robust stability and stabilisation of 2d discrete state delayed systems abstract in this paper we first present sufficient stability and robust stability conditions for discrete linear state delayed 2d systems in terms of linear matrix inequalities all results are obtained with fornasini marchesini delay model but appropriate transformation to the corresponding roesser form is provided as well generalisation to the multiple state delayed case is also given then the stabilisation and robust stabilisation using static state feedback are studied stabilising feedback gain matrices are constructed based on the solutions of certain linear matrix inequalities an numerical example is used to illustrate the effectiveness of the approach

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

two dimensional dissipative control and filtering for roesser model this paper investigates the problems of two dimensional 2 d dissipative control and filtering for a linear discrete time roesser model first a novel sufficient condition is proposed such that the discrete time roesser system is asymptotically stable and 2 d q s r hbox alpha dissipative special cases such as 2 d passivity performance and 2 d h infty performance and feedback interconnected systems are also discussed based on this condition new 2 d q s r hbox alpha dissipative state feedback and output feedback control problems are defined and solved for a discrete time roesser model the design problems of 2 d q s r hbox alpha dissipative filters of observer form and general form are also considered using a linear matrix inequality lmi approach two examples are given to illustrate the effectiveness and potential of the proposed design techniques

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

robust filtering of discrete time linear systems with parameter dependent lyapunov functions robust filtering of linear time invariant discrete time uncertain systems is investigated through a new parameter dependent lyapunov matrix procedure its main interest relies on the fact that the lyapunov matrix used in stability checking does not appear in any multiplicative term with the uncertain matrices of the dynamic model we show how to use such an approach to determine high performance h2 robust filters by solving a linear problem constrained by linear matrix inequalities lmis the results encompass the previous works in the quadratic lyapunov setting numerical examples illustrate the theoretical results

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

angle variable holonomy in adiabatic excursion of an integrable hamiltonian if an integrable classical hamiltonian h describing bound motion depends on parameters which are changed very slowly then the adiabatic theorem states that the action variables i of the motion are conserved here the fate of the angle variables is analysed because of the unavoidable arbitrariness in their definition angle variables belonging to distinct initial and final hamiltonians cannot generally be compared however they can be compared if the hamiltonian is taken on a closed excursion in parameter space so that initial and final hamiltonians are the same the result shows that the angle variable change arising from such an excursion is not merely the time integral of the instantaneous frequency omega dh di but differs from it by a definite extra angle which depends only on the circuit in parameter space not on the duration of the process the 2 form which describes this angle variable holonomy is calculated

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

classical adiabatic angles and quantal adiabatic phase a semiclassical connection is established between quantal and classical properties of a system whose hamiltonian is slowly cycled by varying its parameters round a circuit the quantal property is a geometrical phase shift gamma n associated with an eigenstate with quantum numbers n nl the classical property is a shift delta theta l i in the lth angle variable for motion round a phase space torus with actions i il the connection is delta theta l delta gamma delta nl two applications are worked out in detail the generalised harmonic oscillator with quadratic hamiltonian whose parameters are the coefficients of q2 qp and p2 and the rotated rotator consisting of a particle sliding freely round a non circular hoop slowly turned round once in its own plane

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

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

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

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

analysis of quantum time dependent evolution by the averaged variational principle in this paper we give a general method to solve a time dependent schrodinger equation the formalism developed is based on the quantum variational principle conveniently averaged in addition we apply our method to study the time dependent systems in which the hamiltonians are linear functions of su 1 1 and su 2 lie algebras

stability analysis and stabilization of 2 d singular roesser models abstract this paper addresses the problem of controller design for 2 d singular roesser models sufficient stability conditions are formulated in terms of strict linear matrix inequalities lmis for 2 d singular systems described by the roesser models then a set of sufficient conditions for existence of desired a state feedback controller are obtained numerical examples are provided to demonstrate the effectiveness of the proposed method

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

h sub spl infin filtering of 2 d discrete systems this paper deals with h sub spl infin filtering of two dimensional 2 d linear discrete systems described by a 2 d local state space lss fornasini marchesini 1978 second model several versions of the bounded real lemma of the 2 d discrete systems are established the 2 d bounded real lemma allows us to solve the finite horizon and infinite horizon h sub spl infin filtering problems using a riccati difference equation or a riccati inequality approach further a solution to the infinite horizon h sub spl infin filtering problem based on a linear matrix inequality lmi approach is developed our results extend existing work for one dimensional 1 d systems to the 2 d case and give a state space solution to the bounded realness of 2 d discrete systems as well as 2 d h sub spl infin filtering for the first time numerical examples are given to demonstrate the riccati difference equation approach to the 2 d finite horizon h sub spl infin filtering problem and the lmi approach to the 2 d infinite horizon h sub spl infin filtering problem

merging in maps and in pavings we introduce here a notion of paving extending the notion of map which allows an easy definition of the incidence relations between vertices edges faces and pieces more precisely a paving is a quadruple p b where b is a finite set and are permutations of b such that 2 1 1 and x b x x and x alpha x x if r s m and n are respectively the numbers of pieces faces edges and vertices of p then p r s m n is called the characteristics of p c b is a map and if s m n are respectively the numbers of faces edges and vertices of c then g c r 12 s m n is called the genus of c the merging of two pieces according to a common face is a fundamental operation in pavings the simultaneous studies of merging in maps and in pavings has given a result which links p and g c

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

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

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

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

construction of voronoi diagrams in the plane by using maps abstract an algorithm by guibas and stolfi 1985 constructs for a finite set s of n sites in the plane a triangulation t s of s that strictly refines the delaunay diagram del s when there exists a circle passing through at least four points of s and none of the sites is contained in its interior for this triangulation t s there exist isometries t such that t t s t t s the voronoi diagram vor s is the straight line dual of del s and the substitution of t s into del s leads to needless calculus indeed to the creation of imaginary vertices for vor s we present here a variant of the guibas and stolfi algorithm that determines with the same complexity del s and not a triangulation and uses a simpler data structure we also give approximation tests of collinearity and cocircularity so that for any similitude t of the plane del t s t del s

robust filtering for uncertain nonlinearly parameterized plants we address the robust filtering problem for a wide class of systems whose state space data assume a very general nonlinear dependence in the uncertain parameters our resolution methods rely on new linear matrix inequality characterizations of spl hscr sub 2 and spl hscr sub spl infin performances which in conjunction with suitable linearization transformations of the variables give rise to practical and computationally tractable formulations for the robust filtering problem

delay dependent stability for 2d systems with time varying delay subject to state saturation in the roesser model this paper addresses the problem of delay dependent stability of 2d systems with time varying delay subject to state saturation in the roesser model by introducing diagonally dominant matrices new delay dependent conditions are obtained in terms of linear matrix inequalities lmis where the lower and upper delay bounds along horizontal and vertical directions respectively are known numerical examples are provided to demonstrate the proposed results

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

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

berry s transport and minimization of averaged distances in this paper we consider the metric approach to the berry s transport geometrical part of the adiabatic evolution of any pure or mixed state for possibly degenerate hamiltonians we emphasize that explicit formulae for the transport of such states need the introduction of an averaging procedure in analogy with the classical case this quantum averaging involves multiplying each energy eigenstate by a different phase and then integrating over these phases we show in particular how the transport of non stationary pure states rays and density matrices arise from the minimization of hilbert fubini study and bures averaged distances respectively

berry s phase hannay s angle and coherent states through the use of coherent states describing the action angle variables the authors establish a strict parallelism between berry s phase and hannay s angle in particular they define a geometrical transport for classical tori which leads to hannay s angle as in the case of berry s phase the transport can be associated with the minimization of a distance

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

quantal phase factors accompanying adiabatic changes a quantal system in an eigenstate slowly transported round a circuit c by varying parameters r in its hamiltonian r will acquire a geometrical phase factor exp i c in addition to the familiar dynamical phase factor an explicit general formula for c is derived in terms of the spectrum and eigenstates of r over a surface spanning c if c lies near a degeneracy of c takes a simple form which includes as a special case the sign change of eigenfunctions of real symmetric matrices round a degeneracy as an illustration c is calculated for spinning particles in slowly changing magnetic fields although the sign reversal of spinors on rotation is a special case the effect is predicted to occur for bosons as well as fermions and a method for observing it is proposed it is shown that the aharonov bohm effect can be interpreted as a geometrical phase factor

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

state estimation in discrete m d systems in this study observers and stochastic state estimation for m d systems are considered the analysis uses a wave advance process model in transporting the existing 1 d results to the m d setting a constrained minimization technique is used to compute the optimal state estimator which preserves quarter plane causality the optimal state estimator without the quarter plane causality constraint is also determined a comparison then yields insight into the tradeoff between quarter plane causality and estimator performance

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

robust mixed spl hscr sub 2 spl hscr sub spl infin filtering of 2 d systems this paper deals with several challenging problems of robust filtering for two dimensional 2 d systems first of all new linear matrix inequality lmi characterizations for the spl hscr sub spl infin and spl hscr 2 norms of 2 d systems are introduced and thoroughly established based on these preparatory results convex lmi characterizations for robust spl hscr sub spl infin spl hscr sub 2 and robust mixed spl hscr sub 2 spl hscr sub spl infin filtering are derived the efficiency and viability of the proposed techniques and tools are demonstrated through a set of 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

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

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

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

stability criteria for a class of linear delay partial difference equations this paper is concerned with the linear delay partial difference equation a i j u i 1 j u i j 1 b i j u i j p i j u i j 0 where a i j b i j p i j i j n0 are real sequences sufficient conditions for this equation to be stable are derived some conditions for this equation to be unstable are obtained also

power diagrams properties algorithms and applications the power pow x s of a point x with respect to a sphere s in euclidean d space e d is given by d 2 x z r 2 where d denotes the euclidean distance function and z and r are the center and the radius of s the power diagram of a finite set s of spheres in e d is a cell complex that associates each s in s with the convex domain x in e d operatorname pow x s operatorname pow x t text for all t in s s the close relationship to convex hulls and arrangements of hyperplanes is investigated and exploited efficient algorithms that compute the power diagram and its order k modifications are obtained among the applications of these results are algorithms for detecting k sets for union and intersection problems for cones and paraboloids and for constructing weighted voronoi diagrams and voronoi diagrams for spheres upper space bounds for these geometric problems are derived

oscillation criteria of a class of partial difference equations with delays this paper is concerned with the linear delay partial difference equation aa m 1 n 1 ba m 1 n ca n m n l da m n p m na m s n t 0 where s and t are two nonnegative integers a b c and d are positive constants and p i j i j e n 0 is a double real sequence sufficient conditions for this equation to be oscillatory are derived

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

voronoi diagram in the laguerre geometry and its applications we extend the concept of voronoi diagram in the ordinary euclidean geometry for n points to the one in the laguerre geometry for n circles in the plane where the distance between a circle and a point is defined by the length of the tangent line and show that there is an o n log n algorithm for this extended case the voronoi diagram in the laguerre geometry may be applied to solving effectively a number of geometrical problems such as those of determining whether or not a point belongs to the union of n circles of finding the connected components of n circles and of finding the contour of the union of n circles as in the case with ordinary voronoi diagrams the algorithms proposed here for those problems are optimal to within a constant factor some extensions of the problem and the algorithm from different viewpoints are also suggested

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