assignment for continuous and single rate discrete systems is well understood the eigenstructure assignment for the design of multirate feedback systems is an open topic of research accepting that the problems of intersample ripple are often magnified through multirate control there are advantages in terms of increased freedom for minimizing sensitivity and optimizing robustness to parameter variations a special feature of the mifs class of multirate systems is the ability to introduce extra design freedom in the eigenproblem by a suitable choice of eigenstructure assignment and sample rates the criteria for the selection of minimum sample rates to produce this extra freedom and the implication that this has on the eigenstructure assignment problem are outlined the improved insensitivity properties are demonstrated using an example comparing the performance of multirate and corresponding single rate designs

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

a global tb theorem for compactness and boundedness of calderon zygmund operators abstract we prove a tb theorem that characterizes all calderon zygmund operators that extend compactly on l p r n 1 p the result whose proof does not require the property of accretivity can be used to prove compactness of the double layer potential operator on a wide class of domains the study also provides conditions for boundedness of singular integral operators by means of non accretive testing functions

a two time scale neurodynamic approach to constrained minimax optimization this paper presents a two time scale neurodynamic approach to constrained minimax optimization using two coupled neural networks one of the recurrent neural networks is used for minimizing the objective function and another is used for maximization it is shown that the coupled neurodynamic systems operating in two different time scales work well for minimax optimization the effectiveness and characteristics of the proposed approach are illustrated using several examples furthermore the proposed approach is applied for h infty model predictive control

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

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

an algorithm for computing state feedback in multiinput linear systems a new algorithm is proposed in this note to compute the state feedback for arbitrary pole placement in multiinput linear systems the algorithm has good numerical behavior it also allows the user to adjust the eigenstructure of the resulting feedback system and therefore improve the condition of the problem and computation

the decay of stabilizability with reynolds number in a linear model of spatially developing flows this article characterizes the gradual decay of stabilizability with reynolds number in the linear complex ginzburg landau model of spatially developing ow systems when a single spatially localized actuator is used to apply the control forcing it is shown that technically the system considered is linearly stabilizable for all actuator locations at any reynolds number however as the reynolds number is increased and an increasing number of modes of the open loop system become unstable the control authority on some of these open loop unstable modes is found to be exponentially small using nite precision arithmetic and any given numerical method for computing the feedback gains an e ective upper bound on the reynolds number is reached above which it is not possible to compute a linearly stabilizing control

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

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

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

an innovation representation for nonlinear systems with application to parameter and state estimation abstract an innovation model is derived for a nonlinear stochastic system described by a state variable representation the problem of state and system parameter estimation is solved through identification of the innovation model a recursive prediction error rpe algorithm is derived for the joint system parameter and state estimation through minimization of the innovation variance miv the algorithm is robust against the use of an erroneous model convergence and stability properties of the algorithm are also analyzed in order to ensure stability the algorithm needs an on line stability check at each iteration

the sharp weighted bound for general calderon zygmund operators for a general calderon zygmund operator t on r n it is shown that ktfkl2 w c t sup q a q w q w 1 a k fkl2 w for all muckenhoupt weights w 2 a2 this optimal estimate was known as the a2 conjecture a recent result of perez treil volberg reduced the problem to a testing condition on indicator functions which is verified in this paper the proof consists of the following elements i a variant of the nazarov treil volberg method of random dyadic systems with just one random system and completely without bad parts ii a resulting representation of a general calderon zygmund operator as an average of dyadic shifts and iii improvements of the lacey petermichl reguera estimates for these dyadic shifts which allow summing up the series in the obtained representation

an operator valued tb theorem we establish conditions similar to the tb theorem of david journe and semmes which guarantee the boundedness of an integral transformation t with l x valued kernel on lxp rn where 1 p and x is a banach space with the unconditionality property of martingale differences umd

a finite termination mehrotra type predictor corrector algorithm abstract mehrotra type predictor corrector algorithms are the backbone of most interior point methods based software packages salahi et al m salahi j peng t terlaky on mehrotra type predictor corrector algorithms technical report 2005 4 advanced optimization lab mcmaster university hamilton on canada http www cas mcmaster ca oplab publication in their recent works have shown some ill behaviors of mehrotra s original algorithm which motivated them to modify it in order to achieve the polynomial iteration complexity while preserving its practical efficiency in this paper we analyze the same algorithm from a different perspective and give a condition on the maximum feasible step size in the predictor step violation of which might lead to a very small or even zero step size in the corrector step if the maximum step size in the predictor step is above a certain threshold then we cut it to satisfy the derived condition this enables us to prove that the algorithm terminates finitely

regularization of descriptor systems by output feedback conditions are given under which a descriptor or generalized state space system can be regularized by output feedback it is shown that under these conditions proportional and derivative output feedback controls can be constructed such that the closed loop system is regular and has index at most one this property ensures the solvability of the resulting system of dynamic algebraic equations a reduced form is given that allows the system properties as well as the feedback to be determined the construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way

on regularizing singular systems by decentralized output feedback this paper considers linear time invariant decentralized singular systems which are either nonregular or if they are regular they have impulsive modes it derives algebraic necessary and sufficient conditions for making a singular system both regular and impulse free by decentralized output feedback control laws and decentralized proportional plus derivative output feedback control laws

controllability and observability of second order descriptor systems we analyze controllability and observability conditions for second order descriptor systems and show how the classical conditions for first order systems can be generalized to this case we show that performing a classical transformation to first order form may destroy some controllability and observability properties as an example we demonstrate that the loss of impulse controllability in constrained multibody systems is due to the representation as a first order system to avoid this problem we will derive a canonical form and new first order formulations that do not destroy the controllability and observability properties

feedback controller norm optimization for linear time invariant descriptor systems with pole region constraint an algorithm is proposed to compute a state feedback gain matrix for a linear time invariant regular descriptor system which ensures that i the closed loop system is impulse free and ii all the finite poles are placed within a pre defined stability region in the complex plane the associated design flexibilities are exploited in minimizing upper bounds of the frobenius norm of respective gain matrices a class of linear matrix inequality lmi regions in the complex plane are chosen as constraints for the closed loop finite poles by representing a subset of the nonsingular matrices through solution of an lmi and linearizing the set of matrix inequalities arise in the regional pole finite poles assignment the associated optimizations are formulated as semidefinite programs the effectiveness of the developed algorithm is demonstrated through numerical examples significant reduction in the norm of feedback gain matrix is achieved in a two generator six bus power system

the tb theorem on non homogeneous spaces 0 introduction main objects and results 3 0 1 main results 4 0 2 an application of t1 heorem electric intensity capacity 7 0 3 how to interpret calderon zygmund operator t 9 0 3 1 bilinear form is defined on lipschitz functions 10 0 3 2 bilinear form is defined for smooth functions 11 0 3 3 apriori boundedness 12 0 4 plan of the paper 15

robust pole placement in lmi regions discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality lmi regions a class of convex regions of the complex plane that embraces most practically useful stability regions the focus is on linear systems with static uncertainty on the state matrix for this class of uncertain systems the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary lmi regions the resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities lmis and cover both unstructured and parameter uncertainty these analysis results are then applied to the synthesis of dynamic output feedback controllers that robustly assign the closed loop poles in a prescribed lmi region with some conservatism this problem is again tractable via lmi optimization in addition robust pole placement can be combined with other control objectives such as h sub 2 or h sub spl infin performance to capture realistic sets of design specifications physically motivated examples demonstrate the effectiveness of this robust pole clustering technique

on finding a vertex solution using interior point methods abstract an approach is proposed to generate a vertex solution while using a primal dual interior point method to solve linear programs a controlled random perturbation is made to the cost vector a method to identify the active constraints at the vertex to which the solutions are converging is given this basic method is further refined to save computational effort the proposed approach is tested by using a variation of the primal dual interior point method our method is developed by taking a predictor corrector approach in practice this method takes considerably fewer iterations to solve linear programs than methods described by choi monma and shanno lustig marsten and shanno and domich boggs donaldson and witzgall computational results on problems from the netlib test set are reported to test our approach for finding vertex solutions these results show that one perturbation is enough to force the solutions to converge to a vertex the results indicate that the proposed approach is insensitive to the number of degenerate variables the results also indicate that the effort required to generate a vertex solution is comparable to that required to solve the problem using an interior point method

robust control with pole shifting via performance index modification robust controllers that ensure closed loop eigenvalue placement are designed for linear systems with parametric uncertainties by using an appropriate state weighting matrix choice and a relative stability degree an lmi based algorithm is proposed to provide guaranteed cost controllers that ensure i the closed loop nominal eigenvalues shifting by a pre specified amount ii a prescribed degree of stability for all system uncertainties of a given class a certain level of closed loop performance is also ensured by minimizing the associated guaranteed cost

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

brief augmented gradient flows for on line robust pole assignment via state and output feedback this paper is concerned with robust pole assignment in synthesis of linear control systems via state and output feedbacks first both the pole assignment and robustness requirements are appropriately formulated as two optimization problems then gradient flow models are developed for the on line computation of feedback gain matrices that result in robust pole assignment by solving these two optimization problems a technique is introduced to facilitate the real time matrix inverse involved for realizing the gradient flow models the resulting augmented gradient flows have desired convergence properties simulation results are included to show the effectiveness of the proposed approach

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

the generalized eigenstructure problem in linear system theory the algebraic theory of linear time invariant systems has been studied in large detail during the past few decades and numerous computational algorithms have been developed to solve problems arising in this context in this paper the numerical aspects of a certain class of such algorithms dealing with what the author calls generalized eigenstructure problems are discussed some new and or modified algorithms are presented both the nmnerical stability of the algorithms and the conditioning of the problems they solve are analyzed using numerical criteria

a new design approach to unknown input observers this paper proposes a fundamentally new unknown input observer uio which has uniquely r decoupled modes provides r linearly independent combinations of plant system states and has zero gain to all p unknown inputs the parameter r is adjustable if the plant system satisfies the conditions of the existing uio then r n plant system order and there is no difference between our uio and the existing regular uio however if the plant system satisfies either of the following two significantly more general conditions m p m is the number of plant output measurements and at least one stable transmission zero then 1 n and our uio can still generate some constrained state feedback control signals hence this new uio can completely unify the regular uio r n and the static output feedback r m the two basic feedback structures of modern control theory far from being unified before

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

perturbation theory for homogeneous polynomial eigenvalue problems we consider polynomial eigenvalue problems p a alpha beta x 0 in which the matrix polynomial is homogeneous in the eigenvalue alpha beta uc2 in this framework infinite eigenvalues are on the same footing as finite eigenvalues we view the problem in projective spaces to avoid normalization of the eigenpairs we show that a polynomial eigenvalue problem is well posed when its eigenvalues are simple we define the condition numbers of a simple eigenvalue alpha beta and a corresponding eigenvector x and show that the distance to the nearest ill posed problem is equal to the reciprocal of the condition number of the eigenvector x we describe a bihomogeneous newton method for the solution of the homogeneous polynomial eigenvalue problem homogeneous pep

robust eigenvalue assignment for generalized systems abstract in this paper we examine the problem of robust pole placement using state feedback in generalized systems we develop a robustness theory for the finite generalized spectrum of the system as a partial problem and for the infinite pole placement problem as a second partial problem where perfect conditioning is always achievable we also give bounds between the complete closed loop robust eigenvalue problem and the two partial ones the basic tool that is exploited in the presented theory is the concept of chordal metric in this paper we take advantage of this notion and present a compact theory for the robust eigenvalue assignment problem in generalized systems the proposed theory is easy to implement retrieves the results for the state variable case as a special case and takes advantage of well known computational results

brief paper feedback nash equilibria for linear quadratic descriptor differential games in this paper we consider the non cooperative linear feedback nash quadratic differential game with an infinite planning horizon for descriptor systems of index one the performance function is assumed to be indefinite we derive both necessary and sufficient conditions under which this game has a nash equilibrium

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

computational experience with a primal dual interior point method for linear programming abstract a new comprehensive implementation of a primal dual algorithm for linear programming is described it allows for easy handling of simple bounds on the primal variables and incorporates free variables which have not previously been included in a primal dual implementation we discuss in detail a variety of computational issues concerning the primal dual implementation and barrier methods for linear programming in general we show that in a certain way lustig s method for obtaining feasibility is equivalent to newton s method this demonstrates that the method is in some sense the natural way to reduce infeasibility the role of the barrier parameter in computational practice is studied in detail numerical results are given for the entire expanded netlib test set for the basic algorithm and its variants as well as version 5 3 of minos

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