kobayashi hyperbolic imbeddings into toric varieties our main goal of this article is to give a characterization of an algebraic divisor on an algebraic torus whose complement is kobayashi hyperbolically imbedded into a toric projective variety as an application of our main theorem we prove the following the complement of the union of n 1 hyperplanes in the n dimensional projective space mathbb p n mathbb c in general position and a general hypersurface of degree n in mathbb p n mathbb c is kobayashi hyperbolically imbedded into mathbb p n mathbb c

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

novel delay dependent kalman luenberger type filter design for neutral systems this article presents a new delay dependent condition to design a kalman luenberger type filter for neutral systems where the resulting filter is such that a prescribed level is guaranteed the proposed approach is based on linear matrix inequalities and on lyapunov krasovskii theory also the gu s discretisation method and a slack matrix technique that decouples the system matrices from the lyapunov ones are applied in order to obtain less conservative results than the similar ones two numerical examples are performed to illustrate the advantage of the method proposed

frequency response functions for nonlinear rational models a recursive algorithm which maps a general class of nonlinear rational model defined as the ratio of two polynomial functions into the frequency domain is derived using the harmonic expansion method the new algorithm provides for the first time a direct analytic map from the time domain rational model parameters to the higher order frequency response functions complex nonlinear time domain behaviours can be analysed and interpreted in the frequency domain and simulated examples are included to illustrate the concepts involved

robust spl hscr sub spl infin filtering for uncertain discrete time state delayed systems this paper addresses the problem of robust spl hscr sub spl infin filtering for linear discrete time systems subject to parameter uncertainties in the system state space model and with multiple time delays in the state variables the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain a methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed spl hscr sub spl infin performance for the filtering error irrespective of the uncertainty and the time delays the proposed design is given in terms of linear matrix inequalities which has the advantage in that it can be implemented numerically very efficiently

a digital method of modeling quadratically nonlinear systems with a general random input without assuming particular statistics of the input a practical digital method of estimating linear and quadratic transfer functions of a nonlinear time invariant system that can be described by volterra series of up to second order is presented the method is tested and validated by analyzing input output data of a known quadratically nonlinear system it is used when there is little knowledge about the input statistics or the input is non gaussian it is also noted that the ordinary coherence functions cannot be used in explaining the input output power transfer relationship of a quadratic system excited by a non gaussian input signal with respect to the practical application of the method the relationship between the mean square errors involved in the transfer function estimates and the number of averages taken from the spectral estimation is qualitatively discussed

spectrally and inertially arbitrary sign patterns we introduce some n by n sign patterns which allow for arbitrary spectrum and hence also arbitrary inertia consequently we demonstrate that some known inertially arbitrary patterns are in fact spectrally arbitrary we demonstrate that all inertially arbitrary patterns of order 3 are spectrally arbitrary and classify all spectrally arbitrary patterns of order 3 we illustrate that in general the class of spectrally arbitrary patterns is distinct from the inertially arbitrary patterns and present some observations about inertially arbitrary patterns

a combinatorial converse to the perron frobenius theorem abstract a sign pattern requires allows the perron property if every some matrix with that sign pattern has its special radius among its eigenvalues we characterize those sign patterns that require the perron property which in a sense provides a converse to the classical perron frobenius theorem also a large class of patterns that allow the perron property is identified but a complete characterization remains an open problem

lmi approach to robust h filtering for neutral delay differential systems in this paper we investigate the problems of stability and h filtering for a class of linear neutral delay differential systems a linear matrix inequality approach is proposed to design a robust h filter such that the filtering system remains asymptotically stable and the bound of h norm is minimized the lyapunov stability theory is used for analysis of the system a numerical example illustrate the theoretical results

robust mixed h_2 h_infty filtering for time delay fuzzy systems in this paper a robust mixed h2 hinfin filtering problem for continuous time fuzzy systems subject to parameter uncertainties and multiple time varying delays in state variables is addressed the uncertain systems are expressed as takagi sugeno fuzzy models with linear nominal parts and norm bounded uncertainties the main objective is to design stable filters that minimize a guaranteed cost index and achieve a prescribed hinfin performance under worst case disturbance based on lyapunov theory both delay independent and delay dependent sufficient conditions guaranteeing stability and achieving prescribed performances are stated in terms of linear matrix inequalities therefore stable filters can be obtained easily with existing convex algorithms lastly two examples are given to illustrate the proposed design methodology

a game theory approach to robust discrete time h sub spl infin estimation the deterministic robust estimation problem is formulated in the discrete time case as a zero sum two person difference game in which a statistician plays against nature the statistician tries to estimate a linear combination of the states of an uncertain linear system which is driven by nature saddle point strategies for the statistician in the above game are difficult to find a suboptimal strategy is therefore considered which guarantees an h sub spl infin performance bound on the estimation error different patterns of the information that is available to the statistician are treated and the corresponding fixed point fixed lag and fixed interval smoothing strategies are derived

generalized big picard theorem for pseudo holomorphic maps we show how an appropriate choice for affine connections in the target manifold allows the pseudo holomorphic curves to be realized as harmonic maps as an application we present a generalized big picard theorem for pseudo holomorphic maps between manifolds with almost complex structures

finiteness of the family of rational and meromorphic mappings into algebraic varieties introduction in this paper we deal with the higher dimensional version of de franchis theorem which says that there are only a finite number of nonconstant separable rational mappings of an algebraic curve into a complete algebraic curve with genus greater than 1 kobayashiochiai 11 proved that there are only a finite number of dominant meromorphic mappings onto a complex space of general type and its algebraic proof which covers the positive characteristic case was given by 14 cf also 23 here we shall consider the case where the mappings are not necessarily dominant let k be an algebraically closed field with arbitrary characteristic all algebraic varieties and mappings morphisms in the following will be defined over k let r be an algebraic variety v a smooth complete algebraic variety and t v denote the tangent bundle over v set rank f sup dim r dimtf 1 f t t e r for rational mappings

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

k3 surfaces with involution equivariant analytic torsion and automorphic forms on the moduli space in this paper we introduce an invariant of a k3 surface with 2 action equipped with a 2 invariant kahler metric which we obtain using the equivariant analytic torsion of the trivial line bundle this invariant is shown to be independent of the choice of the kahler metric it can be viewed as a function on the moduli space of k3 surfaces with involution the main result of this paper is that this function can be identified with an automorphic form which characterizes the discriminant locus in particular we show that the ray singer analytic torsion of the trivial line bundle on an enriques surface with ricci flat kahler metric is given by the value of the norm of the borcherds function at its period point

robust spl hscr sub spl infin filtering for discrete time linear systems with uncertain time varying parameters this paper deals with the problem of robust spl hscr sub spl infin filtering for linear discrete time state space models with uncertain time varying parameters the parameters enter affinely into the state space model matrices and their admissible values and variations are assumed to belong to given intervals a method is derived for designing a linear stationary asymptotically stable filter with a prescribed spl hscr sub spl infin performance in spite of large parameter uncertainty the proposed method incorporates information on available bounds on both the admissible values and variation of the uncertain parameters and is based on a lyapunov function with quadratic dependence on the parameters the filter design is given in terms of linear matrix inequalities

robust h filter design with past output measurements for uncertain discrete time systems this paper is concerned with the design of robust filters for uncertain discrete time linear systems the uncertainty is assumed to be time invariant belonging to a polytope an upper bound to the h norm of the transfer function from the system input to the filtering error is used as performance criterion the novelty is that the resulting robust filter has order greater than the order of the system being filtered by incorporating past output measurements the design conditions are expressed in terms of convex problems constrained by linear matrix inequalities performance is assessed through parameter dependent lyapunov functions the results generalize existing robust filtering procedures without bringing in any additional conservatism simple numerical examples illustrate the procedure

improved structure selection for nonlinear models based on term clustering in this paper the concepts of term clusters and cluster coefficients are defined and used in the context of system identification it is argued that if a certain type of term in a nonlinear model is spurious the respective cluster coefficient is small compared with the coefficients of the other clusters represented in the model once the spurious clusters have been detected the corresponding terms can be deleted from the set of candidate terms the consequences of doing this are i a drastic reduction in the size of the set of candidate terms and consequently a substantial gain in computation time is achieved ii the final estimated model is more likely to reproduce the dynamics of the original system and iii the final model is more robust to overparametrization numerical examples are included to illustrate the new procedure

a parameter dependent approach to robust h_ infty filtering for time delay systems this paper is concerned with the problem of robust h infin filtering for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state we utilize the polynomially parameter dependent idea to solve the robust h infin filtering problem with new linear matrix inequality conditions obtained for the existence of admissible filters these conditions are developed based on homogeneous polynomially parameter dependent matrices of arbitrary degree the delay dependence and polynomial parameter dependence guarantee the proposed approach to be potentially less conservative which is shown via a numerical example

reliable finite time h filtering for discrete time delay systems with markovian jump and randomly occurring nonlinearities this paper is concerned with the problem of reliable finite time h filtering for discrete time varying delay systems with markovian jump and randomly occurring nonlinearities rons rons are introduced to model a class of sector like nonlinearities that occur in a probabilistic way according to a two dimensional discrete random variables joint distribution the failures of sensors are quantified by a variable varying in a given interval the time varying delay is unknown with given lower and upper bounds firstly the filtering errr dynamic system is constructed based on an h filter sufficient criteria are provided to guarantee that the resulting filtering error system is stochastic finite time boundedness and stochastic finite time h filtering in both normal and fault cases the gain matrices of the controller and filter are achieved by solving a feasibility problem in terms of linear matrix inequalities with a fixed parameter respectively finally numerical examples are given to demonstrate the effectiveness of the proposed design approach

h filter design for discrete delay systems a new parameter dependent approach this article revisits the problem of h filtering for discrete time systems with a time varying delay in the state and parameter uncertainties residing in a polytope by utilising the polynomially parameter dependent idea a new filter design procedure is proposed which formulates the existence of admissible robust h filters into a set of linear matrix inequalities these conditions are developed based on homogeneous polynomially parameter dependent matrices of an arbitrary degree as the degree grows test of increasing precision is obtained providing less conservative filter designs it is established that the results in the quadratic framework that entail fixed matrices for the entire uncertainty domain and the linearly parameter dependent framework that use linear convex combinations of matrices are special cases of the proposed conditions for the zeroth degree and the first degree respectively moreover in addition to parameter dependence the obtained conditions are also dependent on both

state feedback ℋ control for stochastic time delay nonlinear systems with state and disturbance dependent noise this article focuses on the state feedback control problem for the stochastic nonlinear systems with state and disturbance dependent noise and time varying state delays based on the maxmin optimisation approach both the delay independent and the delay dependent hamilton jacobi inequalities hjis are developed for synthesising the state feedback controller for a general type of stochastic nonlinear systems it is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level for a class of stochastic affine nonlinear systems the delay independent as well as delay dependent matrix valued inequalities are proposed the resulting control system satisfies global asymptotic stability in the mean square sense and the required disturbance attenuation level by modelling the nonlinearities as uncertainties in corresponding stochastic time delay systems the sufficient conditions in terms of a linear matrix inequality lmi and a bili

mapping non linear integro differential equations into the frequency domain a recursive algorithm is derived to compute the generalized frequency response functions for a large class of non linear integro differential equations applications to duffing s equation and a modified van der pol model are discussed

a harmonic probing algorithm for the multi input volterra series it is shown how the conventional harmonic probing algorithm of bedrosian and rice can be extended to deal with the multi input multi output form of the volterra functional series example calculations are presented for both continuous time and discrete time multi input non linear systems subject to multiple sinusoidal inputs

identification of cubic systems using higher order moments of i i d signals a simple method for estimating the volterra kernels of cubic systems with a zero mean i i d input is presented this method significantly reduces the computational complexity of volterra kernel estimation compared to the non i i d and non gaussian input case

recursive algorithm for computing the frequency response of a class of non linear difference equation models abstract a recursive algorithm is developed which is both computationally compact and enables the nth order frequency response functions of a large class of non linear difference equation models to be found without restriction on the order n

mapping nonlinear integro differential equations to a generalized describing function form an algebraic relationship is derived which enables the generalized amplitude dependent describing function to be expressed in terms of the parameters of a general nonlinear integro differential equation the algorithm is not restricted to a specific input but treats the whole class of harmonically related phase independent sinusoidal inputs and is illustrated by a number of examples

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

analysis of the effects of time delay in nonlinear systems using generalised frequency response functions abstract a recursive algorithm for computing the generalised frequency response functions gfrfs of nonlinear time delay systems described by nonlinear differential difference equation models is derived using the operator e n and used to analyse the effects of time delay in nonlinear systems the algorithm shows an explicit relationship between the model parameters and the gfrfs such a relationship provides important insight into the behaviour of nonlinear systems the effect of delay on several properties of nonlinear systems such as harmonic generation gain compression expansion and desensitisation is studied by considering the example of a duffing oscillator with retarded damping results of the studies convincingly demonstrate that the system delay has a significant effect on several important properties of nonlinear systems

potentially nilpotent and spectrally arbitrary even cycle sign patterns abstract an n n sign pattern s n is potentially nilpotent if there is a real matrix having sign pattern s n and characteristic polynomial x n a new family of sign patterns c n with a cycle of every even length is introduced and shown to be potentially nilpotent by explicitly determining the entries of a nilpotent matrix with sign pattern c n these nilpotent matrices are used together with a jacobian argument to show that c n is spectrally arbitrary i e there is a real matrix having sign pattern c n and characteristic polynomial x n i 1 n 1 i i x n i for any real i some results and a conjecture on minimality of these spectrally arbitrary sign patterns are given

on robust h filter design for uncertain neural systems lmi optimization approach this article deals with the robust h filtering problem for neutral delay differential systems with parametric uncertainties a linear matrix inequality lmi approach is proposed to design the robust h filter such that the filtering system remains asymptotically stable and the bound of h norm is minimized the lyapunov stability theory is used for analysis of the system a numerical example is provided to illustrate the validity of proposed design approach

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

brief paper robust h filtering for nonlinear stochastic systems with uncertainties and markov delays this paper investigates the h filtering problem for a class of general nonlinear stochastic systems considering model uncertainties and random time delays governed by markov chains simultaneously the general algebraic hamilton jacobi inequality hji is established first for general nonlinear stochastic systems with uncertainties and random markovian delays then a set of sufficient conditions are derived for the filtering system to achieve stochastic stability in the sense of mean square and the prescribed disturbance attenuation level moreover the developed results are specialized for a special class of nonlinear stochastic systems by presenting the sufficient conditions in terms of matrix inequalities simulation results demonstrate the effectiveness of the proposed approach

technical communique robust h observer design of linear state delayed systems with parametric uncertainty the discrete time case in this note we consider the problem of h observer design for a class of uncertain linear discrete time systems with delayed state and parameter uncertainties the goal of this problem is to design a linear state observer such that for the positive integer state time delay and all admissible norm bounded parameter uncertainties the observation process remains robustly stable and the transfer function from exogenous disturbances to error state outputs meets the prespecified h norm upper bound constraint the observer structure does not depend on the parameter uncertainties a simple effective algebraic methodology is developed to derive the conditions for the existence of the desired robust h observers and the analytical expression of these observers is then characterized in terms of the matrix riccati like equations inequalities we provide a numerical example to demonstrate the validity and the applicability of the proposed approach

a simple criterion for establishing an upper limit to the harmonic excitation level of the duffing oscillator using the volterra series abstract high order frequency response functions based on the volterra series are employed to represent the input output characteristics of the duffing oscillator subject to sinusoidal excitation from these a series representation of a first order frequency response function of the non linear system is obtained and used to derive a simple criterion which provides an estimate of the magnitude of the input sine wave above which the predicted response begins to diverge the criterion results in a small overestimate of the magnitude of the input force excitation at the undamped natural frequency condition although the derived criterion strictly applies only to the duffing oscillator the procedure can be applied generally and is extended to a two degree of freedom system with a non linear cubic stiffness producing a similar criterion to that of the single degree of freedom system

a bound for the magnitude characteristics of nonlinear output frequency response functions part 1 analysis and computation a bound for the magnitude frequency domain characteristics associated with the outputs of a wide class of nonlinear systems is derived as a relatively simple function of the generalized frequency response functions and properties of the system inputs it is shown how the practical computation of the new bound can be easily performed for nonlinear systems with finite but arbitrary order nonlinearities and worked examples are included the paper is divided into two parts in part 1 an expression for the output magnitude bound is derived properties of the result are discussed and general procedures for the practical computation of the bound are developed in part 2 the practical computations associated with applying the bound to the polynomial nonlinear autoregressive model with exogenous input are discussed

delay dependent hbox h _ infty filter design for discrete time fuzzy systems with time varying delays this paper investigates delay dependent hinfin filter design problems for discrete time fuzzy systems with time varying delays first a novel delay dependent piecewise lyapunov krasovskii functional ddplkf is proposed in which both the upper bound of delays and the delay interval are considered based on this ddplkf the delay dependent stability criteria for discrete time systems with constant or time varying delays are obtained respectively then delay dependent full order and reduced order hinfin filter design approaches are proposed the filter parameters can be obtained by solving a set of linear matrix inequalities lmis simulation examples are also given to illustrate the performance of the proposed approaches it is shown that our approaches are less conservative and that the corresponding hinfin filters can achieve better performance than the existing approaches

companion matrix patterns abstract companion matrices especially the frobenius companion matrices are used in algorithms for finding roots of polynomials and are also used to find bounds on eigenvalues of matrices in 2003 fiedler introduced a larger class of companion matrices that includes the frobenius companion matrices one property of the combinatorial pattern of these companion matrices is that up to diagonal similarity they uniquely realize every possible spectrum of a real matrix we characterize matrix patterns that have this property and consequently introduce more companion matrix patterns we observe that each fiedler companion matrix is permutationally similar to a unit hessenberg matrix we provide digraph characterizations of the classes of patterns described and in particular all sparse companion matrices noting that there are companion matrices that are not sparse

induced l sub 2 and generalized h sub 2 filtering for systems with repeated scalar nonlinearities this paper provides complete results on the filtering problem for a class of nonlinear systems described by a discrete time state equation containing a repeated scalar nonlinearity as in recurrent neural networks both induced l sub 2 and generalized h sub 2 indexes are introduced to evaluate the filtering performance for a given stable discrete time systems with repeated scalar nonlinearities our purpose is to design a stable full order or reduced order filter with the same repeated scalar nonlinearities such that the filtering error system is asymptotically stable and has a guaranteed induced l sub 2 or generalized h sub 2 performance sufficient conditions are obtained for the existence of admissible filters since these conditions involve matrix equalities the cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to linear matrix inequalities which can be readily solved by using standard numerical software if these conditions are feasible a desired filter can be easily constructed these filtering results are further extended to discrete time systems with both state delay and repeated scalar nonlinearities the techniques used in this paper are very different from those used for previous controller synthesis problems which enable us to circumvent the difficulty of dilating a positive diagonally dominant matrix a numerical example is provided to show the applicability of the proposed theories

generalized frequency response function matrix for mimo non linear systems recursive algorithms are derived to compute the generalized frequency response function matrix of multi input multioutput mimo non linear systems as an analytical map from both non linear differential equation models and narx non linear auto regressive models with exogenous inputs models of the system the algorithm is computationally compact and exposes the explicit relationship between the model parameters and the elements of the generalized frequency response function matrix and can thus provide important insights into the behaviour of non linear systems

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

spl hscr sub spl infin filtering for continuous time linear systems with delay the problem of spl hscr sub spl infin filtering for continuous time linear systems with time delayed measurement is investigated the authors develop a methodology for designing linear filters which ensure a prescribed bound on the spl lscr sub 2 induced gain from the noise signals to the estimation error filtering problems for time varying systems over a finite horizon as well as stationary infinite horizon filtering for time invariant systems are tackled in the finite horizon case our estimation procedure entails an overdesign that stems from the last d seconds of the time interval 0 t where d is the delay length this overdesign becomes smaller as t increases and it vanishes in the infinite horizon case

robust fault detection with missing measurements this paper investigates the problem of robust fault detection for uncertain systems with missing measurements the parameter uncertainty is assumed to be of polytopic type and the measurement missing phenomenon which appears typically in a network environment is modelled by a stochastic variable satisfying the bernoulli random binary distribution the focus is on the design of a robust fault detection filter or a residual generation system which is stochastically stable and satisfies a prescribed disturbance attenuation level this problem is solved in the parameter dependent framework which is much less conservative than the quadratic approach both full order and reduced order designs are considered and formulated via linear matrix inequality lmi based convex optimization problems which can be efficiently solved via standard numerical software a continuous stirred tank reactor cstr system is utilized to illustrate the design procedures

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

potentially nilpotent sign pattern matrices abstract a sign pattern is said to be potentially nilpotent if it allows nilpotence in this paper a number of qualitative necessary or sufficient conditions for a sign pattern to allow nilpotence are established the sign patterns that allow nilpotence of index 2 are investigated for orders up to three potentially nilpotent sign patterns are characterized potentially nilpotent tree sign patterns are also explored

h sub spl infin filtering for multiple time delay measurements the aim of this paper is to study the h sub spl infin filtering problem for linear continuous time systems with both current and multiple time delay measurements the key technique applied for deriving the filter is the reorganized innovation analysis approach in krein space a necessary and sufficient condition for the existence of an h sub spl infin filter is derived and the solution to the h sub spl infin filter is given in terms of solutions of riccati and matrix differential equations an example is finally presented to show the effectiveness of the proposed approach

describing functions volterra series and the analysis of non linear systems in the frequency domain a relationship between the higher order frequency response functions of the volterra series model and the well known describing function representation for non linear systems is derived it is shown that a large class of generalized describing functions can be derived from the volterra model and that this approach removes the restriction to specific inputs the concept of a worst case transfer function is introduced and examples are included to illustrate the results

sign patterns allowing nilpotence of index 3 suppose p is a property referring to a real matrix we say that a sign pattern a allows p if there exists at least one matrix with the same sign pattern as a that has the property p in this paper we study sign patterns allowing nilpotence of index 3 four methods for constructing sign patterns that allow nilpotence of index 3 are obtained all tree sign patterns that allow nilpotence of index 3 are characterized sign patterns of order 3 that allow nilpotence are identified

hyperbolic embeddedness and extension convergence theorems of j holomorphic curves first we give some characterization of hyperbolic embeddedness in the almost complex case next we study the stability of hyperbolically embedded manifolds under a small perturbation of almost complex structures finally we obtain generalizations and extensions of theorems of kobayashi kiernan kwack and noguchi for almost complex manifolds

allow problems concerning spectral properties of sign pattern matrices a survey abstract an n n sign pattern matrix has entries in 0 this paper surveys the following problems concerning spectral properties of sign pattern matrices sign patterns that allow all possible spectra spectrally arbitrary sign patterns sign patterns that allow all inertias inertially arbitrary sign patterns sign patterns that allow nilpotency potentially nilpotent sign patterns and sign patterns that allow stability potentially stable sign patterns relationships between these four classes of sign patterns are given and several open problems are identified

on the period and base of a sign pattern matrix abstract a square sign pattern matrix a whose entries are or 0 is said to be powerful if all the powers a 1 a 2 a 3 are unambiguously defined for a powerful pattern a if a l a l p with l and p minimal then l is called the base of a and p is called the period of a we characterize irreducible powerful sign pattern matrices and investigate the period and base of a powerful sign pattern matrix we also consider some connections with real matrices and give some significant classes of powerful patterns

delay dependent robust h control of uncertain linear systems with time varying delays abstract this paper proposes an optimization based approach to the robust h control problem of uncertain continuous or discrete time linear time invariant systems with different time varying delays in the state vector and control input of the dynamic equation and controlled output sufficient delay dependent conditions are derived for the control stabilization problem where both the size of the time varying delay and the size of its time derivative in the continuous time case play a crucial role for the closed loop stability with a guaranteed h performance index the solutions that are proposed for the h control problem are similar or less conservative when compared to other recent approaches

robust h filtering for networked systems with multiple state delays in this paper a new robust h filter design problem is studied for a class of networked systems with multiple state delays two kinds of incomplete measurements namely measurements with random delays and measurements with stochastic missing phenomenon are simultaneously considered such incomplete measurements are induced by the limited bandwidth of communication networks and are modelled as a linear function of a certain set of indicator functions that depend on the same stochastic variable attention is focused on the analysis and design problems of a full order robust h filter such that for all admissible parameter uncertainties and all possible incomplete measurements the filtering error dynamics is exponentially mean square stable and a prescribed h attenuation level is guaranteed some recently reported methodologies such as delay dependent and parameter dependent stability analysis approaches are employed to obtain less conservative results sufficient conditions which are dependent

robust filtering for 2 d state delayed systems with nft uncertainties this paper is concerned with the robust filtering problem for two dimensional 2 d state delayed systems with uncertainties represented by nonlinear fraction transformation the authors first establish the stability h sub spl infin performance and generalized h sub 2 performance criteria for the system based on the results the authors propose efficient methods to solve the robust h sub spl infin filtering generalized h sub 2 filtering and mixed generalized h sub 2 h sub spl infin filtering problems by using a parameter dependent lyapunov function approach the methods involve solving linear matrix inequalities two examples are given to show the effectiveness of the proposed approach