on the two block h problem for a class of unstable distributed systems this paper deals with the two block h control problem for distributed plants with finitely many unstable modes we assume that weighting filters in the h mixed sensitivity problem are finite dimensional then the corresponding optimal two block problem can be solved by finding the schmidt pairs of a hankel operator whose symbol is of the form m 2 m 1u u where u r h u h and m2 rh and m1 h are inner and the suboptimal two block problem can be solved by finding the solutions of certain functional equations very similar to the ones satisfied by the schmit pairs of the above mentioned hankel operator in this paper a unified approach is proposed for solving both the optimal and suboptimal two block problems we obtain two systems of linear equations expressed in terms of state space realizations of u and m2 whose solutions give the schmidt pairs of the associated hankel operator and the functions needed for the parametrization of all the suboptimal solutions respectively

krein space approach to h sup spl infin mixed sensitivity minimization for a class of infinite dimensional systems motivated by the computation of the h sup spl infin optimal performance and optimal mixed sensitivity for a class of infinite dimensional systems the author considers the explicit computation of the norm and minimal symbols of a class of hankel plus toeplitz type operators with irrational symbols using the krein space approach the author shows how to explicitly compute the norm and parameterize all the minimal symbols the results are used to obtain a complete solution to the h sup spl infin optimal mixed sensitivity synthesis problem for a class of infinite dimensional systems an explicit formula for computing the h sup spl infin optimal performance and explicit parameterization of all optimal and suboptimal mixed sensitivities an illustrative example is given

an h minimax approach to the design of robust control systems abstract a realistic feedback design problem is posed based on the minimization of a weighted combination of the sensitivity and complementary sensitivity matrices a solution is obtained which makes use of the recently proposed methods for minimizing the sensitivity function alone

closed formulae for a parametric mixed sensitivity problem for pritchard salamon systems the parametric mixed sensitivity problem is posed for the class of irrational transfer matrices with a realization as a pritchard salamon system an exact solution is obtained in terms of two uncoupled standard riccati equations

a hamiltonian based solution to the two block h problem for general plants in h and rational weights a complete skew toeplitz type solution to the two block h 1 problem for innite dimensional stable plants with rational weights is derived with a basis free proof the solution consists of one riccati equation with a rank criterion for a transcendental function of a certain hamiltonian this gives a natural extension of the well known formula for the one block case an example is given to illustrate the result c 2000 elsevier science b v all rights reserved

reducing stochasticity in the north atlantic oscillation index with coupled langevin equations we present a critical investigation of the functional relationship between the two pressure time series routinely used to define the index characterizing the north atlantic oscillation nao well known to regulate global climate variability and change first by a standard markov analysis we show that the standard nao index based on the pressure difference is not optimal in the sense of producing sufficiently reliable forecasts because it contains a dominating stochastic term in the corresponding langevin equation then we introduce a variationally optimized markov analysis involving two coupled langevin equations tailored to produce a nao quasi index having the desired minimum possible stochasticity the variationally optimized markov analysis is very general and can be applied in other physical situations involving two or more time series

mixed sensitivity optimization for a class of unstable infinite dimensional systems abstract in this paper we solve the h mixed sensitivity minimization problem for a class of unstable distributed systems the solution is based on an extension of the skew toeplitz methodology the key mathematical fact used is that the skew toeplitz operators arising in the unstable case are finite rank perturbations of the classical skew toeplitz operators obtained from compressions of rational functions a system of linear equations the singular system is derived for this class of operators from which one can compute the associated singular values and vectors an example is included to illustrate the results

a generalization of the bernstein polynomials abstract we give an interesting generalization of the bernstein polynomials we find sufficient and necessary conditions for uniform convergence by the new polynomials and we generalize the bernstein theorem

a simpler formula for the singular values of a certain hankel operator this paper deals with the problem of computing the singular values and vectors of a hankel operator with symbol m w where m h is arbitrary inner and w h is rational a simplified version of the formula given in 6 is obtained for computing the singular values of the hankel operator this result is applied to the one block h optimal control of siso stable infinite dimensional plants and rational weights using this new formula a simple expression is derived for the h optimal controller whose structure was observed in 9

a note on essential spectra and norms of mixed hankel toeplitz operators in this brief hankel toeplitz operators which occur in feedback theory e g in the minimization of mixed h sensitivity and complementary sensitivity will be considered a method of computing their spectra eigenvectors and norms will be presented for infinite dimensional systems subject to continuous weightings

the four block adamjan arov krein problem abstract this paper is concerned with the mixed sensitivity h design in the most general i e the four block case this problem involves in a crucial manner the so called four block operator the norm of which is the achievable feedback tolerance our objective in this paper is to provide an interpretation for all singular values of these singular values are given an adamjan arov krein interpretation in terms of the l distance of an l function to h l intuitively the singular values of are the various tolerance levels that can be achieved if we allow a various number of unstable poles in the closed loop we finally provide an upper bound on the number of singular values

weighted sensitivity minimization general plants in h and rational weights abstract for general plants in h and rational weighting functions the problem of computing the weighted h optimal sensitivity is considered a general formula is derived for a function whose singularities determine the optimal sensitivity 6 a determinantal expression for the optimal sensitivity is then deduced and related to a conjecture of zhou and khargonekar

fast computation of achievable feedback performance in mixed sensitivity h design the computational bottleneck of the h infty design has been recognized to be the e iteration a computationally demanding direct search of the minimum achievable h infty performance verma and jonckheere showed that the optimal h infty performance can be characterized as the spectral radius of the so called toeplitz plus hankel operator even before the appearance of the toeplitz plus hankel operator in the h infty setting the same operator had already been shown to play a crucial role in the spectral theory of the linear quadratic problem developed by jonckheere and silverman in this paper we exploit this common toeplitz plus hankel operator structure shared by the seemingly unrelated linear quadratic and h infty problems and we construct fast state space algorithms for evaluating the spectral radius of the toeplitz plus hankel operator the salient feature of the algorithm is that the spectral radius can be evaluated with an accuracy predicted by an identifiable error bound from the antistabilizing solution of the algebraic riccati equation of the linear quadratic problem associated with the h infty design

on the state space and frequency domain characterization of h norm of sampled data systems this paper studies the problem of characterization and computation of the h norm of sampled data systems using the time invariant function space model via lifting with the advantage of time invariance the treatment gives an eigenvalue type characterization first in the operator form in the frequency domain and then in the hamiltonian type finite dimensional form the form obtained can be adopted for use with the bisection algorithm for actual computation

computing the l2 induced norm of a compression operator abstract a new computationally viable approach is derived for computing the induced norm of a state space compression operator that is an integral operator defined on the finite length space l2 0 h determining this norm is a crucial component in the control analysis of both delay systems and sampled data systems the technique developed may have application to a wider variety of integral operators

a lifting technique for linear periodic systems with applications to sampled data control abstract a lifting technique is developed for periodic linear systems and applied to the h and h 2 sampled data control problems

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

on combined h h2 suboptimal interpolants abstract based on the authors previous results and those of kaftal et al we give an explicit parametrization of the suboptimal interpolants which satisfy simultaneously an h2 and an h suboptimality criterion

minimax lq stochastic tracking and servo problems it is proved that the separation between feedback and feedforward of the two degree of freedom linear quadratic lq stochastic controller reported by e mosca and g zappa ibid vol 34 p 240 2 1989 can be suitably extended when a linear controller is postulated to the minimax lq stochastic tracking and servo problems besides the relevance of the results the authors show that in some problems the wiener and the h sub infinity approaches can play a fruitful complementary role

fast iterative computation of optimal two block h sup infinity norm the two block h sup infinity optimization problem is discussed in which the most computationally demanding work is the computation of the optimal h sup infinity norm denoted by gamma sub 0 the problem of computing gamma sub 0 can be considered as that of finding a gamma such that mu gamma is equal to 1 some new properties of mu gamma are revealed and studied based on these properties and those found by c c chu and j doyle 1985 and z z wang and j b pearson 1984 a very fast computational algorithm for finding gamma sub 0 is proposed

minimax frequency domain performance and robustness optimization of linear feedback systems it is shown that feedback system design objectives such as disturbance attenuation and rejection power and bandwidth limitation and robustness may be expressed in terms of required bounds of the sensitivity function and its complement on the imaginary axis this leads to a minimax frequency domain optimization problem whose solution is reduced to the solution of a polynomial equation

weighted sensitivity minimization for delay systems in this note we discuss the h infty sensitivity minimization problem for linear time invariant delay systems while the unweighted case reduces to simple nevanlinna pick interpolation the weighted case turns out to be much more complicated and demands certain functional analytic techniques for its solution

on identification of stable systems and optimal approximation abstract approximative modelling of stable continuous time possibly infinite dimensional systems is studied based on an optimal approximation approach both approximation of analytical system representations system approximation as well as approximation of input output data based system estimates system identification are considered while special emphasis is given to approximative modelling in the h and hankel norms the l1 and l2 norm cases are also discussed the model sets considered here are finite dimensional systems and time shifted systems simple delay systems the theory of approximation numbers is shown to provide a convenient tool to study problems of identification of stable continuous time systems in a deterministic framework with close connections to complexity considerations laguerre fourier series methods and hankel operator techniques can be utilized to develop fully practical identification methods for continuous time possibly infinite dimensional systems

on the parametrization of the suboptimal solutions in generalized interpolation abstract we apply methods previously developed to give a explicit parametrization of the suboptimal solutions to the standard h generalized interpolation problem this gives in particular a simple parametrization of all the suboptimal controllers of the standard sensitivity minimization problem

unbiased estimation of langevin dynamics from time series with application to hippocampal field potentials in vitro the last decade showed an increased interest in langevin equations for modeling time series recorded from complex dynamical systems these equations allow to discriminate between deterministic drift and stochastic diffusion components of the recorded time series in practice the estimation of drift and diffusion is often based on approximations of the models dynamics that are valid only for high sampling frequencies also model assessment is not or only indirectly performed potentially leading to false claims in this study we compare the performance of an asymptotically unbiased estimation method with a generally used approximate method demonstrating the necessity of using asymptotically unbiased estimators furthermore we describe how confidence intervals for the unknown parameters can be constructed and how model assessment can be carried out we apply the methodology to local field potentials recorded in vitro from mouse hippocampus from eight genetically different strains the recorded field potentials turn out to be well described by linearly damped langevin equations with parabolic diffusion the modeling enables a dynamical interpretation of the spectral power of the field potentials it reveals that observed spectral power differences in the field potentials across hippocampal regions are associated with differences in the deterministic component of the system and it reveals transiently active current dipoles which are not detectable by conventional methods also all estimated parameters have significant heritabilities which suggests that the langevin equations capture biological relevant aspects of electrical hippocampal activity

a spectral characterization of h optimal feedback performance and its efficient computation abstract we study the spectral properties of a toeplitz hankel operator which arises in the context of the mixed sensitivity h optimization problem and whose largest eigenvalue characterizes the optimal achievable performance 0 the existence of such an operator was first shown by verma and jonckheere 26 who also noted the potential numerical advantage of computing eo through its eigenvalue characterization rather than through the iteration here we investigate this operator in detail with the objective of efficiency computing its spectrum we define an adjoint linear quadratic problem that involves the same toeplitz hankel operator as shown by jonckheere and silverman 13 16 consequently a finite polynomial algorithm allows 0 to be characterized as simply as the largest root of a polynomial finally a computationally more attractive state space algorithm emerges from the h t 8 lq relationship this algorithm yields a very good accuracy evaluation of the performance 0 by solving just one algebraic riccati equation thorough exploitation of this algorithm results in a drastic computation reduction with respect to the standard e iteration

a weighted mixed sensitivity h sub spl infin control design for irrational transfer matrices approximate solutions to a weighted mixed sensitivity h sub spl infin control problem for an irrational transfer matrix are obtained by solving the same problem for a reduced order rational transfer matrix upper and lower bounds for the sensitivity are obtained in terms of the sensitivity for the reduced order model and the approximation error moreover rational suboptimal controllers for the irrational transfer matrix are constructed which achieve a sensitivity close to the minimum

on decoupling the h optimal sensitivity problem for products of plants abstract in this note we show how to solve the h optimal sensitivity problem for a siso plant p s p 1 s p 2 s given the solutions for p 1 s p 2 s this allows us to solve the problem for systems of the form e hs p 0 s where p 0 s is the transfer function of a stable lti finite dimensional system

on the structure of suboptimal h controllers in the sensitivity minimization problem for distributed stable plants in this paper we consider the h sensitivity minimization problem for siso distributed stable systems we elucidate the structure of all the suboptimal h controllers for stable distributed plants with invertible outer parts and rational weights we identify the finite and infinite dimensional parts of the controller the conditions under which one can obtain a finite dimensional suboptimal controller by approximating the infinite dimensional parts of the optimal controller are discussed the case where plant transfer function is continuous on the boundary is also discussed

on cancellation in h optimal controllers abstract this note clarifies the mechanism of pole zero cancellations that appeared in the derivation of the h optimal controller via a solution of the corresponding model matching problem the cancellable factor is explicitly expressed using chain scattering matrix descriptions a simple state space formula of the sub optimal controller is also presented based on the chain scattering forms and we show that there is a mixed sensitivity problem that can be solved by calculating a solution of only one riccati equation in each iteration

an algorithm for super optimal h design the two block case abstract in this paper we consider the strengthened h optimization problem in the two block case an algorithm for the super optimal solution is proposed it is based on results by the authors ieee trans aut control ac 33 833 1988 for the less practical one block case it uses state space models and is numerically implementable a feature of the procedure is an optimality criterion which is a natural generalization of that used in the iterative scheme of doyle lecture notes in advances in multivariable control onr honeywell workshop minneapolis u s a 1984 for the unstrengthened problem

functional models in linear algebra abstract this paper examines the role of functional models in linear algebra and some related areas of application notably linear systems theory this approach adopts an intermidiate level of abstraction somewhere between abstract module theory on the one hand and matrix theory on the other it is a powerful method which simplifies many proofs provides insights and illuminates the less obvious connections between linear algebra and operator theory approximation theory moment problems interpolation and control theory

some remarks on optimal interpolation abstract we give in this note very simple new formula for the optimal solution of a generalized interpolation problem which arises in the weighted sensitivity h minimization for distributed systems this is based on our work on skew toeplitz operators from 2

how to quantify deterministic and random influences on the statistics of the foreign exchange market it is shown that price changes of the u s dollar german mark exchange rates upon different delay times can be regarded as a stochastic marcovian process furthermore we show how kramers moyal coefficients can be estimated from the empirical data finally we present an explicit fokker planck equation which models very precisely the empirical probability distributions in particular their non gaussian heavy tails

on the h optimal sensitivity problem for systems with delays in this paper we extend some of the results of ieee trans automat control ac 31 1986 pp 763 766 to more general delay systems in particular we analyze the effect of the interaction of delays and nonminimum phase zeros on the h infty optimal weighted sensitivity

a generalization of bernstein kantorovic operators abstract in this paper we use a probabilistic setting to introduce a double sequence l k n of linear polynomial operators which includes as particular cases the classical bernstein operators the kantorovic operators and the operators recently introduced by cao for these operators we discuss several approximation properties in particular we deal with the convergence properties according to the way in which the different parameters vary and the preservation of global smoothness and classes of functions determined by concave moduli of continuity a remarkable feature of our approach is that if f is differentiable the approximation properties of both l k nf and its derivatives can be discussed simultaneously throughout the paper probabilistic methods play an important role

methods of solving a polynomial equation for an h sub infinity optimal control problem for a single input single output discrete time system a polynomial equation for the h sub infinity optimal control problem is reduced to a nonlinear algebraic equation two methods are proposed for solving the algebraic equation one method uses the singularity of a linear algebraic equation as the optimality index the other gives an approximate solution by solving an eigenvalue problem a numerical example is presented

computation of the singular values of toeplitz operators and the gap metric it is widely recognized that the computation of gap metric is equivalent to a certain two block h problem i e the gap is equal to the norm of a certain two block operator however it can also be characterized as the smallest singular value of a certain toeplitz operator this paper derives a simple computational method for finding such singular values and the gap between two plants by using a state space approach

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

on the nehari problem for a certain class of l functions appearing in control theory ii abstract in this paper we generalize the results of c foias and a tannenbaum j functional analysis 74 1987 146 159 on the classical nehari problem to a much broader class of operators we relate our results to the computation of the discrete spectrum for a certain class of contractions which appear frequently in control engineering applications

minimax lq exact and inexact model matching problems abstract a mixed h 2 h optimal problem is presented for both disturbance attenuation and model mismatching minimization its solution is in the form of a two degrees of freedom controller whose feedback and feedforward paths can be independently designed if the conditions for exact model matching are not met an inexact model matching problem is addressed this solution provides an effective model matching design methodology for non minimum phase plants

paper uniformly optimal control of linear feedback systems the problem of uniformly optimal control is posed in the context of linear time varying discrete time systems the controller is optimal uniformly over a pre specified set of exogenous signals existence of an optimal controller is proved and a formula for the minimum cost is derived the time invariant case is treated in the frequency domain it is shown that for time invariant systems an optimal time varying controller is no better than an optimal time invariant controller

stochastic time series with strong correlated measurement noise markov analysis in n dimensions an extension and generalization of a recently presented approach for the analysis of langevin type stochastic processes in the presence of strong measurement noise is presented for a stochastic process in n dimensions which is superimposed with strong exponentially correlated gaussian distributed measurement noise it is possible to extract the strength and the correlation functions of the noise as well as polynomial approximations of the drift and diffusion functions of the underlying process

norm preserving dilations and their applications to optimal error bounds the problem is given a b c to find d such that left begin array 20 c a c b d end array right leqq mu here we deal with hilbert space operators a b and c ar

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

on computing the spectral radius of the hankel plus toeplitz operator the square root of the spectral radius of the hankel plus toeplitz operator has been shown to be the achievable performance of the mixed sensitivity h sup infinity design the computation of the spectral radius is the bottleneck in the synthesis of the h sup infinity controller in this paper the spectral properties of the hankel plus toeplitz operator are investigated a finite procedure for computing the spectral radius of the hankel plus toeplitz operator is proposed

sensitivity minimization for arbitrary siso distributed plants abstract in this note we write down an explicit formula for the computation of the optimal sensitivity of an arbitrary single input single output linear invariant distributed plant we moreover discuss the uniqueness of the optimal compensator and work out a design example

sensitivity minimization in an h norm parametrization of all suboptimal solutions a number of problems in the control of linear feedback systems can be reduced to the following we are given three stable rational matrix functions k of sizes p 1 x q 1 p 1 x q 2 and p 2 x q 1 respectively and seek a stable rational q 2 x p 2 matrix function s so as to minimize k s we assume that p 1 q 2 p 2 q 1 and that and have maximal rank q 2 and p 2 respectively on the j axis given a tolerance level sufficiently large we obtain a linear fractional map g f 0 11 g 0 12 0 13 0 21 g 0 22 0 23 1 such that f k s with s stable and f if and only if g is a stable q 2 x p 2 matrix function with g 1 the computation of 0 0 ij 1 i 2 1 j 3 reduces to solving a pair of symmetric wiener hopf factorization problems for the special case where i q2 0 t i p2 0 and k not necessarily stable to which the general case can be reduced we provide explicit state space formulae for 0 in terms of a state space realization of k and the

a stable state space realization in the formulation of h norm computation in the two block hinftyoptimization problem usually we are given the state space realizations of the proper rational matrices r 1 s and r 2 s whose poles are all the open right half plane two problems are studied in the note the first is the evaluation of phi s r 1 s at s s k k 1 2 n where phi s is an inner function whose zeros s k k 1 2 n are the poles of r 1 s this evaluation is essential if chang and pearson s method is used for computing the optimal hinftynorm the problem is solved in state space via the solutions of lyapunov equations neither polynomial matrix manipulations nor numerical pole zero cancellations are involved in the evaluation the second problem is to find a stable state space realization of s s u s r 2 s where u s is an inner matrix this problem arises in the spectral factorization of gamma 2 r 2 ast r 2 doyle and chu had a method for constructing stable s s based on a minimal realization of r 2 s an alternate method is proposed the alternate method does not require a minimal realization of r 2 s and only a lyapunov equation is involved

spectral theory of the linear quadratic and h problems abstract an overview of the spectral theory of the linear quadratic and h problems is presented originally the spectral theory of the linear quadratic problem emerged out of the problem of characterizing the finite time escape of the riccati differential equation as a condition on the spectrum of a toeplitz plus hankel operator later and following an independent line of thought the spectral theory of the h problem emerged as a toeplitz plus hankel operator characterization of the smallest achievable tolerance in feedback design this common toeplitz plus hankel operator structure shared by the linear quadratic and h problems is elucidated by mapping the usual h frequency response specification into the time domain leading to an inequality bound on a quadratic functional precisely induced by the toeplitz plus hankel operator with this deep linear quadratic h connection at hand we derive a linear quadratic solution to the h problem and show that such issues as the adamjan arov krein problem pole zero cancellation in optimal h compensation etc can be fruitfully attacked using simple linear quadratic arguments

an interpolation problem associated with h optimal design in systems with distributed input lags the symbol for infinity appears as superscript in title where indicated by the word infinity in brackets

on the optimal and suboptimal solutions of the mixed sensitivity problem abstract in this note using elementary operator theoretic methods we give a method for the explicit computation of the suboptimal and optimal solutions to the mixed sensitivity problem for stable single input single output distributed systems

an lmi solution to the robust synthesis problem for multi rate sampled data systems in this paper we address the asynchronous multi rate sampled data h synthesis problem necessary and sufficient conditions are given for the existence of a controller achieving the desired performance and the problem is shown to be equivalent to a convex optimization problem expressed in the form of linear operator inequalities in the case where the sample and hold rates are synchronous these operator inequalities reduce to linear matrix inequalities for which standard numerical software is available

operator theoretic approach to the optimal two disk problem the nonstandard two disk problem plays a fundamental role in robust feedback optimization here it is shown via banach space duality theory that its solutions satisfy an extremal identity and may be viewed as a dual extremal kernel of a particular l sup 1 optimization problem a novel operator theoretic framework to characterize explicitly its solutions is developed in particular the two disk optimization is shown to be equal to the induced norm of a specific operator defined on a projective tensor product space involving a non hilbert version of a vector valued h sup 2 space moreover this operator is shown to be a combination of multiplication and toeplitz operators under certain conditions existence of maximal vectors is established leading to an explicit formula for the optimal controller an infinite matrix representation with respect to a canonical basis is derived together with an algorithm to compute it the norm of the relevant operator is approximated by special finite dimensional optimizations whose solutions lead to solving semi definite programming problems involving the computation of a matrix projective tensor norm

simple mixed sensitivity optimal controllers abstract we consider the problem of determining whether frequency domain properties of a nominal system specified by a fixed plant g and a given controller k 0 can be improved by performing weighted mixed sensitivity h optimization the weighting functions for the mixed sensitivity problem are specified in terms of g and k 0 both assumed to be single input single output linear and time invariant we show by way of an inverse problem that for a large class of plant controller pairs the nominal controller k 0 is optimal in that its sensitivity and complementary sensitivity functions can not simultaneously be improved upon by h optimization

the kantorovich variant of an operator defined by d d stancu abstract in this note we introduce kantorovich variant of the operators considered by stancu 1998 based on two nonnegative parameters here we prove an approximation theorem with the help of bohman korovkin s principle and find the estimate of the rate of convergence by means of modulus of smoothness and lipschitz type function for these operators in the last section of the paper we show the convergence of the operators by illustrative graphics in mathematica to certain functions

analysis of time series from stochastic processes analysis of time series from stochastic processes governed by a langevin equation is discussed several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the fokker planck equation the coefficients are estimated directly from a time series the applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting

reverse discrete time riccati equation and extended nehari s problem abstract necessary and sufficient conditions for the existence of the anticausal stabilizing solution to the so called reverse discrete time riccati equation are derived under very relaxed conditions imposed on the initial data further a suboptimal solution of prescribed tolerance to the extended nehari s problem is constructed

analytic system problems and j lossless coprime factorization for infinite dimensional linear systems abstract this paper extends the coprime factorization approach to the synthesis of internally stabilizing controllers satisfying an h norm bound to a class of systems with irrational transfer matrices using the coprime factorization description the h control problem can be reduced to two stable analytic system problems such problems have solutions if and only if a certain j lossless factorization exists the full h synthesis problem is shown to be equivalent to the solution of two nested j lossless factorizations if the irrational transfer matrix has a state space realization then the known state space formulas for the h control problem may be recovered using the relationship between j lossless factorizations and solutions of riccati equations however the results derived here are valid for a larger class of infinite dimensional systems

robust h state feedback control for linear systems with state delay and parameter uncertainty this paper addresses the problem of robust h state feedback control design for linear systems with state delay and parameter uncertainty based on a positive definite solution of a modified algebraic riccati equation the proposed robust h static state feedback controller stabilizes uncertain time delay systems independently of delays and guarantees an h norm bound constraint on disturbance attenuation for all admissible uncertainties furthermore it is shown that no advantage can be obtained from the use of a proper linear dynamic state feedback compared with the use of static state feedback illustrative examples are given to demonstrate the applicability of the proposed approach

optimal mixed sensitivity for siso distributed plants the authors extend previous results for the single input single output siso mixed sensitivity problem for distributed parameter systems to a more general setting in which the transfer function of the plant to be controlled has both irrational stable and irrational unstable parts these developments were originally motivated by the computation of the infimal h sup spl infin norm of the weighted mixed sensitivity for the irrational transfer function model of a damped flexible beam