capacity results on multiple input single output wireless optical channels this paper derives upper and lower bounds on the capacity of the multiple input single output free space optical intensity channel with signal independent additive gaussian noise subject to both an average intensity and a peak intensity constraint in the limit where the signal to noise ratio snr tends to infinity the asymptotic capacity is specified while in the limit where the snr tends to zero the exact slope of the capacity is given

on the capacity of free space optical intensity channels upper and lower bounds are derived on the capacity of the free space optical intensity channel this channel has a nonnegative input representing the transmitted optical intensity which is corrupted by additive white gaussian noise to preserve the battery and for safety reasons the input is constrained in both its average and its peak power for a fixed ratio of the allowed average power to the allowed peak power the difference between the upper and the lower bound tends to zero as the average power tends to infinity and their ratio tends to one as the average power tends to zero when only an average power constraint is imposed on the input the difference between the bounds tends to zero as the allowed average power tends to infinity and their ratio tends to a constant as the allowed average power tends to zero

maximal parabolic regularity for divergence operators including mixed boundary conditions abstract we show that elliptic second order operators a of divergence type fulfill maximal parabolic regularity on distribution spaces even if the underlying domain is highly non smooth the coefficients of a are discontinuous and a is complemented with mixed boundary conditions applications to quasilinear parabolic equations with non smooth data are presented

the golden code a 2 spl times 2 full rate space time code with nonvanishing determinants in this paper the golden code for a 2 spl times 2 multiple input multiple output mimo system is presented this is a full rate 2 spl times 2 linear dispersion algebraic space time code with unprecedented performance based on the golden number 1 spl radic 5 2

quadratic extension field codes for free space optical intensity communications in this paper we propose a space time code construction with a symbol rate of two for free space optical multiple input multiple output fso mimo communication systems unlike the radio frequency space time coding design that deals with complex symbols holding phase and magnitude information the phase detection in wireless optical communications remains very challenging this restricts optical mimo codes to carry positive magnitude information belonging to a finite range to meet these requirements we propose to design the fso mimo codes considering first the whole real space mathbb r followed by a bipolar to unipolar conversion to fit in the intensity margin we consider the mimo configurations with two or four transmitters lasers we base our shape preserving construction on quadratic extension fields that linearly combine the real symbols to form a full diversity space time code with a symbol rate equal to two for each configuration we show how to optimize the choice of the algebraic field numbers to jointly optimize the non vanishing code determinant and the bipolar to unipolar attenuation factor

a necessary and sufficient condition for the stability of nonnegative interval discrete systems the stability of nonnegative discrete systems with interval uncertainty is discussed for this class of system a necessary and sufficient condition for the stability is provided when all elements of the system matrix are assumed to be specified by intervals an illustrative example is used as a guideline to demonstrate the effectiveness of the result simple computational tests are suggested and their usefulness in this framework is discussed the possible extension of this result to more general classes of systems is addressed

a new fast algorithm for robust stability analysis of linear control systems with linearly dependent parametric uncertainties abstract in this paper a fast algorithm is proposed for the computation of stability margins in parameter space for linear control systems subject to structured uncertainties the case in which plant transfer function coefficients are affine in a set of physical uncertain parameters is considered the paper shows also how the proposed algorithm can be used to solve another interesting problem in robust control analysis i e the determination of the region of pole location of a closed loop control system including an entire family of uncertain plants

numerical identification of a robin coefficient in parabolic problems this paper studies a regularization approach for an inverse problem of estimating a spatially and temporally dependent robin coefficient arising in the analysis of convective heat transfer the parameter to state map is analyzed especially a differentiability result is established a regularization approach is proposed and the properties e g existence and optimality system of the functional are investigated a finite element method is adopted for discretizing the continuous optimization problem and the convergence of the finite element approximations as the mesh size and temporal step size tend to zero is established numerical results by the conjugate gradient method for oneand two dimensional problems are presented

robust control with structure perturbations the problem of making a given stabilizing controller robust so that the closed loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant the problem is treated in the state space and transfer function domains in the state space domain a stability hypersphere is determined in the parameter space using lyapunov theory the radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere in the transfer function domain a corresponding stability margin is defined and optimized on the basis of the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed loop characteristic polynomial the design algorithms are illustrated by examples

conditions on the boundary of the zero set and application to stabilization of systems with uncertainty abstract we describe an analytic method for finding the location of the zero set of a vector valued function which depends on m real variables and n complex parameters we apply the method to robust stabilization of multivariable linear feedback systems we find exact measures of the extent of permissible perturbations in the plant and or the compensator that maintain feedback stability

free space optical communication with nonzero boresight pointing errors the performance of free space optical fso communication systems is compromised by atmospheric fading and pointing errors the pointing errors are widely considered as a combination of two components boresight and jitter a statistical model is investigated for pointing errors with nonzero boresight by taking into account the laser beamwidth detector aperture size and jitter variance a novel closed form probability density function pdf is derived for this new nonzero boresight pointing error model furthermore we obtain closed form pdf for the composite lognormal turbulence channels and finite series approximate pdf for the composite gamma gamma turbulence channels which is suitable for terrestrial fso applications impaired by building sway we conduct error rate analysis of on off keying signaling with intensity modulation and direct detection over the lognormal and gamma gamma fading channels asymptotic error rate analysis and outage probability of such a system are also presented based on the derived composite pdfs it is shown that the boresight can only affect the coding gain while the diversity order is determined by the atmospheric fading effect as well as the pointing error effect

capacity achieving probability measure for conditionally gaussian channels with bounded inputs a conditionally gaussian channel is a vector channel in which the channel output given the channel input has a gaussian distribution with well behaved input dependent mean and covariance we study the capacity achieving probability measure for conditionally gaussian channels subject to bounded input constraints and average cost constraints many practical communication systems including additive gaussian noise channels certain optical channels fading channels and interference channels fall within this framework subject to bounded input constraint and average cost constraints we show that the channel capacity is achievable and we derive a necessary and sufficient condition for a probability measure to be capacity achieving under certain conditions the capacity achieving measure is proved to be discrete

on maximal parabolic regularity for non autonomous parabolic operators abstract we consider linear inhomogeneous non autonomous parabolic problems associated to sesquilinear forms with discontinuous dependence of time we show that for these problems the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 2 this allows us to prove maximal parabolic l r regularity for discontinuous non autonomous second order divergence form operators in very general geometric settings and to prove existence results for related quasilinear equations

a quasi orthogonal space time block code it has been shown that a complex orthogonal design that provides full diversity and full transmission rate for a space time block code is not possible for more than two antennas previous attempts have been concentrated in generalizing orthogonal designs which provide space time block codes with full diversity and a high transmission rate we design rate one codes which are quasi orthogonal and provide partial diversity the decoder of the proposed codes works with pairs of transmitted symbols instead of single symbols

gradient based estimation of manning s friction coefficient from noisy data we study the numerical recovery of manning s roughness coefficient for the diffusive wave approximation of the shallow water equation we describe a conjugate gradient method for the numerical inversion numerical results for one dimensional models are presented to illustrate the feasibility of the approach also we provide a proof of the differentiability of the weak form with respect to the coefficient as well as the continuity and boundedness of the linearized operator under reasonable assumptions using the maximal parabolic regularity theory

a dual result to kharitonov s theorem a dual problem to kharitonov s problem involving a diamond instead of a rectangle is considered the results show that a family of polynomials with coefficients varying in the diamond is strictly hurwitz if and only if eight one dimensional exposed edges of the diamond are strictly hurwitz

a note on robust pole placement pole placement algorithm in single input single output siso systems is discussed with respect to the corresponding real stability radius of the resulting closed loop polynomial

perfect space time codes for any number of antennas in a recent paper perfect n times n space time codes were introduced as the class of linear dispersion space time st codes having full rate nonvanishing determinant a signal constellation isomorphic to either the rectangular or hexagonal lattices in 2n 2 dimensions and uniform average transmitted energy per antenna consequence of these conditions include optimality of perfect codes with respect to the zheng tse diversity multiplexing gain tradeoff dmt as well as excellent low signal to noise ratio snr performance yet perfect space time codes have been constructed only for two three four and six transmit antennas in this paper we construct perfect codes for all channel dimensions present some additional attributes of this class of st codes and extend the notion of a perfect code to the rectangular case

simple robust stability tests for polynomials with real parameter uncertainty in this paper we consider several problems related to the robust stability of polynomials whose coefficients depend on real parameters we first show that if these parameters appear linearly in the coefficients the computation of the largest stability hypercube with a fixed centre does not require a frequency sweep its size can be determined by considering a finite set of frequencies we also demonstrate that for some polynomials where the coefficients themselves are polynomials in the parameters the determination of stability can be made in a manner that involves a single frequency sweep and where at each frequency a finite number of simple tests are carried out the methods are based on the nyquist theorem and value set ideas and the approach provides analytical solutions

approximately universal codes over slow fading channels performance of reliable communication over a coherent slow fading multiple input multiple output mimo channel at high signal to noise ratio snr is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains this paper studies the problem of designing codes that optimally tradeoff the diversity and multiplexing gains the main contribution is a precise characterization of codes that are universally tradeoff optimal i e they optimally tradeoff the diversity and multiplexing gains for every statistical characterization of the fading channel this characterization is referred to as approximate universality the approximation is in the connection between error probability and outage capacity with diversity and multiplexing gains respectively the characterization of approximate universality is then used to construct new coding schemes as well as to show optimality of several schemes proposed in the space time coding literature

robustness measures for linear systems with application to stability radii of hurwitz and schur polynomials in this paper we consider robustness measures stability radii for system matrices which are subjected to structured real and complex perturbations of the form a a bdc where b c are given matrices our object is twofold a to present a number of new results mainly concerning the real stability radius and its differences from the complex one b to give an overview of our approach to the robustness analysis of linear state space systems including basic properties and characterizations of the complex stability radius applying the results to the special case where a is in companion form and b 0 0 0 1 t we are able to determine stability radii for hurwitz and schur polynomials under arbitrary complex and real affine perturbations of the coefficient vector computable formulae are obtained and illustrated by several examples

maximal polytopic stability domains in parameter space for uncertain systems abstract some results on the stability and pole location of families of uncertain systems with characteristic polynomial coefficients affected by structured perturbations are presented the case in which the coefficients are affine in a set of system physical parameters is considered assuming that the parameters are subject to polytopic perturbations of a given structure for these cases which often arise in system stability robustness analysis as for example in the robustification of controllers for multivariable closed loop systems a procedure is given to estimate maximal stability polytopic regions in the space of parameters this result is also used to derive simple necessary and sufficient conditions for the discrete time stability of convex combinations of two polynomials

closest point search in lattices in this semitutorial paper a comprehensive survey of closest point search methods for lattices without a regular structure is presented the existing search strategies are described in a unified framework and differences between them are elucidated an efficient closest point search algorithm based on the schnorr euchner 1995 variation of the pohst 1981 method is implemented given an arbitrary point x spl isin spl ropf sup m and a generator matrix for a lattice spl lambda the algorithm computes the point of spl lambda that is closest to x the algorithm is shown to be substantially faster than other known methods by means of a theoretical comparison with the kannan 1983 1987 algorithm and an experimental comparison with the pohst 1981 algorithm and its variants such as the viterbo boutros see ibid vol 45 p 1639 42 1999 decoder modifications of the algorithm are developed to solve a number of related search problems for lattices such as finding a shortest vector determining the kissing number computing the voronoi 1908 relevant vectors and finding a korkine zolotareff 1873 reduced basis

on space time coding with pulse position and amplitude modulations for time hopping ultra wideband systems in this work we propose novel families of space time st block codes that can be associated with impulse radio ultra wideband ir uwb communication systems the carrier less nature of this nonconventional totally real transmission technique necessitates the construction of new suitable coding schemes in fact the last generation of complex valued st codes namely the perfect codes cannot be associated with ir uwb systems where the phase reconstitution at the receiver side is practically infeasible on the other hand while the perfect codes were considered mainly with quadrature amplitude modulation qam and hexagonal hex constellations ir uwb systems are often associated with pulse position modulation ppm and hybrid ppm pam pulse amplitude modulation constellations in this paper instead of adopting the classical approach of constructing st codes over infinite fields or for the perfect codes we study the possibility of constructing modulation specific codes that are exclusive to ppm and ppm pam the proposed full rate codes are totally real information lossless and have a uniform average energy per transmit antenna they permit to achieve a full diversity order with any number of transmit antennas in some situations the proposed schemes have an optimal nonvanishing coding gain and satisfy all the construction constraints of the perfect codes in addition to the constraint of being totally real simulations performed over realistic indoor uwb channels showed that the proposed schemes outperform the best known codes constructed from cyclic division algebras

stabilization of linear systems with fixed order controllers abstract this paper deals with the problem of stabilizing a linear time invariant plant with a feedback compensator of fixed dynamic order this is an important unsolved problem in control theory because existing solutions to the regulator problem can only generate controllers that are of high enough order that arbitrary pole placement becomes possible in general the dynamic order of controllers can be much lower if only stabilization is desired in the transfer function domain a new necessary condition for stabilizability by a fixed order controller is derived this result which can be used sequentially to derive a lower bound on the order of a stabilizing controller is based on a classical result 1873 of linear programming known as gordan s theorem of the alternative the stabilization algorithm successively selects hurwitz vectors to make the largest stability hypersphere intersect a linear subspace determined by the plant parameters and the order of the controller occurrence of such an intersection is a sufficient condition for stabilizability and the intersection also determines a stabilizing compensator the algorithm is illustrated by practical examples which demonstrate that a large reduction in controller order is achievable by this method

a geometric approach to stabilization by output feedback in this paper we present a geometric approach to the stabilizability of linear systems by output feedback the geometric approach is completely analysed for both discrete time and continuous time single input single output systems two examples are worked out in detail to illustrate the theoretical development we also show how our approach can be extended to dyadic systems the simplicity of the geometric approach in the special case when the number of inputs or outputs is one less than the order of the system is illustrated with the help of examples present address bell laboratories south plainfield new jersey 07080 u s a

invariance of the strict hurwitz property for polynomials with perturbed coefficients given a strictly hurwitz polynomial f lambda lambda n a n 1 lambda n 1 a n 2 lambda n 2 a 1 lambda a 0 it is of interest to know how much the coefficients a i can be perturbed while simultaneously preserving the strict hurwitz property for systems with n leq 4 maximal intervals of the a i are given in a recent paper by guiver and bose 1 in this note a theorem of kharitonov is exploited to obtain a general result for polynomials of any degree

robustness of pole location in perturbed systems abstract in this paper we present some results on robustness of location of roots of polynomials in given regions of the complex plane for unknown but bounded perturbations on the polynomial coefficients a geometric approach in coefficient space is exploited to derive maximal deviations in a given class of admissible perturbations of characteristic polynomial coefficients of an uncertain linear system from their nominal values preserving system poles in a given region of the complex plane it is also shown that the solution of this problem can be used to give computationally feasible necessary and sufficient conditions such that all the roots of the members of a family of polynomials lie in a given open region of the complex plane this last result can be considered an extension of the result of the well known theorem of kharitonov it is also outlined how the proposed technique can be used to deal with families of polynomials with linearly correlated coefficient perturbations

sensitivities of stability constraints and their applications let the real polynomial a s a 0 a 1 s a n s n with the coefficients being known differentiable functions a k x be given and let the constraints g i x 0 determine the strictly hurwitz property of the polynomial a s a simple and efficient method to calculate the derivatives partial g i x partial x j is proposed then the application of the method to the problem of stability of polynomials under coefficient perturbation by gradient optimization is discussed also a theorem characterizing the stability region and the newly introduced regions of nondestabilizing perturbations is given

state space measures of robustness of pole locations for structured and unstructured perturbations abstract measures of pole location robustness for linear feedback systems are derived from a state space model of the system the robustness tests ensure that the eigenvalues of the perturbed systems matrix a e remain in a desired region d of the complex plane containing the eigenvalues of the nominal system matrix a the region d may be any open set of the complex plane whatsoever the results are expressed in terms of induced matrix norms and apply to structured perturbations of the form e b c where b and c define the structure of e and may be nonsquare matrices rank one perturbations e of minimal norm and with the given structure that will cause a e to have an eigenvalue outside of d are constructed for the cases when the matrix norm is induced by the vector 1 norm or the vector norm the advantages of having robustness measures for several matrix norms that can be computed are illustrated with a simple example that demonstrates how the conservatism of single tests can be reduced using several tests i e several matrix norms a method for computing numerically the robustness measures for particular norms is presented it can be used to compute with a guaranteed degree of accuracy the maximum of the norm of the frequency response of a system

the robustness properties of univariate and multivariate reciprocal polynomials the author investigates the robustness properties of univariate and multivariate reciprocal polynomials that are nonzero on the unit circle and the unit polycircle respectively he shows that any polytope of univariate reciprocal polynomials are nonzero on the unit circle if and only if a set of real valued rationals corresponding to its vertices are entirely either positive or negative on the unit circle ensuring that these vertex rationals are entirely either positive or negative on the unit circle can be carried out by the tests described by lakshmanan 1992 when these existing tests are combined with the results contained in this paper it provides a complete procedure for testing the nonzeroness of polytopes of univariate reciprocal polynomials over the unit circle he shows that this result generalizes to the case of multivariate polynomials for any polytope of multivariate polynomials to be nonzero on the unit polycircle it is necessary and sufficient that a set of real valued multivariate rationals corresponding to its vertices are entirely either positive or negative on the unit polycircle again by using the test the positivity or the negativity of the vertex rationals can be ensured as well thereby resulting in a complete procedure for testing the nonzeroness of an entire polytope of multivariate reciprocal polynomials over the unit polycircle although he develops the results for polytopic families he then extends those results to the case of non polytopic reciprocal polynomial families

aw1 p estimate for solutions to mixed boundary value problems for second order elliptic differential equations on demontre que sous des hypotheses plutot faibles une solution d un probleme aux valeurs limites mixte pour une equation elliptique d ordre 2 est dans l espace de sobolev w 1 p pour p 2

optimal control for the thermistor problem this paper is concerned with the state constrained optimal control of the two dimensional thermistor problem a quasi linear coupled system of a parabolic and elliptic pde with mixed boundary conditions this system models the heating of a conducting material by means of direct current existence uniqueness and continuity for the state system are derived by employing maximal elliptic and parabolic regularity by similar arguments the linearized state system is discussed while the adjoint system involving measures is investigated using a duality argument these results allow us to derive first order necessary conditions for the optimal control problem

complete characterization of the spherical spectral set the problem of computing the spectral set of any given spherical family of polynomials is considered an algorithm based on the decomposition of the spectral set in three disjoint subsets with relate points having the same dimension of the back image in the parameter space is devised moreover the structure of the polynomial function which characterizes the main subset is analyzed such an analysis leads to significant simplifications for boundary generation and bounds computation of the spectral set

perfect space time block codes in this paper we introduce the notion of perfect space time block codes stbcs these codes have full rate full diversity nonvanishing constant minimum determinant for increasing spectral efficiency uniform average transmitted energy per antenna and good shaping we present algebraic constructions of perfect stbcs for 2 3 4 and 6 antennas

explicit space time codes achieving the diversity multiplexing gain tradeoff a recent result of zheng and tse states that over a quasi static channel there exists a fundamental tradeoff referred to as the diversity multiplexing gain d mg tradeoff between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space time st code this tradeoff is precisely known in the case of independent and identically distributed i i d rayleigh fading for tgesnt nr 1 where t is the number of time slots over which coding takes place and nt nr are the number of transmit and receive antennas respectively for t nt case we present two general techniques for building d mg optimal rectangular st codes from their square counterparts a byproduct of our results establishes that the d mg tradeoff for all tgesnt is the same as that previously known to hold for tgesnt n r 1

an algorithm for the computation of the structured complex stability radius abstract perturbed state space models of the form x a bdc x are considered where a b c are given matrices a is stable and d is an unknown complex perturbation matrix a reliable and efficient algorithm for the computation of the norm of the minimal norm destabilizing matrix d is presented the performance of the algorithm and possible applications are illustrated

one extending hypersphere method to handle dominant pole assignment it is pointed out that the stability hypersphere approach presented by c b soh et al see ibid vol ac 32 p 239 244 mar 1987 can be extended to handle the case where the region is not simply connected the extension is useful in application such as dominant pole assignment and filter design where the separation of zeros is required

on the stability properties of polynomials with perturbed coefficients given a polynomial p c s s n t 1 s n 1 t n 0 which is hurwitz or p d z z n t 1 z n 1 t n 0 which has zeros only within or on the unit circle it is of interest to know how much the coefficients t j can be perturbed while preserving the stability properties in this note a method is presented for obtaining the largest hypersphere centered at t t t 1 t n containing only polynomials which are stable

a universal lattice code decoder for fading channels we present a maximum likelihood decoding algorithm for an arbitrary lattice code when used over an independent fading channel with perfect channel state information at the receiver the decoder is based on a bounded distance search among the lattice points falling inside a sphere centered at the received point by judicious choice of the decoding radius we show that this decoder can be practically used to decode lattice codes of dimension up to 32 in a fading environment

pole assignment with robust stability this paper uses convex analysis for the pole assignment design of discrete time siso systems incorporating robust stability against norm bounded parametric perturbations in the plant transfer function the method involves designing an overparameterized pole assignment controller for the nominal plant with the overparameterization chosen to reduce the size of changes in the closed loop characteristic equation which result from plant perturbations sufficiency bounds on the l sub p norm of the perturbation guaranteeing stability are obtained