iterative regularization for elliptic inverse problems elliptic inverse problems can be formulated using coefficient dependent energy least squares functionals resulting in a smooth convex objective functional a variational inequality emerges as a necessary and sufficient optimality condition the principle of iterative regularization when coupled with the auxiliary problem principle results in a strongly convergent scheme for the solution of elliptic inverse problems

control of an unstable reaction diffusion pde with long input delay abstract a smith predictor like design for compensation of arbitrarily long input delays is available for general controllable possibly unstable lti finite dimensional systems such a design has not been proposed previously for problems where the plant is a pde we present a design and stability analysis for a prototype problem where the plant is a reaction diffusion parabolic pde with boundary control the plant has an arbitrary number of unstable eigenvalues and arbitrarily long delay with an unbounded input operator the predictor based feedback design extends fairly routinely within the framework of infinite dimensional backstepping however the stability analysis contains interesting features that do not arise in predictor problems when the plant is an ode the unbounded character of the input operator requires that the stability be characterized in terms of the h 1 rather than the usual l 2 norm of the actuator state the analysis involves an interesting structure of interconnected pdes of parabolic and first order hyperbolic types where the feedback gain kernel for the undelayed problem becomes an initial condition in a pde arising in the compensator design for the problem with input delay space and time variables swap their roles in an interesting manner throughout the analysis

indentification of some source densities of the distribution type abstract in this paper we investigate the solvability of an ill posed two dimensional fredholm integral equation of the first kind which allows the solutions of distribution type the problem is first transformed into a well posed differential integral equation using output least squares approach with a regularization of bounded variations a globally convergent iterative method is proposed and some numerical results are presented the methodology discussed may be applied for the identification of the boundary shape of the defects of a dielectric material or the interface between different materials

finite spectrum assignment problem for systems with delay in state variables this correspondence is concerned with the finite spectrum assignment problem for linear systems with delay in state variables a systematic procedure for constructing the feedback law is presented on the basis of advanced elementary row operations on matrices with two variables s and z e sh

an observer of systems with delays in state variables the paper is concerned with the design of an observer of systems with delays in state variables and control it is shown on the basis of the finite spectrum assignment theory that if the system is spectrally observable there exists an observer which can estimate the state variables of the system as fast as desired a systematic design procedure of the observer is presented the advantage of the proposed method is that the observer is constructed without preliminary knowledge of the open loop spectrum in contrast with the design method based on the spectral decomposition

strongly pseudoconvex cr structures over small balls part i an a priori estimate the purpose of the present series of papers is to develop the theory of harmonic integrals on strongly pseudoconvex cr structures over small balls along the line developed by d c spencer c b morrey j j kohn and l nirenberg 5 6 7 8 for strongly pseudoconvex complex manifolds we consider a strongly pseudoconvex cr structure on a manifold of real dimension 2n 1 in part i we establish the a priori estimate for the neumann boundary value problem on the complex associated with the structure in the case the structure is induced by an embedding in c and restricted to a small ball of special type provided i c q c n 3 where q is the degree of differential forms we consider in part ii we derive the regularity theorem of solutions of the neumann boundary value problem based on the a priori estimate of part i as an application we prove in part il that when n 5 the structure is realized on a neighborhood of a reference point by an embedding in cn we note here that l nirenberg gave an example of a strongly pseudoconvex cr structure which cannot be induced by such an embedding when n 2 9 l boutet de monvel proved that in the case of such structures over a compact manifold we can find such an embedding when n 3 1 there are two major differences between the cases of strongly pseudoconvex integrable almost complex structures and cr structures firstly the principal parts of the associated laplacians in cr structures are no longer elliptic secondly we have characteristic points on the boundary as a result when we follow over the predecessor s calculation in our case we end up with terms which may not be absorbed in the main non negative terms fortunately these leftover terms depend mostly on the levi form of the cr structure and the hessian form with respect to the cr structure of the equation of the boundary of our

fredholm property of a family of operators on the five dimensional heisenberg group abstract an expansion in euclidean spherical harmonics on the ball in the heisenberg group of dimension five decomposes the dirichlet problem for the laplacian in an infinite number of two dimensional problems fundamental solutions are obtained for each of the partial differential operators in these problems thus reducing them further via layer potentials to one dimensional integral equations the main result in this article states that the corresponding integral operators are fredholm in appropriate weighted l 2 spaces

on spectral controllability of multi input time delay systems abstract it is proved that under certain verifiable conditions spectral controllability of a linear system with commensurate state delays and with m inputs m 1 implies the existence of an n 1 vector b contained in the image of the control matrix b such that the system with b replaced by b is spectrally controllable both the necessity and the sufficiency of these conditions are shown a procedure to construct b is given and an example is discussed

stabilization of linear systems with non commensurate delays a stabilization method for linear systems with non commensurate delays in both state and control variables is presented this method is obtained by combining the algebraic stabilization method with the finite spectrum assignment method the present method can stabilize systems that algebraic methods cannot

on the stability of equivariant embedding of compact cr manifolds with circle action we prove the stability of the equivariant embedding of compact strictly pseudoconvex cr manifolds with transversal cr circle action under circle invariant deformations of the cr structures

finite spectrum assignment problem for systems with multiple commensurate delays in state variables abstract this paper is concerned with the finite spectrum assignment problem for systems with multiple commensurate delays in state variables the necessary and sufficient condition for finite spectrum assignability is clarified a systematic design procedure which can straightforwardly yield a control law is presented

feedback controllers for a wind tunnel model involving a delay analytical design and numerical simulation an application of a finite spectrum assignment method for time delay systems to a feedback control of mach number in a wind tunnel is presented the linearized model of mach number control is a system of three state equations with a delay in one of the state variables the proposed feedback is a linear combination of state variables and weighted integrals of some of the state variables over a period equal to time delay the spectrum of the closed loop system is finite and consists of three eigenvalues that can be placed arbitrarily four possible variants of the feedback control law are presented the calculation of feedback coefficients is very simple which makes it possible to update the controller s parameters on line with the changes of the operating point an extensive numerical simulation of the system dynamics and the feedback controllers was done and led to several conclusions in particular a very good settling time under problem constraints has been obtained and several nice features of the proposed feedback controller have been demonstrated

finite spectrum assignment and observer for multivariable systems with commensurate delays this paper is concerned with control of multivariable systems with commensurate delays the purpose of this paper is to enlarge the class of finite spectrum assignable systems to spectrally controllable multivariable systems with commensurate delays by overcoming an infinite number of eigenvalues which are contained in the system and make control very complex it is proved that if the system is spectrally controllable there is a delayed feedback matrix such that the closed loop system is spectrally controllable through a single input combining this result with previous ones about single input systems it is verified that spectral controllability is equivalent to finite spectrum assignability for multivariable systems with commensurate delays an observer for the system with delayed outputs is presented by using these results the multivariable system can be regulated as desired without preliminary knowledge of open loop eigenvalues and a stability test of transcendental functions whenever the system is spectrally controllable and spectrally observable

linear systems with commensurate time delays stability and stabilization independent of delay notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays constructive methods for determining a stabilizing feedback are also presented the last part of the paper deals with a standard type of observer and regulator with the requirement that the closed loop system be stable independent of delay

reduced order observers for linear neutral delay systems the problem of reduced order observers design for linear neutral delay systems is investigated sufficient conditions for the existence of these observers are given first the general case is presented then under more restrictive conditions a simple design method is developed for some special cases based on linear matrix inequality lmi and linear matrix equality lme formulation independent of delays stability criteria are derived a systematic design method of these observers is presented

approximate inverse method for stable analytic continuation in a strip domain numerical analytic continuation is in general an ill posed problem and some special regularization methods are needed in this paper we apply the approximate inverse method to deal with the problem in a strip domain w z x iy c x r 0 y

observers for discrete time systems with multiple delays a systematic approach to design observers for discrete time systems with multiple delays under general conditions is presented the main feature of the proposed technique is that necessary and sufficient conditions for asymptotic stability are derived while the observer s order is independent from the number of delays and is equal to the state dimension to illustrate the efficiency of the proposed technique two numerical examples are provided

the range of the tangential cauchy riemann operator over a small ball in this paper we study the closed range property of tangential cauchy riemann equations of an abstract cr structure over a small ball let d be the set x e r 1 1x1 4 kuranishi 141 and akahori 11 have studied the l theory

finite spectrum assignment of linear systems with a class of non commensurate delays this paper is concerned with finite spectrum assignment of linear systems with non commensurate delays it is proved that if a feedforward pass between states variables does not have multi non commensurate delays in parallel but only one or no delay in series then the system is finite spectrum assignable even though the feedback pass has multi non commensurate delays in parallel

an asymptotic modal observer for linear autonomous time lag systems a full state vector observer is derived for a class of linear autonomous time lag systems represented by differential equations the major features of the approach are 1 an observer is constructed just for the set of unstable or poorly damped modes of the delayed system once they have been determined and 2 the design is accomplished by using a partial fraction expansion separating the unstable part from the system and then applying well known finite dimensional state vector techniques a procedure for the construction is given along with some numerical results to illustrate the simplicity of the observer

recursive predictor design for state and output feedback controllers for linear time delay systems this paper presents a recursive method to design state and output feedback controllers for mimo block feedforward linear systems with delays in the inputs outputs and interconnections between the blocks the resulting controller is of predictor type which means that it contains finite integrals over past state and input values the method is a generalization of the well known model reduction approach for systems with input delay a recursive procedure replaces delay terms with non delay ones step by step from the top of the cascade structure down controller gains are computed for the proxy system without delays while the construction guarantees the same closed loop poles for the delay system and the proxy one the observer is designed by applying the duality argument and the separation principle is also shown to apply

an eigenvalue based approach for the stabilization of linear time delay systems of neutral type an eigenvalue based approach for the stabilization of linear neutral functional differential equations is presented which extends the recently developed continuous pole placement method for delay equations of retarded type the approach consists of two steps first the stability of the associated difference equation is determined and a procedure is applied to compute the supremum of the real parts of its characteristic roots which corresponds to computing the radius of the essential spectrum of the solution operator of the neutral equation no restrictions are made on the dimension of the system and the number of delays also the effect of small delay perturbations is explicitly taken into account as a result of this first step the stabilization problem of the neutral equation is reduced to a problem involving only a finite number of characteristic roots as a second step stabilization is achieved by shifting the rightmost or unstable characteristic roots to the left half plane in a quasi continuous way by applying small changes to the controller parameters and meanwhile monitoring other characteristic roots with a large real part a numerical example is presented

finite dimensional approximate observers for a class of transportation systems finite dimensional approximate observers are designed for linear functionals of the state of distributed parameter transportation systems a systematic design procedure is presented in which the observer parameters can be optimized for maximal accuracy of observation the maximal attainable accuracy can be improved by increasing either the observer s dynamical order or the number of point and or distributed measurements the eigenvalue spectrum of the observation error dynamics is freely assignable

stabilization of linear distributed control systems with unbounded delay in this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space we characterize those systems that can be stabilized using a feedback control as consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control

strongly pseudoconvex cr structures over small balls part iii an embedding theorem the purpose of the present paper is to prove that any germ of strongly pseudoconvex cr structure on a manifold of real dimension 9 is realized by an embedding in the complex euclidean space of real codimension 1 it is well known that the above is true as formal power series hence we find an embedding such that the induced structure is very close to the given one on a small neighborhood of the reference point we correct our embedding by newton s method we then apply the moser nash procedure cf 4 to prove that the sequence of embeddings obtained by the successive correction converges on a sufficiently small neighborhood of the reference point to an embedding which realizes the given structure to explain how the correction is made let d be the differential operator in the complex associated with the given structure when f f f is an approximating embedding defined on u we set ox dfx if we can find gx such that dga on and f g is still an embedding f is completely corrected unfortunately we do not know how to find such a g however the neumann boundary value problem in parts i and ii for the differential operator df which is associated with the induced structure is a tool to handle such question by newton s method we mean that we make the best correction using df instead of d this is done as follows oa is not a differential form in the complex of df hence we replace 01 oj by its projection o on to the complex of df note that 0a may no longer be in the kernel of df and our domain may not be distinguished we first construct a distinguished distance function tf on u and consider a ball u tf r

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

feedback stabilization of linear autonomous time lag systems a stabilization theory which employs well established finite dimensional control system tools is developed for the stabilization of linear autonomous time lag systems the main ideas include 1 a set whose elements are matrices each of which is a left zero of the system characteristic quasi polynomial matrix and 2 a linear transformation which reduces the delay system to a delay free system whose state matrix is a direct sum of n elements of the matrix set where n is some positive integer from the definition of this matrix set it is shown that each of its elements inherits its spectrum from that of the delay system so that by design the system unstable poles may be embedded in the spectrum of the delay free system under the assumption of spectral stabilizability it is then shown how to obtain a stabilizing feedback control law on the basis of the delay free system numerical examples are presented to confirm the theory

dynamic compensation of siso systems over a principal ideal domain the polynomial equation approach and some concepts from algebraic geometry are employed in compensator design for a class of linear single input single output siso systems with coefficients from a principal ideal domain pid

an observer for time lag systems a full state vector observer is derived for a class of linear differential state delayed control systems the approach dualizes a feedback stabilization theory based on the reducing transformation technique a major feature of the approach is that the observer or the combined controller observer can be designed by well known finite dimensional state vector methods once the set of unstable and poorly damped modes of the system has been determined

a necessary condition for spectral controllability of delay systems on the basis of finite laplace transforms abstract this paper is concerned with spectral controllability of systems with multiple commensurate delays in the state variables a necessary condition for spectral controllability is presented on the basis of finite laplace transforms it is closely related to the finite spectrum assignment problem physical meanings of it are also discussed

output stabilization of time varying input delay systems using interval observation technique the output stabilization problem for a linear system with an unknown bounded time varying input delay is considered the interval observation technique is applied in order to obtain guaranteed interval estimate of the system state the procedure of the interval observer synthesis uses lower and upper estimates of the unknown delay and requires to solve a special silvester s equation the interval predictor is introduced in order to design a linear stabilizing feedback the control design procedure is based on linear matrix inequalities lmi the theoretical results are supported by numerical simulations and compared with a control design scheme based on a luenberger like observer

an internal state decomposition approach to a discrete time h2 control problem with irrational input non minimum phase property abstract an internal state decomposition approach to a class of discrete time h 2 control problems with irrational non minimum phase property at the control input is proposed this is a generalization of the state variable transformation to derive the discrete time smith predictor for a single input delay system the h 2 optimal controller is derived using the orthogonality principle in h 2 space as a direct consequence of the state decomposition the characterization of the optimal cost by the previous and alternative truncation operators is also discussed

evaluating and approximating fir filters an approach based on functions of matrices most of the controllers designed for systems with timedelays involve finite impulse response fir filters in their structure in particular prediction based controllers for systems with input output delays we present theory algorithms and software to evaluate the frequency response to approximate the filters by stable linear timeinvariant systems and to compute their induced cal l 2 gain the approach is based on the theory of functions of matrices in the approach pole zero cancelations in frequency domain representations are explicitly taken into account

nonexistence of homotopy formula for 0 1 forms on hypersurfaces in mathbb c 3 soit g une 0 1 forme definie sur une hypersurface strictement convexe dans c 3 et on suppose que b g 0 mais b g est petit on considere la resolution locale approchee de l equation b u g

on controllability and observability of time delay systems this paper deals with controllability and observability properties of time delay systems in the state space r n times l p in particular we prove the equivalence of spectral controllability and approximate null controllability moreover it is shown that the necessary condition for approximate f controllability obtained recently by manitius is also sufficient and a verifiable and matrix type criterion for f controllability is derived for systems with commensurate delays finally we introduce the dual observability notion of approximate controllability and prove that the control system is exactly null controllable if and only if the transposed delay system tis continuously finally observable

on necessary and sufficient conditions for regulation of linear systems over rings necessary and sufficient conditions are given for regulation of linear systems over rings using observers and causal dynamic state feedback systems with the polynomial fractional representation property the results are then used to obtain stabilizability conditions for systems over integers delay differential systems systems over polynomial rings and to obtain conditions to make a 2 d system nonrecursive

on the control of linear systems whose coefficients are functions of parameters the stabilization and regulation of linear discrete time systems whose coefficients depend on one or more parameters is studied for linear systems whose coefficients are continuous functions of real or complex parameters respectively analytic or rational functions of real parameters it is shown that reachability of the system for all values of the parameters implies that the system can be stabilized using gains that are also continuous analytic rational functions of the parameters closed form expressions for a collection of stabilizing gains are given in terms of the reachability gramian for systems which are stabilizable for all values of the parameters it is shown that continuous analytic rational stabilizing gains can be computed from a finite time solution to a riccati difference equation whose coefficients are functions of the parameters these results are then applied to the problem of tracking and disturbance rejection in the case when both the plant and the exogenous signals contain parameters

linear functional observers for systems with delays in state variables this paper is concerned with the design of linear functional state observers for systems with delays in state variables in particular the necessary and sufficient conditions for the existence of the rth order observers are given sufficient conditions for the stability dependent of delays and stability independent of delays are derived using linear matrix in equality formulation a systematic design method of these observers is presented numerical examples are given to illustrate this method

adaptive backstepping controller design for stochastic jump systems in this technical note we improve the results in a paper by shi et al in which problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps were considered however the system considered is switching stochastically between different subsystems the dynamics of the jump system can not stay on each sliding surface of subsystems forever therefore it is difficult to determine whether the closed loop system is stochastically stable in this technical note the backstepping techniques are adopted to overcome the problem in a paper by shi et al the resulting closed loop system is bounded in probability it has been shown that the adaptive control problem for the markovian jump systems is solvable if a set of coupled linear matrix inequalities lmis have solutions a numerical example is given to show the potential of the proposed techniques

time delay systems design of delay free and low order observers this note provides a comprehensive treatment on the design of functional observers for linear systems having a time varying delay in the state variables the designed observers possess attractive features of being low order and delay free and hence they are cost effective and easy to implement existence conditions are derived and a design procedure for finding low order observers is given

strictly pseudoconvex domains in c n the theory which we have developed so far will be expanded in two ways 1 in this chapter we shall use the cauchy fantappie calculus to transform the bochner martinelli kernel into a kernel adapted to strictly pseudoconvex domains in n and prove a number of finiteness and vanishing theorems for these domains 2 in the next chapter we shall pass from n to arbitrary hermitian manifolds and establish the analogue of the bmk formula in that context obtaining along the way the hodge decomposition theorem on compact manifolds both lines of thought will merge in the subsequent chapters and lead to a solution of the levi problem and finiteness theorems for strictly pseudoconvex manifolds as well as to a solution of the overline partial neumann problem to be formulated later

observers design for linear time delay systems abstract in this contribution we propose a simple and useful approach to design observers for discrete time systems with delays in the state and output variables the main feature is that the necessary and sufficient conditions for the existence of such observer are derived the stability analysis is performed by the lyapunov approach where the obtained conditions are expressed in terms of a modified riccati equation numerical examples are provided to show efficiency of the proposed observer

output feedback stabilization of delay systems via generalization of the transformation method the left characteristic matrix equation l c m e of a delay system has been employed to develop a state feedback stabilization theory for delay systems analogously the right characteristic matrix equation r c m e has led to the development of an observer theory for this class of systems the characteristic matrix equation approach however only permits the relocation of integral multiples of n poles where n represents the system order this restriction is removed in this work through a generalization of the l c m e and r c m e in a manner which permits the stabilization of an arbitrary but finite number of unstable modes the resulting state feedback controller and state estimator permit the output feedback stabilization of the most general linear autonomous delay system under the minimal assumptions of spectral stabilizability and detectability

on the spectral controllability of delay differential equations a computable necessary and sufficient condition is proved for the spectral controllability of a class of linear hereditary systems and a counterexample is given to a previously published result

finite dimensional observers for delay systems a finite dimensional observer theory is formulated for a class of point delayed systems the observer is characterized by the fact that it directly generates a finite dimensional feedback controller for this class of systems the theory is based on a preliminary approximation theory which allows the delay system to be exponentially approximated by a system of ordinary differential equations

strongly pseudoconvex cr structures over small balls part ii a regularity theorem the purpose of the present paper is to prove the regularity theorem for the solution of the generalized neumann boundary value problem for a strongly pseudoconvex cr structure say t over a small ball this will be based on the a priori estimate established in i namely we take an admissible distance function t to a reference point cf 2 12 in i and consider a sufficiently small ball ur t r denote by d the differential operator in the complex associated with 0t and consider the metric given by a levi form set b dt which is a function of u we consider the hilbert space of l2 norm with weight factor b2a 11 11 a and a denoting its norm and inner product respectively let ad be the adjoint of d set qa u v du dv a ad u ad v a for 0t q forms u v the generalized neumann boundary value problem is to solve the following equation for a given 0t q form a and an unknown 0t q form u withuldt 0

on matrix fraction representations for linear systems over commutative rings this paper deals with the problem of existence of polynomial matrix fraction representations for transfer matrices of linear systems over rings as well as the related realization theory these representations are then used in establishing new results for various classes of systems including split systems the relevance of these results to the regulation of various nonclassical classes of linear systems for example delay differential systems two dimensional systems etc is also discussed

regulation of split linear systems over rings coefficient assignment and observers a theory of regulators is developed for finite free split linear systems over a commutative ring k this is achieved by developing a theory of coefficient assignment and observers it is shown that the problem of coefficient assignment can be solved for reachable systems by using dynamic state feedback for strongly observable systems it is shown that observers with arbitrary dynamics can be constructed internal stability of observer and state feedback configuration is considered explicitly some examples are given to illustrate these techniques

further study of spectral controllability of systems with multiple commensurate delays in state variables the paper presents a necessary and sufficient condition for spectral controllability of systems with multiple commensurate delays in state variables on the basis of finite laplace transforms