reduced order generalized h_ infty filtering for linear discrete time systems with application to channel equalization this paper investigates the problem of reduced order generalized h infty filtering for linear discrete time systems generalized h infty filtering covers standard h infty filtering as a special case and can make use of the frequency domain characteristics of practical signals moreover reduced order filters are more attractive than full order ones regarding implementability by virtue of the generalized bounded real lemma a new necessary and sufficient condition is proposed for analyzing the generalized h infty performance of the filtering error system to compute reduced order generalized h infty filters a necessary and sufficient condition is then derived in terms of matrix inequalities to solve which iterative linear matrix inequality algorithms are further developed in addition the proposed filter design method is applied to cope with the channel equalization problem examples are finally presented for illustrating the proposed method

reduced order h_ infty filter design for delta operator systems over multiple frequency intervals in this article a reduced order h infty filter is designed for a delta operator system over multiple frequency intervals by nonsmooth optimization techniques subdifferential analysis is generalized in delta domain for minimizing the maximum value of the h infty performance over the multiple frequency intervals based on the subdifferential analysis an efficient descent algorithm is developed to obtain the reduced order h infty filter compared with some existing algorithms the proposed descent algorithm not only reduces computational complexities but also improves the h infty performance numerical examples are presented to demonstrate effectiveness of the proposed descent algorithm

a class of cubic splines obtained through minimum conditions a class of cubic spline minimizing some special functional is investigated this class is determined by the solution of a quadratic programming problem in which the minimizing function depends linearly on a parameter a 2 for a 1 2 natural splines are obtained for a 1 the spline minimizing the mean value of the third derivative is obtained it is shown that this spline has the best convergence order

robust control via concave minimization local and global algorithms this paper is concerned with the robust control problem of linear fractional representation lft uncertain systems depending on a time varying parameter uncertainty our main result exploits a linear matrix inequality lmi characterization involving scalings and lyapunov variables subject to an additional essentially nonconvex algebraic constraint the nonconvexity enters the problem in the form of a rank deficiency condition or matrix inverse relation on the scalings only it is shown that such problems but also more generally rank inequalities and bilinear constraints can be formulated as the minimization of a concave functional subject to lmi constraints first of all a local frank and wolfe 1956 feasible direction algorithm is introduced in this context to tackle this hard optimization problem exploiting the attractive concavity structure of the problem several efficient global concave programming methods are then introduced and combined with the local feasible direction method to secure and certify global optimality of the solutions computational experiments indicate the viability of our algorithms and in the worst case they require the solution of a few lmi programs

superposition signaling in broadcast interference networks it is known that superposition signaling in gaussian interference networks is capable of improving the achievable rate region however the problem of maximizing the rate gain offered by superposition signaling is computationally prohibitive even in the simplest case of two user single input single output interference networks this paper examines superposition signaling for the general multiple input multiple output broadcast gaussian interference networks the problem of maximizing either the sum rate or the minimal user s rate under superposition signaling and dirty paper coding is solved by a computationally efficient path following procedure which requires only a convex quadratic program for each iteration but ensures convergence at least to a locally optimal solution numerical results demonstrate the substantial performance advantage of the proposed approach

interpolation and approximation of 3 d and 4 d scattered data abstract given a set of 3 d or 4 d scattered data methods are presented that yield a bivariate or trivariate function that interpolate or approximate the given data the subroutine package includes hardy s multiquadric interpolant and multistage methods with many options available to the user thus several different interpolation and approximation methods can be generated the options available in the multistage methods can be effectively used if the data set is noisy rapidly varying or nonuniformly distributed the computational and storage requirements for the multistage methods are linear in the number of data points thus they are efficient on large data sets

nonfragile h_ infty filtering of continuous time fuzzy systems this paper is concerned with the problem of nonfragile h filtering for a class of continuous time fuzzy systems attention is focused on the design of a filter such that the filtering error system preserves a prescribed h performance where the filter to be designed is assumed to have gain variations by using the quadratic lyapunov function approach and adding slack matrix variables sufficient conditions for designing the nonfragile h filter are proposed in terms of solutions to a set of linear matrix inequalities lmis finally a simulation example will be given to show the efficiency of the proposed design methods

general variational approach to the interpolation problem abstract the talmi and gilat variational approach to the interpolation problem in arbitrary dimension is presented together with the corresponding physical model the connection of this approach to some known spline methods is demonstrated and new interpolation functions are derived for one two and three dimensional cases they are designed to be flexible through the use of meaningful parameters and to give good approximations of both the function itself and its derivatives as well

l sub 2 optimal filter reduction a closed loop approach this paper is concerned with the problem of order reduction of a full order kalman filter for a stable linear signal model so that the steady state filtering error variance associated with the reduced order filter is minimized by an orthogonal parameterization the above problem is formulated to minimize the filtering error variance over a set of orthogonal matrices both continuous and iterative algorithms are derived to compute an optimal reduced order filter the algorithms are shown to possess good properties including the desirable convergence property the proposed algorithms are simple and effective numerical examples are presented to demonstrate the effectiveness and the significant advantages of the proposed algorithms over the existing open loop methods such as the well known balanced truncation method

some splines produced by smooth interpolation the spline theory can be derived from two sources the algebraic one where splines are understood as piecewise smooth functions satisfying some continuity conditions and the variational one where splines are obtained via minimization of some quadratic functionals with constraints we show that the general variational approach called smooth interpolation introduced by talmi and gilat covers not only the cubic spline but also the tension spline called also spline in tension or spline with tension in one or more dimensions we show the results of a 1d numerical example that present the advantages and drawbacks of the tension spline

adaptive walks and extreme value theory we study biological evolution in a high dimensional genotype space in the regime of rare mutations and strong selection the population performs an uphill walk which terminates at local fitness maxima assigning fitness randomly to genotypes we show that the mean walk length is logarithmic in the number of initially available beneficial mutations with a prefactor determined by the tail of the fitness distribution this result is derived analytically in a simplified setting where the mutational neighborhood is fixed during the adaptive process and confirmed by numerical simulations

universality classes of interaction structures for nk fitness landscapes kauffman s nk model is a paradigmatic example of a class of stochastic models of genotypic fitness landscapes that aim to capture generic features of epistatic interactions in multilocus systems genotypes are represented as sequences of l binary loci the fitness assigned to a genotype is a sum of contributions each of which is a random function defined on a subset of k le l loci these subsets or neighborhoods determine the genetic interactions of the model whereas earlier work on the nk model suggested that most of its properties are robust with regard to the choice of neighborhoods recent work has revealed an important and sometimes counter intuitive influence of the interaction structure on the properties of nk fitness landscapes here we review these developments and present new results concerning the number of local fitness maxima and the statistics of selectively accessible that is fitness monotonic mutational pathways in particular we develop a unified framework for computing the exponential growth rate of the expected number of local fitness maxima as a function of l and identify two different universality classes of interaction structures that display different asymptotics of this quantity for large k moreover we show that the probability that the fitness landscape can be traversed along an accessible path decreases exponentially in l for a large class of interaction structures that we characterize as locally bounded finally we discuss the impact of the nk interaction structures on the dynamics of evolution using adaptive walk models

smooth interpolation of scattered data by local thin plate splines abstract an algorithm and the corresponding computer program for solution of the scattered data interpolation problem is described given points x k y k f k k 1 n a locally defined function f x y which has the property f x k y k f k k 1 n is constructed the algorithm is based on a weighted sum of locally defined thin plate splines and yields an interpolation function which is differentiable the program is available from the author

continuous time analysis eigenstructure assignment and h sub 2 synthesis with enhanced linear matrix inequalities lmi characterizations this note describes a new framework for the analysis and synthesis of control systems which constitutes a genuine continuous time extension of results that are only available in discrete time in contrast to earlier results the proposed methods involve a specific transformation on the lyapunov variables and a reciprocal variant of the projection lemma in addition to the classical linearizing transformations on the controller data for a wide range of problems including robust analysis and synthesis multichannel h sub 2 stateand output feedback syntheses the approach leads to potentially less conservative linear matrix inequality lmi characterizations this comes from the fact that the technical restriction of using a single lyapunov function is to some extent ruled out in this new approach moreover the approach offers new potentials for problems that cannot be handled using earlier techniques an important instance is the eigenstructure assignment problem blended with lyapunov type constraints which is given a simple and tractable formulation

punctuated evolution for the quasispecies model abstract biological evolution in a sequence space with random fitnesses is studied within eigen s quasispecies model a strong selection limit is employed in which the population resides at a single sequence at all times evolutionary trajectories start at a randomly chosen sequence and proceed to the global fitness maximum through a small number of intermittent jumps the distribution of the total evolution time displays a universal power law tail with exponent 2 simulations show that the evolutionary dynamics is very well represented by a simplified shell model in which the sub populations at local fitness maxima grow independently the shell model allows for highly efficient simulations and provides a simple geometric picture of the evolutionary trajectories

low nonconvexity rank bilinear matrix inequalities algorithms and applications in robust controller and structure designs a branch and bound bb algorithm for solving a general class of bilinear matrix inequality bmi problems is proposed first linear matrix inequality lmi constraints are incorporated into bmi constraints in a special way to take advantage of useful information on nonconvex terms then the nonconvexity of the bmi is centralized in coupling constraints so that when the latter are omitted we get a relaxed lmi problem for computing lower bounds as in our previous developments the branching is performed in a reduced dimensional space of complicating variables this makes the approach practical even with a large dimension of overall variables applications of the algorithm to several test problems of robust control are discussed

parameter dependent h filter design for lpv systems and an autopilot application abstract this paper considers the design problem of parameter dependent h filters for linear parameter varying lpv systems whose parameters are measurable conditions for existence of parameter dependent lyapunov function are proposed via parametrical linear matrix inequality lmi constraints based on the solutions to the lmis an algorithm for the gain matrices of lpv filter is presented the design method is applied to a missile system to demonstrate the effectiveness

evolutionary accessibility of modular fitness landscapes a fitness landscape is a mapping from the space of genetic sequences which is modeled here as a binary hypercube of dimension l to the real numbers we consider random models of fitness landscapes where fitness values are assigned according to some probabilistic rule and study the statistical properties of pathways to the global fitness maximum along which fitness increases monotonically such paths are important for evolution because they are the only ones that are accessible to an adapting population when mutations occur at a low rate the focus of this work is on the block model introduced by a s perelson and c a macken proc natl acad sci usa 92 9657 1995 where the genome is decomposed into disjoint sets of loci modules that contribute independently to fitness and fitness values within blocks are assigned at random we show that the number of accessible paths can be written as a product of the path numbers within the blocks which provides a detailed analytic description of the path statistics the block model can be viewed as a special case of kauffman s nk model and we compare the analytic results to simulations of the nk model with different genetic architectures we find that the mean number of accessible paths in the different versions of the model are quite similar but the distribution of the path number is qualitatively different in the block model due to its multiplicative structure a similar statement applies to the number of local fitness maxima in the nk models which has been studied extensively in previous works the overall evolutionary accessibility of the landscape as quantified by the probability to find at least one accessible path to the global maximum is dramatically lowered by the modular structure

gain scheduled filtering for time varying discrete systems this paper deals with the design of gain scheduled filters whose state space realization depends on real time parameters of plants similar to well recognized advantages of gain scheduled controllers in control theory gain scheduled filters are expected to provide enhanced performance in comparison with customary nonadjustable filters our construction technique is based on nonlinear fractional transformation nft representations of systems that are a generalization of widely used linear fractional transformation lft representations both generalized h sub 2 and h sub spl infin discrete time filter design problems are investigated together with their extension to mixed designs this study leads to new linear matrix inequality lmi formulations which in turn provide an effective and reliable design tool the proposed design technique is finally evaluated in the light of simulation examples

brief paper stability and h2 objective characterizations in control a comparative study this paper is concerned with stability and h 2 objective characterizations in control new forms of alternative lmi characterizations are presented for continuous time stability and h 2 objective a key relationship between the alternative characterizations for continuous time systems and the existing discrete time versions is illustrated the existing enhanced lmi characterization for continuous time systems called the reciprocal projection lemma is revisited and an alternative proof is provided with a new interpretation an e embedded lmi characterization is presented for a comparative study with the reciprocal projection lemma and for numerical analysis on the conservativeness of synthesis conditions through an application in control it is discussed that when applied to multi objective problems in control the alternative characterizations in this paper lead to an lmi solution with further significant conservativeness reduction compared to the reciprocal projection lemma in addition through the comparison with the existing dilated lmi condition it is shown that the dilated condition is an equivalent continuous time counterpart of the existing discrete time versions

an optimization algorithm for checking feasibility of robust h infinity control problem for linear time varying uncertain systems an algorithm for checking feasibility of the robust h control problem for systems with time varying norm bounded uncertainty is suggested this algorithm is an iterative procedure on each step of

optimal linear filtering under parameter uncertainty this paper addresses the problem of designing a guaranteed minimum error variance robust filter for convex bounded parameter uncertainty in the state output and input matrices the design procedure is valid for linear filters that are obtained from the minimization of an upper bound of the error variance holding for all admissible parameter uncertainty the results provided generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured assuming the order of the uncertain system is known the optimal robust linear filter is proved to be of the same order as the order of the system in the present case of convex bounded parameter uncertainty the basic numerical design tools are linear matrix inequality lmi solvers instead of the riccati equation solvers used for the design of robust filters available in the literature to date the paper that contains the most important and very recent results on robust filtering is used for comparison purposes in particular it is shown that under the same assumptions our results are generally better as far as the minimization of a guaranteed error variance is considered some numerical examples illustrate the theoretical results

successive interference mitigation in multiuser mimo channels motivated by the work of dahrouj and yu in applying the han kobayashi transmission strategy for mitigating the intercell interference in a multi cell multi user multiple input single output interference network miso in this paper considers splitting messages into private and common parts in a multi cell multi user mimo in specifically the covariances of the private messages and common messages are designed to optimize either the sum rate or the minimal rate the common messages and private messages are decoded in sequence using successive decoding this paper shows how these difficult optimization problems can be adequately solved by means of d c d ifference of c oncave functions optimization over a simple convex set numerical and simulation results also reveal the great advantage of our proposed solutions for various types of ins in particular the proposed solutions are shown to outperform the algorithm developed by dahrouj and yu for the simpler case of the miso in

robust output feedback controller design via local bmi optimization the problem of designing a globally optimal full order output feedback controller for polytopic uncertain systems is known to be a non convex np hard optimization problem that can be represented as a bilinear matrix inequality optimization problem for most design objectives in this paper a new approach is proposed to the design of locally optimal controllers it is iterative by nature and starting from any initial feasible controller it performs local optimization over a suitably defined non convex function at each iteration the approach features the properties of computational efficiency guaranteed convergence to a local optimum and applicability to a very wide range of problems furthermore a fast but conservative lmi based procedure for computing an initially feasible controller is also presented the complete approach is demonstrated on a model of one joint of a real life space robotic manipulator

relay beamforming designs in multi user wireless relay networks based on throughput maximin optimization beamforming design for multi user wireless relay networks under the criterion of maximin information throughput is an important but also very hard optimization problem due to its nonconvex nature the existing approach to reformulate the design as a matrix rank one constrained optimization problem is highly inefficient this paper exploits the d c difference of two convex functions structure of the objective function and the convex structure of the constraints in such a global optimization problem to develop efficient iterative algorithms of very low complexity to find the solutions both cases of concurrent and orthogonal transmissions from sources to relays are considered numerical results indicate that the proposed algorithms provide solutions that are very close to the upper bound on the solution of the non orthogonal source transmissions case and are almost equal to the optimal solution of the orthogonal source transmissions case this demonstrates the ability of the developed algorithms to locate approximations close to the global optimal solutions in a few iterations moreover the proposed methods are superior to other methods in both performance and computation complexity

polyharmonic splines generated by multivariate smooth interpolation abstract polyharmonic splines of order m satisfy the polyharmonic equation of order m in n variables moreover if employed as basis functions for interpolation they are radial functions we are concerned with the problem of construction of the smooth interpolation formula presented as the minimizer of suitable functionals subject to interpolation constraints for n 1 this is the principal motivation of the paper we show a particular procedure for determining the interpolation formula that in a natural way leads to a linear combination of polyharmonic splines of a fixed order possibly complemented with lower order polynomial terms if it is advantageous for the interpolant in the problem solved to be a polyharmonic spline we can construct such an interpolant directly using the multivariate smooth approximation technique the smoothness of the spline can be a priori chosen smooth interpolation can be very useful e g in signal processing computer aided geometric design or construction of geographic information systems a 1d computational example is presented

δ exceedance records and random adaptive walks we study a modified record process where the kth record in a series of independent and identically distributed random variables is defined recursively through the condition with a deterministic sequence called the handicap for constant and exponentially distributed random variables it has been shown in previous work that the process displays a phase transition as a function of between a normal phase where the mean record value increases indefinitely and a stationary phase where the mean record value remains bounded and a finite fraction of all entries are records park et al 2015 phys rev e 91 042707 here we explore the behavior for general probability distributions and decreasing and increasing sequences focusing in particular on the case when matches the typical spacing between subsequent records in the underlying simple record process without handicap we find that a continuous phase transition occurs only in the exponential case but a novel kind of first order transition emerges when is increasing the problem is partly motivated by the dynamics of evolutionary adaptation in biological fitness landscapes where corresponds to the change of the deterministic fitness component after k mutational steps the results for the record process are used to compute the mean number of steps that a population performs in such a landscape before being trapped at a local fitness maximum

suboptimal reduced order filtering through an lmi based method this paper addresses the reduced order filtering design problem for continuous time linear systems the h2 and hinfin norms of the estimation error used as performance criteria are discussed and a new linear matrix inequalities lmi based method for reduced order filter design is proposed differently from the methods available in the literature to date the one presented here does not solve the associated nonconvex problem by means of an appropriate optimization procedure it is based on the a priori determination of a certain matrix that simultaneously rends convex the problem to be solved and reduces the suboptimality degree of the solution its efficiency is tested by means of two examples the first one borrowed from the literature allows the comparison of our method for the h2 norm case with three earlier techniques one of them being the well known balanced truncation the second one of higher order consists of the estimation of the displacement of a tapered bar using an hinfin norm criterion

dc optimization approach to robust controls the optimal scaling value problem the optimal scaling problem osp for constant scaling in output feedback control is an inherently difficult nonconvex problem for which in general existing local search algorithms can at best locate a local solution however it can be restated as a problem of globally minimizing a convex function under dc constraints i e constraints that can be expressed in terms of differences of convex functions a particular structure of this dc optimization problem is that it becomes convex when a relatively small number of complicating variables are held fixed we propose alternative branch and bound algorithms for osp which exploit this structure by branching upon the complicating variables and use adaptive sub division strategies to speed up the convergence to the global solution

a new design of robust h2 filters for uncertain systems abstract in this paper a structured polynomial parameter dependent approach is proposed for robust h 2 filtering of linear uncertain systems given a stable system with parameter uncertainties residing in a polytope with s vertices the focus is on designing a robust filter such that the filtering error system is robustly asymptotically stable and has a guaranteed estimation error variance for the entire uncertainty domain a new polynomial parameter dependent idea is introduced to solve the robust h 2 filtering problem which is different from the quadratic framework that entails fixed matrices for the entire uncertainty domain or the linearly parameter dependent framework that uses linear convex combinations of s matrices this idea is realized by carefully selecting the structure of the matrices involved in the products with system matrices linear matrix inequality lmi conditions are obtained for the existence of admissible filters and based on these the filter design is cast into a convex optimization problem which can be readily solved via standard numerical software both continuous and discrete time cases are considered the merit of the methods presented in this paper lies in their less conservatism than the existing robust filter design methods as shown both theoretically and through extensive numerical examples

a periodic basis system of the smooth approximation space the paper is primarily devoted to the problem of smooth interpolation of data in 1d in addition to the exact interpolation of data at nodes we are also concerned with the smoothness of the interpolating curve and its derivatives the interpolating curve is defined as the solution of a variational problem with constraints the system of functions exp i kx k being an integer is taken for the basis of the space where we measure the smoothness of the result it also generates the functions used for the interpolation itself choosing different norms when measuring the smoothness we arrive at different interpolating functions we also mention the problem of smooth curve fitting data smoothing we discuss the proper choice of different norms for this way of approximation and present the results of several 1d numerical examples that show the advantages and drawbacks of smooth interpolation

an augmented lagrangian method for a class of lmi constrained problems in robust control theory we present a new approach to a class of non convex lmi constrained problems in robust control theory the problems we consider may be recast as the minimization of a linear objective subject to linear matrix inequality lmi constraints in tandem with non convex constraints related to rank deficiency conditions we solve these problems using an extension of the augmented lagrangian technique the lagrangian function combines a multiplier term and a penalty term governing the non convex constraints the lmi constraints due to their special structure are retained explicitly and not included in the lagrangian global and fast local convergence of our approach is then obtained either by an lmi constrained newton type method including line search or by a trust region strategy the method is conveniently implemented with available semi definite programming sdp interior point solvers we compare its performance to the wellknown d k iteration scheme in robust control two test problems are investigated and

gain scheduled open loop system design for lpv systems using polynomially parameter dependent lyapunov functions abstract this paper addresses the design problem of full order gain scheduled gs open loop systems such as gs filters and gs inverse systems which are independent of unmeasurable parameters for linear parameter varying lpv systems in which the state space matrices are polynomially parameter dependent using structured polynomially parameter dependent lyapunov functions pdlfs in which some conservatism is admitted we propose design methods for our addressed problems via parametrically affine linear matrix inequality lmi conditions that are easily solved via semi definite programming for parametrically affine lpv systems including polytopic systems our design methods theoretically encompass existing methods which use structured quadratically pdlfs our proposed methods include robust open loop system design as a special case several numerical examples are introduced to demonstrate the effectiveness of our methods

the speed of evolution in large asexual populations we consider an asexual biological population of constant size n evolving in discrete time under the influence of selection and mutation beneficial mutations appear at rate u and their selective effects s are drawn from a distribution g s after introducing the required models and concepts of mathematical population genetics we review different approaches to computing the speed of logarithmic fitness increase as a function of n u and g s we present an exact solution of the infinite population size limit and provide an estimate of the population size beyond which it is valid we then discuss approximate approaches to the finite population problem distinguishing between the case of a single selection coefficient g s s s b and a continuous distribution of selection coefficients analytic estimates for the speed are compared to numerical simulations up to population sizes of order 10300

robust state estimation for uncertain neural networks with time varying delay the robust state estimation problem for a class of uncertain neural networks with time varying delay is studied in this paper the parameter uncertainties are assumed to be norm bounded based on a new bounding technique a sufficient condition is presented to guarantee the existence of the desired state estimator for the uncertain delayed neural networks the criterion is dependent on the size of the time varying delay and on the size of the time derivative of the time varying delay it is shown that the design of the robust state estimator for such neural networks can be achieved by solving a linear matrix inequality lmi which can be easily facilitated by using some standard numerical packages finally two simulation examples are given to demonstrate the effectiveness of the developed approach

robust reduced order unbiased filtering for uncertain systems this paper presents a simple solution to the robust unbiased functional reduced order filtering problem in the case of uncertain systems described by integral quadratic constraint iqc the existence condition of the unbiased filter is expressed through a rank relation then the filter is designed via linear matrix inequalities coupled with an equality constraint the results obtained in this paper are applicable to unstable systems the approach is illustrated by a numerical example

on bounded real matrix inequality dilation we discuss a variation of dilated matrix inequalities for the conventional bounded real matrix inequality and other similarly structured inequalities here system matrices are separated from lyapunov matrix to allow the use of different lyapunov matrices in multi objective and robust problems the search involves a bounded scalar parameter that enters the problem nonlinearly and is dealt with a line search to demonstrate the benefits of the new dilated matrix inequalities over the conventional ones an example of controller synthesis with 2 gain performance measure control for a system with polytopic uncertainty robust problem has been studied it is shown that for the resulting robust problem the performance obtained via the dilated form is at least equal to that of the conventional one also the connection between the proposed dilated form and the full block s procedure is discussed

robust semidefinite programming problems with general nonlinear parameter dependence two conservative approaches are proposed to a semidefinite programming problem nonlinearly dependent on uncertain parameters these approaches are applicable to general nonlinear parameter dependence not necessarily polynomial or rational they are based on the mild assumption that the parameter dependence is expressed as the difference of two convex functions the first approach uses constant bounds on the parameter dependence optimization of the bounds is reduced to convex nonsmooth minimization the second approach uses parameter dependent bounds for a less conservative result optimization of the bounds is immediate when the centroid is computable for the parameter set numerical examples are presented for illustration of the approaches

d c optimization approach to robust control feasibility problems the feasibility problem for constant scaling in output feedback control is considered this is an inherently difficult problem since the set of feasible solutions is non convex and may be disconnected nevertheless we show that this problem can be reduced to the global minimization of a concave function over a convex set or alternatively to the global minimization of a convex program with an additional reverse convex constraint thus this feasibility problem belongs to the realm of d c optimization a new field which has recently emerged as an active promising research direction in nonconvex global optimization by exploiting the specific d c structure of the problem several algorithms are proposed which at every iteration require solving only either convex or linear subproblems analogous algorithms with new characterizations are proposed for the bilinear matrix inequality bmi feasibility problem

robust and reduced order filtering new lmi based characterizations and methods this paper addresses several challenging problems of robust filtering we derive new linear matrix inequality lmi characterizations of minimum variance or h sub 2 performance and demonstrate that they allow the use of parameter dependent lyapunov functions while preserving tractability of the problem the resulting conditions are less conservative than earlier techniques which are restricted to fixed not parameter dependent lyapunov functions the remainder of the paper discusses reduced order filter problems new lmi based nonconvex optimization formulations are introduced for the existence of reduced order filters and several efficient optimization algorithms of local and global optimization are proposed nontrivial and less conservative relaxation techniques are presented as well the viability and efficiency of the proposed approaches are then illustrated through computational experiments and comparisons with existing methods