frequency domain pole assignment and exact model matching for delay systems frequency domain pole assignment and exact model matching for delay systems are considered with the knowledge that the delay plant is not necessarily stable as for pole assignment for the delay plant the state space approach which is also called the time domain approach is already known the frequency domain approach which is much more fruitful than the time domain approach has not previously been developed and is solved in this paper as for exact model matching which is not only of a higher level but is also a more agreeable design method neither the time domain nor the frequency domain approach has been reported a newly developed frequency domain exact model matching approach is presented in this paper

a modified smith predictor and controller for unstable processes with time delay an integrated design procedure is developed for a modified smith predictor and associated controller for linear time delay systems having transfer functions of the form k 1 a exp st b where a and b are monic polynomials in s of degree n l and n respectively a is hurwitz and b has a single right half plane root at s for l 1 2 3 an augmented pi controller guarantees asymptotic stability for t less than an l dependent limit the procedure for l 3 is extended to l 4 with the introduction of derivative action into the controller design arguments are on root locus topology and on nyquist analysis applied to an auxiliary system

subproper and regular splittings for restricted rectangular linear system iterative schemes for approximating a solution to restricted rectangular but consistent linear system of equations ax b email protected t are considered the methods are based upon so called subproper splitting a m n which is a generalization of the concept of subproper splitting introduced by neumann and studied further by berman and neumann and others we give a necessary and sufficient condition on the splitting such that the iterative sequence converges to a solution of ax b in the case of email protected at for every x 0 where email protected c m x n and t is a subspace of c n monotonicity and the concept of regular subproper splitting are used to determine a necessary and a sufficient condition for the convergence of the iterative scheme finally we present two numerical examples to verify our conclusions

a cramer rule for minimum norm t least squares s solution of inconsistent linear equations abstract in this paper the minimum norm t least squares s solution of inconsistent linear equations ax y a c m n r y r a is given a determinantal form and reduces to common cramer s rule if a is nonsingular

a simpler dgmres dgmres is an algorithm to solve the drazin inverse solution of large scale and sparse consistent or inconsistent singular linear systems with an arbitrary index in this paper we present a simpler version of this algorithm

general balance and treatment permutations abstract many equi replicate designs whether ordinary block designs or multi stratum designs have a structure which is left unchanged by a group g of permutations of the treatments this group g is often used in the construction of the design a survey of the properties of such designs is given and useful necessary conditions on g are found for such a design to be generally balanced if g is abelian then the necessary conditions are satisfied in this case explicit formulas for the efficiency factors are given

note on the relation between pole zero location and input output behaviour of siso systems and its influence on controller design linear time invariant completely controllable and observable systems can be described for example by state equations transfer functions or time responses due to specific test signals all these descriptions are uniquely related for a given system where different state representations are possible by use of equivalence transformations however a whole class of different systems characterized by an infinite number of different pole zero patterns exhibits the same input output behaviour within drawing accuracy i e the plots coincide to the point of indistinguishability this effect is demonstrated and it may have implications on such fields as system modelling model order reduction and controller design

feedback minimax sensitivity and optimal robustness in this paper we look for feedbacks that minimize the sensitivity function of a linear single variable feedback system represented by its frequency responses sensitivity to disturbances and robustness under plant perturbations are measured in a weighted h infty norm in an earlier paper zames proposed an approach to feedback design involving the measurement of sensitivity by multiplicative seminorms which have certain advantages over the widely used quadratic norm in problems where there is plant uncertainty or where signal power spectra are not fixed but belong to sets the problem was studied in a general setting and some h infty examples were solved here a detailed study of the single variable case is undertaken the results are extended to unstable plants and explicit formulas for the general situation of a finite number of right half plane rhp plant zeros or poles are provided the q or approximate inverse parametrization of feedbacks that maintain closed loop stability is extended to the ease of unstable plants the h infty and wiener hopf approaches are compared

design of pole placing controllers for stable and unstable systems with pure time delay abstract based on improved low order dead time approximants or starting from an overall approximation of linear time invariant systems with pure time delay pole placing controller design is applied this procedure yields excellent results for stable and unstable systems the main advantage of this approach is the use of well known state feedback control methods which can be used to shape the closed loop response in a desired manner as long as the approximations are of sufficient quality the closed loop transients of model and original loop coincide within small error limits

adjusting exchangeable beliefs summary we consider geometrically the practical theoretical and computational treatment of second order exchangeability within bayes linear analysis we establish bayes linear sufficiency for sample means through the representation theorem for second order exchangeable beliefs interrelationships between collections of bayes linear belief adjustments are analysed through the resolution transforms induced by a second order exchangeable sample it is shown that the resolution transforms for the underlying population structure and for the prediction of future observables have essentially the same form whatever the sample size these results are applied to simplify general adjustments of beliefs given second order exchangeable data we illustrate the theory by analysing a problem concerning exchangeable regressions

adaptive posicast controller for time delay systems with relative degree n 2 in this paper we present an adaptive posicast controller that deals with parametric uncertainties in linear systems with delays it is assumed that the plant has no right half plane zeros and the delay is known the adaptive controller is based on the smith predictor and finite spectrum assignment with time varying parameters adjusted online a novel lyapunov krasovskii functional is used to show semi global stability of the closed loop error equations the controller is applied to engine fuel to air ratio control the implementation results show that the adaptive posicast controller significantly improves the closed loop performance when compared to the case with the existing baseline controller

optimal model matching control for time delay systems model matching control for time delay systems is formulated as an optimization problem in h2 norm space as well as h norm space wiener hopf techniques and the theory of optimal interpolation are successfully employed to treat this model matching problem including perfect and imperfect model matching cases prior to this work for time delay systems only the problem of perfect model matching control had been considered and no attempt had been made to examine that of imperfect model matching control with the optimization approach presented here an optimal model matching control scheme is constructed for the imperfect model matching case to produce perfect model matching results whenever possible

algebraic multigrid methods for laplacians of graphs abstract classical algebraic multigrid theory relies on the fact that the system matrix is positive definite we extend this theory to cover the positive semidefinite case as well by formulating semiconvergence results for these singular systems for the class of irreducible diagonal dominant singular m matrices we show that the requirements of the developed theory hold and that the coarse level systems are still of the same class if the c f splitting is good enough an important example for matrices that are irreducible diagonal dominant m matrices are laplacians of graphs recent shape optimizing methods for graph partitioning require to solve singular linear systems involving these laplacians we present convergence results as well as experimental results for numerous graphs arising from finite element discretizations with up to 10 6 vertices

on the convergence of splittings for semidefinite linear systems abstract recently lee et al young ju lee jinbiao wu jinchao xu ludmil zikatanov on the convergence of iterative methods for semidefinite linear systems siam j matrix anal appl 28 2006 634 641 introduce new criteria for the semi convergence of general iterative methods for semidefinite linear systems based on matrix splitting the new conditions generalize the classical notion of p regularity introduced by keller h b keller on the solution of singular and semidefinite linear systems by iterations siam j numer anal 2 1965 281 290 in view of their results we consider here stipulations on a splitting a m n which lead to fixed point systems such that the iterative scheme converges to a weighted moore penrose solution to the system ax b our results extend the result of lee et al to a more general case and we also show that it requires less restrictions on the splittings than keller s p regularity condition to ensure the convergence of iterative scheme

a note on properties of splittings of singular symmetric positive semidefinite matrices recently benzi and szyld have published an important paper 1 concerning the existence and uniqueness of splittings for singular matrices however the assertion in theorem 3 9 on the inheriting property of p regular splitting for singular symmetric positive semidefinite matrices seems to be incorrect as a complement of paper 1 in this short note we point out that if a matrix t is resulted from a p regular splitting of a symmetric positive semidefinite matrix a then splittings induced by t are not all p regular

on the solution of singular linear systems of algebraic equations by semiiterative methods for a square matrixt n n where i t is possibly singular we investigate the solution of the linear fixed point problemx tx c by applying semiiterative methods sim s to the basic iterationx0 n xk tck 1 c k 1 such problems arise if one splits the coefficient matrix of a linear systemax b of algebraic equations according toa m n m nonsingular which leads tox m 1nx m 1b tx c even ifx tx c is consistent there are cases where the basic iteration fails to converge namely ift possesses eigenvalues 1 with 1 or if 1 is an eigenvalue oft with nonlinear elementary divisors in these cases and also ifx tx c is incompatible we derive necessary and sufficient conditions implying that a sim tends to a vector hat x which can be described in terms of the drazin inverse of i t we further give conditions under which hat x is a solution or a least squares solution of i t x c

a parameter adaptive control structure for linear multivariable systems this paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous time linear multivariable system represented by an m times m strictly proper transfer matrix t s provided t s has no right half plane zeros the controller parameters can be directly estimated from input output data the paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design this information is a natural extension of that required in the scalar case

finite spectrum assignment for multivariable delay systems in the frequency domain a frequency domain approach to arbitrary finite spectrum assignment for multivariable delay systems is developed and a practical example is presented for illustration

an adaptive smith controller for time delay systems with relative degree n 2 abstract this paper addresses the control of time delay systems whose relative degree does not exceed two an adaptive smith controller together with an adaptive law similar to the delay free case is proposed by using lyapunov krasovskii functionals for an appropriate model transformation of the original system semiglobal stability of the closed loop system and asymptotic convergence of the output error is established strict positive realness together with the low relative degree of the plant is exploited to establish the stability properties robustness properties of the adaptive controller are briefly discussed

feedback and optimal sensitivity model reference transformations multiplicative seminorms and approximate inverses in this paper the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization stable feedback schemes obtainable from a given plant are parameterized salient properties of sensitivity reducing schemes are derived and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity the theory is developed for input output systems in a general setting of banach algebras and then specialized to a class of multivariable time invariant systems characterized by n times n matrices of h infty frequency response functions either with or without zeros in the right half plane the approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity and on the concept of an approximate inverse approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction an indicator of approximate invertibility called a measure of singularity is introduced the measure of singularity of a linear time invariant plant is shown to be determined by the location of its right half plane zeros in the absence of plant uncertainty the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure in particular if there are no right half plane zeros sensitivity can be made arbitrarily small the feedback schemes used in the optimization of sensitivity resemble the lead lag networks of classical control design some of their properties and methods of constructing them in special cases are presented

control of internally delayed plants by using only input output signals abstract control of internally delayed plants using only input output signals is considered frequency domain techniques using two variable polynomial algebra are used consistently the restriction imposed on the plant is moderate pole placement as well as exact model matching is examined in detail the control law obtained is simpler than that obtained via time domain techniques the synthesis method differs in the case when a 0 0 and the case when a 0 0 for the former case finite pole assignment and matching to a finite dimensional reference model is realizable but for the latter case it is not

condition number related with generalized inverse a t s 2 and constrained linear systems in this paper we introduce a pq norm and discuss the condition number of the generalized inverse at s 2 we get some results on the condition numbers with respect to at s 2 and constrained linear systems ax b x t which are similar to the regular inverse a 1 and nonsingular linear systems ax b finally we investigate the structured perturbation of the generalized inverse at s 2

frequency domain finite spectrum assignment for delay systems with multiple poles a general finite spectrum assignment method for delay systems with possibly multiple poles is presented and an example is provided for illustration

globally stable adaptive controller for systems with delay we propose a globally stable finite spectrum assignment adaptive controller for systems with delay it is assumed that the process is minimum phase though not necessarily stable and the delay is known it is shown that the plant output asymptotically tracks a reference model output with all signals remaining bounded

on necessary conditions for convergence of stationary iterative methods for hermitian semidefinite linear systems abstract in an earlier paper frommer et al 2008 5 we gave sufficient conditions in terms of an energy seminorm for the convergence of stationary iterations for solving linear systems whose coefficient matrix is hermitian and positive semidefinite in this paper we show in which cases these conditions are also necessary and show that they are not necessary in others

adaptive control of delay system the result of exact model matching for delay systems developed by the author is extended to the adaptive control of delay systems likewise using results from the adaptive control of systems without delay the principle of constructing adaptive systems for delay plants is also very simple and clear

on the perturbation and subproper splittings for the generalized inverse at s 2 of rectangular matrix a abstract in this paper the perturbation and subproper splittings for the generalized inverse at s 2 the unique matrix x such that xax x r x t and n x s are considered we present lower and upper bounds for the perturbation of at s 2 convergence of subproper splittings for computing the special solution at s 2 b of restricted rectangular linear system ax b x t are studied for the solution at s 2 b we develop a characterization therefore we give a unified treatment of the related problems considered in literature by ben israel berman hanke neumann plemmons etc

transfer function synthesis using frequency response data an improved method for transfer function synthesis from measured frequency response data is presented the improvement is due to a new scheme of matrix adaptation that eliminates measurement dependent inaccuracies step by step arbitrary coefficients can be set to any preassigned values so that account can be taken of previous knowledge of the investigated system an extension to integrating systems is developed the efficiency of the proposed method is demonstrated for an example taken from the literature

decomposition and bayesian analysis of invariant normal linear models abstract using the theory of linear group representations we analyse the normal linear model with known sampling covariance structure invariant under a symmetry group and sampling mean structure equivariant under the same group in particular assuming an invariant normal prior distribution on the parameter space the problem of bayesian inference is shown to decompose naturally into several independent subproblems within any such subproblem if additional irreducibility conditions hold it is shown that the posterior expectation of any parameter is a fixed scalar multiple of its unique unbiased estimator and similarly the posterior covariance of any two parameters is a fixed scalar multiple of the prior covariance the theoretical framework is illustrated with reference to experimental designs

preconditionings and splittings for rectangular systems recently eiermann marek and niethammer have shown how to applysemiiterative methods to a fixed point systemx tx c which isinconsistent or in whichthe powers of the fixed point operator t have no limit to obtain iterative methods which converge to some approximate solution to the fixed point system in view of their results we consider here stipulations on apreconditioning qax qb of the systemax b and separately on asplitting a m n which lead to fixed point systems such that with the aid of a semiiterative method the iterative scheme converges to a weighted moore penrose solution to the systemax b we show in several ways that to obtain a meaningful limit point from a semiiterative method requires less restrictions on the splittings or the reconditionings than those which have been required in the classical picard iterative method see e g the works of berman and plemmons berman and neumann and tanabe we pay special attention to the case when the weighted moore penrose solution which is sought is the minimal norm least squares solution toax b

model reference adaptive control of multivariable plants with delays the design and complete stability analysis for the model reference adaptive control mrac of multivariable plants with input and or output delays are presented in this paper a modified estimation error which enables us to solve the non commutativity problem and the stability issue in the multivariable case is introduced in the adaptive law for updating the controller parameters a generalized controller structure which achieves stable model plant transfer matrix matching in the presence of delays is developed for the multivariable mrac scheme based on a unified framework it is shown that the proposed adaptive control scheme guarantees the global stability and asymptotic zero tracking error for the closed loop system

symmetry models and hypotheses for structured data layouts on peut utiliser des proprietes de symetrie pour deriver des tests valides d hypotheses nulles et pour construire des modeles statistiques appropries pour les donnees on developpe des idees generales et on les illustre dans le contexte d une classification a deux criteres