bilateral locally testable languages we give an algebraic characterization of a new variety of languages that will be called bilateral locally testable languages and denoted as blt given k 0 the membership of a word x to a blt k bt language can be decided by means of exploring the segments of length k of x as well as considering the order of appearance of those segments when we scan the prefixes and the suffixes of x in this paper we also characterize the syntactic semigroup of blt languages in terms of the equations of the variety they belong to as well as in terms of the join of two previously studied varieties

survey paper transfer functions of distributed parameter systems a tutorial in this tutorial article the rich variety of transfer functions for systems described by partial differential equations is illustrated by means of several examples under various boundary conditions an important feature is the strong influence of the choice of boundary conditions on the dynamics and on system theoretic properties such as pole and zero locations properness relative degree and minimum phase it is sometimes possible to design a controller using the irrational transfer function and several such techniques are outlined more often the irrational transfer function is approximated by a rational one for the purpose of controller design various approximation techniques and their underlying theory are briefly discussed

approximation of linear distributed parameter systems by delay systems the present work addresses continuous time approximation of distributed parameter systems governed by linear one dimensional partial differential equations while approximation is usually realized by lumped systems that is finite dimensional systems we propose to approximate the plant by a time delay system within the graph topology we prove that if the plant admits a coprime factorization in the algebra of bibo stable systems any linear distributed parameter plant can be approximated by a time delay system governed by coupled differential difference equations considerations on stabilization and state space realization are carried out a numerical method for constructive approximation is also proposed and illustrated

controller reduction in the two block h optimal design for distributed plants abstract in this paper we consider a two block mixed h sensitivity minimization problem for a class of siso possibly unstable infinite dimensional systems the main issue addressed here is the problem of reducing the order of h optimal controllers it is well known that the optimal controllers for distributed plants are infinite dimensional here we obtain a finite dimensional controller from approximations of the optimal controller in the gap metric topology we show that under certain mild conditions one can obtain a finite dimensional stabilizing controller achieving a performance arbitrarily close to the optimum we also provide an explicit bound for the performance deviation this bound depends on the approximations of the infinite dimensional parts of the optimum controller an example involving an unstable delay system is given to illustrate the computational aspects of this approach

approximate controllability results for analytic resolvent integro differential inclusions in hilbert spaces abstractin this work we consider a nonlinear resolvent integro differential evolution inclusions in hilbert spaces this paper deals with the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces we use bohnenblust karlin s fixed point theorem to establish a set of sufficient conditions for the approximate controllability for nonlinear resolvent integro differential inclusions in hilbert spaces further we extend the result to study the approximate controllability concept with non local conditions an example is presented to demonstrate the obtained theory

on stabilization and the existence of coprime factorizations shows that any transfer function matrix whose elements belong to the quotient field of h sub infinity and which is stabilizable has a matrix fraction representation over h sub infinity which is coprime in the sense that a matrix bezout identity can be satisfied

on the varieties of languages associated with some varieties of finite monoids with commuting idempotents abstract eilenberg has shown that there is a one to one correspondence between varieties of finite monoids and varieties of recognizable languages in this paper we give a description of a variety of languages close to the class of piecewise testable languages considered by i simon the corresponding variety of monoids is the variety of j trivial monoids with commuting idempotents this result is then generalized to the case of finite monoids with commuting idempotents whose regular d classes are groups from a given variety of groups

approximate controllability of partial neutral functional differential systems of fractional order with state dependent delay we prove the approximate controllability of control systems governed by a class of partial neutral functional differential systems of fractional order with state dependent delay in an abstract space sufficient conditions for approximate controllability of the control systems are established provided the approximate controllability of the corresponding linear control systems the results are obtained by using the krasnoselskii schaefer type fixed point theorem with the fractional power of operators an example is provided to illustrate the main results

comments on grimble s comments on stein s comments on rolloff of h sup infinity optimal controllers in m j grimble s comments see ibid vol 35 p 762 5 1990 the polynomial systems approach to h sup infinity is shown to have an advantage over the state space approach in that improper weighting functions can be used allowing one to obtain controllers that roll off at high frequencies it is shown that the same controller can be found with the state space approach using a simple problem reformulation

an approximation theory of solutions to operator riccati equations for h infty control as in the finite dimensional case the appropriate state feedback for the infinite dimensional h infty disturbance attenuation problem may be calculated by solving a riccati equation this operator riccati equation can rarely be solved exactly we approximate the original infinite dimensional system by a sequence of finite dimensional systems and consider the corresponding finite dimensional disturbance attenuation problems we make the same assumptions required in approximations for the classical linear quadratic regulator problem and show that the sequence of solutions to the corresponding finite dimensional riccati equations converge strongly to the solution to the infinite dimensional riccati equation furthermore the corresponding finite dimensional feedback operators yield performance arbitrarily close to that obtained with the infinite dimensional solution

existence of a class of fractional neutral integro differential systems with state dependent delay in banach spaces in this manuscript we tend to implement krasnoselskii s fixed point theorem along with fractional calculus and operator semigroups to come up with a new set of sufficient conditions for the existence of a class of fractional neutral integro differential systems fnids with state dependent delay sdd in banach spaces an illustration is additionally provided to demonstrate the obtained theories

well posedness of h optimal control problems this paper considers the effect of perturbations of a nominal single input single output linear plant or a band of uncertainty on the solution to certain frequency domain optimal control problems weighted h infty sensitivity minimization mixed and robust sensitivity minimization will be considered along with problems of more general type a brief discussion of h p optimal control problems will also be given typical examples will be presented where optimal sensitivity does not depend continuously on the plant ill posedness and conditions for well posedness will be given it is demonstrated that similar discontinuities can occur for more general problems also suggested are ways of defining an optimization problem so that continuous dependence of the infimum is ensured

linearized stability in periodic functional differential equations with state dependent delays in this paper we study stability of periodic solutions of a class of nonlinear functional differential equations fdes with state dependent delays using the method of linearization we show that a periodic solution of the nonlinear fde is exponentially stable if the zero solution of an associated linear periodic linear homogeneous fde is exponentially stable

existence results for an impulsive fractional integro differential equation with state dependent delay in this paper we have a tendency to implement different fixed point theorem banach contraction principle krasnoselskii s 18 and schaefer s 18 coupled with solution operator to analyze the existence and uniqueness results for an impulsive fractional integro differential equations ifide with state dependent delay sdd in banach spaces finally cases are offered to demonstrate the concept

robust stabilization of infinite dimensional systems by finite dimensional controllers abstract the problem of robustly stabilizing an infinite dimensional system with transfer function g subject to an additive perturbation is considered it is assumed that g b 0 of systems introduced by callier and desoer 3 the perturbation satisfies w1 w2 c now write w1gw2 g1 g1 where g1 is rational and totally unstable and g2 is stable generalizing the finite dimensional results of glover 12 this family of perturbed systems is shown to be stabilizable if and only if min g 1 the smallest hankel singular value of g 1 a finite dimensional stabilizing controller is then given by k w 2 k 1 i g 2 k 1 1 w 1 where 2 is a rational approximation of g2 such that g 2 g 2 min g 1 and k1 robustly stabilizes g1 to margin the feedback system g k will then be stable if w1 w2

convergence of controllers designed using state space techniques in this paper coprime factorization theory is used to examine convergence of finite dimensional controllers for infinite dimensional systems designed using approximations under assumptions of uniform stabilizability detectability the controllers stabilize the original system for large enough model order and the corresponding sequence of closed loops converge

moment stability via resolvent operators of fractional stochastic differential inclusions driven by fractional brownian motion in this manuscript we consider a class of fractional stochastic differential inclusions driven by fractional brownian motion in hilbert space with hurst parameter h 12 1 sufficient conditions for the existence and asymptotic stability of mild solutions are derived in mean square moment by employing fractional calculus analytic resolvent operators and bohnenblustkarlins fixed point theorem the effectiveness of the obtained theoretical results is illustrated by an example

learning in varieties of the form v li from positive data grammatical inference and finite semigroup theory are continuously developing nevertheless it seems that they are not interacting too much we propose in this paper an inference method for languages that belong to varieties of the form v li many well known families of languages like locally testable reversible dot depth one etc are of that form the method unifies existing algorithms for inference of some of those families and can be applied to some others that had not been inferred yet it uses a result about the cascade product in which one of the factors is a transducer and the second is the automaton obtained by inferring the base case of the family using the transduction of the sample as input

periodicity in a food limited population model with toxicants and state dependent delays abstract with the help of a continuation theorem based on gaines and mawhin s coincidence degree easily verifiable criteria are established for the global existence of positive periodic solutions of a food limited population model with toxicant and state dependent delays that is du t dt u t r t a t u t j 1 m b j t u t j t u t k t c t u t j 1 m d j t u t j t u t where r t k t a t bj t dj t j 1 2 m are continuous real valued periodic functions with period 0 and r t k t a t 0 bj t dj t 0 j 1 2 m are periodic continuous functions with period 0 j j are periodic with respect to their first arguments some new results are obtained

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

tutorial review h optimal controller design for a class of distributed parameter systems this paper is a tutorial on a frequency domain design method for the two block h optimal control of a class of siso distributed parameter systems uncertainties in the system are assumed to be unmodelled dynamics represented in the form of either multiplicative or additive or coprime factor perturbations of a nominal infinite dimensional plant performance of the closed loop system is measured in terms of the energy amplification from external input signals to the outputs of interest in this paper transfer functions of the nominal plant and the weights are used in order to derive a solution to two block h control problems the solution presented here uses results from operator theory the h optimal performance and controller in this method are computed from a finite set of linear equations

the linear regulator problem for parabolic systems we present an approximation framework for computation in finite dimensional spaces of riccati operators that can be guaranteed to converge to the riccati operator in feedback controls for abstract evolution systems in a hilbert space it is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems

a skew toeplitz approach to the h optimal control of multivariable distributed systems in this paper the problem of the h infty optimization of multivariable distributed systems in the four block setting is studied this work is based on several previous papers and employs the skew toeplitz framework developed in operator theory adv appl 32 1988 pp 21 43 operator theory adv appl 32 1988 pp 93 112 operator theory and integral equations 11 1988 pp 726 767 j functional anal 74 1987 pp 146 159 siam j math anal 19 1988 pp 1081 1091

brief every stabilizing dead time controller has an observer predictor based structure this paper considers the stabilization problem for linear time invariant systems with a single delay h in the feedback loop two parametrizations of all stabilizing controllers are derived in terms of a state space realization of the rational part of the plant these parametrizations have simple structures and clear interpretations the first is in the form of a generalized dead time compensator smith predictor and the second is in the observer predictor form applications of the proposed parametrization to the h 2 optimization and the robust stabilization problems are discussed

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

a new exploration on existence of fractional neutral integro differential equations in the concept of atangana baleanu derivative abstract in this paper we investigate a new fractional derivative with mittag leffler kernels ab derivative to the fractional neutral integro differential equations in banach spaces the results are based on fixed point theorems then we implement a suitable examples and illustrate it by graphical methods with variation of fractional order

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

linear quadratic optimal control of hereditary differential systems infinite dimensional riccati equations and numerical approximations recent theory of infinite dimensional riccati equations is applied to the linear quadratic optimal control problem for hereditary differential systems and it is shown that for most such problems the operator solutions of the riccati equations are of trace class i e nuclear with special attention to trace norm convergence an abstract approximation theory is developed and applied to a particular approximation scheme numerical examples are given problems on both finite and infinite time intervals are studied for both the hereditary system and the approximating systems in the infinite time problem characteristic equations are derived for the closed loop eigenvalues and formulas for the corresponding eigenvectors are given

controllability results for a class of fractional semilinear integro differential inclusions via resolvent operators this paper deals with the controllability of fractional integro differential inclusions the results are obtained by using bohnenblust karlin s fixed point theorem further we extend the result to study the controllability concept with nonlocal conditions finally an example is also given to illustrate our main results in this paper we consider a class of fractional integro differential inclusions in banach spaces this paper deals with the controllability for fractional integro differential control systems first we establishes a set of sufficient conditions for the controllability of fractional semilinear integro differential inclusions in banach spaces via resolvent operators we use bohnenblust karlin s fixed point theorem to prove our main results further we extend the result to study the controllability concept with nonlocal conditions an example is also given to illustrate our main results

analytic controllability of time dependent quantum control systems the question of controllability is investigated for a quantum control system in which the hamiltonian operator components carry explicit time dependence which is not under the control of an external agent we consider the general situation in which the state moves in an infinite dimensional hilbert space a drift term is present and the operators driving the state evolution may be unbounded however considerations are restricted by the assumption that there exists an analytic domain dense in the state space on which solutions of the controlled schrodinger equation may be expressed globally in exponential form the issue of controllability then naturally focuses on the ability to steer the quantum state on a finite dimensional submanifold of the unit sphere in hilbert space and thus on analytic controllability a relatively straightforward strategy allows the extension of lie algebraic conditions for strong analytic controllability derived earlier for the simpler time independent system in which the d

the linear quadratic control problem for infinite dimensional systems with unbounded input and output operators this paper establishes a general semigroup framework for solving quadratic control problems with infinite dimensional state space and unbounded input and output operators

on h sub 2 control of systems with multiple i o delays the h2 optimal control problem of systems with multiple i o delays is solved the problem is tackled by first transforming it to what is called the two sided regulator problem the latter is solved using orthogonal projection arguments and spectral factorization the resulting controller is an interconnection of rational blocks nonrational blocks having finite impulse response and delay operators all of which are implementable

cauchy problem for fractional diffusion equations abstract we consider an evolution equation with the regularized fractional derivative of an order 0 1 with respect to the time variable and a uniformly elliptic operator with variable coefficients acting in the spatial variables such equations describe diffusion on inhomogeneous fractals a fundamental solution of the cauchy problem is constructed and investigated

fractional telegraph equations we investigate several aspects of the fractional telegraph equations in an effort to better understand the anomalous diffusion processes observed in blood flow experiments in the earlier work eckstein et al electron j differential equations conf 03 1999 39 50 the telegraph equation d 2 u 2adu au 0 was used where d d dt a nd it was shown that as t tends to infinity u is approximated by v w here 2adv av 0 here a d 2 dx 2 on l 2 r o ra can be a more general nonnegative selfadjoint operator in this paper the concern is with the fractional telegraph equation e 2 u 2aeu au 0 where e d and 0 1 after solving this equation it is shown that u is approximated

a sufficient condition to polynomially compute a minimum separating dfa the computation of a minimal separating automaton msa for regular languages has been studied from many different points of view from synthesis of automata or grammatical inference to the minimization of incompletely specified machines or compositional verification in the general case the problem is np complete but this drawback does not prevent the problem from having a real application in the above mentioned fields in this paper we propose a sufficient condition that guarantees that the computation of the msa can be carried out with polynomial time complexity

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

existence of s asymptotically ω periodic solutions for fractional order functional integro differential equations with infinite delay abstract we study s asymptotically periodic solutions of the abstract fractional equation u 1 a u f t u t 1 2 where a is a linear operator of sectorial type 0

on the mixed sensitivity minimization for systems with infinitely many unstable modes in this note we consider a class of linear time invariant systems with infinitely many unstable modes by using the parameterization of all stabilizing controllers and a data transformation we show that h controllers for such systems can be computed using the techniques developed earlier for infinite dimensional plants with finitely many unstable modes

mild solutions for class of neutral fractional functional differential equations with not instantaneous impulses this article contains the existence results of the mild solutions of an abstract semilinear neutral fractional differential equations with not instantaneous impulses the results are proved by using the theory of analytic resolvent family and fixed point theorems one application involving partial differential equations with impulses are presented

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

right and left locally testable languages the aim of this paper is to give a denition as well as an algebraic characterization of two new varieties of languages that will be referred to as right respectively left locally testable languages and denoted as rlt resp llt both families strictly contain the class of locally testable languages given k 0 the membership of a word x to a rlt k rt language can be decided by means of exploring the prex and sux of length k 1o fx and the segments of length k as well as considering the order of appearance of those segments when we scan the prexes of x membership of x to a k lt can be decided in a similar way but we have to change the word prexes for suxes in the above description in this paper we also show that s is a syntactic semigroup of a k rt resp k lt language if and only if the local subsemigroups of s are idempotents and right resp left repetition free c 2000 elsevier science b v all rights reserved

robust stabilization of delay systems by approximation of coprime factors given a delay system with transfer function g s h2 s h1 s where h1 s 01npi s e is and h2 s 02nqi s e is with 0 0 1 n1 0 0 n2 the pi being polynomials of degree i and i 0for i 0 and the qi polynomials of degree di 0 for each i the robust stabilization of a class of perturbed coprime factors of this system is considered asymptotic estimates are obtained based on recent results on the approximation and stabilization of normalized coprime factors an explicit formula is given for the normalized coprime factor stability margin for the case of a multivariable transfer function of the form g s e str s with r rational

unstable and nonproper weights in h control an h control problem is examined in which the controller can and need only stabilize a part of the generalized closed loop due to unstable weights the procedure is a simple extension of known results and is computationally the easiest method available

ill posed distributed parameter systems a control viewpoint the use of linear time invariant distributed parameter systems ltidpss as models of physical processes is considered from a control viewpoint specifically classes of ltidpss exhibiting properties which potentially limit their usefulness in feedback design are defined and termed ill posed the structure of these classes is investigated within a general mathematical framework which encompasses many distributed parameter systems of engineering interest within this framework necessary and sufficient conditions are derived which completely characterize these classes and establish their equivalence

slowly oscillating periodic solutions of autonomous state dependent delay equations more than a dozen years since the peak of activity on the question of the existence of periodic slowly oscillating solutions of autonomous delay differential equations following the early work of jones l wright 2 and grafton 3 the work of nussbaum 4 51 is to be specially noted for providing several new fixed point results and a global bifurcation theorem which are particularly useful for proving the existence of periodic solutions other important works include those of hadeler and tomiuk 6 kaplan and yorke 7 chow 8 chow and hale 9 alt lo 111 and walther 12 131 see hale s book 14 for an overview to the best of our knowledge only nussbaum 5 and alt 1 l considered the question of the existence of periodic solutions of autonomous state dependent delay differential equations nussbaum considered a special equation 0 3 below in 5 but did not prove a general result alt 1 l considered more complicated integral threshold type state dependent delays which have arisen in various models in epidemiology and structured population models alt obtained a theorem for a general class of state dependent equations on which we comment below the lack of results on periodic solutions for state dependent equations is probably explained by the fact that it is not clear what kinds of state dependent delays are interesting or natural and on a lack of compelling examples of such equations arising from plausible mathematical models however some recent papers of belair and mackey 15 and belair 16 contain some interesting state dependent delay equations arising in economics and population biology state dependent delays of threshold type arise naturally in structured population models see lo 111 the motivation for this paper stems from consideration of the innocent looking equation x t kx t r x t 0 1 where r x is bell shaped e g r x 01 emxz 1 01 0 i 01 5 1 if k 7r 2 and r o 1 then the zero solution of 0 1 is unstable a formal linearization would yield z t kz t 1 which is known to be unstable for

periodic solutions for differential equations with state dependent delay and positive feedback existence of a nontrivial periodic orbit and a homoclinic orbit connecting 0 to the periodic orbit is shown for the differential equation x t x t f x t r r r x t with state dependent delay and positive feedback here 0 f and r are smooth real functions with r 0 1 and f 0

approximation of delay systems a case study abstract the approximation of delay systems is studied a numerically well behaved method for computing hankel optima rational approximations for delay systems is presented based on certain properties of hankel matrices and the theory of laguerre polynomials the cf method of trefethen and certain pade approximations of delay systems are also considered the importance of a certain wiener algebra property in the analysis of the rational approximation of an important class of delay systems in the l norm and the hankel norm is shown completing certain results presented in the literature for systems satisfying certain nuclearity or absolute continuity conditions a case study and numerical comparison is presented for the approximation of the parametric family of first order stable delay systems g s exp s ts 1 numerical experience indicates that l optimized cf approximations based on short truncated maclaurin series give in general somewhat smaller l approximation errors than hankel optim

over testable languages abstract in this paper we give a combinatorial description of the languages that are both locally and piecewise testable we call such languages over testable the locally testable semigroups were discovered in the study of finite automata the definition of locally testable semigroup is similar to that of locally testable language if we consider words over the alphabet which is the set of all elements of a semigroup s then such a word determines an element of s the product of the letters of the word a semigroup s is locally testable if whenever two words over the alphabet s have the same factors of a fixed length k and the same prefix and suffix of length k 1 then the products of the letters of these words are equal a natural extension of locally testable semigroups is obtained by dropping the condition about the prefix and suffix we call such semigroups strongly locally testable we prove in this paper that the family of strongly locally testable semigroups is exactly the intersection of the variety of locally idempotent and commutative semigroups and that of j trivial semigroups in particular a language is over testable if and only if its syntactic semigroup is strongly locally testable we use this algebraic characterization to derive a simple family of generators for the variety of over testable languages

approximation of unstable infinite dimensional systems using coprime factors abstract the effectiveness of comprime factor techniques in l 2 and l model reduction of unstable linear systems is analysed asymptotic estimates are given of the achievable error in the stable and unstable parts of the approximate system measured in a number of different norms some involving the associated hankel operators the chordal metric is introduced as a measure of approximation and is shown to yield the graph topology finally it is deduced that asymptotically optimal l 2 and l convergence rates can be obtained for a large class of unstable systems

h output feedback of infinite dimensional systems via approximation abstract as in the finite dimensional case a state space based controller for the infinite dimensional h disturbance attenuation problem may be calculated by solving two riccati equations these operator riccati equations can rarely be solved exactly we approximate the original infinite dimensional system by a sequence of finite dimensional systems the solutions to the corresponding finite dimensional riccati equations are shown to converge to the solution of the infinite dimensional riccati equations furthermore the corresponding finite dimensional controllers yield performance arbitrarily close to that obtained with the infinite dimensional controller

h sup spl infin optimal and suboptimal controllers for infinite dimensional siso plants this paper presents a simple formula for h sup spl infin optimal and suboptimal controllers for unstable siso distributed plants with rational weighting functions the controller is expressed in terms of i inner and outer parts of the plant ii a finite dimensional spectral factor obtained from the weighting functions and iii a rational function satisfying certain interpolation conditions under certain genericity assumptions this rational function is of dimension less than or equal to n sub 1 l 1 n sub 1 l in the suboptimal case where l is the number of unstable poles of the plant and n sub 1 is the order of the sensitivity weighting function there are 2 n sub 1 l 2 n sub 1 l 1 in the suboptimal case linear equations which determine this rational function these linear equations can be written directly from the structure of the controller

local varieties of completely regular monoids the aim of this paper is to apply recent deep rcsults on completely regular semigrotips to questions about categories arising in connection with the theory of recognizable languages a variety pseudovariety v of monoids is local if any finite category whose local monoids belong to v divides a member of v in the sense of b tilson 1 21 see below our main theorem 7 1 essentially states that a monoid variety which satisfies an identity x l x n 0 that is which consists of completely regular semigroups is local whenever all the labels on its pol ik ladder are local see below for the definitions as an immediate consequence every nontrivial monoid variety consisting of orthogroups is local an orthogroup is a completely regular semigroup whose idempotents form a subsemigroup further it quickly follows that any nontrivial pseudovariety of monoids consisting of orthogro ps is also local at the core of the paper is a study of congruences on locally completely regular categories those for which each local monoid is completely regular pseudovarieties of monoids arise naturally via the well known correspondence between regular languages and finite monoids e g 1 13 it has lately been realized that for some purposes they are best studied within the framework of pseudovarieties of categories locality of a pseudo

closed form h infinity optimal control for a class of infinite dimensional systems h infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators diffusion equations are an important example in this class explicit formulas for the optimal state feedback controller as well as the optimal state estimator are given unlike traditional methods for h infinity synthesis no iteration is needed to obtain the optimal solution moreover the optimal performance for both the state feedback and state estimation problems are explicitly calculated this is shown to be useful for problems of h infinity optimal actuator and sensor location furthermore the results can be used in testing and bench marking of general purpose algorithms for h infinity synthesis the results also apply to finite dimensional systems

approximation theory for linear quadratic guassian optimal control of flexible structures this paper presents approximation theory for the linear quadratic gaussian optimal control problem for flexible structures whose distributed models have bounded input and output operators the main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator which is infinite dimensional design of the optimal compensator separates into an optimal linear quadratic control problem and a dual optimal state estimation problem the solution to each problem lies in the solution to an infinite dimensional riccati operator equation the approximation scheme in the paper approximates the infinite dimensional lqg problem with a sequence of finite dimensional lqg problems defined for a sequence of finite dimensional usually finite element or modal approximations of the distributed model of the structure two riccati matrix equations determine the solution to each approximating problem the finite dimensional equations for numerical approximation

finite dimensional compensators for infinite dimensional systems via galerkin type approximation in this paper existence and construction of stabilizing compensators for linear time invariant systems defined on hilbert spaces are discussed an existence result is established using galerkin type approximations in which independent basis elements are used instead of the complete set of eigenvectors a design procedure based on approximate solutions of the optimal regulator and optimal observer via galerkin type approximation is given and the schumacher approach is used to reduce the dimension of compensators a detailed discussion for parabolic and hereditary differential systems is included

existence results for fractional neutral integro differential equations with state dependent delay in this paper we study the existence of mild solutions for a class of abstract fractional neutral integro differential equations with state dependent delay the results are obtained by using the leray schauder alternative fixed point theorem an example is provided to illustrate the main results

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