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

the envelope of spectral power for stochastic processes it is well known that the maximum likelihood ml spectral estimate represents an envelope on spectral power which is consistent with estimated covariance lags however in computing the envelope the ml method allows for spectra corresponding to complex valued stochastic processes we study the respective envelope for processes constrained to be real valued at the outset the resulting envelope is less conservative than the one provided by the ml method a closed form expression exists for the new envelope

robust l_ infty induced filtering and control of stochastic systems with state multiplicative noise linear continuous time systems with stochastic uncertainties in their state space model are considered the problems of induced l state feedback control and filtering are solved for the stationary case in both problems the cost function is defined to be the expected value of the standard induced l performance index with respect to the uncertain parameters an example that demonstrates the applicability of the theory is given

an extended robust h _infty filter for nonlinear constrained uncertain systems in this correspondence a robust filter is proposed to effectively estimate the system states in the case where system model uncertainties as well as disturbances are present the proposed robust filter is constructed based on the linear approximation methods for a general nonlinear uncertain system with an integral quadratic constraint we also derive the important characteristic of the proposed filter a modified hinfin performance index analysis results show that the proposed filter has robustness against disturbances such as process and measurement noises and against parameter uncertainties simulation results show that the proposed filter provides a performance improvement

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

quantitative mixing results and inner functions we study in this paper estimates on the size of the sets of points which are well approximated by orbits of other points under certain dynamical systems we apply the results obtained to the particular case of the dynamical system generated by inner functions in the unit disk of the complex plane

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

a small gain theorem for linear stochastic systems abstract a well known result in linear control theory is the so called small gain theorem stating that if given two plants with transfer matrix functions t 1 and t 2 in h such that t 1 and t 2 when coupling t 2 to t 1 such that u 2 y 1 and u 1 y 2 one obtains an internally stable closed system the aim of the present paper is to describe a corresponding result for stochastic systems with state dependent white noise

state feedback control of systems with multiplicative noise via linear matrix inequalities we consider lti systems perturbed by parametric uncertainties modeled as white noise disturbances we show how to maximize via state feedback control the smallest norm of the noise intensity vector producing instability in the mean square sense using convex optimization over linear matrix inequalities we also show how to maximize performance robustness where performance is measured by expected output energy with either bounded initial conditions and zero inputs classical lqg cost or zero initial conditions and deterministic inputs of bounded energy a generalization of the h norm

some remarks on general nonlinear stochastic h_ infty control with state control and disturbance dependent noise this technical note studies the nonlinear stochastic h control of ito type differential systems with all the state control input and external disturbance dependent noise x u v dependent noise for short a sufficient condition is given for the finite infinite horizon h control of such a system by means of an hamilton jacobi inequality hji instead of three coupled hamilton jacobi equations hjes as in previous literature

robust fuzzy filter design for a class of nonlinear stochastic systems this paper describes the robust hinfin fuzzy filtering design for a class of nonlinear stochastic systems the system dynamic is modelled by itocirc type stochastic differential equations for general nonlinear stochastic systems the hinfin filter can be obtained by solving a second order nonlinear hamilton jacobi inequality in general it is difficult to solve the second order nonlinear hamilton jacobi inequality in this paper using fuzzy approach takagi sugeno t s fuzzy model the hinfin fuzzy filtering design for the nonlinear stochastic systems can be given via solving linear matrix inequalities lmis instead of a second order hamilton jacobi inequality when the worst case fuzzy disturbance is considered a near minimum variance fuzzy filtering problem is also solved by minimizing the upper bound on the variance of the estimation error the near minimum variance fuzzy filtering problem under the worst case fuzzy disturbance is also characterized in terms of linear matrix inequality problem lmip which can be efficiently solved by the convex optimization techniques simulation examples are provided to illustrate the design procedure and expected performance

robust h estimation of stationary discrete time linear processes with stochastic uncertainties the problem of h filtering of stationary discrete time linear systems with stochastic uncertainties in the state space matrices is addressed where the uncertainties are modeled as white noise the relevant cost function is the expected value with respect to the uncertain parameters of the standard h performance a previously developed stochastic bounded real lemma is applied that results in a modified riccati inequality this inequality is expressed in a linear matrix inequality form whose solution provides the filter parameters the method proposed is applied also 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 h2 h filtering for the above system is also treated the theory developed is demonstrated by a simple tracking example

robust h filtering for discrete nonlinear stochastic systems with time varying delay this is the postprint version of the article the official published version can be accessed from the link below 2007 elsevier inc

finite horizon h_ infty filtering with missing measurements and quantization effects in this paper a new h filtering approach is developed for a class of discrete time varying systems subject to missing measurements and quantization effects the missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval 0 1 the measured output is quantized by a logarithmic quantizer attention is focused on the design of a stochastic h filter such that the h estimation performance is guaranteed over a given finite horizon in the simultaneous presence of probabilistic missing measurements quantization effects as well as external non gaussian disturbances a necessary and sufficient condition is first established for the existence of the desired time varying filters in virtue of the solvability of certain coupled recursive riccati difference equations rdes owing to its recursive nature the proposed rde approach is shown to be suitable for online application without the need of increasing the problem size the simulation experiment is carried out for the mobile robot localization problem with non gaussian disturbances missing measurements and quantization effects the effectiveness of the proposed method is demonstrated in the numerical example

h 2 and h_ infty robust filtering for discrete time linear systems this paper investigates robust filtering design problems in h2 and h infty spaces for discrete time systems subjected to parameter uncertainty which is assumed to belong to a convex bounded polyhedral domain it is shown that by a suitable change of variables both design problems can be converted into convex programming problems written in terms of linear matrix inequalities lmi the results generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured then assuming the order of the uncertain system is known the optimal guaranteed performance h2 and h infty filters are proven to be of the same order as the order of the system comparisons with robust filters for systems subjected to norm bounded uncertainty are provided in both theoretical and practical settings in particular it is shown that under the same assumptions the results here are generally better as far as the minimization of a guaranteed cost expressed in terms of h2 or h infty norms is considered some numerical examples illustrate the theoretical results

diophantine approximation and cantor sets we provide an explicit construction of elements of the middle third cantor set with any prescribed irrationality exponent this answers a question posed by kurt mahler

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

the dimensions of a non conformal repeller and an average conformal repeller in this paper using thermodynamic formalism for the sub additive potential upper bounds for the hausdorff dimension and the box dimension of non conformal repellers are obtained as the sub additive bowen equation the map f only needs to be c 1 without additional conditions we also prove that all the upper bounds for the hausdorff dimension obtained in earlier papers coincide this unifies their results furthermore we define an average conformal repeller and prove that the dimension of an average conformal repeller equals the unique root of the sub additive bowen equation

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

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

a dynamical dimension transference principle for dynamical diophantine approximation diophantine approximation in dynamical systems concerns the diophantine properties of the orbits in classic diophantine approximation the powerful mass transference principle established by beresnevich and velani provides a general principle to the dimension for a limsup set in this paper we aim at finding a general principle for the dimension of the limsup set arising in a general expanding dynamical system more precisely let x t be a topological dynamical system where x is a compact metric space and t x rightarrow x is an expanding continuous transformation given y o in x we consider the following limsup set mathcal w t f driven by the dynamical system x t begin aligned big x in x x in b z e s n f log t z text for some z in t n y o text with infinitely many n in mathbb n big end aligned where log t is a function reflecting the local conformality of the transformation t f is a non negative continuous function over x and s n f log t z denotes the ergodic sum f log t z cdots f log t t n 1 z by proposing a dynamical ubiquity property assumed on the system x t we obtain that the dimensions of x and mathcal w t f are both related to the bowen manning mccluskey formulae namely the solution to the pressure functions begin aligned texttt p t log t 0 text and texttt p t log t f 0 text respectively end aligned we call this phenomenon a dynamical dimension transference principle because of its partial analogy with the mass transference principle this general principle unifies and extends some known results which were considered only separatedly before these include the b adic expansions expanding rational maps over julia sets inhomogeneous diophantine approximation on the triadic cantor set and finite conformal iterated function systems

h sub 2 and h sub spl infin robust filtering for convex bounded uncertain systems investigates robust filtering design problems in h sub 2 and h sub spl infin spaces for continuous time systems subjected to parameter uncertainty belonging to a convex bounded polyhedral domain it is shown that by a suitable change of variables both designs can be converted into convex programming problems written in terms of linear matrix inequalities the results generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured then assuming the order of the uncertain system is known the optimal guaranteed performance h sub 2 and h sub spl infin filters are proven to be of the same order as the order of the system a numerical example illustrate the theoretical results

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

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

static output feedback of state multiplicative systems with application to altitude control a linear parameter dependent approach for designing a constant output feedback controller for a linear time invariant system with stochastic multiplicative wiener type noise that achieves a minimum bound on either the stochastic h 2 or the h performance level is introduced a solution is achieved also for the case where in addition to the stochastic parameters the system matrices reside in a given polytope in this case a parameter dependent lyapunov function is introduced which enables the derivation of the required constant gain via a solution of a set of linear matrix inequalities that corresponds to the vertices of the uncertainty polytope the stochastic uncertainties appear in both the dynamic and the measurement matrices of the system the problems are solved using the expected value of the standard performance index over the stochastic parameters the theory developed is applied to an altitude control example

robust energy to peak filter design for stochastic time delay systems abstract this paper considers the robust energy to peak filtering problem for uncertain stochastic time delay systems the stochastic uncertainties appear in both the dynamic and the measurement equations and the state delay is assumed to be time varying attention is focused on the design of full order and reduced order filters guaranteeing a prescribed energy to peak performance for the filtering error system sufficient conditions are formulated in terms of linear matrix inequalities lmis and the corresponding filter design is cast into a convex optimization problem which can be efficiently handled by using standard numerical algorithms in addition the results obtained are further extended to more general cases where the system matrices also contain uncertain parameters the most frequently used ways of dealing with parameter uncertainties including polytopic and norm bounded characterizations have been taken into consideration with convex optimization problems obtained for the design of desired robust energy to peak filters

finite horizon h_ 2 h_ infty control for discrete time stochastic systems with markovian jumps and multiplicative noise in this note we consider the finite horizon mixed h 2 h control problem for discrete time stochastic linear systems subject to markov jump parameters and multiplicative noise firstly we derive a stochastic bounded real lemma sbrl which is used to establish a necessary and sufficient condition for the existence of the mixed h 2 h control via the solvability of four coupled difference matrix valued recursions cdmrs moreover a state feedback h 2 h controller is designed by means of the solutions of cdmrs

state feedback h_ infty control for a class of nonlinear stochastic systems this paper discusses the h infty control problem for a class of nonlinear stochastic systems with both state and disturbance dependent noise by means of hamilton jacobi equations both infinite and finite horizon nonlinear stochastic h infty control designs are developed some results on nonlinear h infty control of deterministic systems are generalized to a stochastic setting we introduce some useful concepts such as zero state observability and zero state detectability which together with the stochastic lasalle invariance principle yield some valuable consequences in infinite horizon nonlinear stochastic h infty control

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

brief paper a delay decomposition approach to l2 l filter design for stochastic systems with time varying delay this paper investigates the problem of l 2 l filter design for a class of stochastic systems with time varying delay the addressed problem is the design of a full order linear filter such that the error system is asymptotically mean square stable and a prescribed l 2 l performance is satisfied in order to develop a less conservative filter design a new lyapunov krasovskii functional lkf is constructed by decomposing the delay interval into multiple equidistant subintervals and a new integral inequality is established in the stochastic setting then based on the lkf and integral inequality the delay dependent conditions for the existence of l 2 l filters are obtained in terms of linear matrix inequalities lmis the resulting filters can ensure that the error system is asymptotically mean square stable and the peak value of the estimation error is bounded by a prescribed level for all possible bounded energy disturbances finally two examples are given to illustrate the effectiveness of the proposed method

reduced order h filtering for singular systems abstract this paper solves the problem of reduced order h filtering for singular systems the purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is regular impulse free or causal stable and satisfies a prescribed h performance level one major contribution of the present work is that necessary and sufficient conditions for the solvability of this problem are obtained for both continuous and discrete singular systems these conditions are characterized in terms of linear matrix inequalities lmis and a coupling non convex rank constraint moreover an explicit parametrization of all desired reduced order filters is presented when these inequalities are feasible in particular when a static or zeroth order h filter is desired it is shown that the h filtering problem reduces to a convex lmi problem all these results are expressed in terms of the original system matrices without decomposition which makes the design procedure simple and directly last but not least the results have generalized previous works on h filtering for state space systems an illustrative example is given to demonstrate the effectiveness of the proposed approach

robust stability analysis and state feedback synthesis for discrete time systems characterized by random polytopes this paper deals with discrete time linear systems whose state transition is determined by a sequence of random matrices having uncertain distributions in representing random matrices with uncertain distributions we use random polytopes whose vertices are random matrices with given fixed distributions for such systems characterized by random polytopes we first tackle a problem of analyzing robust second moment exponential stability in particular we show a linear matrix inequality based robust stability condition that can be solved through sample based evaluation of the associated expectations the confidence level for such sample based analysis is ensured by the central limit theorem then we extend the results about analysis toward robust stabilization state feedback synthesis in such a way that the confidence level arguments can be facilitated we also provide numerical examples illustrating our analysis and synthesis framework

stochastic h sub spl infin tracking with preview for state multiplicative systems the problem of finite horizon h sub spl infin tracking for linear time varying systems with stochastic parameter uncertainties is investigated we consider three tracking patterns depending on the nature of the reference signal i e whether it is perfectly known in advance measured on line or previewed in a fixed time interval ahead the stochastic uncertainties appear in both the dynamic and measurement matrices of the system for each of the above three cases a game theory approach is applied for the state feedback case where given a specific reference signal the controller plays against nature which chooses the initial condition and the energy bounded disturbance the problems are solved using an expected value of the standard performance index over the stochastic parameters where necessary and sufficient conditions are found for the existence of a saddle point equilibrium the infinite horizon time invariant tracking problem is also solved the theory developed is demonstrated by a simple tracking example

hausdorff dimension of measures via poincare recurrence we study the quantitative behavior of poincare recurrence in particular for an equilibrium measure on a locally maximal hyperbolic set of a c1 diffeomorphism f we show that the recurrence rate to each point coincides almost everywhere with the hausdorff dimension d of the measure that is inf k 0 fkx b x r r d this result is a non trivial generalization of work of boshernitzan concerning the quantitative behavior of recurrence and is a dimensional version of work of ornstein and weiss for the entropy we stress that our approach uses different techniques furthermore our results motivate the introduction of a new method to compute the hausdorff dimension of measures

technical communique h output feedback control of discrete time systems with state multiplicative noise linear discrete time systems with stochastic uncertainties in their state space model are considered the problem of dynamic output feedback control is solved via a new approach for both the finite horizon and the stationary cases in both cases a cost function is defined which is the expected value of the standard h performance index with respect to the uncertain parameters an example is given which demonstrates the applicability of the theory

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

signal estimation via selective harmonic amplification music redux the technique known as multiple signal classification music is a semi empirical way to obtain pseudo spectra that highlight the spectral energy distribution of a time series it is based on a certain canonical decomposition of a toeplitz matrix formed out of an estimated autocorrelation sequence the purpose of this paper is to present an analogous canonical decomposition of the state covariance matrix of a stable linear filter driven by a given time series accordingly the paper concludes with a modification of music the new method starts with filtering the time series and then estimating the covariance of the state of the filter this step in essence improves the signal to noise ratio snr by amplifying the contribution to the actual value of the state covariance of a selected harmonic interval where spectral lines are expected to reside then the method capitalizes on the canonical decomposition of the filter state covariance to retrieve information on the location of possible spectral lines the framework requires uniformly spaced samples of the process

the ergodic theory of shrinking targets to any dynamical system equipped with a metric we associate a class of well approximable sets in the case of an expanding rational map of the riemann sphere acting on its julia set we estimate and in some cases compute the hausdorff dimension of the associated well approximable sets the methods used show a clear link between distortion properties and the type of results obtained in this paper via ergodic theory and ubiquity

reduced order h sub spl infin filtering for stochastic systems this paper deals with the reduced order h sub spl infin filtering problem for stochastic systems necessary and sufficient conditions are obtained for the existence of solutions to the continuous time and discrete time problems in terms of certain linear matrix inequalities lmis and a coupling nonconvex rank constraint condition furthermore when these conditions are feasible an explicit parametrization of all desired reduced order filters corresponding to a feasible solution is given in particular when the reduced order filter is restricted to be a static one then simple conditions expressed by lmis only without any rank constraints are derived and a parametrization of all solutions is also given finally an illustrative example is provided to show the effectiveness of the proposed approach

min max kalman filtering abstract the problem of h optimal state estimation of linear continuous time systems that are measured with an additive white noise is addressed the relevant cost function is the expected value of the standard h performance index with respect to the measurement noise statistics the solution is obtained by applying the matrix version of the maximum principle to the solution of the min max problem in which the estimator tries to minimize the mean square estimation error and the exogenous disturbance tries to maximize it while being penalized for its energy the solution is given in terms of two coupled riccati difference equations from which the filter gains are derived in the case where an infinite penalty is imposed on the energy of the exogenous disturbance the celebrated kalman filter is recovered in the stationary case where all the signals are stationary an upper bound on the solutions of the coupled riccati equations is obtained via a solution of coupled linear matrix inequalities the resulting filter then guarantees a bound on the estimation error covariance matrix an illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the position

brief paper on detectability of stochastic systems we discuss notions of detectability for stochastic linear control systems of ito type a natural concept of detectability requires a non zero output if the state process is unstable we show that this property can equivalently be characterized by a generalized version of the hautus test the proof is based on spectral theory for positive operators

filtering for discrete fuzzy stochastic systems with sensor nonlinearities this paper deals with the filtering problem for discrete time fuzzy stochastic systems with sensor nonlinearities there exist time varying parameter uncertainties and random noise depending on state and external disturbance the characteristic of nonlinear sensor is handled by a decomposition method by means of the parallel distributed compensation technique the design method of the robust h filter is presented sufficient conditions for the stochastic stability of the filtering error systems are derived such that the filter parameters can be explicitly obtained simulation results are given to illustrate the proposed method

spectral estimation via selective harmonic amplification the state covariance of a linear filter is characterized by a certain algebraic commutativity property with the state matrix of the filter and also imposes a generalized interpolation constraint on the power spectrum of the input process this algebraic property and the relationship between state covariance and the power spectrum of the input allow the use of matrix pencils and analytic interpolation theory for spectral analysis several algorithms for spectral estimation are developed with resolution higher than state of the art

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

on the discrete time bounded real lemma with application in the characterization of static state feedback h controllers abstract this paper deals with the discrete time bounded real lemma and its application in the characterization of all static state feedback h controllers for discrete time systems we first present two versions of the discrete time bounded real lemma the results apply to non minimal stable state space realizations and are given in terms of either the positive semi definite strong solution or the positive semi definite stabilizing solution of a discrete algebraic riccati equation based on the discrete time bounded real lemma we obtain a characterization of all static state feedback h controllers for discrete time systems as an application of the parameterization of all static state feedback h controllers we develop a solution to the discrete time h control problem via static output feedback also a numerical procedure is proposed to determine an output feedback gain

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

a mass transference principle and the duffin schaeffer conjecture for hausdorff measures a hausdorff measure version of the duffin schaeffer conjecture in metric number theory is introduced and discussed the general conjecture is established modulo the original conjecture the key result is a mass transference principle which allows us to transfer lebesgue measure theoretic statements for lim sup subsets of r k to hausdorff measure theoretic statements in view of this the lebesgue theory of lim sup sets is shown to underpin the general hausdorff theory this is rather surprising since the latter theory is viewed to be a subtle refinement of the former

static h2 and h output feedback of discrete time lti systems with state multiplicative noise abstract a parameter dependent approach for designing static output feedback controller for linear time invariant systems with state multiplicative noise is introduced which achieves a minimum bound on either the stochastic h 2 or the h performance levels a solution is obtained also for the case where in addition to the stochastic parameters the system matrices reside in a given polytope in this case a parameter dependent lyapunov function is described which enables the derivation of the required constant feedback gain via a solution of a set of linear matrix inequalities that correspond to the vertices of the uncertainty polytope the stochastic parameters appear in both the dynamics and the input matrices of the state space model of the system the problems are solved using the expected value of the standard performance indices over the stochastic parameters the theory developed is demonstrated by a simple example

dimensions and measures in infinite iterated function systems the hausdorff and packing measures and dimensions of the limit sets of iterated function systems generated by countable families of conformal contractions are investigated conformal measures for such systems reflecting geometric properties of the limit set are introduced proved to exist and to be unique the existence of a unique invariant probability equivalent to the conformal measure is derived our methods employ the concepts of the perron frobenius operator symbolic dynamics on a shift space with an infinite alphabet and the properties of the above mentioned ergodic invariant measure a formula for the hausdorff dimension of the limit set in terms of the pressure function is derived fractal phenomena not exhibited by finite systems are shown to appear in the infinite case in particular a variety of conditions are provided for hausdorff and packing measures to be positive or finite and a number of examples are described showing the appearance of various possible combinations for these quantities one example given special attention is the limit set associated to the complex continued fraction expansion in particular lower and upper estimates for its hausdorff dimension are given a large natural class of systems whose limit sets are dimensionless in the restricted sense is described

quantitative recurrence results letx be a probability measure spacex x endowed with a compatible metricd so that x d has a countable base it is well known that ift x x is measure preserving then almost all pointsx x are recurrent i e lim begin array 20 c inf n geqq 1 end array d x t n x 0 we show that under the additional assumption that the hausdorff measureh x ofx is finite for some 0 this result can be strengthened lim begin array 20 c inf n geqq 1 end array left n 1 alpha d x t n x right infty for almost all pointsx x a number of applications are considered

on a problem of k mahler diophantine approximation and cantor sets let k denote the middle third cantor set and mathcal a 3 n n 0 1 2 ldots given a real positive function let w mathcal a psi denote the set of real numbers x in the unit interval for which there exist infinitely many p q in mathbb z times mathcal a such that x p q q the analogue of the hausdorff measure version of the duffin schaeffer conjecture is established for w mathcal a psi cap k one of the consequences of this is that there exist very well approximable numbers other than liouville numbers in k an assertion attributed to k mahler explicit examples of irrational numbers satisfying mahler s assertion are also given

h sub 2 optimal linear robust sampled data filtering design using polynomial approach a new frequency domain approach to robust multi input multi output mimo linear filter design for sampled data systems is presented the system and noise models are assumed to be represented by polynomial forms that are not perfectly known except that they belong to a certain set the optimal design guarantees that the error variance is kept below an upper bound that is minimized for all admissible uncertainties the design problem is cast in the context of h sub 2 via the polynomial matrix representation of systems with norm bounded unstructured uncertainties the sampled data mix of continuous and discrete time systems is handled by means of a lifting technique however it does not increase the dimensionality or alter the computational cost of the solution the setup adopted allows dealing with several filtering problems a simple deconvolution example illustrates the procedure

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

logarithm laws for flows on homogeneous spaces in this paper we generalize and sharpen d sullivan s logarithm law for geodesics by specifying conditions on a sequence of subsets at t n of a homogeneous space g g a semisimple lie group an irreducible lattice and a sequence of elements ft of g under which t n ftx at is infinite for a e x g the main tool is exponential decay of correlation coefficients of smooth functions ong besides the general higher rank version of sullivan s result as a consequence we obtain a new proof of the classical khinchin groshev theorem on simultaneous diophantine approximation and settle a conjecture recently made by m skriganov

robust h sub spl infin filtering for nonlinear stochastic systems this paper describes the robust h sub spl infin filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance dependent noise we assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by ito spl circ type stochastic differential equations for general nonlinear stochastic systems the h sub spl infin filter can be obtained by solving second order nonlinear hamilton jacobi inequalities when the worst case disturbance is considered in the design procedure a mixed h sub 2 h sub spl infin filtering problem is also solved by minimizing the total estimation error energy it is found that for a class of special nonlinear stochastic systems the h sub spl infin filtering design can be given via solving several linear matrix inequalities instead of hamilton jacobi inequalities a few examples show that the proposed methods are effective