local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in banach spaces abstract in this work we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in banach spaces we suppose that the undelayed part admits a resolvent operator in the sense of grimmer r grimmer resolvent operators for integral equations in a banach space transactions of the american mathematical society 273 1982 333 349 the delayed part is assumed to be locally lipschitz firstly we show the existence of the mild solutions secondly we give sufficient conditions ensuring the existence of strict solutions

parametric output feedback controller design abstract a parameterization of fixed gain output feedback controllers which will assign a complete set of distinct eigenvalues to a given state space system is presented the main result is a compact parametric expression for the output feedback controller gain matrix explicitly characterized by two sets of free parameters the set of n closed loop system eigenvalues and a set of mr n design parameters for n state r input m output systems the free design parameters are determined by a sequential design procedure which automatically satisfies the basic orthogonality constraints on the left and right closed loop eigenvectors under the condition m r n the principal benefits of the explicit characterization of a parametric class of output feedback controllers lie in the ability to directly accommodate various different design criteria an illustration of the parametric output feedback design procedure is given by way of approximating the optimal full state regulator response of a fifth order pilot plant evaporator model

approximate controllability of semi linear neutral integro differential systems with finite delay abstract this paper considers the approximate controllability of semilinear neutral integrodifferential systems with finite delay in hilbert space since the considered equation admits nonlinear terms involving spatial derivatives the fraction power theory and norm are used to discuss the problem so that the established results can be applied to them the results are obtained by using the sadovskii fixed point theorem and the theory of analytic resolvent operator an example is presented to illustrate the applications of the obtained results

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

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

a robust optimal model matching control a deductive design approach is proposed to develop an optimal feedback control while preserving quantitative robustness and noise rejection properties the design procedure involves the minimization of a suitably selected performance index to reflect a required model matching following objective gradient projection schemes applied to the performance index and feasible constraints are used to accomplish the design tradeoff a mechanical manipulator control system example is employed as a vehicle to illustrate the overall design selection and optimization uncertainty of the system description is included as a feature of the example

a polynomial approach to eigenstructure assignment using projection with eigenvalue trade off a novel eigenstructure assignment method is presented which trades exact closed loop eigenvalue location against an improvement in the associated closed loop eigenvector match against membership of a desired set via either constrained or unconstrained optimizations the polynomial approach removes the dependence of the cost functions on the closed loop eigenvector by describing the allowable desired eigenvector subspace as a function of the eigenvalue location a fixed wing aircraft example is used to demonstrates the benefit of eigenvalue trade off over basic projection

on eigenstructure assignment in linear multivariable systems the eigenvalue assignment approach of brogan 1 2 is generalized and extended to the assignment of the entire closed loop eigenstructure of linear multivariable systems the set of assignable eigenvectors and generalized eigenvectors emerges naturally in the solution and is given moreover in an explicit parametric form two numerical examples are worked out to demonstrate the application of the procedure

multi component multiphase porous flow an axiomatic foundation for models of multi component multiphase porous flow appearing ubiquitously in the engineering literature is developed this unifies and extends various disparate and empirical formulations appearing in the literature constitutive restrictions are derived from an appropriate statement of the second law of thermodynamics and the corresponding dissipation inequalities establish stability of solutions the convexity properties and variational structure of these models are elucidated

resolvent operators for integral equations in a banach space conditions are given which ensure the existence of a resolvent operator for an integrodifferential equation in a banach space the resolvent operator is similar to an evolution operator for nonautonomous differential equations in a banach space as in the finite dimensional case this operator is used to obtain a variation of parameters formula which can be used to obtain results concerning the asymptotic behaviour of solutions and weak solutions

wellposedness and wave propagation for a class of integrodifferential equations in banach space in recent years there has been an increasing interest in the mathematical treatment of problems which originate in the theory of viscoelastic materials in such problems the constitutive relations for these materials incorporate the history of the strain or the strain rate and in the linear theory lead to linear volterra integrodifferential equations with infinite memory in a banach space x the purpose of this paper is to examine the problems of wellposedness and wave propagation for one such equation in particular we are concerned with equations of the form x t 4 x r j f t s x s ds al

semilinear integrodifferential equations with nonlocal initial conditions abstract of concern is the cauchy problem for semilinear integrodifferential equations with nonlocal initial conditions under general and natural hypotheses we establish some new theorems about the existence and uniqueness of solutions for the cauchy problem as a consequence we unify and extend the corresponding theorems given previously for the cauchy problem for differential equations or integrodifferential equations with nonlocal initial conditions moreover we present two examples one of which comes from heat conduction in materials with memory to show that the existing results are not applicable to them in contrast with ours

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

eigenstructure assignment via linear state feedback control in fahmy and o reilly 1982 a b a parametric solution for the linear state feedback eigenstructure assignment problem is developed this approach is here modified in such a way as to accommodate the case where the set of closed loop eigenvalues and the set of open loop eigenvalues have elements in common it is particularly shown that each common eigenvalue introduces a number of partially free design parameter vectors in addition to the original free ones the paper concludes with illustrative numerical examples

eigenstructure assignment in multivariable linear systems abstract a new design method of regulators using state feedback is developed this method not only assigns eigenvalues to the closed loop system but also assigns parts of the closed loop eigenvector structure illustration of the method in the case of a two link manipulator is included a new robustness measure is introduced

eigenvalue clustering in subregions of the complex plane eigenvalue clustering in subregions of the complex plane is investigated for multivariable linear feedback systems critical constraints of all the eigenvalues of a perturbed system causing it to stay within a specified region of the nominal system arc discussed a design procedure is developed for the selection of a parametrized class of state feedback gains for eigenvalue clustering an illustration of the method for the case of a bounded frequency region is included

on parametric state feedback design an explicit parametric expression for the controller gain matrix in linear state variable feedback is derived it involves both the case where the set of closed loop eigenvalues does not include any open loop eigenvalue and the case where the two eigenvalue sets have elements in common some advantages of this new explicit parameterization of the controller gain matrix are illustrated by two numerical examples

existence of solutions for neutral integro differential equations with state dependent delay in this paper we study the existence and regularity of solutions for a neutral functional integro differential equation with state dependent delay in banach space the mild solutions are investigated by sadovskii fixed point theorem under compactness condition for the resolvent operator and the theory of fractional power and a norm are also used in the discussion since the nonlinear terms of the system involve spacial derivatives the strict solutions are obtained under holder continuity condition hence this work extends and develops the existed results on this topic in the end an example is provided to illustrate the application of the obtained results

analytic resolvent operators for integral equations in banach space on etudie l equation integrodifferentielle x t a 0 x t 0 t b t s x s ds f t t 0 x 0 x 0 ed a x et l equation integrale x t 0 t a t s x s ds f t dans un espace de banach x les operateurs a a 0 b t et a t sont des operateurs clos sur x a domaine dense

state decomposition for singular perturbation order reduction a modal approach singular perturbation techniques for order reduction are based on decomposing the high order system into two parts approximation of the high order system dynamics by the low order model is mainly dependent on this partition this paper introduces a measure for the degree of dependence of the state variables on the high order dominant eigenvalues by means of this measure it is not only possible to find an appropriate decomposition yielding a good low order model but also to get an indication of the order of the reduced model two illustrative examples demonstrate the main results

holder continuous solutions for integro differential equations and maximal regularity we characterize existence and uniqueness of solutions for a linear integro differential equation in holder spaces our method is based on operator valued fourier multipliers the solutions we consider may be unbounded concrete equations of the type we study arise in the modeling of heat conduction in materials with memory

micro structure models of diffusion in fissured media abstract two diffusion models are developed which recognize the local geometry of the individual cells or storage sites and the exchange of flux on the micro scale of these cells the cauchy problems for these model systems are shown to be resolved by holomorphic semigroups and various classical models are obtained as limits of these disributed micro structure models

dynamical order assignment for linear descriptor systems this paper considers the problem of dynamical order assignment for linear descriptor systems by derivative feedback control the approach is based on an ability to adjust the number of infinite non dynamical modes of the system within a permissible range increasing the dynamical order enables the designer to implement specific otherwise unrealizable control strategies on the other hand dynamical order reduction simplifies the design procedures for a large scale system the solution is obtained by imbedding the descriptor space problem in an equivalent state space problem where a zero value eigenvalue with a prescribed geometric multiplicity is assigned to a linear state system by proportional feedback control

existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions abstract in this work we establish several results about the existence and regularity of solutions for some neutral partial differential equations with nonlocal conditions we assume that the linear part generates a strongly continuous semigroup on a general banach space

polar factorization and monotone rearrangement of vector valued functions given a probability space x p and a bounded domain r in rd equipped with the lebesgue measure 1 i normalized so that 10 i i it is shown under additional technical assumptions on x and q that for every vector valued function u e lp x p rd there is a unique polar factorization u v s where is a convex function defined on r and s is a measure preserving mapping from x p into q i i provided that u is nondegenerate in the sense that p u e 0 for each lebesgue negligible subset e of rd through this result the concepts of polar factorization of real matrices helmholtz decomposition of vector fields and nondecreasing rearrangements of real valued functions are unified the monge amgre equation is involved in the polar factorization and the proof relies on the study of an appropriate monge kantorovich problem

existence results for partial neutral functional differential equations with unbounded delay abstract we prove the existence of mild solutions for a partial neutral functional integrodifferential equation with unbounded delay using the leray schauder alternative