conservative arrays multidimensional modulation codes for holographic recording in holographic storage two dimensional arrays of binary data is optically recorded in a medium via an interference process to ensure optimum operation of a holographic recording system it is desirable that the patterns of 1s light and 0s no light in the recorded array satisfy the following modulation constraint in each row and column of the array there are at least t transitions of the type 1 spl rarr 0 or 0 spl rarr 1 for a prescribed integer t a two dimensional array with this property is said to be a conservative array of strength t in general an n dimensional conservative array of strength t is a binary array having at least t transitions in each column extending in any of the n dimensions of the array we present an algorithm for encoding unconstrained binary data into an n dimensional conservative array of strength t the algorithm employs differential coding and error correcting codes using n binary codes one per dimension with minimum hamming distance d spl ges 2t 3 we apply a certain transformation to an arbitrary information array which ensures that the number of transitions in each dimension is determined by the minimum distance of the corresponding code

a linear programming oriented procedure for quadratic stabilization of uncertain systems abstract this paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty a constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain some experiments are presented

the positive capacity region of two dimensional run length constrained channels a binary sequence satisfies a one dimensional d k constraint if every run of zeros with possible exception of the first and the last runs has length at least d and at most k a binary two dimensional array satisfies a d k constraint if each row and each column satisfies the one dimensional d k constraint few models have been proposed in the literature to handle two dimensional data the diamond model the square model the hexagonal model and the triangular model the constraints in the different directions might be asymmetric and hence many kind of constraints are defined depending on the number of directions in the model for example a two dimensional array in the diamond model satisfies a d1 k1 d2 k 2 constraint if it satisfies the one dimensional d1 k1 constraint horizontally and the one dimensional d 2 k2 constraint vertically in this correspondence the region in which the capacity is zero or positive in the various models is examined asymmetric constraints in the diamond model and symmetric constraints in the other models are considered in particular an almost complete solution for asymmetric constraints in the diamond model is provided

two dimensional runlength constrained arrays with equal horizontal and vertical constraints a binary array is a d1 k1 d2 k 2 runlength constrained array if the runs of zeros in every row and column have length at least d1 and at most k1 and the runs of ones in every row and column have length at least d2 and at most k2 such arrays arise in the context of digital storage devices writing n m n d1 k1 d2 k2 for the number of d1 k 1 d2 k2 runlength constrained arrays of size mtimesn the capacity c d1 k1 d2 k2 is defined to be limm nrarrinfin 1 mn log2n m n d1 k 1 d2 k2 let d2 be an integer such that d2 ges 1 the paper shows that c 1 d2 delta d2 d2 is positive when delta ges 2 but is zero when delta les 1

partial characterization of the positive capacity region of two dimensional asymmetric run length constrained channels a binary sequence satisfies a one dimensional d k run length constraint if every run of zeros has length at least d and at most k a two dimensional binary pattern is d sub 1 k sub 1 d sub 2 k sub 2 constrained if it satisfies the one dimensional d sub 1 k sub 1 run length constraint horizontally and the one dimensional d sub 2 k sub 2 run length constraint vertically for given d sub 1 k sub 1 d sub 2 and k sub 2 the asymmetric two dimensional capacity is defined as c sub d1 k1 d2 k2 lim sub m n spl rarr spl infin 1 mn log sub 2 n sub m n sup d1 k1 d2 k2 where n sub m n sup d1 k1 d2 k2 denotes the number of d sub 1 k sub 1 d sub 2 k sub 2 constrained m spl times n binary patterns we determine whether the capacity is positive or is zero for many choices of d sub 1 k sub 1 d sub 2 k sub 2

h _ infty filtering for discrete time state delayed systems with finite frequency specifications this article researches the problem of finite frequency ff h filtering for linear discrete time state delayed systems the disturbance is assumed to reside in low middle high frequency ranges to reduce the conservatism of the results delay partitioning idea is used to derive a new ff bounded real lemma brl by applying the generalized kalman yakubovich popov lemma two equivalent approaches to the proof of the proposed ff brl are given respectively starting from transfer function and lyapunov krasovskii functional a new ff h filter design method is proposed in terms of solving a set of linear matrix inequalities finally a numerical example clearly demonstrates the merits and effectiveness of the proposed method

multiobjective output feedback control via lmi optimization this paper presents an overview of a linear matrix inequality lmi approach to the multiobjective synthesis of linear output feedback controllers the design objectives can be a mix of h sub spl infin performance h sub 2 performance passivity asymptotic disturbance rejection time domain constraints and constraints on the closed loop pole location in addition these objectives can be specified on different channels of the closed loop system when all objectives are formulated in terms of a common lyapunov function controller design amounts to solving a system of linear matrix inequalities the validity of this approach is illustrated by a realistic design example

entropy bounds for constrained two dimensional random fields the maximum entropy and thereby the capacity of two dimensional 2 d fields given by certain constraints on configurations is considered upper and lower bounds are derived a new class of 2 d processes yielding good lower bounds is introduced asymptotically the process achieves capacity for constraints with limited long range effects the processes are general and may also be applied to e g data compression of digital images results are given for the binary hard square model which is a 2 d run length limited model and some other 2 d models with simple constraints

on the kalman yakubovich popov lemma the purpose of this note is to present a new elementary proof for the multivariable k y p lemma a minimum of linear algebra and finite dimensional convexity theory is used

passivity analysis and passification for uncertain signal processing systems the problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers decision feedback equalizers and digital and analog filters equally important is the problem of passification where a compensator needs to be designed for a given system to become passive this paper considers these two problems for a large class of systems that involve uncertain parameters time delays quantization errors and unmodeled high order dynamics by characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints iqcs we present solutions to the problems of robust passivity analysis and robust passification more specifically for the analysis problem we determine if a given uncertain system is passive for all admissible uncertainty satisfying the iqcs similarly for the problem of robust passification we are concerned with finding a loop transformation such that a particular part of the uncertain signal processing system becomes passive for all admissible uncertainty the solutions are given in terms of the feasibility of one or more linear matrix inequalities lmis which can be solved efficiently

brief paper robust finite frequency h filtering for uncertain 2 d roesser systems this paper investigates the problem of robust finite frequency ff h filtering for two dimensional 2 d roesser models with polytopic uncertainties our attention is focused on designing filters guaranteeing the robustly asymptotic stability and ff h disturbance attenuation level of the filtering error system by the parameter dependent idea and the generalized kalman yakubovich popov lemma for 2 d roesser models the existence conditions of robust ff h filters are obtained in terms of solving an optimization problem which is more general than the existing results an example is given to validate the proposed methods the contribution of the paper is twofold 1 systematic methods are proposed for designing ff h filters for roesser models 2 an improved strategy has been presented to deal with the robust h filter design for roesser models

on the capacity of two dimensional run length constrained channels two dimensional binary patterns that satisfy one dimensional d k run length constraints both horizontally and vertically are considered for a given d and k the capacity c sub d k is defined as c sub d k lim sub m n spl rarr spl infin log sub 2 n sub m n sup d k mn where n sub m n sup d k denotes the number of m spl times n rectangular patterns that satisfy the two dimensional d k run length constraint bounds on c sub d k are given and it is proven for every d spl ges 1 and every k d that c sub d k 0 if and only if k d 1 encoding algorithms are also discussed

fluctuations in coagulating systems ii in this paper we consider coagulation processes in large but finite systems and study the time dependent behavior of the nonequilibrium fluctuations in the cluster size distribution for this purpose we apply van kampen s expansion to a master equation describing coagulation processes and derive an approximate fokker planck equation for the probability distribution of the fluctuations first we consider two exactly soluble models corresponding to the choicesk i j i jandk i j 1 for the rate constants in the fokker planck equation for these models and monodisperse initial conditions we calculate the probability distribution of the fluctuations and the equal time and two time correlation functions for general initial conditions we study the behavior of the fluctuations at large cluster sizes and in the scaling limit next we consider in general homogeneous rate constants with the propertyk i j a k ai aj for alla 0 and we give asymptotic expressions for the equal time correlation functions at large cluster sizes and in the scaling limit in the scaling limit we find that the fluctuations show relatively simple scaling behavior for all homogeneous rate constantsk i j

generalized kalman yakubovich popov lemma for 2 d fm lss model this paper is concerned with the generalized kalman yakubovich popov kyp lemma for 2 d fornasini marchesini local state space fm lss systems by carefully analyzing the feature of the states in 2 d fm lss models a linear matrix inequality lmi characterization for a rectangular finite frequency region is constructed and then by combining this characterization with s procedure a generalized kyp lemma is proposed for 2 d fm lss models as applications of the developed kyp lemma new conditions are further derived for designing controllers guaranteeing finite frequency positive realness of the closed loop systems where both state feedback and dynamic output feedback control laws are considered finally two illustrative examples clearly show the effectiveness of the proposed results the main contribution of the paper is trifold 1 a novel characterization for a finite frequency region has been developed 2 a generalized kyp lemma has been proposed including the existing bounded realness and positive realness results as special cases and 3 systematic methods for finite frequency positive real control of 2 d systems have been presented

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

brief paper a generalized kyp lemma based approach for disturbance rejection in data storage systems this paper is concerned with disturbance rejection for data storage systems which applies microactuator to expand its servo bandwidth an approach based on the generalized kalman yakubovic popov kyp lemma together with the youla parameterization is proposed which allows us to suppress disturbances of particular frequencies within or beyond the servo bandwidth via convex optimization the rejection of narrowband high frequency disturbances is achieved by using this approach simulation together with implementation results demonstrate the simplicity and effectiveness of the design method as compared with the traditional frequency weighting method

bounds on the capacity of constrained two dimensional codes bounds on the capacity of constrained two dimensional 2 d codes are presented the bounds of calkin and wilf see siam j discr math vol 11 no 1 p 54 60 1998 apply to first order symmetric constraints the bounds are generalized in a weaker form to higher order and nonsymmetric constraints results are given for constraints specified by run length limits or a minimum distance between pixels of a given value

positive real control for 2 d discrete delayed systems via output feedback controllers this paper considers the problem of positive real control for two dimensional 2 d discrete delayed systems in the fornasini marchesini second local state space model attention is focused on the design of dynamic output feedback controllers which guarantee that the closed loop system is asymptotically stable and the closed loop transfer function is extended strictly positive real we first present a sufficient condition for extended strictly positive realness of 2 d discrete delayed systems based on this a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality lmi when the lmi is feasible an explicit parametrization of a desired output feedback controller is presented finally we provide a numerical example to demonstrate the application of the proposed method

shannon capacity of m ary redundant multitrack runlength limited codes we consider multiamplitude multitrack runlength limited d k constrained channels with and without clock redundancy we calculate the shannon capacities of these channels and present some simple 100 efficient codes to compute capacity a constraint graph equivalent to the usual runlength limited constraint graph is used the introduced graph model has the vertex labeling independent of number of tracks to be written on in parallel which provides computational savings when the number of tracks is large we show that increasing the number of tracks written on in parallel provides significant increase of per track capacity for the more restrictive clocking constraint case i e when k d but it does not have much influence on the channel capacity when k spl ges d

capacity bounds for the three dimensional 0 1 run length limited channel the capacity c sub 0 1 sup 8 of a three dimensional 0 1 run length constrained channel is shown to satisfy 0 522501741838 spl les c sub 0 1 sup 8 spl les 0 526880847825

generalized kyp lemma unified frequency domain inequalities with design applications the celebrated kalman yakubovic spl caron popov kyp lemma establishes the equivalence between a frequency domain inequality fdi and a linear matrix inequality and has played one of the most fundamental roles in systems and control theory this paper first develops a necessary and sufficient condition for an s procedure to be lossless and uses the result to generalize the kyp lemma in two aspects the frequency range and the class of systems and to unify various existing versions by a single theorem in particular our result covers fdis in finite frequency intervals for both continuous discrete time settings as opposed to the standard infinite frequency range the class of systems for which fdis are considered is no longer constrained to be proper and nonproper transfer functions including polynomials can also be treated we study implications of this generalization and develop a proper interface between the basic result and various engineering applications specifically it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain phase properties in several frequency ranges the method is illustrated by numerical design examples of digital filters and proportional integral derivative controllers

brief paper h filtering for 2d markovian jump systems this paper is concerned with the problem of h filtering for 2d discrete markovian jump systems the mathematical model of 2d jump systems is established upon the well known roesser model our attention is focused on the design of a full order filter which guarantees the filtering error system to be mean square asymptotically stable and has a prescribed h disturbance attenuation performance sufficient conditions for the existence of a desired filter are established in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently solved by using commercially available numerical software a numerical example is provided to illustrate the effectiveness of the proposed design method

writing sequences on the plane the problem of arranging two dimensional arrays of data into one dimensional sequences comes up in image processing color quantization and optical and magnetic data recording a good arrangement should enable the one dimensional sequences to be modeled as markov chains or shifts of finite type since this is not possible in general two dimensional data is most commonly scanned by rows columns or diagonals we look into three unusual ways to write a sequence in the plane by penrose tilings by space filling curves and by cylindrical and spiral lattices we show how penrose tilings can be used to record information and how some spiral lattices can be used for quantization of color spaces