brief robust h filtering for uncertain impulsive stochastic systems under sampled measurements this paper is concerned with the problem of robust h filtering for uncertain impulsive stochastic systems under sampled measurements the parameter uncertainties are assumed to be time varying norm bounded the aim is to design a stochastically stable filter using the locally sampled measurements which ensures both the robust stochastic stability and a prescribed level of h performance for the filtering error dynamics for all admissible uncertainties a sufficient condition for the existence of such a filter is proposed in terms of certain linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given an example is provided to demonstrate the effectiveness of the proposed approach

inverse wave scattering with discontinuous wave speed the inverse scattering problem on the line is studied for the generalized schrodinger equation d2 dx2 k2h x 2 q x where h x is a positive piecewise continuous function with positive limits h as x this equation in the frequency domain describes the wave propagation in a nonhomogeneous medium where q x is the restoring force and 1 h x is the variable wave speed changing abruptly at various interfaces a related riemann hilbert problem is formulated and the associated singular integral equation is obtained and proved to be uniquely solvable the solution of this integral equation leads to the recovery of h x in terms of the scattering data consisting of q x a reflection coefficient either of h and the bound state energies and norming constants some explicitly solved examples are provided

time dependent inverse scattering from gradient type interfaces using an exact solution in the context of one dimensional linear wave propagation a gradient type interface is a point at which the velocity profile of a scattering medium suffers a jump in first derivative in this paper a time domain approach to scattering from such an interface leads to an integrodifferential equation involving the kernel of the reflection operator impulse response which can be solved exactly if the velocity profile is piecewise parabolic this special case provides the basis for an approximate numerical scheme to solve the inverse scattering problem recover the velocity profile from reflection data for a general velocity profile the algorithm is fast and affords good results if the velocity profile is nearly parabolic or the interest is in short time only a detailed error estimate for the approximation is provided

discontinuous inverse eigenvalue problems on considere des problemes de sturm liouville inverses dans lesquels les fonctions propres ont une discontinuite dans un point interieur on montre que si le potentiel est connu sur la moitie de l intervalle et si une condition limite est donnee alors le potentiel et l autre condition limite sont determines de facon unique par les valeurs propres

approximate finite dimensional filtering for polynomial states over polynomial observations in this article the mean square filtering problem for polynomial system states over polynomial observations is studied proceeding from the general expression for the stochastic ito differentials o

filtering on sampled data systems with parametric uncertainty the paper is concerned with the problem of robust h sub spl infin filtering for a class of systems with parametric uncertainties and unknown time delays under sampled measurements the parameter uncertainties considered are real time varying and norm bounded appearing in the state equation an approach has been proposed for the designing of h sub spl infin filters using sampled measurements which would guarantee a prescribed h sub spl infin performance in the continuous time context irrespective of the parameter uncertainties and unknown time delays both cases of finite and infinite horizon filtering are studied it has been shown that the above robust h sub spl infin filtering problem can be solved in terms of differential riccati inequalities with finite discrete jumps

filtering for stochastic systems driven by poisson processes this paper investigates the filtering problem for stochastic systems driven by poisson processes by utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator this paper transforms the expectation of stochastic integral with respect to the poisson process into the expectation of lebesgue integral then based on this this paper designs an filter such that the filtering error system is mean square asymptotically stable and satisfies a prescribed performance level finally a simulation example is given to illustrate the effectiveness of the proposed filtering scheme

brief paper robust stability and h control of uncertain impulsive systems with time delay this paper investigates the problems of robust stability stabilization and h control for uncertain impulsive systems with time delay the parametric uncertainties are assumed to be time varying and norm bounded three classes of impulsive systems with time delay are considered the systems with stable stabilizable continuous dynamics and unstable unstabilizable discrete dynamics the systems with unstable unstabilizable continuous dynamics and stable stabilizable discrete dynamics and the systems where both the continuous time dynamics and the discrete time dynamics are stable stabilizable for each class of system by using the lyapunov function and razumikhin type techniques sufficient conditions for robust stability stabilization and h control are developed in terms of linear matrix inequalities numerical examples are given which illustrate the applicability of the theoretical results

model reduction of uncertain systems with multiplicative noise based on balancing this paper investigates the problem of model reduction based on balancing for uncertain discrete time systems with multiplicative noise such systems can be considered as linear systems with both deterministic and stochastic uncertainties two linear matrix inequalities lmis are proposed to find the balancing transformation through which the original uncertain model with multiplicative noise is balanced the reduced order model with the same structure as that of the original one is obtained by truncating the balanced model an upper bound of the model reduction error is guaranteed based on the derived model reduction error bound an optimization problem is suggested so that the solutions of the lmis can be uniquely found and the model reduction error is ensured to be small

eigenvalue bounds spectral partitioning and metrical deformations via flows we present a new method for upper bounding the second eigenvalue of the laplacian of graphs our approach uses multi commodity flows to deform the geometry of the graph we embed the resulting metric into euclidean space to recover a bound on the rayleigh quotient using this we show that every n vertex graph of genus g and maximum degree d satisfies 2 g eo g 1 3d n this recovers the o d n bound of spielman and teng for planar graphs and compares to kelner s bound of o g 1 poly d n but our proof does not make use of conformal mappings or circle packings we are thus able to extend this to resolve positively a conjecture of spielman and teng by proving that 2 g e o dh6log h n whenever g is kh minor free this shows in particular that spectral partitioning can be used to recover o sn sized separators in bounded degree graphs that exclude a fixed minor we extend this further by obtaining nearly optimal bounds on 2 for graphs that exclude small depth minors in the sense of plotkin rao and smith consequently we show that spectral algorithms find separators of sublinear size in a general class of geometric graphs moreover while the standard sweep algorithm applied to the second eigenvector may fail to find good quotient cuts in graphs of unbounded degree our approach produces a vector that works for arbitrary graphs this yields an alternate proof of the well known nonplanar separator theorem of alon seymour and thomas that states that every excluded minor family of graphs has o sn node balanced separators

on sturm liouville operators with discontinuity conditions inside an interval abstract in this study transformation operator some properties of kernel properties of spectral characteristics and also uniquiness theorems for the inverse problems are studied for a class of sturm liouville differential operators which have discontinuity conditions inside a finite interval

stability and stabilization of switched linear systems with mode dependent average dwell time in this paper the stability and stabilization problems for a class of switched linear systems with mode dependent average dwell time mdadt are investigated in both continuous time and discrete time contexts the proposed switching law is more applicable in practice than the average dwell time adt switching in which each mode in the underlying system has its own adt the stability criteria for switched systems with mdadt in nonlinear setting are firstly derived by which the conditions for stability and stabilization for linear systems are also presented a numerical example is given to show the validity and potential of the developed techniques

trace and inverse problem of a discontinuous sturm liouville operator with retarded argument abstract in this study a discontinuous boundary value problem with retarded argument and with transmission conditions at the point of discontinuity is investigated regularized sums from the eigenvalues oscillations of eigenfunctions and the solutions of inverse nodal problem for the problem are obtained in the special case that the transmission coefficient 1 and retarded argument 0 in the results obtained below coincide with corresponding results in the classical sturm liouville operator

fuzzy controller design for nonlinear impulsive fuzzy systems with time delay the stabilization problem is investigated for continuous time takagi sugeno t s fuzzy systems with time delay and impulsive effects in this paper some delay independent and delay dependent stabilization approaches are developed for both state feedback and observer based feedback cases which are based on the lyapunov krasovskii functional approach and a parallel distributed compensation scheme the time delay is dealt by lyapunov theory allied with the halanay lemma the restriction on the interval between each impulsive instant and output sampled instant needs not be equal to or less than a constant scalar but it only requires an inequality satisfaction when the impulsive effects vanish the results can be extended to the corresponding sufficient conditions for the cases of a nonlinear continuous time delay system with a state feedback and observer based sampled output feedback finally some examples are given to demonstrate the effectiveness of the proposed method

single source shortest paths in h minor free graphs we present an algorithm for the single source shortest paths sssp problem in directedh minor free graphs for every fixed h if g is a graph with n vertices having integer edge lengths and s is a designated source vertex of g the algorithm runs in o n 1 1 5 2logl o n 1 3 9 2logl time where l is the absolute value of the smallest edge length the algorithm computes the shortest paths and the distances from s to all vertices of the graph or else provides a certificate that g is not h minor free our result improves an earlier o n 1 5logl time algorithm for this problem which follows from a general sssp algorithm of goldberg

every minor closed property of sparse graphs is testable abstract suppose g is a graph of bounded degree d and one needs to remove n of its edges in order to make it planar we show that in this case the statistics of local neighborhoods around vertices of g is far from the statistics of local neighborhoods around vertices of any planar graph g in fact a similar result is proved for any minor closed property of bounded degree graphs the main motivation of the above result comes from theoretical computer science using our main result we infer that for any minor closed property p there is a constant time algorithm for detecting if a graph is far from satisfying p this in particular answers an open problem of goldreich and ron stoc 1997 20 who asked if such an algorithm exists when p is the graph property of being planar the proof combines results from the theory of graph minors with results on convergent sequences of sparse graphs which rely on martingale arguments

mean square stability analysis of impulsive stochastic differential equations with delays in this article based on lyapunov krasovskii functional method and stochastic analysis theory we obtain some new criteria ensuring mean square stability of trivial solution of a class of impulsive stochastic differential equations with delays as an application a class of stochastic impulsive neural network with delays has been discussed one illustrative example has been provided to show the effectiveness of our results

h filtering for a class of uncertain nonlinear systems abstract this paper investigates the problem of h filtering for a class of uncertain continuous time nonlinear systems with real time varying parameter uncertainty and unknown initial state we develop an infinite horizon h filtering methodology which provides both robust stability and a guaranteed h performance for the filtering error irrespective of the parameter uncertainty

the strong perfect graph theorem a graph g is perfect if for every induced subgraph h the chromatic number of h equals the size of the largest complete subgraph of h and g is berge if no induced subgraph of g is an odd cycle of length at least five or the complement of one the strong perfect graph conjecture berge 1961 asserts that a graph is perfect if and only if it is berge a stronger conjecture was made recently by conforti cornu ejols and vuiskovi c that every berge graph either falls into one of a few basic classes or admits one of a few kinds of separation designed so that a minimum counterexample to berge s conjecture cannot have either of these properties in this paper we prove both of these conjectures

inverse nodal problems of discontinuous sturm liouville operator abstract we study inverse nodal problems for the second order differential operator with discontinuity inside a finite interval in particular we solve the uniqueness reconstruction and stability problems using the nodal set of its eigenfunctions furthermore we show that the space of discontinuous sturm liouville operators characterized by b q h h a 1 a 2 l 1 0 1 r 4 such that 0 1 q x d x 0 is homeomorphic to the partition set of the space of quasinodal sequences which are all admissible sequences x x n j n 2 j 1 n 1 which form sequences that converge to q h h and 2 a 2 a 1 a 1 1 individually

h sub infinity minimum error state estimation of linear stationary processes a state estimator is derived which minimizes the h sub infinity norm of the estimation error power spectrum matrix two approaches are presented the first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution the second approach establishes a duality between the problem of h sub infinity filtering and the problem of unconstrained input h sub infinity optimal regulation using this duality previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding kalman filter the two approaches usually lead to different results they are compared by a simple example which also demonstrates a clear advantage of the h sub infinity estimate over the conventional l sub 2 estimate

on quasi stability for impulsive differential systems on developpe une theorie de la stabilite relativement a une solution donnee de systemes differentiels impulsifs une telle etude conduit a un mecanisme complique et les notions de stabilite doivent etre modifiees

stability analysis of systems with impulse effects the authors establish conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulse effects described by systems of nonlinear time varying ordinary differential equations under mild additional assumptions these sufficient conditions turn out to be necessary as well for the case of time invariant systems with impulse effects described by nonlinear ordinary differential equations the above results are used to establish conditions under which the uniform asymptotic stability of equilibria can be deduced from the linearizations of such systems

inverse nodal and inverse spectral problems for discontinuous boundary value problems inverse nodal and inverse spectral problems are studied for second order differential operators on a finite interval with discontinuity conditions inside the interval uniqueness theorems are proved and a constructive procedure for the solution is provided

brief h control and filtering of discrete time stochastic systems with multiplicative noise linear discrete time systems with stochastic uncertainties in their state space matrices are considered the problems of finite horizon filtering and output feedback control are solved taking into account possible cross correlations between the uncertain parameters in both problems a cost function is defined which is the expected value of the relevant standard h performance index with respect to the uncertain parameters a solution to the filtering problem is obtained first by applying the adjoint system and deriving a bounded real lemma for this system this solution guarantees a prescribed estimation level of accuracy while minimizing an upper bound on the covariance of the estimation error the solution of the filtering problem is also extended to the infinite horizon case the results of the filtering problem are used to solve the corresponding output feedback problem a filtering example is given where a comparison is made with the results obtained using bounded uncertainty design techniques

nearly tight bounds on the contiguity and linearity of cographs in this paper we show that the contiguity and linearity of cographs on n vertices are both o logn moreover we show that this bound is tight for contiguity as there exists a family of cographs on n vertices whose contiguity is w logn we also provide an w logn loglogn lower bound on the maximum linearity of cographs on n vertices as a by product of our proofs we obtain a min max theorem which is worth of interest in itself stating equality between the rank of a tree and the minimum height of one of its path partitions

a decoupled approach to filter design for stochastic systems abstractthis paper presents a new theorem to guarantee the almost sure exponential stability for a class of stochastic triangular systems by studying only the stability of each diagonal subsystems this result allows to solve the filtering problem of the stochastic systems with multiplicative noises by using the almost sure exponential stability concept two kinds of observers are treated the full order and reduced order cases

robustness analysis for parameter matrices of global exponential stability time varying delay systems abstract this paper analyzes the robustness of global exponential stability time varying delay systems subjected to parameter uncertainty given a globally exponentially stable time varying delay systems the problem to be addressed herein is how much parameter uncertainty the systems can withstand to be globally exponentially stable we characterize the upper bounds of the parameter uncertainty for the systems to sustain global exponential stability moreover we prove theoretically that for globally exponentially stable systems if additive parameter uncertainty is smaller than the derived upper bounds arrived at here then the perturbed systems are guaranteed to also be globally exponentially stable a numerical example is provided to illustrate the theoretical result

robust h filters for markovian jump linear systems under sampled measurements abstract in this paper a new class of markovian jump linear system model with polytopic parameter uncertainty continuous disturbance and discrete disturbance is introduced the transition rate matrix of the markov process and the parameters of the system are either exactly known or unknown but belong to a given polytope the general criteria for the stochastic stability of this model and the method for designing a robust stable linear time invariant h filter under sampled measurements are derived in terms of certain linear matrix inequalities lmis finally a numerical example is given to show that the method is effective and feasible

brief paper h functional filtering for stochastic bilinear systems with multiplicative noises this paper deals with the design of a reduced order h filter for a stochastic bilinear system with a prescribed h norm criterion the considered system is bilinear in control and with multiplicative noises in the dynamics and in the measurement equations the problem is transformed into the search of a unique gain matrix by using sylvester like constraints the approach is based on the resolution of lmi and is then easily implementable

a novel approach to output feedback control of fuzzy stochastic systems this paper investigates the problem of hankel norm output feedback controller design for a class of t s fuzzy stochastic systems the full order output feedback controller design technique with the hankel norm performance is proposed by the fuzzy basis dependent lyapunov function approach and the conversion on the hankel norm controller parameters sufficient conditions are established to design the controllers such that the resulting closed loop system is stochastically stable and satisfies a prescribed performance the desired output feedback controller can be obtained by solving a convex optimization problem which can be efficiently solved by standard numerical algorithms finally a henon map system is used to illustrate the effectiveness of the proposed techniques

integral equation methods for the inverse problem with discontinuous wave speed the recovery of the coefficient h x in the one dimensional generalized schrodinger equation d2 dx2 k2h x 2 q x where h x is a positive piecewise continuous function with positive limits h as x is studied the large k asymptotics of the wave functions and the scattering coefficients are analyzed a factorization formula is given expressing the total scattering matrix as a product of simpler scattering matrices using this factorization an algorithm is presented to obtain the discontinuities in h x and h x h x in terms of the large k asymptotics of the reflection coefficient when there are no bound states it is shown that h x is recovered from an appropriate set of scattering data by using the solution of a singular integral equation and the unique solvability of this integral equation is established an equivalent marchenko integral equation is derived and is shown to be uniquely solvable the unique recovery of h x from the solution of this marchenko equation is presented some expli

frequency domain wave splitting techniques for plane stratified bianisotropic media a plane harmonic electromagnetic wave obliquely incident on a plane stratified bianisotropic medium with multiple discontinuities in the parameters is considered a covariant wave splitting approach based on the use of the formula of integration by parts for multiplicative integrals and the impedance concept is presented it encompasses various types of decomposition of the total internal field into two waves propagating in opposite directions including the physical and vacuum wave splittings treated earlier in the literature and provides a convenient means for both analytical investigation and numerical calculation of evolution operators green s functions and impedance tensors of split waves as well as characteristic matrices and reflection and transmission tensors of stratified bianisotropic media the potentialities of the approach are illustrated by its application to the problems of reflection transmission and guided propagation and by generalizing the method of multiple reflections to the case of stratified bianisotropic media

filtering and smoothing in an h sup infinity setting the problems of filtering and smoothing are considered for linear systems in an h sup infinity setting i e the plant and measurement noises have bounded energies are in l sub 2 but are otherwise arbitrary two distinct situations for the initial condition of the system are considered the initial condition is assumed known in one case while in the other the initial condition is not known but the initial condition the plant and measurement noise are in some weighted ball of r sup n xl sub 2 finite horizon and infinite horizon cases are considered necessary and sufficient conditions are presented for the existence of estimators both filters and smoothers that achieve a prescribed performance bound and algorithms that result in performance within the bounds are developed in case of smoothers the optimal smoother is also presented the approach uses basic quadratic optimization theory in a time domain setting as a consequence of which both linear time varying and time invariant systems can be considered with equal ease in the smoothing problem for linear time varying systems one considers only the finite horizon case

uniqueness theorems for differential pencils with eigenparameter boundary conditions and transmission conditions abstract inverse spectral problems are considered for differential pencils with boundary conditions depending polynomially on the spectral parameter and with a finite number of transmission conditions we give formulations of the associated inverse problems such as titchmarsh weyl theorem hochstadt lieberman theorem and mochizuki trooshin theorem and prove corresponding uniqueness theorems the obtained results are generalizations of the similar results for the classical sturm liouville operator on a finite interval

design of a stable state feedback controller based on the multirate sampling of the plant output a new type of controller is proposed which detects the ith plant output n sub i times during a period of t sub 0 and changes the plant inputs once during t sub 0 it is shown that an arbitrary state feedback can be realized by such controllers if the plant is observable this implies for instance that arbitrary symmetric pole assignment is possible if the plant is controllable it is also shown that if the plant has no zeros at the origin the state transition matrix of the controller itself can be set arbitrarily without changing the state feedback to be realized that is to say inversely expressed any state feedback can be equivalently realized by a controller with any prescribed degree of stability

robust h filter design for neutral stochastic uncertain systems with time varying delay abstract in this paper the robust h filtering problem for a class of neutral stochastic systems is discussed the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delay the parameter uncertainties are assumed to be time varying norm bounded using the stochastic lyapunov stability theory and ito s differential rule a full order filter is designed for all admissible uncertainties and time varying delay which is expressed in the form of linear matrix inequality lmi the dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable while achieving a prescribed stochastic robust h performance level at the end of this paper a numerical example is given to demonstrate the usefulness of the proposed method

h sub infinity control and filtering for sampled data systems h sub infinity control and filtering problems for sampled data systems are studied necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified h sub infinity performance bound when these conditions hold explicit formulas for a controller and a filter satisfying the h sub infinity performance bound are also given

random walks and forbidden minors i an n 1 2 o 1 query one sided tester for minor closed properties on bounded degree graphs let g be an undirected bounded degree graph with n vertices fix a finite graph h and suppose one must remove varepsilon n edges from g to make it h minor free for some small consta

moment stability of discontinuous stochastic dynamical systems in this note we establish new lyapunov and lagrange stability results in the pth mean for a class of discontinuous stochastic dynamical systems we apply these results in the qualitative analysis of a class of digital feedback control systems that are subjected to multiplicative and additive disturbances in the plants the present results constitute natural extensions of our earlier results for discontinuous deterministic dynamical systems

inverse spectral problems for the sturm liouville operator with discontinuity abstract in this work we consider the sturm liouville operator on a finite interval 0 1 with discontinuous conditions at 1 2 we prove that if the potential is known a priori on a subinterval b 1 with b 1 2 then parts of two spectra can uniquely determine the potential and all parameters in discontinuous conditions and boundary conditions for the case b 1 2 parts of either one or two spectra can uniquely determine the potential and a part of parameters

inverse problems for nonabsorbing media with discontinuous material properties one dimensional electromagnetic and elastic inverse problems are formulated for media with discontinuous material properties in addition an impedence mismatch between source and medium is allowed the measured data for either problem is shown to generate a reflection kernel which is used in the solution of the inverse problem the solution algorithm itself is a time domain technique which is a special case of previously obtained results for absorbing media

a decomposition theory for binary linear codes the decomposition theory of matroids initiated by paul seymour in the 1980s has had an enormous impact on research in matroid theory this theory when applied to matrices over the binary field yields a powerful decomposition theory for binary linear codes in this paper we give an overview of this code decomposition theory and discuss some of its implications in the context of the recently discovered formulation of maximum likelihood ml decoding of a binary linear code over a binary input discrete memoryless channel as a linear programming problem we translate matroid theoretic results of grotschel and truemper from the combinatorial optimization literature to give examples of nontrivial families of codes for which the ml decoding problem can be solved in time polynomial in the length of the code one such family is that consisting of codes for which the codeword polytope is identical to the koetter vontobel fundamental polytope derived from the entire dual code cperp however we also show that such families of codes are not good in a coding theoretic sense either their dimension or their minimum distance must grow sublinearly with code length as a consequence we have that decoding by linear programming when applied to good codes cannot avoid failing occasionally due to the presence of pseudocode words

robust h sub spl infin filtering of stationary continuous time linear systems with stochastic uncertainties the problem of applying h sub spl infin filters on stationary continuous time linear systems with stochastic uncertainties in the state space signal model is addressed these uncertainties are modeled via white noise processes the relevant cost function is the expected value of the standard h sub spl infin performance index with respect to the uncertain parameters the solution is obtained via a stochastic bounded real lemma that results in a modified riccati inequality this inequality is expressed in the form of a linear matrix inequality whose solution provides the filter parameters the method proposed is also applied to the case where in addition to the stochastic uncertainty other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope the problem of mixed h sub 2 h sub spl infin filtering for the above system is also treated the theory developed is demonstrated by a practical example