the discrete time h control problem with measurement feedback this paper is concerned with the discrete time h infty control problem with measurement feedback it follows that as in the continuous time case the existence of an internally stabilizing controller that makes the h infty norm strictly less than 1 is related to the existence of stabilizing solutions to two algebraic riccati equations however in the discrete time case the solutions of these algebraic riccati equations must satisfy extra conditions

large derivatives backward contraction and invariant densities for interval maps in this paper we study the dynamics of a smooth multimodal interval map f with non flat critical points and all periodic points hyperbolic repelling assuming that dfn f c as n holds for all critical points c we show that f satisfies the so called backward contracting property with an arbitrarily large constant and that f has an invariant probability which is absolutely continuous with respect to lebesgue measure and the density of belongs to lp for all p lmax lmax 1 where lmax denotes the maximal critical order of f in the appendix we prove that various growth conditions on the derivatives along the critical orbits imply stronger backward contraction

analysis of h 2 and h performance of discrete periodically time varying controllers abstract this paper presents analysis of the h 2 and h performance of discrete linear periodically time varying controllers for control of linear time invariant plants using a frequency domain lifting approach the analysis distinguishes periodically time varying control from time invariant control to show that the multiple transfer channels of the system time varying dynamics amplify the overall system gain such a result can provide deeper insights into the system time varying mechanism and clarify how the time varying dynamics acts and degrades the system performance quantitatively the paper presents necessary and sufficient conditions under which a linear time invariant controller can be found to provide strictly better control than periodically time varying controllers

finite approximations of frobenius perron operators a solution of ulam s conjecture to multi dimensional transformations abstract we prove that ulam s piecewise constant approximation algorithm is convergent for computing an absolutely continuous invariant measure associated with a piecewise c2 expanding transformation or a jablonski transformation s 0 1 n rn 0 1 n this solves an extension of ulam s conjecture to multi dimensions and generalizes the convergence result given by t y li for one dimensional transformations

error analysis of nitsche s mortar method optimal a priori and a posteriori error estimates are derived for three variants of nitsche s mortar finite elements the analysis is based on the equivalence of nitsche s method and the stabilised mixed method nitsche s method is defined so that it is robust with respect to large jumps in the material and mesh parameters over the interface numerical results demonstrate the robustness of the a posteriori error estimators

a constructive approach to approximate linear periodic systems in this note the problem on approximating a linear periodic system with period n by a periodic model with period m 0 m n is revisited different from the existing results the proposed method is based on state space representations and the approximation performance is evaluated using hinfin norms under this framework both finite impulse response fir and infinite impulse response iir periodic systems can be efficiently approximated by using a constructive linear matrix inequality approach finally some numerical examples are given to illustrate the effectiveness of the proposed approach

a direct approach to conformational dynamics based on hybrid monte carlo recently a novel concept for the computation ofessentialfeatures of the dynamics of hamiltonian systems such as molecular dynamics has been proposed the realization of this concept had been based on subdivision techniques applied to the frobenius perron operator for the dynamical system the present paper suggests an alternative but related concept that merges the conceptual advantages of the dynamical systems approach with the appropriate statistical physics framework this approach allows us to define the phrase conformation in terms of the dynamical behavior of the molecular system and to characterize the dynamical stability of conformations in a first step the frequency of conformational changes is characterized in statistical terms leading to the definition of some markov operatortthat describes the corresponding transition probabilities within the canonical ensemble in a second step a discretization oftvia specific hybrid monte carlo techniques is shown to lead to astochasticmatrixp with these theoretical preparaions an identification algorithm for conformations to be presented in a later paper is applicable it is demonstrated that the discretization oftcan be restricted to few essential degrees of freedom so that the combinatorial explosion of discretization boxes is prevented and biomolecular systems can be attacked numerical results for the n pentane molecule and the triribonucleotide adenylyl 3 5 cytidylyl 3 5 cytidin are given and interpreted

the spectral analysis of frobenius perron operators abstract it is known that the frobenius perron operator p s l 1 0 1 l 1 0 1 associated with a transformation s from 0 1 to itself with inf s 1 is quasi compact as an operator on the banach space bv 0 1 of functions of bounded variation in l 1 0 1 and thus p s bv 0 1 bv 0 1 possesses only the finite peripheral spectrum and in particular 1 is an isolated eigenvalue of p s in this paper we show that under mild conditions on s the spectrum of p s l 1 x l 1 x is either the closed unit disk c 1 or a cyclic subset of c 1

a multirate digital controller for model matching abstract this paper presents a multirate digital controller which comprises a stable linear time invariant system with a multirate sampling scheme this controller is capable of arbitrary zero assignment pole assignment and model matching and it is applicable to plants with unstable zeros the stable controller also provides improved system intersample performance a controller design procedure is derived an example is given to illustrate the design and the system performance

time varying versus time invariant compensation for rejection of persistent bounded disturbances and robust stabilization it is shown that time varying compensation does not improve the optimal rejection of persistent bounded disturbances this result is obtained by exploiting a key observation that any time varying compensator which yields a given degree of disturbance rejection must do so uniformly over time thereby removing any advantage of time variation this key observation is exploited to show that time varying compensation does not improve the optimal rejection of disturbances regardless of the norm used to measure the disturbances thus absolutely summable finite energy or persistent bounded disturbances may be treated in the same manner it is shown that time varying compensation does not help in the bounded input bounded output robust stabilization of time invariant plants with unstructured uncertainty in doing so it is also shown that the small gain theorem is both necessary and sufficient for the bounded input bounded output stability of certain linear time varying plants subject to unstructured linear time varying perturbations

linear periodically time varying discrete time systems aliasing and lti approximations linear periodically time varying lptv systems are abundant in control and signal processing examples include multirate sampled data control systems and multirate filter bank systems in this paper several ways are proposed to quantify aliasing effect in discrete time lptv systems these are associated with optimal time invariant approximations of lptv systems using operator norms

a finite element method for the frobenius perron operator equation we present a finite element framework to numerically solve the absolutely continuous invariant measure associated with a non singular transformation both convergence analysis and error estimates of the method are given for a class of mappings in r n

linear time varying h 2 optimal control of sampled data systems abstract the goal in this paper is twofold first it is shown that linear time varying control is in general superior to linear time invariant lti control for lti plants with an h 2 criterion an expression for the optimal performance using time varying control is derived and a condition under which there is no advantage in using linear time varying control over lti control is determined second the h 2 optimal control of continuous time systems is studied via dual rate sampled data controllers it is shown that such a problem can be recast via the lifting technique as a standard lti h 2 problem in discrete time a design procedure for the dual rate h 2 optimal controller is proposed

approximating the invariant measures of randomly perturbed dissipative maps abstract we present a method for approximating the invariant measure of a randomly perturbed mappingsofrd cases where the unperturbed mapping is singular are considered as are cases where the sizes of random jumps are unbounded existence of an invariant measure and convergence of the scheme are proved when the mapping has strong contraction properties the implementation is designed to be useful in experimental situations where the map is known only approximately and the distribution of the noise is unknown under the same contraction conditions we also prove that the invariant measure the stationary measure of the associated markov chain is approached exponentially under iteration of the perturbed map independent of the starting point

performance of periodically time varying controllers for sampled data control analyzes performance of periodically time varying sampled data controllers for l sub p deterministic and uniform disturbance rejection for a given linear periodic sampled data controller controlling a linear time invariant continuous time plant it is shown that a linear time invariant controller can be found to give better l sub p sampled data control than the time varying controller the performance analysis is in time domain using convexity properties of the l sub p signal space

a lifting technique for linear periodic systems with applications to sampled data control abstract a lifting technique is developed for periodic linear systems and applied to the h and h 2 sampled data control problems

h sub 2 optimal inverse of periodic fir digital filters the objective of this correspondence is to design a fixed order h sub 2 optimal inverse filter of a given periodic fir digital filter in the presence of measurement noise the problem is solved by using a linear matrix inequality lmi approach to an equivalent time invariant h sub 2 optimization problem constructed by applying the lifting technique to the original periodic problem an example is given to demonstrate the effectiveness of the proposed design approach

all optimal hankel norm approximations of linear multivariable systems and their l error bounds the problem of approximating a multivariable transfer function g s of mcmillan degree n by s of mcmillan degree k is considered a complete characterization of all approximations that minimize the hankel norm is derived the solution involves a characterization of all rational functions s f s that minimize where s has mcmillan degree k and f s is anticavisal the solution to the latter problem is via results on balanced realizations all pass functions and the inertia of matrices all in terms of the solutions to lyapunov equations it is then shown that where k 1 g s is the k l st hankel singular value of g s and for one class of optimal hankel norm approximations the method is not computationally demanding and is applied to a 12 state model

analysis of time varying control strategies for optimal disturbance rejection and robustness analysis of linear time invariant systems that are controlled by time varying controllers is given the problems of disturbance rejection and robustness are formulated and analyzed using functional analytic methods which reveal the properties that are common to these problems the theoretical development presented uses the theory and techniques of nuclear operators and their relation with the duality theory of tensor products of banach spaces the authors show how time varying compensation offers no advantage over time invariant compensation for the problem of disturbance rejection over general signal spaces in both continuous and discrete time and for the problem of l sub infinity robust stabilization of time invariant plants in addition another application of the theory for the problem of norm minimization subject to a norm constraint is presented

h 2 performance of continuous time periodically time varying controllers abstract this paper uses a frequency domain approach to the analysis of h 2 performance of continuous time periodically time varying controllers for control of linear time invariant plants it is shown that the time varying dynamics of the periodic controller deteriorates the closed loop system h 2 performance and a linear time invariant controller can be found to provide strictly better h 2 control of the system

approximations of frobenius perron operators via interpolation abstract let s 0 1 0 1 be a chaotic map and let p l1 0 1 l1 0 1 be the corresponding frobenius perron operator we propose a piecewise linear approximations method based on interpolation that can be efficiently used to compute a fixed density of p the convergence of the method for a class of mappings is proved and numerical results are also presented

skew symmetric nitsche s formulation in isogeometric analysis dirichlet and symmetry conditions patch coupling and frictionless contact abstract a simple skew symmetric nitsche s formulation is introduced into the framework of isogeometric analysis iga to deal with various problems in small strain elasticity essential boundary conditions symmetry conditions for kirchhoff plates patch coupling in statics and in modal analysis as well as signorini contact conditions for linear boundary or interface conditions the skew symmetric formulation is parameter free for contact conditions it remains stable and accurate for a wide range of the stabilization parameter several numerical tests are performed to illustrate its accuracy stability and convergence performance we investigate particularly the effects introduced by nitsche s coupling including the convergence performance and condition numbers in statics as well as the extra outlier frequencies and corresponding eigenmodes in structural dynamics we present the hertz test the block test and a 3d self contact example showing that the skew symmetric nitsche s formulation is a suitable approach to simulate contact problems in iga

nonlinear time varying controllers for robust stabilization in this paper we consider the problem of robust stabilizallon for a certain class of plants with unstructured infinite dimensional uncertainty we demonstrate that for the problem of robustly stabilizing this class of plants linear time invariant controllers perform as well as nonlinear time varying nltv ones ihis in particular implies that adaptive control laws offer no advantage as far as the problem of robust stabilization of this class of plants is concerned as a corollary we demonstrate that the small gain theorem is both necessary and sufficient for a certain class of nltv operators

high order approximation of the frobenius perron operator we formulate a general convergence theory for the finite dimensional projection approximation of the fixed point of a class of linear operators in particular we explore the relation with the standard framework of stability and consistency of the approximation imply convergence applications include the frobenius perron operator p s corresponding to a nonsingular measurable transformation from 0 1 to itself numerical experiments are also given to support the theoretical analysis

symmetric and non symmetric variants of nitsche s method for contact problems in elasticity theory and numerical experiments a general nitsche method which encompasses symmetric and non symmetric variants is proposed for frictionless unilateral contact problems in elasticity the optimal convergence of the method is established both for two and three dimensional problems and lagrange affine and quadratic finite element methods two and three dimensional numerical experiments illustrate the theory

optimal convergence for discrete variational inequalities modelling signorini contact in 2d and 3d without additional assumptions on the unknown contact set the basic h 1 finite element error estimate of order h with only h 2 regularity on the solution has not been yet established for the simplest two dimensional signorini problem approximated by a discrete variational inequality or the equivalent mixed method and linear finite elements to obtain an optimal error bound in this basic case and also when considering more general cases e g the three dimensional problem quadratic finite elements additional assumptions on the exact solution in particular on the unknown contact set see z belhachmi and f ben belgacem math comp 72 2003 pp 83 104 s hueber and b wohlmuth siam j numer anal 43 2005 pp 156 173 b wohlmuth a popp m gee and w wall comput mech 49 2012 pp 735 747 had to be used in this paper we consider finite element approximations of the two dimensional and three dimensional signorini problems with linear and quadratic finite elements in the analysis we remove all the additional assumptions and pr

double standard maps we investigate the family of double standard maps of the circle onto itself given by f a b x 2x a b pi sin 2 pi x mod 1 where the parameters a b are real and 0 b 1 similarly to the well known family of arnold standard maps of the circle a a b x x a b 2 pi sin 2 pi x mod 1 any such map has at most one attracting periodic orbit and the set of parameters a b for which such orbit exists is divided into tongues however unlike the classical arnold tongues that begin at the level b 0 for double standard maps the tongues begin at higher levels depending on the tongue moreover the order of the tongues is different for the standard maps it is governed by the continued fraction expansions of rational numbers for the double standard maps it is governed by their binary expansions we investigate closer two families of tongues with different behavior

the penalty free nitsche method and nonconforming finite elements for the signorini problem we design and analyse a nitsche method for contact problems compared to the seminal work of chouly and hild siam j numer anal 51 2013 pp 1295 1307 our method is constructed by expressing the contact conditions in a nonlinear function for the displacement variable instead of the lateral forces the contact condition is then imposed using the nonsymmetric variant of nitsche s method that does not require a penalty term for stability nonconforming piecewise affine elements are considered for the bulk discretization we prove optimal error estimates in the energy norm

discretization of the frobenius perron operator using a sparse haar tensor basis the sparse ulam method the global macroscopic behavior of a dynamical system is encoded in the eigenfunctions of the associated frobenius perron operator for systems with low dimensional long term dynamics efficient techniques exist for a numerical approximation of the most important eigenfunctions cf m dellnitz and o junge siam j numer anal 36 1999 pp 491 515 they are based on a projection of the operator onto a space of piecewise constant functions supported on a neighborhood of the attractor ulam s method in this paper we develop a numerical technique which makes ulam s approach applicable to systems with higher dimensional long term dynamics it is based on ideas for the treatment of higher dimensional partial differential equations using sparse grids c zenger sparse grids in parallel algorithms for partial differential equations kiel 1990 vieweg braunschweig 1991 pp 241 251 h j bungartz and m griebel acta numer 13 2004 pp 147 269 here we use a sparse haar tensor basis as the underlying approximation space we develop the technique establish statements about its complexity and convergence and present two numerical examples

a posteriori error estimates for markov approximations of frobenius perron operators abstract we present lower and upper error bounds under the bv norm for piecewise linear markov finite approximations to frobenius perron operators in terms of the bv norm of the residuals so that a posteriori error estimates can be given numerical results using the monte carlo implementation are presented to support the theoretical analysis

paper uniformly optimal control of linear feedback systems the problem of uniformly optimal control is posed in the context of linear time varying discrete time systems the controller is optimal uniformly over a pre specified set of exogenous signals existence of an optimal controller is proved and a formula for the minimum cost is derived the time invariant case is treated in the frequency domain it is shown that for time invariant systems an optimal time varying controller is no better than an optimal time invariant controller

on the approximation of invariant measures given a discrete dynamical system defined by the map x x the density of the absolutely continuous a c invariant measure if it exists is the fixed point of the frobenius perron operator defined on l1 x ulam proposed a numerical method for approximating such densities based on the computation of a fixed point of a matrix approximation of the operator t y li proved the convergence of the scheme for expanding maps of the interval g keller and m blank extended this result to piecewise expanding maps of the cube in n we show convergence of a variation of ulam s scheme for maps of the cube for which the frobenius perron operator is quasicompact we also give sufficient conditions on for the existence of a unique fixed point of the matrix approximation and if the fixed point of the operator is a function of bounded variation we estimate the convergence rate

a posteriori error estimates for a discontinuous galerkin approximation of second order elliptic problems several a posteriori error estimators are introduced and analyzed for a discontinuous galerkin formulation of a model second order elliptic problem in addition to residual type estimators we introduce some estimators that are couched in the ideas and techniques of domain decomposition results of numerical experiments are presented

generalized sample hold functions frequency domain analysis of robustness sensitivity and intersample difficulties over the past 5 years there has been substantial interest in the use of generalized sample hold functions for control in this correspondence the authors use a tool which is novel in this context namely amplitude modulation theory the authors employ this tool to analyze the quantitative and qualitative features of the intersample behavior in a frequency domain setting this offers new theoretical and practical insights into the method the authors conclusion is that the perceived benefits come at substantial cost which makes its practical use questionable

poincare friedrichs inequalities for piecewise h 1 functions poincare friedrichs inequalities for piecewise h1 functions are established they can be applied to classical nonconforming finite element methods mortar methods and discontinuous galerkin methods

robustness of discrete periodically time varying control under lti unstructured perturbations investigates robustness of linear periodically time varying lptv control of discrete linear time invariant lti plants subject to lti unstructured perturbations the note first derives a necessary and sufficient condition for robust stability of an lptv system subject to lti perturbations which is less conservative than the well known small gain condition it then presents a quantitative analysis on the robustness of lptv control under lti unstructured perturbations in comparison with that of lti control it is shown that under the normal value of the controller period suggested in the previous literature the stability margin is deteriorated by lptv control if lti unstructured perturbations are considered hence lti control is superior to lptv control in this respect

h deconvolution filtering of 2 d digital systems this paper deals with the problem of two dimensional 2 d digital system deconvolution under the h performance specification the 2 d digital system under consideration is expressed by the fornasini marchesini local state space fm lss model for a given 2 d digital system a 2 d deconvolution filter is designed to reconstruct the 2 d signal to meet a prescribed h performance specification a key analytical means for the deconvolution filter design is the 2 d bounded realness property derived in this paper applying this property the 2 d h deconvolution filter design is formulated into a convex optimization problem characterized by linear matrix inequalities lmis a procedure for the design of an h deconvolution filter for a given 2 d digital system with measurement noise is developed first the lmi approach to the 2 d h deconvolution filtering problem is further extended to the 2 d h robust deconvolution filtering problem with polytopic modeling uncertainties in the 2 d system the obtained results on the 2 d deconvolution filtering and robust deconvolution filtering problems are demonstrated with examples

computing the invariant measure and the lyapunov exponent for one dimensional maps using a measure preserving polynomial basis we consider a generalisation of ulam s method for approximating invariant densities of one dimensional maps rather than use piecewise constant polynomials to approximate the density we use polynomials of degree n which are defined by the requirement that they preserve the measure on n 1 neighbouring subintervals over the whole interval this results in a discontinuous piecewise polynomial approximation to the density we prove error results where this approach is used to approximate smooth densities we also consider the computation of the lyapunov exponent using the polynomial density and show that the order of convergence is one order better than for the density itself together with using cubic polynomials in the density approximation this yields a very efficient method for computing highly accurate estimates of the lyapunov exponent we illustrate the theoretical findings with some examples

a penalty free nonsymmetric nitsche type method for the weak imposition of boundary conditions in this paper we show that the nonsymmetric version of nitsche s method for the weak imposition of boundary conditions is stable without penalty term for nonconforming elements we prove the same result for the symmetric formulation as well we prove optimal h 1 error estimates and l 2 error estimates that are suboptimal with half an order in h both the pure diffusion and the convection diffusion problems are discussed

a direct approach to h sub 2 optimal deconvolution of periodic digital channels this paper studies the h sub 2 optimal deconvolution problem for periodic finite impulse response fir and infinite impulse response iir channels it shows that the h sub 2 norm of a periodic filter can be directly quantified in terms of periodic system matrices and linear matrix inequalities lmis without resorting to the commonly used lifting technique the optimal signal reconstruction problem is then formulated as an optimization problem subject to a set of matrix inequality constraints under this framework the optimization of both the fir and iir periodic deconvolution filters can be made convex solved using the interior point method and computed by using the matlab lmi toolbox the robust deconvolution problem for periodic fir and iir channels with polytopic uncertainties are further formulated and solved also by convex optimization and the lmis compared with the lifting approach to the design of periodic filters the proposed approach is simpler yet more powerful in dealing with multiobjective deconvolution problems and channel uncertainties especially for iir deconvolution filter design the obtained solutions are applied to the design of an optimal filterbank yielding satisfactory performance

vibrational feedback control zeros placement capabilities it is shown that in addition to closed loop pole placement vibrational feedback controllers lead in the sense specified below to a possibility of open loop zeros assignability on this basis the superior performance characteristics of continuous time periodic controllers discovered in 3 6 are explained

robust perron cluster analysis in conformation dynamics the key to molecular conformation dynamics is the direct identification of metastable conformations which are almost invariant sets of molecular dynamical systems once some reversible markov operator has been discretized a generalized symmetric stochastic matrix arises this matrix can be treated by perron cluster analysis a rather recent method involving a perron cluster eigenproblem the paper presents an improved perron cluster analysis algorithm which is more robust than earlier suggestions numerical examples are included

finite approximations of markov operators in this paper we survey some recent developments in the numerical analysis of markov operators and in particular frobenius perron operators associated with chaotic discrete dynamical systems

optimal approximate inverse of linear periodic filters we propose a method for constructing optimal causal approximate inverse for discrete time single input single output siso causal periodic filters in the presence of measurement noise the analysis is based on block signals and multi input multi output mimo time invariant models for periodic filters the objective function to be minimized is the asymptotic block mean square error the optimization problem is formulated in terms of transfer matrices as an optimal model matching problem with nonsquare model and plant based on an inner outer factorization on the transpose of the plant rational matrix it is shown that the problem can be further reduced to one with a lower dimensional square model and plant which is then solved in the time domain and a closed form solution is obtained a lower bound on the objective function is given it is shown that the lower bound can be asymptotically achieved as the order of the optimal transfer matrix increases the proposed method is extended to mimo periodic systems numerical examples are used to illustrate the performance of the proposed approximate inverse

a nitsche based method for unilateral contact problems numerical analysis we introduce a nitsche based formulation for the finite element discretization of the unilateral contact problem in linear elasticity it features a weak treatment of the non linear contact conditions through a consistent penalty term without any additional assumption on the contact set we can prove theoretically its fully optimal convergence rate in the h1 norm for linear finite elements in two dimensions which is o h 1 2 when the solution lies in h 3 2 0 1 2 an interest of the formulation is that conversely to lagrange multiplier based methods no other unknown is introduced and no discrete inf sup condition needs to be satisfied

error estimates of the markov finite approximation of the frobenius perron operator in the practical application of the modern ergodic theory one of the main problems is related to the computation of the absolutely continuous invariant measures for nonsingular transformations on measure spaces see lasota and mackey l a simple example is constructed in li 2 to show that the round off error can completely dominate the calculation if one is to compute the invariant measure directly using a sequence of cesaro sums an alternative is to compute the invariant density function for the frobenius perron operator p l 0 1 l 0 1 associated with the nonsingular measurable transformations s 0 11 0 11 the frobenius perron operator p is defined by

a general framework for linear periodic systems with applications to h sup infinity sampled data control the authors present a framework for dealing with continuous time periodic systems the main tool is a lifting technique which provides a strong correspondence between continuous time periodic systems and certain types of discrete time time invariant systems with infinite dimensional input and output spaces despite the infinite dimensionality of the input and output spaces a lifted system has a finite dimensional state space if the original system does this fact permits rather constructive methods for analyzing these systems as a demonstration of the utility of this framework the authors use it to describe the continuous time i e intersample behavior of sampled data systems and to obtain a complete solution to the problem of parameterizing all controllers that constrain the l sup 2 induced norm of a sampled data system to within a certain bound

a dual rate digital compensator for zero assignment abstract this paper considers design of a simple dual rate digital compensator drdc for assignment of system zeros the drdc comprises a linear time invariant system with a dual rate sampling scheme it is shown that zeros of a discrete system can be arbitrarilassigned by drdc corresponding to the block sampling period and that drdc is applicable to non minimum phase plants a design procedure and an example are given

the h 2 problem for sampled data systems m for sampled data systems in this paper we pose and give a complete solution to an analog of the h2 problem for sampled data system we motivate and develop a natural generalization of the h2 cost to periodic systems which is then applied to the continuous time closed loop mapping in a sampled data control system it is shown that the cost criterion developed is actually a norm in an space of hilbert schmidt operator valued functions we give state space solutions to the optimal and suboptimal controllers synthesis problems in this new norm by establishing an equivalent standard h2 problem

h sub 2 optimal sampled data control the h sub 2 optimal control of continuous time linear time invariant systems by sampled data controllers is discussed two different solutions state space and operator theoretic are given in both cases the h sub 2 sampled data problem is shown to be equivalent to a certain discrete time h sub 2 problem other topics discussed include input output stability of sampled data systems performance recovery in digital implementation of analog controllers and sampled data control of systems with the possibility of multiple time delays

the computation of lyapunov exponents via spatial integration with application to blowout bifurcations we propose a new method for the numerical approximation of the largest lyapunov exponent this method is based on the computation of a spatial average with respect to an underlying natural invariant measure rather than on a long term simulation of the dynamical system this approach is particularly advantageous for the detection of blowout bifurcations of a synchronous chaotic state and we illustrate this fact for a system of two coupled duffing oscillators

invariant measures for interval maps with critical points and singularities abstract we prove that under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative cusp map admits an ergodic invariant probability measures which is absolutely continuous with respect to lebesgue measure

on the approximation of complicated dynamical behavior we present efficient techniques for the numerical approximation of complicated dynamical behavior in particular we develop numerical methods which allow us to approximate sinai ruelle bowen srb measures as well as almost cyclic behavior of a dynamical system the methods are based on an appropriate discretization of the frobenius perron operator and two essentially different mathematical concepts are used our idea is to combine classical convergence results for finite dimensional approximations of compact operators with results from ergodic theory concerning the approximation of srb measures by invariant measures of stochastically perturbed systems the efficiency of the methods is illustrated by several numerical examples

periodically time varying memory state feedback controller synthesis for discrete time linear systems in this paper we deal with discrete time linear periodic time invariant systems with polytopic type uncertainties and propose a new linear matrix inequality lmi based method for robust state feedback controller synthesis in stark contrast with existing approaches that are confined to memoryless static controller synthesis we explore dynamical controller synthesis and reveal a particular periodically time varying memory state feedback controller ptvmsfc structure that allows lmi based synthesis in the context of robust controller synthesis we prove rigorously that the proposed design method encompasses the well known extended lmi based static controller synthesis methods as particular cases through numerical experiments we demonstrate that the suggested design method is indeed effective in achieving less conservative results under both periodic and time invariant settings we finally derive a viable test to verify that the designed robust ptvmsfc is exact in the sense that it attains the best achievable robust performance this exactness verification test works fine in practice and we will show via a numerical example that exact robust control is indeed attained by designing ptvmsfcs even for such a problem where the standard memoryless static state feedback fails

model matching for discrete time periodic systems with time varying relative degree and order abstract this paper extends the well known solution for the linear time invariant model matching problem to discrete time periodic systems with time varying relative degree and order it is shown that a key step to the design of a periodic output feedback controller is to compute the stable inverse of the periodic system using input output equations this problem is solved and model matching is achieved with system internal stability

markov finite approximation of frobenius perron operator the problem of existence and computation of absolutely continuous invariant measures for nonsingular transformations on measure spaces is one of the main concerns in the modern ergodic theory 3 lasota and yorke have established the existence of the invariant measures for a class of nonsingular measurable transformations s from 0 l to itself 4 later in 6 li and yorke gave a sufficient condition for the uniqueness of this invariant density and thus for the ergodicity of the mapping the classical birkhoff s individual ergodic theorem says that if u is an ergodic invariant probability measure under s then for any measurable set a c 0 11 the time average lim 1 n c ax s x which measures the average time spent in a under iteration of s exists to be i for p almost all x where xa is the characteristic function of a 1 on a and 0 off a this seems to suggest that we may use the cesaro sum of the above form to calculate the invariant measure a simple and important example in 5 however shows that the computer round off error can completely dominate the calculation and make the implementation difficult in order to overcome this difficulty li 5 proposed a rigorous numerical procedure which can be implemented on a computer with negligible round off error problem a mapping s 0 l 0 l is called piecewise c2 if there is a partition 0 a a a 1 of 0 l such that for k 1 r the restriction sk of s on uk a is a c2 function which can be extended to the closed interval ak i ak as a c2 function s need not be continuous at the point ak for a c 0 11 we write s a for x s x e a throughout the paper we assume s is a nonsingular measurable transformation i e s is measurable and for any measurable subset a c 0 l with m a 0 m s a 0 here m denotes the lebesgue measure on 0 11 the operator ps l 0 1 l 0 1 defined by