properly embedded minimal planar domains in 1997 collin proved that any properly embedded minimal surface in r 3 with nite topology and more than one end has

robust state estimation for singularly perturbed systems abstractthis paper deals with the design of interval observers for singularly perturbed linear systems the full order system is first decoupled into slow and fast subsystems then using the cooperativity theory an interval observer is designed for the slow and fast subsystems assuming that the measurement noise and the disturbances are bounded and the singular perturbed parameter is uncertain this decoupling leads to two observers that estimate the lower and upper bounds for the feasible state domain a numerical example shows the efficiency of the proposed technique

some results involving hermite base polynomials and functions using operational methods this paper is an attempt to stress the usefulness of the operational methods in the theory of special functions using operational methods we derive summation formulae and generating relations involving various forms of hermite base polynomials and functions

robust exact differentiation via sliding mode technique abstract the main problem in differentiator design is to combine differentiation exactness with robustness in respect to possible measurement errors and input noises the proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal such an order of the differentiation error is shown to be the best possible one when the only information known on the base signal is an upper bound for lipschitz s constant of the derivative

interval estimation for lpv systems applying high order sliding mode techniques in this paper the problem of design of interval observers for linear parameter varying lpv systems containing non detectable or non strongly observable parts is addressed firstly a high order sliding mode hosm method is applied to the strongly observable subsystem obtained by an appropriate change of coordinates to estimate the state and its derivative secondly this information is used to decrease the level of uncertainty in the rest of the system which leads to improvement of accuracy of the set membership estimates generated by an interval observer moreover it is shown that hosm techniques allows us to relax the applicability conditions of standard interval observer design methods the efficiency of the proposed approach is demonstrated through simulation examples

coupled boundary interval observer for lpv systems subject to uncertainties in input output and parameters abstract the topic of this publication is the design of interval observers for lpv systems under consideration of parameter input and output uncertainties that are described by bounded intervals in the course of the design also time varying bounds of the parameter intervals are considered representing the case when parameters are measured with an unknown but bounded measurement error in this case an existing approach is extended to handle these parameter uncertainties the effectiveness of the approach is demonstrated by two numerical examples

brief paper interval observer design for consistency checks of nonlinear continuous time systems this paper deals with fault detection for nonlinear continuous time systems a procedure based on interval analysis is proposed to build a guaranteed qlpv quasi linear parameter varying approximation of the nonlinear model the interval qlpv approximation makes it possible to derive two point observers which estimate respectively the lower and the upper bound of the state vector using cooperativity theory a set guaranteed to contain the actual value of the residual is then designed the modelling uncertainties and measurement errors are taken into account at the design stage the proposed methodology is illustrated through numerical simulations

the dynamics theorem for properly embedded minimal surfaces in this paper we prove two theorems the first one is a structure result that describes the extrinsic geometry of an embedded surface with constant mean curvature possibly zero in a homogeneously regular riemannian three manifold in any small neighborhood of a point of large almost maximal curvature we next apply this theorem and the quadratic curvature decay theorem in meeks et al j differ geom arxiv 1308 6439 to deduce compactness descriptive and dynamics type results concerning the space d m of non flat limits under dilations of any given properly embedded minimal surface m in r 3

bending the helicoid we construct colding minicozzi limit minimal laminations in open domains in mathbb r 3 with the singular set of c 1 convergence being any properly embedded c 1 1 curve by meeks c 1 1 regularity theorem the singular set of convergence of a colding minicozzi limit minimal lamination mathcal l is a locally finite collection s mathcal l of c 1 1 curves that are orthogonal to the leaves of the lamination thus our existence theorem gives a complete answer as to which curves appear as the singular set of a colding minicozzi limit minimal lamination in the case the curve is the unit circle mathbb s 1 1 in the x 1 x 2 plane the classical bjorling theorem produces an infinite sequence of complete minimal annuli h n of finite total curvature which contain the circle the complete minimal surfaces h n contain embedded compact minimal annuli overline h n in closed compact neighborhoods n n of the circle that converge as n to infty to mathbb r 3 x 3 axis in this case we prove that the overline h n converge on compact sets to the foliation of mathbb r 3 x 3 axis by vertical half planes with boundary the x 3 axis and with mathbb s 1 1 as the singular set of c 1 convergence the overline h n have the appearance of highly spinning helicoids with the circle as their axis and are named bent helicoids

brief paper global sliding mode observer with adjusted gains for locally lipschitz systems a state observer design procedure is proposed for nonlinear locally lipschitz systems with high relative degree from the available for measurements output to the nonlinearity the possible presence of disturbances is taken into account the solution is based on logic based control and the high order super twisting observer the approach is applicable to nonlinear systems with bounded solutions

complete proper minimal surfaces in convex bodies of mathbbr 3 consider a convex domain b of r 3 we prove that there exist complete minimal surfaces which are properly immersed in b we also demonstrate that if d and dare convex domains with d bounded and the closure of d contained in dthen any minimal disk whose boundary lies in the boundary of d can be approximated in any compact subdomain of d by a complete minimal disk which is proper in d we apply these results to study the so called type problem for a minimal surface we demonstrate that the interior of any convex region of r 3 is not a universal region for minimal surfaces in the sense explained by meeks and perez in 9

uniqueness of the riemann minimal examples we prove that a properly embedded minimal surface in r 3 of genus zero with infinite symmetry group is a plane a catenoid a helicoid or a riemann minimal example we introduce the language of hurwitz schemes to understand the underlying moduli space of surfaces in our setting

hosm observer for a class of non minimum phase causal nonlinear mimo systems a higher order sliding mode observer is proposed for asymptotic identification of the full state vector and the vector of unknown inputs for mimo nonlinear causal systems with unstable internal dynamics the problem is addressed via consistent application of exact higher order sliding mode differentiators in conjunction with the method of stable system center a numerical example illustrates the performance of the proposed algorithm

the calabi yau conjectures for embedded surfaces in this talk i will discuss the proof of the calabi yau conjectures for embedded surfaces this is joint work with bill minicozzi cm9 the calabi yau conjectures about surfaces date back to the 1960s much work has been done on them over the past four decades in particular examples of jorge xavier from 1980 and nadirashvili from 1996 showed that the immersed versions were false we will show here that for embedded surfaces i e injective immersions they are in fact true their original form was given in 1965 in ca where e calabi made the following two conjectures about minimal surfaces see also s s chern page 212 of ch conjecture 1 prove that a complete minimal hypersurface in r must be unbounded calabi continued it is known that there are no compact minimal submanifolds of r or of any simply connected complete riemannian manifold with sectional curvature 0 a more ambitious conjecture is conjecture 2 a complete minimal hypersurface in r has an unbounded projection in every n 2 dimensional flat subspace

the structure of singly periodic minimal surfaces the only properly embedded minimal surface with more than one topological end and a cont inuous g roup of symmetries is the catenoid considering periodic minimal surfaces with more than one end a surface in n 3 is periodic if it is invariant under an infinite discrete g roup of isometrics that act freely on 1r3 the only classical examples are those discovered by riemann the riemann examples possess a quite special set of properties 1 they have an infinite number of flat annular ends 1 2 they are invariant under a nontrivial t ranslat ion t 3 the surfaces t h a v e genus 1 and 2 ends 4 the surfaces t have total curvature equal to 8 zr mot iva ted by the riemann examples we established the existence of an infinite family of proper ly embedded periodic minimal surfaces d k each with an infinite number of ends 1 these surfaces which are discussed below see sect 1 2 on rigidity also have an infinite number of flat annular ends and are invariant under a t ranslat ion t the quot ient of these surfaces by t is a surface of genus 2 k 1 with two ends and total curvature 8 r e k 1 k l we have been able to twis t each of these new surfaces that is we construct surfaces with the same properties that are invariant under screw motions t r where r is a rota t ion a round an axis in the direction of t see sect 1 3 below together with the catenoid and the examples of riemann these new surfaces comprise all the known properly embedded minimal surfaces with more than one topological end whose symmetry g roup contains an infinite discrete subgroup these examples share m a n y of the properties of the riemann examples a major goal of this paper is to show that this is not accidental

design of interval observer for a class of uncertain unobservable nonlinear systems this paper investigates the interval observer design for a class of nonlinear continuous systems which can be represented as a superposition of a uniformly observable nominal subsystem with a lipschitz nonlinear perturbation it is shown in this case there exists an interval observer for the system that estimates the set of admissible values for the state consistent with the output measurements an illustrative example of the observer application is given with simulation results

the space of embedded minimal surfaces of fixed genus in a 3 manifold v fixed genus this paper is the fifth and final in a series on embedded minimal surfaces following our earlier papers on disks we prove here two main structure theorems for itnonsimply connected embedded minimal surfaces of any given fixed genus the first of these asserts that any such surface without small necks can be obtained by gluing together two oppositely oriented double spiral staircases the second gives a pair of pants decomposition of any such surface when there are small necks cutting the surface along a collection of short curves after the cutting we are left with graphical pieces that are defined over a disk with either one or two sub disks removed a topological disk with two sub disks removed is called a pair of pants both of these structures occur as different extremes in the two parameter family of minimal surfaces known as the riemann examples

interval observers for time varying discrete time systems this techical note deals with interval state observer design for time varying discrete time systems the problem of a similarity transformation computation which connects a time varying matrix and its nonnegative representation is studied three solutions are proposed for a generic time varying system a system with positive state and for a particular class of periodical systems numerical simulations are provided to demonstrate advantages of the developed techniques

a note on interval observer design for unknown input estimation this paper addresses the problem of interval observer design for unknown input estimation in linear time invariant systems although the problem of unknown input estimation has been widely studied in the literature the design of joint state and unknown input observers has not been considered within a set membership context while conventional interval observers could be used to propagate with some additional conservatism unknown inputs by considering them as disturbances the proposed approach allows their estimation under the assumption that the measurement noise and the disturbances are bounded lower and upper bounds for the unmeasured state and unknown inputs are computed numerical simulations are presented to show the efficiency of the proposed approach

strict lyapunov functions for the super twisting algorithm a method to construct a family of strict lyapunov functions i e with negative definite derivative for the super twisting algorithm without or with perturbations is provided this second order sliding modes algorithm is widely used to design controllers observers and exact differentiators the proposed lyapunov functions ascertain finite time convergence provide an estimate of the convergence time and ensure the robustness of the finite time or ultimate boundedness for a class of perturbations wider than the classical ones for this algorithm since the lyapunov functions and their derivatives are quadratic forms the operation with them is as simple as for linear time invariant systems

interval observer design for continuous time switched systems under known switching and unknown inputs this paper deals with unknown input estimation for switched linear systems in an unknown but bounded error ubbe framework based on a known switching signal and under the fulfilment of the relati

robust interval observers and stabilization design for discrete time systems with input and output for a family of nonlinear discrete time systems with input output and uncertain terms a new interval observer is designed its main feature is that it is composed of two copies of classical observers this interval observer applies in the presence of unknown bounded nonlinear terms and additive disturbances and is used to achieve asymptotic stability through an appropriate choice of dynamic output feedback an illustrative example completes the presentation

the local picture theorem on the scale of topology we prove a descriptive theorem on the extrinsic geometry of an embedded minimal surface of injectivity radius zero in a homogeneously regular riemannian threemanifold in a certain small intrinsic neighborhood of a point of almost minimal injectivity radius this structure theorem includes a limit object which we call a minimal parking garage structure on r 3 whose theory we also develop

incomplete 2d hermite polynomials properties and applications incomplete forms of two variable two index hermite polynomials are introduced their link with laguerre polynomials is discussed and it is shown that they are a useful tool to study quantum mechanical harmonic oscillator entangled states the possibility of developing the theory of complete 2d hermite polynomials from the point of view of the incomplete forms is analyzed too the orthogonality properties of the associated harmonic oscillator functions are finally discussed

generating functions involving hermite laguerre polynomials using operational methods in this paper some generating functions involving 3 variable hermite laguerre polynomials are derived by using operational methods further generating functions for the polynomials related to hermite laguerre polynomials are also obtained as applications of the main results

optimal interval observers for discrete time linear switched systems the main goal of this paper is to present a methodology to design interval observers for discrete time linear switched systems affected by bounded but unknown disturbances two design techniques a

an unknown input interval observer for lpv systems under l2 gain and l gain criteria abstract this paper investigates the design of an unknown input interval observer for linear parameter varying systems the proposed method provides a solution to the decoupling conditions under l 2 gain and l gain performance level it is shown that the design of the unknown input interval observer parameters can be formulated as a sdp problem the major advantages with regard to other solutions is that first it does not require the explicit knowledge of a time varying state transformation for the estimation error dynamics to satisfy the meztler property rather it is shown how such a property can be formulated as a part of the sdp optimization process second decoupling and l 2 l constraints are formulated on the thickness of the interval length in spite of half the interval length the proposed methodology is illustrated on a numerical academic example

the geometry of minimal surfaces of finite genus i curvature estimates and quasiperiodicity let mathcal m be the space of properly embedded minimal surfaces in 3 with genus zero and two limit ends normalized so that every surface m mathcal m has horizontal limit tangent plane at infinity and the vertical component of its flux equals one we prove that if a sequence m i i mathcal m has the horizontal part of the flux bounded from above then the gaussian curvature of the sequence is uniformly bounded this curvature estimate yields compactness results and the techniques in its proof lead to a number of consequences concerning the geometry of any properly embedded minimal surface in 3 with finite genus and the possible limits through a blowing up process on the scale of curvature of a sequence of properly embedded minimal surfaces with locally bounded genus in a homogeneously regular riemannian 3 manifold

brief paper near optimal interval observers bundle for uncertain bioreactors in this paper we design an interval observer for the estimation of unmeasured variables of uncertain bioreactors the observer is based on a bounded error observer as proposed in lemesle v gouze j l 2005 hybrid bounded error observers for uncertain bioreactor models bioprocess and biosystems engineering 27 311 318 that makes use of a loose approximation of the bacterial kinetics we first show how to generate guaranteed upper and lower bounds on the state provided that known intervals for the initial condition and the uncertainties are available these so called framers depend on a tuning gain they can be run in parallel and the envelope provides the best estimate an optimality criterion is introduced leading to the definition of an optimal observer we show that this criterion provides directly a gain set containing the best framers the method is applied to the estimation of the total biomass of an industrial wastewater treatment plant demonstrating its efficiency

the strong halfspace theorem for minimal surfaces d hoffman and w h meeks iii department of mathematics university of massachusetts amherst ma 01003 usa in 6 jorge and xavier constructed examples of complete nonplanar minimal surfaces contained between two parallel planes in 3 recently rosenberg and toubiana have found complete minimally immersed annuli that are proper in an open slab 1 12 on the basis of these and other results the question has arisen as to whether or not there could exist a properly immersed minimal surface in 3 that was contained between two parallel planes the answer is negative an immediate consequence of the following theorem

the classical theory of minimal surfaces we present here a survey of recent spectacular successes in classical minimal surface theory we highlight this article with the theorem that the plane the helicoid the catenoid and the one parameter family frtgt2 0 1 of riemann minimal examples are the only complete properly embedded minimal planar domains in r 3 the proof of this result depends primarily on work of colding

simple factor dressing and the lopez ros deformation of minimal surfaces in euclidean 3 space the aim of this paper is to investigate a new link between integrable systems and minimal surface theory the dressing operation uses the associated family of flat connections of a harmonic map to construct new harmonic maps since a minimal surface in 3 space is a willmore surface its conformal gauss map is harmonic and a dressing on the conformal gauss map can be defined we study the induced transformation on minimal surfaces in the simplest case the simple factor dressing and show that the well known lopez ros deformation of minimal surfaces is a special case of this transformation we express the simple factor dressing and the lopez ros deformation explicitly in terms of the minimal surface and its conjugate surface in particular we can control periods and end behaviour of the simple factor dressing this allows to construct new examples of doubly periodic minimal surfaces arising as simple factor dressings of scherk s first surface

interval observer design for continuous time linear parameter varying systems abstract this paper studies interval observer design for linear parameter varying systems subject to uncertainties in parameters input and output based on a general assumption that these uncertainties are unknown but bounded by known intervals a novel interval observer is presented to estimate the bounds of state to attenuate the effect of uncertainties and obtain tight state intervals a novel l norm based design method is proposed numerical simulations are conducted to demonstrate the performance of the proposed method

functional interval observer for discrete time systems with disturbances abstract this paper further investigates the design problem of the functional interval observer for discrete time systems with disturbances two methods are given to design functional interval observers given monotone system theory a luenberger like functional interval observer is constructed and sufficient conditions are achieved by sylvester equations in the first method the second approach is known as the two step method an h functional observer of the system is presented by the h technique and then the approach of the zonotope is used to estimate its upper and lower boundaries to improve the estimation accuracy the above methods are applied to two examples for comparison and to show the correctness

higher genus riemann minimal surfaces riemann surfaces constitute a one parameter family of embedded minimal surfaces which are periodic and have infinitely many horizontal planar ends the surfaces in this family are foliated by circles or straight lines in this paper we prove the existence of a one parameter family of embeded minimal surfaces which have infinitely many horizontal planar ends and have genus k for k 1 37 riemann surfaces as their flux is nearly vertical can be understood as a sequence of parallel planes connected by slightly bent catenoidal neks the surfaces we construct are obtained by replacing one of these catenoidal necks by a member of the family of minimal surfaces discovered by c costa d hoffman and w meek

structure theorems for singular minimal laminations in this paper we apply our local removable singularity theorem and local structure theorems for embedded minimal surfaces and minimal laminations in r 3 proven in 16 15 to obtain global structure theorems for certain possibly singular minimal laminations of r 3 we will use theorems 1 3 and theorem 1 6 below in 14 to prove that a complete embedded minimal surface in r 3 with finite genus and a countable number of ends is proper theorem 1 6 will also be applied in 13 to obtain bounds on the index and the topology of complete embedded minimal surfaces of fixed genus and finite topology in r 3

switched observers for switched linear systems with unknown inputs two state observers are designed for some classes of switched linear systems with unknown inputs the design of the proposed observers assumes that all switching subsystems fulfill a property of strong detectability that allows to implement suitable reduced order unknown input switched observers the synthesis of the observers is based on the feasibility of a certain system of lmis two main schemes are presented for the case when the set of possible unknown input distribution matrices are linearly dependent an observer is suggested that guarantees the asymptotic state reconstruction without imposing any slow switching dwell time constraint about the sequence of the switching times for the general case the existence of a minimal average dwell time for every switching sequence is assumed by appropriate lyapunov analysis the convergence of the state estimate is proven to be exponential in both cases simulation results confirm the predicted performance

interval observers for linear time invariant systems with disturbances it is shown that for any time invariant exponentially stable linear system with additive disturbances time varying exponentially stable interval observers can be constructed the technique of construction relies on the jordan canonical form that any real matrix admits and on time varying changes of coordinates for elementary jordan blocks which lead to cooperative linear systems the approach is applied to detectable linear systems

design of interval observers and controls for pdes using finite element approximations synthesis of interval state estimators is investigated for the systems described by a class of parabolic partial differential equations pdes first a finite element approximation of a pde is constructed and the design of an interval observer for the derived ordinary differential equation is given second the interval inclusion of the state function of the pde is calculated using the error estimates of the finite element approximation finally the obtained interval estimates are used to design a dynamic output stabilizing control the results are illustrated by numerical experiments with an academic example and the black scholes model of financial market

the space of embedded minimal surfaces of fixed genus in a 3 manifold iv locally simply connected this paper is the fourth in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed 3manifold the key is to understand the structure of an embedded minimal disk in a ball in r3 this was undertaken in cm3 cm4 and the global version of it will be completed here see the discussion around figure 12 for the local case and cm15 for some more details our main results are theorem 0 1 the lamination theorem and theorem 0 2 the one sided curvature estimate the lamination theorem is stated in the global case where the lamination is in fact a foliation the first four papers of this series show that every embedded minimal disk is either a graph of a function or is a double spiral staircase where each staircase is a multivalued graph this is done by showing that if the curvature is large at some point and hence the surface is not a graph then it is a double spiral staircase like the helicoid to prove that such a disk is a double spiral staircase we showed in the first three papers of the series that it is built out of n valued graphs where n is a fixed number in this paper we will deal with how the multi valued graphs fit together and in particular prove regularity of the set of points of large curvature the axis of the double spiral staircase the first theorem is the global version of the statement that every embedded minimal disk is a double spiral staircase

multivariable lagrange expansion and generalization of carlitz srivastava mixed generating functions abstract families of mixed generating functions generalizing those of the carlitz srivastava type are derived here by applying methods based on the multivariable extension of the lagrange expansion it is also shown that the combination with techniques of operational nature offers a wide flexibility to explore a wealth of mixed bilateral generating functions for special functions with many variables

non periodic riemann examples with handles we show the existence of 1 parameter families of non periodic complete embedded minimal surfaces in euclidean space with infinitely many parallel planar ends in particular we are able to produce finite genus examples and quasi periodic examples of infinite genus

the space of embedded minimal surfaces of fixed genus in a 3 manifold iii planar domains this paper is the third in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed 3 manifold in cm3 cm5 we describe the case where the surfaces are topologically disks on any fixed small scale although the focus of this paper general planar domains is more in line with cm6 we will prove a result here namely corollary iii 3 5 below which is needed in cm5 even for the case of disks roughly speaking there are two main themes in this paper the first is that stability leads to improved curvature estimates this allows us to find large graphical regions these graphical regions lead to two possibilities

interval state estimation for a class of nonlinear systems the goal of this technical note is to design interval observers for a class of nonlinear continuous time systems the first part of this work shows that it is usually possible to design an interval observer for linear systems by means of linear time invariant changes of coordinates even if the system is not cooperative this result is extended to a class of nonlinear systems using partial exact linearisations the proposed observers guarantee to enclose the set of system states that is consistent with the model the disturbances and the measurement noise moreover it is only assumed that the measurement noise and the disturbances are bounded without any additional information such as stationarity uncorrelation or type of distribution the proposed observer is illustrated through numerical simulations

the geometry of minimal surfaces of finite genus ii nonexistence of one limit end examples we demonstrate that a properly embedded minimal surface in 3 with finite genus cannot have one limit end

some uniqueness and nonexistence theorems for embedded minimal surfaces thanks to the works of callahan costa hoffman karcher meeks rosenberg wei etc see for example 1 2 3 5 8 11 12 16 20 we dispose now of a large number of properly embedded minimal surfaces in the euclidean space ir other than the classical examples all those surfaces can be viewed as minimal surfaces with finite total curvature properly embedded in complete flat three manifolds the most basic invariants associated to a surface of this type are its topology and its periodicity it is an interesting problem to decide if the simplest examples like the catenoid the helicoid the scherk s surfaces or the riemann example can be characterized in terms of some of these invariants in the non periodic case there are two important uniqueness theorems in this direction the first one obtained by schoen 17 characterizes the catenoid as the only complete minimal surface embedded

interval observer design and control of uncertain non homogeneous heat equations the problems of state estimation and observer based control for heat non homogeneous equations under distributed in space point measurements are considered first an interval observer is designed in the form of partial differential equations pdes without galerkin projection second conditions of boundedness of the interval observer solutions with non zero boundary conditions and measurement noise are proposed third the obtained interval estimates are used to design a dynamic output feedback stabilizing controller the advantages of the pde based interval observer over the approximation based one are clearly shown in the numerical example

an easy design for interval observers this paper deals with the problem of interval estimation the proposed approach is based on the use of successive derivatives in continuous time or forward measurements in discrete time in an alg

on design of interval observers with sampled measurement new design of interval observers for continuous time systems with discrete time measurements is proposed for this purpose new conditions of positivity for linear systems with sampled feedbacks are obtained a sampled data stabilizing control is synthesized based on provided interval estimates efficiency of the obtained solution is demonstrated on examples

the space of embedded minimal surfaces of fixed genus in a 3 manifold ii multi valued graphs in disks this paper is the second in a series where we give a description of the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed 3 manifold the key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in r 3 we show here that if the curvature of such a disk becomes large at some point then it contains an almost flat multi valued graph nearby that continues almost all the way to the boundary this will be proved by showing the existence of small multi valued graphs near points of large curvature and then using the extension result for multi valued graphs proved in the first paper in this series there are two local models for embedded minimal disks by an embedded disk we mean a smooth injective map from the closed unit ball in r 2 into r 3 one model is the plane or more generally a minimal graph the other is a piece of a helicoid in the first four papers of this series we will show that every embedded minimal disk is either a graph of a function or is a double spiral staircase like a helicoid recall that a double spiral staircase consists of two spiral staircases that spiral together around a common axis one inside the other this will be done by showing that if the curvature is large at some point and hence the surface is not a graph then it is a double spiral staircase to prove that it is a double spiral staircase we will first prove that it is built out of n valued graphs where n is a fixed number these n valued graphs are like a single spiral staircase connecting n floors the existence of the n valued graphs was initiated in the first paper and will be completed here the third and fourth papers of this series will deal with how the multi valued graphs fit together and in particular prove regularity of the set of points of large curvature the axis of the double spiral staircase

interval observers for continuous time lpv systems with l 1 l 2 performance an approach to interval observer design for linear parameter varying lpv systems is proposed it is assumed that the vector of scheduling parameters in lpv models is not available for measurement two different interval observers are constructed for nonnegative systems and for a generic case stability conditions are expressed in terms of matrix inequalities which can be solved with respect to the observer gains using standard numerical solvers applying l 1 l 2 framework the robustness and estimation accuracy with respect to model uncertainty are analyzed the efficiency of interval estimation for lpv models is demonstrated through numerical experiments for a microfluidic system and an academic example

a less conservative lmi condition for robust cal d stability of polynomial matrix polytopes a projection approach this technical note investigates the problem of checking robust d stability of a polytope of polynomial matrices finsler s projection lemma is taken to derive a new sufficient condition in terms of a linear matrix inequality lmi feasibility problem the basic idea behind this condition is to lift the existing stability condition into the one of larger space by means of finsler s lemma and based on it to introduce additional decision variables examples are given to show that the proposed condition can yield less conservative results than the previous one

linear interval observers under delayed measurements and delay dependent positivity new interval observers are designed for linear systems with time varying delays in the case of delayed measurements interval observers employ positivity and stability analysis of the estimation error system which in the case of delayed measurements should be delay dependent new delay dependent conditions of positivity for linear systems with time varying delays are introduced efficiency of the obtained solution is demonstrated by examples

interval observer for a class of uncertain nonlinear singular systems this paper investigates the problem of observer design for a general class of linear singular time delay systems in which the time delays are involved in the state the output and the known input if there exists the involvement of the delay could be multiple which however is rarely studied in the literature sufficient conditions are proposed which guarantee the existence of a luenberger like observer for the general system

the space of embedded minimal surfaces of fixed genus in a 3 manifold i estimates off the axis for disks this paper is the first in a series where we describe the space of all embedded minimal surfaces of fixed genus in a fixed but arbitrary closed riemannian 3 manifold the key for understanding such surfaces is to understand the local structure in a ball and in particular the structure of an embedded minimal disk in a ball in r3 with the flat metric this study is undertaken here and completed in cm6 these local results are then applied in cm7 where we describe the general structure of fixed genus surfaces in 3 manifolds there are two local models for embedded minimal disks by an embedded disk we mean a smooth injective map from the closed unit ball in r2 into r3 one model is the plane or more generally a minimal graph the other is a piece of a helicoid in the first four papers of this series we will show that every embedded minimal disk is either a graph of a function or is a double spiral staircase where each staircase is a multi valued graph this will be done by showing that if the curvature is large at some point and hence the surface is not a graph then it is a double spiral staircase to prove that such a disk

technical communique an observation algorithm for nonlinear systems with unknown inputs this paper deals with the design of unknown input observers for nonlinear systems an algorithm which determines if the state and the unknown input of the system can be recovered in finite time is introduced this algorithm leads to the transformation of the system into an extended block triangular observable form suitable for the design of finite time observers the proposed method is useful to relax some restrictive conditions of the existing nonlinear unknown input observer design procedures

h infinity set membership observer design for discrete time lpv systems this paper presents a new set membership observer design method for discrete time linear parameter varying systems the real process is assumed to be perturbed by unknown but bounded disturbances

technical communique nonlinear bounded error state estimation of continuous time systems this paper presents a first study on the application of interval analysis and consistency techniques to state estimation of continuous time systems described by nonlinear ordinary differential equations the approach is presented in a bounded error context and the resulting methodology is illustrated by an example

adding one handle to half plane layers in this paper we build properly embedded singly periodic minimal surfaces which have infinite total curvature in the quotient by the period these surfaces are constructed by adding a handle to the toroidal half plane layers defined by h karcher the technics that use is to solve a jenkins serrin problem over a strip domain and to consider the conjugate minimal surface to the graph