gravity interpretation using the mellin transform the mellin transform of the gravity effect of a buried sphere and two dimensional horizontal circular cylinder and the first horizontal derivative of the gravity effect of a two dimensional thin fault layer are derived the transformed functions are bounded by two asymptotes they are analyzed and procedures are formulated excluding the asymptotic regions for the extraction of the body parameters the application of the mellin transform is tested on simulated models as well as on two field examples 1 the humble dome gravity anomaly near houston usa and 2 the louga gravity anomaly usa

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 connection between normalized coprime factorizations and linear quadratic regulator theory given a transfer matrix described by a minimal state space triple a method is given for computing state space realizations for the numerator and denominator of a normalized stable right coprime factorization for the transfer matrix the method involves the solution of an algebraic riccati equation it allows the use of existing computational state space algorithms in finding normalized stable right coprime factorizations and avoids explicit calculations of spectral factors

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

formulas for hankel singular values and vectors for a class of input delay systems this paper gives explicit formulas for hankel singular values and vectors for a class of multiple input delay systems the class consists of systems whose gramian is reducible to an integral operator with semi separable kernel this structure is exploited in deriving a transcendental equation for singular values

robust controller design for delay systems in the gap metric a robust stabilization problem in the gap metric is discussed for a system with delays in control the authors derive a design procedure of robust controllers based on finite dimensional ricatti equations and it is shown that the resulting controller has a structure of observer based predictive action by employing completing the square argument a game theoretic interpretation is also provided on the trade off between the initial uncertainties and attenuating the disturbance caused by plant uncertainties

robust control with respect to coprime factors of infinite dimensional positive real systems it is shown that infinite dimensional positive real systems can be robustly stabilized with respect to coprime factor perturbations with a robustness margin of at least 1 square root 2 this result is applied to dissipative colocated systems which arise in pde models of flexible structures

closed form boundary state feedbacks for a class of 1 d partial integro differential equations in this paper a problem of boundary stabilization of a class of linear parabolic partial integro differential equations p i des in one dimension is considered using the method of backstepping avoiding spatial discretization required in previous efforts the problem is formulated as a design of an integral operator whose kernel is required to satisfy a hyperbolic p i de the kernel p i de is then converted into an equivalent integral equation and by applying the method of successive approximations the equation s well posedness and the kernel s smoothness are established it is shown how to extend this approach to design optimally stabilizing controllers an adaptation mechanism is developed to reduce the conservativeness of the inverse optimal controller and the performance bounds are derived for a broad range of physically motivated special cases feedback laws are constructed explicitly and the closed loop solutions are found in closed form a numerical scheme for the kernel p i de is proposed its numerical effort compares favorably with that associated with operator riccati equations

robust stabilization bibo stability distance notions and robustness optimization abstract this paper studies robust stabilization of both linear shift invariant causal systems in an lp setting and linear time invariant causal continuous time systems in an lp p 1 or setting two key technical results in the paper establish the existence of lp and lp stable normalized coprime factorizations for discrete time and continuous time systems respectively which have coprime factorizations as lp and lp stable operators several distance measures for systems are then introduced including the graph metric the function the gap between the graphs of the systems and the projection gap it is shown that these distance measures lead to the weakest convergence notions for systems for which closed loop stability is a robust property the function can be computed using the dahleh pearson theory for l1 l1 optimal control robustness optimization in a directed p function is shown to be closely related to robustness optimization for bibo stable normalized coprime factor perturbations this result connects the stability margin of dahleh for coprime factor perturbations to the function these considerations are further supported by a robustness result in terms of the projection gap

detection of multivariate cyclostationarity this paper derives an asymptotic generalized likelihood ratio test glrt and an asymptotic locally most powerful invariant test lmpit for two hypothesis testing problems 1 is a vector valued random process cyclostationary cs or is it wide sense stationary wss 2 is a vector valued random process cs or is it nonstationary our approach uses the relationship between a scalar valued cs time series and a vector valued wss time series for which the knowledge of the cycle period is required this relationship allows us to formulate the problem as a test for the covariance structure of the observations the covariance matrix of the observations has a block toeplitz structure for cs and wss processes by considering the asymptotic case where the covariance matrix becomes block circulant we are able to derive its maximum likelihood ml estimate and thus an asymptotic glrt moreover using wijsman s theorem we also obtain an asymptotic lmpit these detectors may be expressed in terms of the loeve spectrum the cyclic spectrum and the power spectral density establishing how to fuse the information in these spectra for an asymptotic glrt and lmpit this goes beyond the state of the art where it is common practice to build detectors of cyclostationarity from ad hoc functions of these spectra

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

spline approximation for retarded systems and the riccati equation the purpose of this paper is to introduce a new spline approximation scheme for retarded functional differential equations the special feature of this approximation scheme is that it preserves the product space structure of retarded systems and approximates the adjoint semigroup in a strong sense these facts guarantee the convergence of the solution operators for the differential riccati equation in a strong sense numerical findings indicate a significant improvement in the convergence behaviour over both the averaging and the previous spline approximation scheme

on a least squares approach to depth determination from gravity data discussion and reply in his paper gupta was able to transform the problem of depth estimation of buried structures into a problem of finding a solution of a nonlinear equation in the form of f z 0 gupta also indicated that such a numerical approach is found to be capable of determining optimum depths particularly from residual anomaly profiles even if small segments of the gravity profiles are observed no doubt this numerical approach has its point of view both in theory and practice over any other depth estimation techniques such as those defined by the half g max rule nettleton 1940 1942 telford et al 1976 however gupta s technique would be much more effective if applied not to residuals but to derivative anomalies particularly when the regional field has few extrema in it this is obviously due to the following

spectral factorization and lq optimal regulation for multivariable distributed systems a necessary and sufficient condition is proved for the existence of a bistable spectral factor with entries in the distributed proper stable transfer function algebra x1d49c in the context of distributed multivariable convolution systems with no delays a by product is the existence of a normalized coprime fraction of the transfer function of such a possibly unstable system with entries in the algebra of fractions over x1d49c we next study semigroup state space systems sgb with bounded sensing and control having a transfer function with entries in and consider its standard lq optimal regulation problem having an optimal state feedback operator k0 for a system sgb a formula is given relating any spectral factor of a transfer function coprime fraction power spectral density to k0 a by product is the description of any normalized coprime fraction of the transfer function in terms of k0 finally we describe an alternative way of finding the solution operator k0 of the lq problem using spectral factor

on the least squares residual anomaly determination this paper discusses an approach to determine the least squares optimum order of the regional surface which when subtracted from the bouguer gravity anomaly data minimizes distortion of the residual component of the field the least squares method was applied to theoretical composite gravity fields each consisting of a constant residual component sphere or vertical cylinder and a regional component of different order using successively increasing orders of polynomial regionals for residual determination the overall similarity between each two successive residual maps was determined by computing the correlation factor between the mapped variables similarity between residual maps of the lowest orders verified by good correlation may generally be considered a criterion for determining the optimum order of the regional surface and consequently the least distorted residual component the residual map of the lower order in this well correlated doublet is considered the most plausible one and may be used

dynamic stabilization of regular linear systems we consider a general class of infinite dimensional linear systems called regular linear systems for which convenient representations are known to exist both in time and in frequency domain for this class of systems we investigate the concepts of stabilizability and detectability in particular their invariance under feedback and their relationship to exponential stability we introduce two concepts of dynamic stabilization the first formulated as usual with the plant and the controller connected in feedback and the second with two feedback loops even for finite dimensional systems the second concept stabilization with an internal loop in the controller is more general we argue that the more general concept is the natural one and we derive sufficient conditions under which an observer based stabilizing controller with an internal loop can be constructed

observability of nontrivial small solutions for neutral systems abstract in this paper we introduce the concept of observability of nontrivial small solutions for neutral functional differential equations with a single point delay and prove a matrix type criterion

robust stabilization in the gap metric controller design for distributed plants the problem of robustness in the gap metric for infinite dimensional systems is considered the problem of computing the optimal controller and the optimal robustness radius for a class of systems whose normalized coprime factors have elements which are h sub infinity functions with continuous boundary values is studied the underlying hankel and related operators which are important in the gap optimization problem are studied and relations between their singular values and vectors are established a computational approach to the optimal robustness problem is developed for single input single output systems whose transfer function is an inner function in h sub infinity times a rational function the procedure is applied to a general first order delay system and a closed form formula is obtained for the optimal controller the frequency response plots of the compensated system for various values of time delay are examined

a new method for shape and depth determinations from gravity data we have developed a simple method to determine simultaneously the shape and depth of a buried structure from residualized gravity data using filters of successive window lengths the method is similar to euler deconvolution but it solves for shape and depth independently the method involves using a relationship between the shape factor and the depth to the source and a combination of windowed observations the relationship represents a parametric family of curves window curves for a fixed window length the depth is determined for each shape factor the computed depths are plotted against the shape factors representing a continuous monotonically increasing curve the solution for the shape and depth of the buried structure is read at the common intersection of the window curves this method can be applied to residuals as well as to the bouguer gravity data of a short or long profile length the method is applied to theoretical data with and without random errors and is tested on a known field example from the united states in all cases the shape and depth solutions obtained are in good agreement with the actual ones

robust controllers for uncertain linear multivariable systems abstract this paper is addressed to three distinct yet related topics in the design of controllers for imprecisely known linear multivariable systems in the first part it is supposed that the plant to be stabilized is subject to additive or multiplicative uncertainties and necessary and sufficient conditions are derived for the existence of a controller that stabilizes all plants within this band of uncertainty in the second part in contrast with the first part it is supposed that the number of unstable poles of the plant to be stabilized is not precisely known the type of plant uncertainty is the so called stable factor uncertainty and necessary and sufficient conditions are given for robust stabilization in the third part the model of uncertainty is a ball in the space of rational matrices metrized by the so called graph metric and sufficient conditions for robust stabilization are derived

ir uwb transmitted reference systems with partial channel knowledge a receiver design based on the statistical invariance principle this paper deals with detection algorithms for impulse radio ultrawideband transmitted reference systems for binary modulation schemes we propose a novel detector that operates on the partial autocorrelations of the received signal as computed over time intervals bins of size less than the symbol period assuming that the receiver has knowledge of the partial autocorrelations of the channel response over those bins we derive the minimum error probability detector mepd in doing so we exploit some invariance properties of the detection problem under consideration it turns out that the receiver adopting such a strategy is superior to a conventional tr system the more so the smaller the bin size is also we address the problem of estimating the partial autocorrelations of the channel response and propose a simple solution by exploiting a training sequence the impact of the estimation errors on the receiver performance is shown to be marginal

optimal robustness in the gap metric the application of the gap metric to robust stabilization of feedback systems is considered in particular a solution to the problem of robustness optimization in the gap metric is presented the problem of robust stabilization under simultaneous plant controller perturbations is addressed and the least amount of combined plant controller uncertainty measured by the gap metric that can cause instability of a nominally stable feedback system is determined included are a detailed summary of the main properties of the gap metric and the introduction of a dual metric called the t gap metric a key contribution of this study is to show that the problem of robustness optimization in the gap metric is equivalent to robustness optimization for normalized coprime factor perturbations this settles the question as to whether maximizing allowable coprime factor uncertainty corresponds to tolerating the largest ball of uncertainty in a well defined metric

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

robust stabilizability of normalized coprime factors the infinite dimensional case the problem of robustly stabilizing a linear system subject to h bounded perturbations in the numerator and the denominator of its normalized left coprime factorization is considered for a class of infinite dimensional systems this class has possible unbounded finite rank input and output operators which include many delay and distributed systems the optimal stability margin is expressed in terms of the solutions of the control and filter algebraic riccati equations

realisation and approximation of linear infinite dimensional systems with error bounds the class of linear infinite dimensional systems with finite dimensional inputs and outputs whose impulse response h satisfies h in l 1 cap l 2 0 infty mathbb c p times m and induces a nuclear hankel operator is said to be of nuclear type for this class of systems it is shown that balanced or output normal realisations always exist and their truncations converge to the original system in various topologies furthermore explicit l infty bounds on the transfer function errors l 1 and l 2 bounds on the impulse response errors and hilbert schmidt and nuclear bounds on the hankel operator errors are obtained these truncations also generate an approximating sequence to the optimal hankel norm approximations to the original system and various error bounds of these approximants are deduced

on the relationship between the glrt and umpi tests for the detection of signals with unknown parameters the generalized likelihood ratio test glrt is widely used in signal processing applications such as image processing wireless communications medical imaging classification and signal detection however the glrt does not have many known properties other than that it is invariant uniformly most powerful invariant umpi for problems that fit the linear model and asymptotically n spl rarr spl infin umpi in general since it is invariant it belongs to the class of tests for which the umpi test is optimal in this paper we consider a general class of detection problems in which unknown signal parameters imply a problem invariance that can be described analytically by orthogonal subgroups this invariance is natural for problems with unknown signal parameters and for example include those of the matched subspace detectors of scharf and friedlander we derive the glrt and umpi detectors for this general signal class for the case of gaussian noise an expression is found that relates the two test statistics showing the umpi statistic to be the sum of two terms one of which is the glrt using this we find that the glrt and umpi tests are asymptotically equivalent as signal to noise ratio snr approaches infinity or as probability of false alarm approaches zero these results are illustrated by extending an example given by nicolls and de jager to show the analytic relationship between the glrt and umpi tests the results indicate that the performance between the tests becomes close at signal to noise ratios snrs associated with operating points of the receiver operating curve that are typically of interest in signal detection applications

coprime factorization for regular linear systems mild sufficient conditions are given for the existence of a doubly coprime factorization of the transfer function of a regular linear system as well as formulae for such a factorization the results are illustrated by two examples of delay systems one of which has infinitely many unstable poles

robustly stabilizing controllers for dissipative infinite dimensional systems with collocated actuators and sensors we derive formulas for normalized doubly coprime factorizations over h for a class of nonexponentially stabilizable systems using these results we solve the problem of robust stabilization with respect to normalized coprime factor perturbations for a class of infinite dimensional systems s a b b d with finite rank inputs and outputs and dissipative operator a these systems are not exponentially stabilizable we give a parameterization of controllers that achieve a given robustness margin

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

gravity interpretation using correlation factors between successive least squares residual anomalies the correlation factors between successive least squares residual or regional gravity anomalies from a buried sphere a two dimensional 2 d horizontal cylinder and a vertical cylinder and the first horizontal derivative of the gravity from a 2 d thin faulted layer are computed correlation values are used to determine the depth to the center of the buried structure and the radius of the sphere or the cylinder and the thickness of the fault are estimated the method can be applied not only to residuals but also to the bouguer anomaly profile consisting of the combined effect of a residual component due to a purely local structure and a regional component represented by a polynomial of any order the method is easy to apply and may be automated if desired it can also be applied to the derivative anomalies of the gravity field the validity of the method is tested on two field examples from the united states and denmark

optimal invariant detection of a sinusoid with unknown parameters a uniformly most powerful test does not exist for the problem of detecting a sinusoid of unknown amplitude phase and frequency in complex white gaussian noise of unknown variance the problem is shown to be invariant to scale and modulation transformations using invariance principles it is found that the uniformly most powerful invariant umpi test does not exist a test is derived that is umpi if it is given that the signal to noise ratio snr is known for snr unknown the derived test can be used as an upper performance bound for any invariant test suboptimal tests are typically implemented such as the generalized likelihood ratio and locally most powerful tests which are also scale and modulation invariant it is shown analytically that as snr approaches zero the locally most powerful invariant test performance approaches the umpi performance bound and as the snr becomes large the generalized likelihood ratio test performance approaches the performance of the umpi bound computer simulation examples indicate that the generalized likelihood ratio test performance is close to the umpi bound particularly in the low probability of false alarm region of the receiver operating characteristic curve

locally most powerful invariant tests for correlation and sphericity of gaussian vectors in this paper we study the existence of locally most powerful invariant tests lmpit for the problem of testing the covariance structure of a set of gaussian random vectors the lmpit is the optimal test for the case of close hypotheses among those satisfying the invariances of the problem and in practical scenarios can provide better performance than the typically used generalized likelihood ratio test glrt the derivation of the lmpit usually requires one to find the maximal invariant statistic for the detection problem and then derive its distribution under both hypotheses which in general is a rather involved procedure as an alternative wijsman s theorem provides the ratio of the maximal invariant densities without even finding an explicit expression for the maximal invariant we first consider the problem of testing whether a set of n dimensional gaussian random vectors are uncorrelated or not and show that the lmpit is given by the frobenius norm of the sample coherence matrix second we study the case in which the vectors under the null hypothesis are uncorrelated and identically distributed that is the sphericity test for gaussian vectors for which we show that the lmpit is given by the frobenius norm of a normalized version of the sample covariance matrix finally some numerical examples illustrate the performance of the proposed tests which provide better results than their glrt counterparts

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

three least squares minimization approaches to depth shape and amplitude coefficient determination from gravity data three different least squares approaches are developed to determine successively the depth shape shape factor and amplitude coefficient related to the radius and density contrast of a buried structure from the residual gravity anomaly by defining the anomaly value g max at the origin on the profile the problem of depth determination is transformed into the problem of solving a nonlinear equation f z 0 formulas are derived for spheres and cylinders knowing the depth and applying the least squares method the shape factor and the amplitude coefficient are determined using two simple linear equations in this way the depth shape and amplitude coefficient are determined individually from all observed gravity data a procedure is developed for automated interpretation of gravity anomalies attributable to simple geometrical causative sources the method is applied to synthetic data with and without random errors in all the cases examined the maximum error in depth shape and amplitude coeffic

shape and depth solutions from gravity data using correlation factors between successive least squares residuals the gravity anomaly expression produced by most geologic structures can be represented by a continuous function in both shape shape factor and depth variables with an amplitude coefficient related to the mass correlation factors between successive least squares residual gravity anomalies from a buried vertical cylinder horizontal cylinder and sphere are used to determine the shape and depth of the buried geologic structure for each shape factor value the depth is determined automatically from the correlation value the computed depths are plotted against the shape factor representing a continuous correlation curve the solution for the shape and depth of the buried structure is read at the common intersection of correlation curves this method can be applied to a bouguer anomaly profile consisting of a residual component caused by local structure and a regional component this is a powerful technique for automatically separating the bouguer data into residual and regional polynomial components this method is tested on theoretical examples and a field example in both cases the results obtained are in good agreement with drilling results

robustly stabilizing controllers with respect to left coprime factor perturbations for infinite dimensional linear systems we solve the problem of robust stabilization with respect to left coprime factor perturbations for a large class of irrational transfer functions with a realization in terms of unbounded operators the key condition is that the associated dynamical system and its dual should satisfy a finite cost condition so that two optimal cost operators exist we obtain an explicit parameterization of infinitely many robustly stabilizing controllers in terms of these optimal cost operators and the generating operators of the realization

spectral properties of finite dimensional perturbed linear semigroups abstract many interesting cauchy problems arising in applications can be treated as finite dimensional perturbations of relatively simple problems in most applications these perturbations take place via boundary conditions it is the aim of this paper to investigate such cauchy problems and especially the spectral properties of the corresponding generators some general results are obtained that unify several well known results for functional differential equations and age dependent population dynamics applications to control problems as well as some nonlinear generalizations will appear in forthcoming papers

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

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

a least squares approach to depth determination from gravity data the present paper deals with a numerical approach to determine the depth of a buried structure from the residual anomaly the problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of the form f z 0 formulas have been derived for a sphere vertical and horizontal cylinders and for a vertical fault thin plate approximation the procedure is applied to synthetic data with and without random errors finally a field example is presented in which the depth to a fault is estimated at 3 8 km and verified from drilling results

backstepping observers for a class of parabolic pdes in this paper we design exponentially convergent observers for a class of parabolic partial integro differential equations p i des with only boundary sensing available the problem is posed as a problem of designing an invertible coordinate transformation of the observer error system into an exponentially stable target system observer gain output injection function is shown to satisfy a well posed hyperbolic pde that is closely related to the hyperbolic pde governing backstepping control gain for the state feedback problem for several physically relevant problems the observer gains are obtained in closed form the observer gains are then used for an output feedback design in both collocated and anti collocated setting of sensor and actuator the order of the resulting compensator can be substantially lowered without affecting stability explicit solutions of a closed loop system are found in particular cases

robust stabilization of normalized coprime factor plant descriptions with h sub infinity bounded uncertainty the problem of robustly stabilizing a family of linear systems is explicitly solved in the case where the family is characterized by h sub infinity bounded perturbations to the numerator and denominator of the normalized left coprime factorization of a nominal system this problem can be reduced to a nehari extension problem directly and gives an optimal stability margin all controllers satisfying a suboptimal stability margin are characterized and explicit state space formulas are given

linear state space systems in infinite dimensional space the role and characterization of joint stabilizability detectability several fundamental results from the theory of linear state space systems in finite dimensional space are extended to encompass a class of linear state space systems in infinite dimensional space the results treated are those pertaining to the relationship between input output and internal stability the problem of dynamic output feedback stabilization and the concept of joint stabilizability detectability a complete structural characterization of jointly stabilizable detectable systems is obtained the generalized theory applies to a large class of linear state space systems assuming only that i the evolution of the state is governed by a strongly continuous semigroup of bounded linear operators ii the state space is hilbert space iii the input and output spaces are finite dimensional and iv the sensing and control operators are bounded general conclusions regarding the fundamental structure of control theoretic problems in infinite dimensional space can be drawn from these results