short communication characterization of fuzzy topologies by s neighbourhood systems using chang s definition of a fuzzy topological space or fts for short 1 we introduce the notion of s neighbourhoods of a fuzzy point by which we succeed to characterize a fuzzy topology this answers warren s open question 4

linearization of time delay systems by input output injection and output transformation in the present paper necessary and sufficient geometric conditions for the equivalence of a single input single output nonlinear time delay system under bicausal change of coordinates and regular output transformation to a linear weakly observable time delay system up to input output injection are given the obtained results are then applied to the observer design problem

non linear observer design by transformation into a generalized observer canonical form an observer design method for a certain class of non linear single output systems is introduced the characteristic feature of this method consists of the fact that it does not require any linearization in the way that the given non linear system is approximated by a linear one the present paper deals with the derivation of a transformation of the considered non linear system into a generalized observer canonical form gocf which enables a systematic observer design similar to the linear one based on the well known linear observer canonical form to assign conditions for its existence the transformation into the gocf is carried out in two steps via a generalized observability canonical form gobcf in contrast to previous forms used for linear systems the two non linear canonical forms presented here also depend on the time derivatives of the input variables this means that the resulting observer has to be supplied not only with the input and output variables of the given system but also with deri

on regularity axioms in fuzzy neighbourhood spaces abstract two notions of regularity in fuzzy neighbourhood spaces fns s have been introduced one by t m g ahsanullah and the other by the authors we prove that those two notions coincide we then characterize a regular fns as a fns whose level topologies for all 0

restricted dynamic observer error linearizability following the general dynamic observer error linearization problem state equivalence to a triangular nonlinear observer canonical form with index d and the restricted dynamic observer error linearization problem are defined in this paper the necessary and sufficient conditions for the above two problems are given since our proofs are constructive a desired state transformation can also be found in the theorem

metrization theorems in l topological spaces abstract in this paper some characterizations of a pointwise uniformity are presented in l fuzzy set theory a new hausdorff separation axiom compatible with pointwise metric is introduced urysohn metrization theorem and alexandroff urysohn metrization theorem in general topology are generalized to l topology

on r l o we prove there exists a somewhat simpler description of l and its fuzzy topology than the one given by hutton 2 and a considerably simpler description of than the one given by rodabaugh 4 as a result of this simplification we are able to give a direct proof of the continuity of an open problem in 4

on fuzzy pseudo normed vector spaces abstract we provide a method for introducing fuzzy pseudo metric topologies on sets and fuzzy pseudo normed topologies on vector spaces over r or c which will be fuzzy linear topologies we define fuzzy pseudo metrics for pairs of crisp points and fuzzy pseudo norms for crisp points as fuzzy real numbers 0 as defined by hutton we define the associated fuzzy open balls with crisp points for their centres and fuzzy real numbers 0 for their radii these form a basis for the associated fuzzy pseudo metric topology the axioms governing fuzzy pseudo metric and fuzzy pseudo norm are straightforward extensions for the corresponding axioms in the crisp case the formulation conforms with zadeh s extension principle we show that katsaras concept of fuzzy seminorm fuzzy sets and systems 12 1984 143 154 is equivalent to ours in the sense that both concepts will result in same fuzzy linear topologies

brief nonlinear observer design via passivation of error dynamics we present a new design scheme of nonlinear state observers global full order asymptotic observers through passivation of the error dynamics in order to consider passivity of the error dynamics for the observer problem we place a conceptual input and output on the generalized error dynamics which also includes the plant and the strictness of passivity is extended with respect to a set in which the estimation error becomes zero then output feedback passivation for the error dynamics will lead to the construction of a state observer it is also shown that a nonlinear observer is generally vulnerable to measurement disturbance in the sense that even an arbitrarily small measurement disturbance can lead to a blowup of the error state however due to the passivity of the error dynamics the proposed nonlinear injection gain can be easily modified for the observer to be robust to measurement disturbances

time scaling for observer design with linearizable error dynamics in this paper we consider the problem of observer design for dynamical systems with scalar output by linearization of the error dynamics via coordinate change output injection and time scaling we present necessary and sufficient conditions which guarantee the existence of a coordinate change and output dependent time scaling such that in the new coordinates and with respect to the new time the system has linear error dynamics

an algorithm for system immersion into nonlinear observer form siso case the class of nonlinear systems that can be put into nonlinear observer form linear system with output injection can be broadened if we employ the system immersion we provide an immersion algorithm for siso nonlinear systems with relative degree r the proposed algorithm is an extension of the previous results and does not require the relative degree 1 assumption in addition it is seen that the immersion can always be computed via algebraic computations and simple integrations except in a very special case in which the relative degree equals the system dimension in this case only one first order differential equation appears in the algorithm

algebraic conditions for state equivalence to a discrete time nonlinear observer canonical form abstract algebraic necessary and sufficient conditions for a single output discrete time system to be state equivalent to a generalized nonlinear observer canonical form with or without output transformation are derived our algebraic conditions are easier to verify for researchers unaccustomed to differential geometry in addition our proofs are constructive and contain the state and output transformations for generalized nonlinear observer canonical forms

a block triangular nonlinear observer normal form abstract the nonlinear observer normal form is generalized to a block triangular observer normal form which can be interpreted as a series connection of subsystems in observer form based on this new form exponential observers can be designed using methods from the linear case necessary and sufficient conditions for the existence of state transformations into this normal form are given

discrete time observer error linearizability via restricted dynamic systems in this technical note we define the observer error linearization problem of a discrete time autonomous nonlinear system via a restricted dynamic system this is the dual to restricted dynamic feedback linearization in a loose sense necessary and sufficient conditions for this problem are obtained in terms of the index

dynamic observer error linearization in this paper a new framework of observer error linearization problem is proposed the main idea of our approach is twofold the one is to introduce an auxiliary dynamics whose input is the system output and the other is to transform the augmented system into an observable linear system with an injection term which contains the system output as well as the state of the auxiliary dynamics it is a natural extension of the recently developed dynamic observer error linearization where the injection term contains only newly defined output it is also shown that whenever an n dimensional system is immersible into an n d dimensional linear system up to an output injection then it can be also dynamically observer error linearizable in our sense with a d dimensional auxiliary dynamics moreover we show that the converse is not true by providing a counterexample which implies that our approach is applicable to a strictly wider class of systems than that of the system immersion method

brief paper observer forms for perspective systems the estimation of three dimensional position information from two dimensional images in computer vision systems can be formulated as a state estimation problem for a nonlinear perspective dynamic system the multi output state estimation problem has been treated by several authors using methods for nonlinear observer design this paper shows that a perspective system can be transformed to two observer forms and provides constructive methods for arriving at the transformations these observer forms lead to straightforward observer designs first it is shown that using an output transformation the system admits an observer form which leads to an observer with linear error dynamics a second observer design is based on a time scaled block triangular form both designs assume a commonly used observability condition the designs are demonstrated in simulation

semi induced fuzzy topologies abstract induced fuzzy topologies were first introduced by wong 15 and weiss 14 they were studied by lowen who called them topologically generated fuzzy topologies 7 an induced fuzzy topology includes its modification topology we generalize induced fuzzy topologies to semi induced fuzzy topologies viz those which include their modification topologies the yet more general fuzzy topologies of structure c are also introduced the fully stratified fuzzy topological spaces of structure c are precisely the fuzzy neighbourhood spaces of lowen 4 in subsequent papers this relationship will be established and benefited from the two axioms of semi induction and structure c hold trivially for crisp fuzzy topologies we call such axioms fuzzy structural axioms in fuzzy topology in this paper we analyze the axioms of structure c semi induction and induction in this context we show how these axioms are linked to the three structural asioms of structures a b and d introduced by us in 11 the basic notions and results pertaining to structures a b and d are compiled in the first section the behaviour of warren s fuzzy boundary in semi induced fuzzy topological spaces fts s for short is also explained

reduced order dynamic observer error linearisation a natural extension of observer error linearisation this paper introduces the concept of reduced order dynamic observer error linearisation rdoel for multi output systems which is the problem of transforming a nonlinear system into a nonlinear observer canonical form with the aid of auxiliary dynamics the proposed rdoel framework is not only a modified version of dynamic observer error linearisation doel but also a natural extension of observer error linearisation oel we provide three necessary conditions for the rdoel problem and then derive a necessary and sufficient condition described in terms of lie algebras of vector fields furthermore from the result we also give a geometric necessary and sufficient condition for the oel problem which has not yet been completely established in the case where a diffeomorphism on the output of general form is considered

linear fuzzy neighborhood spaces some of the properties of linear fuzzy neighborhood spaces are studied a special class of these spaces is the family of all fuzzy linear spaces whose topology is given by probabilistic seminorms as in the classical case it is shown that a linear fuzzy neighborhood space is probabilistic normable iff it is hausdorff and it has an n bounded convex fuzzy neighborhood of zero

an efficient method for observer design with approximately linear error dynamics exact error linearization is a well known full order observer design method which yields linear time invariant stable error dynamics in normal form coordinates the difficult procedure associated with exact error linearization has led to the simpler extended luenberger observer design however extended luenberger observers can only guarantee a first order approximation to the exact error linearization design this paper provides an explicit formula involving only derivative lie derivative and bracket and matrix inversion operations for computing an nth order approximation of the exact error linearization observer hence the proposed method is a computational simple tool for designing observers for systems admitting exact error linearization observers two examples demonstrate the application of the method

the observer error linearization problem via dynamic compensation linearization by output injection has played a key role in the observer design for nonlinear control systems for almost three decades in this paper following some recent works ge ometric necessary and sufficient conditions are derived for the existence of a dynamic compensator solving the problem under regular output transformation an algorithm which computes a compensator of minimal order is given

constructive algorithm for system immersion into non linear observer form there exists a class of non linear systems which cannot be transformed into a non linear observer form an observable linear system up to output injection via diffeomorphism but can be immersed into a higher dimensional non linear observer form this class of systems can be characterized by a differential equation called characteristic equation if the system is an n dimensional system and it is immersible into n m dimensional observer form the characteristic equation involves n m 1 unknowns where n m unknowns are for the state immersion and one for the output transformation in general one should solve these unknowns simultaneously which makes the characterization difficult after investigating the algebraic structure of the characteristic equation we present an algorithm to check the immersibility under a constant rank assumption using the algorithm one can check the immersibility iteratively since only one unknown is involved at each step of the algorithm

on fuzzy metric spaces abstract in this paper we introduce the concept of a fuzzy metric space the distance between two points in a fuzzy metric space is a non negative upper semicontinuous normal and convex fuzzy number properties of fuzzy metric spaces are studied and some fixed point theorems are proved

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input abstract the transformation of nonlinear multi input multi output systems x f x u y h x u into an observer canonical form with reduced dependency on derivatives of the input is studied necessary and sufficient conditions for its existence and a straightforward algorithm for obtaining the canonical model are derived the proposed method involves the solution of a nonlinear algebraic equation system and systems of first order linear partial differential equations the nonlinear canonical form obtained permits global observer error linearization and it is a stage in the design of nonlinear observers the method is illustrated by an example

invariant probabilistic metrizability of fuzzy neighbourhood groups we introduce the notions of n local compactness and n openess in fuzzy neighbourhood spaces and in fuzzy neighbourhood groups together with some characterizations for them in particular we prove that a fuzzy neighbourhood space is n locally compact if and only if its level spaces for all 0 1 are locally compact a similar criterion is established for n open functions we also introduce the notion of fuzzy absolute value functions on groups we show that there exists a 1 1 correspondence between invariant fuzzy probabilistic pseudo metrics on groups and fuzzy absolute value functions we establish theorems on fuzzy probabilistic pseudo metrizability of fuzzy neighbourhood groups finally fuzzy probabilistic metrizability of quotient fuzzy neighbourhood groups is also taken into account

new algebraic geometric conditions for the linearization by input output injection the goal of this paper is twofold it unifies and generalizes existing results on input output injection linearization of nonlinear systems the problem is solved as a realization problem since it is based on the analysis of the structure of the input output differential equation the necessary and sufficient conditions are derived from a simplified and constructive procedure for clarity the paper is limited to the case of single output systems exterior differential systems are extensively used throughout the paper giving constructive conditions

on the uniform observability of discrete time nonlinear systems in constructing an observer for a discrete time nonlinear system the system is commonly required to satisfy a certain kind of uniform observability condition that is the state should always be reconstructible from observation windows of a specific length irrespective of the values of the state and inputs in this technical note it is proved that this uniform requirement is unnecessary in the sense that if the initial state and inputs are on a compact set then the uniform observability is derived from its non uniform counterpart

observer design for a class of nonlinear systems a viable design methodology to construct observers for a class of nonlinear systems is developed the proposed technique is based on the off line solution of a riccati equation and can be solved using commercially available software packages for globally valid results the class of systems considered is characterized by globally lipschitz nonlinearities local results relax this assumption to only a local requirement for a more general description of nonlinear systems the methodology yields approximate observers locally the proposed theory is used to design an observer for a single link flexible joint robot this observer estimates the robot link variables based on the joint measurements

input output linearization approach to state observer design for nonlinear system presents a state observer for a class of nonlinear systems based on the input output linearization while the previous result presented state observers for nonlinear systems of full relative degree we proposed a procedure fur the design of nonlinear state observers which do not require the hypothesis of full relative degree assuming that there exists a global state observer for internal dynamics and that some functions are globally lipschitz we can design a globally convergent state observer it is also shown that if the zero dynamics are locally exponentially stable then there exists a local state observer an example is given to illustrate the proposed design of nonlinear state observers

linearization by output injection and nonlinear observers abstract observers can easily be constructed for those nonlinear systems which can be transformed into a linear system by change of state variables and output injection necessary and sufficient conditions for the existence of such a transformation are given

a state observer for nonlinear systems and its application to ball and beam system in this paper we present a state observer for single input single output nonlinear systems which fail to have well defined relative degree it is shown that there exists a local state observer for a nonlinear system if it has robust relative degree n the proposed observer utilizes the coordinate change which transforms a system into an approximate normal form the proposed method is applied to a ball and beam system and simulation results show that substantial improvement in the performance was achieved compared with other local observers

on fuzzy metrizability abstract in this paper we answer two questions raised by m a erceg j math anal appl 69 1979 205 230 precisely we show that the fuzzy unit interval is never t0 except in the standard case and that a fuzzy pseudo metrizable t0 space is metrizable in the sense of erceg ibid hence the two definitions of metrizable space given in b hutton and i reilly fuzzy sets and systems3 1980 93 104 and erceg ibid are equivalent

a level topologies criterion for lowen fuzzy uniformizability throughout x will be a nonempty set we consider a subset m of x as a crisp fuzzy set and denote this again by m we denote the strong cut of a fuzzy set e ix by and its weak cut by e i

comments on state observers and state feedback controllers for a class of non linear systems the new non linear observer canonical form introduced by hauksdottir and fenton 1988 is compared with the known non linear observer canonical form it is pointed out that the new canonical form does not satisfy essential requirements for an observer canonical form and hence should not be denoted as such

h filter design for a class of nonlinear discrete time singular systems this paper deals with the h filter design problem for a class of discrete time lipschitz nonlinear singular systems the approach is based on the parameterisation of the obtained algebraic constraints from the estimation errors sufficient conditions for the existence of the filters which guarantee stability and the worst case filter error energy over all bounded energy disturbances is minimised are given the method also unifies the design for the full order reduced order minimal order filters for discrete time systems the presented results are less conservative than those existing in the literature this is due to the introduction of new slack variables application to systems with unknown input is presented via a numerical example

brief paper h observers design for a class of nonlinear singular systems the present paper is devoted to the h observer or filter design problem for a class of lipschitz nonlinear singular systems the approach is based on the parameterization of the obtained algebraic constraints from the estimation errors sufficient conditions for the existence of the observers which guarantee stability and the worst case observers error energy over all bounded energy disturbances is minimized are given the method also unifies the design for the full order reduced order minimal order observers for continuous time systems it can be seen that the obtained conditions when applied to linear systems are also necessary a numerical example is given to show the applicability of our results

linearization by generalized input output injection abstract the problem under interest is the linearization of nonlinear mimo systems by generalized input output injection in order to design observers with linear error dynamics the method is based on the study of the structure of the input output differential equations thus the problem is solved as a realization problem in this note one considers the linearization under two kinds of inout output injection in the first case the transformation depends on the output and time derivatives of the input whereas in the second case derivatives of both the input and the output are considered necessary and sufficient conditions are obtained which generalize the ones on standard input output injection linearization

a unified h adaptive observer synthesis method for a class of systems with both lipschitz and monotone nonlinearities abstract this paper investigates the problem of the h adaptive observer design for a class of nonlinear dynamical systems the main contribution consists in providing a unified synthesis method for systems with both lipschitz and monotone nonlinearities not necessarily lipschitz thanks to the innovation terms into the nonlinear functions m arcak p kokotovic observer based control of systems with slope restricted nonlinearities ieee transactions on automatic control 46 7 2001 1146 1150 and to the differential mean value theorem a zemouche m boutayeb g i bara observers for a class of lipschitz systems with extension to h performance analysis systems and control letters 57 1 2008 18 27 the stability analysis leads to the solvability of a linear matrix inequality lmi with several degrees of freedom for simplicity we start by presenting the result in an h adaptive free context furthermore we propose an h adaptive estimator that extends easily the obtained results to systems with unknown parameters in the presence of disturbances we show in particular that the matching condition in terms of an equality constraint required in several works is not necessary and therefore allows reducing the conservatism of the existing conditions performances of the proposed approach are shown through a numerical example with a polynomial nonlinearity

pseudo closure operators in fuzzy neighbourhood base spaces abstract fuzzy neighbourhood base spaces and dual fuzzy neighbourhood spaces are two special types of fuzzy topological spaces they were introduced by morsi as useful tools for the theory explanation and application of lowen s fuzzy neighbourhood systems the notion of the pseudoclosure operator of a fuzzy topological space was introduced by mashhour et al as a tool in establishing a necessary and sufficient condition for the productivity of fuzzy kuratowski operators pseudo closure operators carry partial information about the fuzzy closure operators of their respective spaces we establish relationships between the pseudo closure operators of fuzzy neighbourhood base spaces their fuzzy closure operators and their level topologies we provide counterexamples to disprove other nonvalid relationships we also study some categorical aspects of the operation of taking the pseudo closure operators of fuzzy topological spaces

extended output depending normal form this paper concerns the design of a nonlinear observer through a transformation of a nonlinear system into an observer form that supports a high gain observer sufficient geometrical condition is deduced to guarantee the existence of change of coordinates allowing the transformation of a nonlinear system into the proposed normal form the result is highlighted by studying the susceptible exposed infected and recovered seir model

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

recursive nonlinear observer design beyond the uniform observability we propose a recursive design scheme of a state observer for multiple input multiple output partly lower triangular nonlinear systems the design begins from the subdynamics far from the output and propagates to the subdynamics close to the output recalling the backstepping scheme for nonlinear control the proposed class of systems is fairly general since it includes nonuniformly observable and or detectable multioutput systems error convergence to zero is proved assuming boundedness of inputs a posteriori i e after the design which is preferable whereas most results in the literature assume the boundedness a priori i e before the design a global observer is proposed with the global lipschitz condition of the system but without any restriction on the size of lipschitz coefficient the lipschitz condition can be removed when a semiglobal observer is of interest

fuzzy topological vector spaces ii abstract some of the properties of fuzzy topological vector spaces are investigated also there are given necessary and sufficient conditions for a family of fuzzy sets in a vector space e to be the family of all neighborhoods of zero for a fuzzy linear topology

non linear observer design by reduced generalized observer canonical form a non linear canonical form observer design approach for multi input multi output systems y h x u with linearizable error dynamics is proposed in the paper the method involves a transformation of the original non linear system in a reduced generalized observer canonical form rgocf by a non linear state transformation the name reduced comes from the fact that this non linear canonical form has a reduced dependency on derivatives of the inputs necessary and sufficient conditions for transformability are derived and a transformation algorithm based on those conditions is developed the non linear observer is firstly designed in the canonical coordinates of the rgocf and then it is presented in the original and observability coordinates a final example including simulation is given for illustration

online exact differentiation and notion of asymptotic algebraic observers in recent years the availability of computer based methods has created a revival of interests in exploring algebraic methods in nonlinear context this paper proposes a new approach to algebraic nonlinear observer design after giving the notion of algebraic observability and based on a novel algorithm of exact differentiation the formulation of the nonlinear observer is realized via the construction of a set of linear time varying differentiators an example of a chemical reaction is given to show the effectiveness of our approach

partial observer normal form for nonlinear system in this paper we investigate the estimation problem for a class of partially observable nonlinear systems for the proposed partial observer normal form ponf necessary and sufficient conditions are deduced to guarantee the existence of a change of coordinates which can transform the studied system into the proposed ponf examples are provided to illustrate the effectiveness of the proposed results

verifiable conditions for multioutput observer error linearizability the verifiable necessary and sufficient conditions for the multioutput observer error linearization problem have not been found over the last three decades in this technical note we give the unverifiable necessary and sufficient conditions which are more specific than the ones in the literature using these conditions a verifiable sufficient condition also necessary with additional restriction on the problem is derived since our proofs are constructive a desired state transformation can also be found in the theorem also our algorithmic conditions can be easily implemented by a matlab programming

design of an extended unknown input observer with stochastic robustness techniques and evolutionary algorithms the paper deals with the problem of designing an unknown input observer for discrete time non linear systems in particular with the use of the lyapunov method it is shown that the proposed observer is convergent under certain non restrictive conditions based on the achieved results a general solution for increasing the convergence rate is proposed and implemented with the use of stochastic robustness techniques in particular it is shown that the problem of increasing the convergence rate of the observer can be formulated as a stochastic robustness analysis task that can be transformed into a structure selection and parameter estimation problem of a non linear function which can be solved with the b spline approximation and evolutionary algorithms the final part of the paper shows an illustrative example based on a two phase induction motor the presented results clearly exhibit the performance of the proposed observer

lower semicontinuous convex relaxation in optimization we relate the argmin sets of a given function not necessarily convex or lower semicontinuous and its lower semicontinuous convex hull by means of explicit characterizations involving an appropriate concept of asymptotic functions this question is connected to the subdifferential calculus of the legendre fenchel conjugate function the final expressions which also involve a useful extension of the fenchel subdifferential introduced in r correa and a hantoute set valued var anal 18 2010 pp 405 422 are then written exclusively by means of primal objects relying on the initial function this work extends to the infinite dimensional setting of some related results given in j benoist and j b hiriart urruty siam j math anal 27 1996 pp 1661 1679

nonlinear observer design via an extended observer canonical form based on the theory of designing unknown input observers an extended nonlinear observer canonical form is introduced observers can easily be constructed for those systems which can be transformed into this canonical form necessary and sufficient conditions for the existence of such transformation are derived and furthermore an algorithm for calculating this transformation in given

the urysohn lemma for fuzzy neighbourhood spaces abstract the framework fns of lowen s fuzzy neighbourhood spaces is a special environment for the study of fuzzy topology it encompasses its own metrics uniformities and proximities among other interesting constructions this is a fresh and fast growing field of research it promises to develop quickly to a calculus which combines depth with applicability within this framework we establish the urysohn lemma for the mashhour morsi axiom of n normality the formulation employs the mashhour morsi n euclidean space as the suitable fuzzy analogue of the real line the proof makes use of the artico moresco fuzzy proximities the lowen fuzzy uniformities and the mashhour morsi axiom of n complete regularity

a state observer for nonlinear systems a state observer design methodology for a class of nonlinear systems is proposed the nonlinear observer design methodology is in fact an extension of linear observer design techniques using transformations related to linear observability matrices

fuzzy neighborhood spaces abstract in this paper we introduce a subcategory of the category of fuzzy topological spaces and we prove basic properties of this subcategory the main idea behind these spaces is the notion of fuzzy neighborhoods which enables us to introduce a local theory of fuzzy topologies

observability through delayed measurements a new approach to state observers design an original approach for the construction of state observers for dynamic systems is presented in this article new notions of observability delay observability and delay drift observability useful for the development of the observer equations and for the convergence proof are introduced and compared with other standard observability concepts in particular it is shown that delay drift observability is an extension of the well known drift observability property the construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form which is a common feature of many other approaches a numerical example is reported where a system that is not drift observable is considered in this case the proposed observer is easily constructed and performs well

observers for a class of lipschitz systems with extension to h performance analysis abstract in this paper observer design for a class of lipschitz nonlinear dynamical systems is investigated one of the main contributions lies in the use of the differential mean value theorem dmvt which allows transforming the nonlinear error dynamics into a linear parameter varying lpv system this has the advantage of introducing a general lipschitz like condition on the jacobian matrix for differentiable systems to ensure asymptotic convergence in both continuous and discrete time systems such sufficient conditions expressed in terms of linear matrix inequalities lmis are established an extension to h filtering design is obtained also for systems with nonlinear outputs a comparison with respect to the observer method of gauthier et al a simple observer for nonlinear systems applications to bioreactors ieee trans automat control 37 6 1992 875 880 is presented to show that the proposed approach avoids high gain for a class of triangular globally lipschitz systems in the last section academic examples are given to show the performances and some limits of the proposed approach the last example is introduced with the goal to illustrate good performances on robustness to measurement errors by avoiding high gain

fuzzy uniform spaces in this paper we introduce the notion of fuzzy uniform spaces in section 2 we give some basic results and show how a fuzzy topology is derived from a fuzzy uniformity in sections 3 and 4 we prove that the notions which are introduced are good extensions and we prove that the category of uniform spaces is nicely injected in the category of fuzzy uniform spaces finally in section 5 we prove some basic results

immersion of non linear systems into linear systems up to output injection characteristic equation approach there exists a class of non linear systems which cannot be transformed into non linear observer form via diffeomorphism but can be immersed into higher dimensional non linear observer form this paper investigates when n dimensional non linear systems can be immersed into n m dimensional non linear systems in non linear observer form and provides a necessary and sufficient condition we also present an algorithm to check the immersibility in general at the first step of the algorithm one should solve a differential equation with m 1 unknowns rather than solving one with n m unknowns simultaneously when a solution to the differential equation can be obtained the immersibility can be checked by a recursive algorithm moreover when 2m n a straightforward algorithm is provided to check the immersibility

observers for a class of nonlinear singular systems this technical note considers the observers design for a class of nonlinear singular systems the approach is based on the new parameterization of the generalized sylvester equations solutions the conditions for the existence of these observers are given and sufficient conditions for their stability are derived using linear matrix inequalities lmis formulation reduced order minimal order and full order observers are designed by a unified method a numerical example is presented to demonstrate the effectiveness of the developed method

semi global observer for multi output nonlinear systems abstract we present an explicit form of nonlinear observers for a class of multi input multi output systems observer construction for multi output nonlinear systems is not a trivial extension of single output case especially when the global error convergence is of interest in this paper we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself and the overall system has a block triangular form for each subsystem hence the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed the construction is based on the saturation of some estimates which is originated by khalil and esfandiari for the use of semi global output feedback control