nonlinear unknown input observability extension of the observability rank condition this paper provides an extension of the observability rank condition to nonlinear systems driven by both known and unknown inputs in particular the systems here considered are characterized by dynamics that are nonlinear in the state and linear in the inputs and characterized by a single unknown input or disturbance and multiple known inputs additionally it is assumed that the unknown input is a differentiable function of time up to a given order the goal of the paper is not to design new observers for these systems but to provide the analytic condition in order to check the weak local observability of the state this condition is simple and can be easily and automatically applied to the nonlinear systems mentioned above independently of their complexity and type of nonlinearity in particular the complexity of the analytic condition is comparable to the complexity of the standard method to check the state observability in the case without unknown inputs i e the observability rank condition this is a fundamental practical and unexpected advantage as for the observability rank condition the proposed analytic condition is based on the computation of the observable codistribution similarly to the case of only known inputs the observable codistribution is obtained by recursively computing the lie derivatives of the outputs along the vector fields that characterize the dynamics however in correspondence of the unknown input the corresponding vector field must be suitably rescaled additionally the lie derivatives of the outputs must also be computed along a new set of vector fields that are obtained by recursively performing suitable lie bracketing of the vector fields that define the dynamics in practice the entire observable codistribution is obtained by a very simple recursive algorithm finally it is shown that the recursive algorithm converges in a finite number of steps and the criterion to establish that the convergence has been reached is provided the proposed analytic extension of the observability rank condition is illustrated by checking the weak local observability of several nonlinear systems driven by known inputs and a single disturbance

technical communique a note on fractional order derivatives of periodic functions in this paper it is shown that the fractional order derivatives of a periodic function with a specific period cannot be a periodic function with the same period the fractional order derivative considered here can be obtained based on each of the well known definitions grunwald letnikov definition riemann liouville definition and caputo definition this concluded point confirms the result of a recently published work proving the non existence of periodic solutions in a class of fractional order models also based on this point it can be easily proved the absence of periodic responses in a wider class of fractional order models finally some examples are presented to show the applicability of the paper achievements in the solution analysis of fractional order systems

technical communique on the existence of periodic solutions in time invariant fractional order systems periodic solutions and their existence are one of the most important subjects in dynamical systems fractional order systems like integer ones are no exception to this rule tavazoei and haeri 2009 have shown that a time invariant fractional order system does not have any periodic solution in this article this claim has been investigated and it is shown that although in any finite interval of time the solutions do not show any periodic behavior when the steady state responses of fractional order systems are considered periodic orbits can be detected

unknown input observers for switched nonlinear discrete time descriptor systems in this paper a linear matrix inequality technique for the state estimation of discrete time nonlinear switched descriptor systems is developed the considered systems are composed of linear and nonlinear parts an observer giving a perfect unknown input decoupled state estimation is proposed sufficient conditions of global convergence of observers are proposed numerical examples are given to illustrate this method

observers for lipschitz non linear systems in an interesting paper r rajamani and y m cho have proposed a systematic methodology to design observers they have introduced a new problem relation between distance to unobservability and convergence of luenberger like observers a result for the convergence of the observer has also been given they have presented a quantity denoted by i claimed as the distance to unobservability we show that this number is not actually the distance from the system to the set of unobservable systems moreover the result for the observer is incorrect we provide a counterexample for the result of convergence in this paper results for convergence are obtained with additional strengthened hypothesis to correct rajamani and cho s result the results are used to design an observer for a now classical single link flexible robot joint the behaviour of the observer to noisy output is quite satisfactory

computation of eigenvector derivatives with repeated eigenvalues using a complete modal space this paper presents a complete modal space cms method that is an exact modal expansion method there is no modal truncation error existing in the derivation

brief extension of minimum variance estimation for systems with unknown inputs in this paper we address the problem of minimum variance estimation for discrete time time varying stochastic systems with unknown inputs the objective is to construct an optimal filter in the general case where the unknown inputs affect both the stochastic model and the outputs it extends the results of darouach and zasadzinski automatica 33 1997 717 where the unknown inputs are only present in the model the main difficulty in treating this problem lies in the fact that the estimation error is correlated with the systems noises this fact leads generally to suboptimal filters necessary and sufficient conditions for the unbiasedness of this filter are established then conditions under which the estimation error and the system noises are uncorrelated are presented and an optimal estimator and a predictor filters are derived sufficient conditions for the existence of these filters are given and sufficient conditions for their stability are obtained for the time invariant case a numerical example is given in order to illustrate the proposed method

on uniform observation of nonuniformly observable systems abstract in 4 7 9 12 classes of nonlinear systems are considered for which observers can be designed although observability of nonlinear systems is known to be dependent on the input the proposed observers have the property that the estimation error decays to zero irrespective of the input in the first part of this paper it is shown that this phenomenon follows from a common property of these systems for all of them the unobservable states with respect to some input are in some sense stable in the linear case these systems are called detectable and for this reason a reduced order observer can be designed in the second part is given a more general class of nonlinear systems for which such an observer can be designed

optimum approximation for residual stiffness in linear system identification a new method of system identification uti 1 i zes projector m atrix theory and the moorepenrose generalized inverse to derive an analytical stiffness matrix which when combined with the analytical mass matrix will more closely p redict modal test results weighting matrices a re used to enforce connectivity and make weighted corrections to the original analytical stiffness matrix a simple and straightforward mathematical formulation is obtained the method is compared and contrasted with other methods found in the literature and a simple numerical example is presented

maximum number of frequencies in oscillations generated by fractional order lti systems in this paper relation between the inner dimension of a fractional order lti system and the maximum number of frequencies which exist in oscillations generated by the system is investigated the considered system is defined in pseudo state space form and the orders of its involved fractional derivatives are rational numbers between zero and one first an upper bound is derived for the maximum number of frequencies then using the restricted difference bases concept a new method is introduced to design a multifrequency oscillatory fractional order system finally based on the proposed method some lower bounds are derived for the maximum number of frequencies obtainable in solutions of a fractional order system having a fixed inner dimension

iterative computation of modal sensitivities the computation of frequency and mode shape sensitivities with respect to design parameters is essential to many structural optimization and finite element updating algorithms approximating the gradients may lead to poor estimates and loss of convergence but on the other hand the cost of exact methods such as nelson s nelson r simplified calculations of eigenvector derivatives a1aa journal vol 14 no 9 1976 pp 1201 1205 is often not acceptable for industrial size models the present study thus analyses existing approximation methods suggests a first order improvement of fox and kapoor s modal basis fox r and kapoor m rate of change of eigenvalues and eigenvectors a1aa journal vol 6 no 12 1968 pp 2426 242 9 and proposes a residual iteration technique allowing accurate computations of modeshape sensitivities an engine cover model and a model of the ariane 5 main cryogenic stage are used to analyze for models of realistic sizes the accuracy and computational costs of the proposed methods

non existence of finite time stable equilibria in fractional order nonlinear systems we note that in the literature it is often taken for granted that for fractional order system without delays whenever the system trajectory reaches the equilibrium it will stay there in fact this is the well known phenomenon of finite time stability however in this paper we will prove that for fractional order nonlinear system described by caputo s or riemann liouville s definition any equilibrium cannot be finite time stable as long as the continuous solution corresponding to the initial value problem globally exists in addition some examples of stability analysis are revisited and linear lyapunov function is used to prove the asymptotic stability of positive fractional order nonlinear systems

observers for lipschitz nonlinear systems this paper presents some fundamental insights into observer design for the class of lipschitz nonlinear systems the stability of the nonlinear observer for such systems is not determined purely by the eigenvalues of the linear stability matrix the correct necessary and sufficient conditions on the stability matrix that ensure asymptotic stability of the observer are presented these conditions are then reformulated to obtain a sufficient condition for stability in terms of the eigenvalues and the eigenvectors of the linear stability matrix the eigenvalues have to be located sufficiently far out into the left half plane and the eigenvectors also have to be sufficiently well conditioned for ensuring asymptotic stability based on these results a systematic computational algorithm is then presented for obtaining the observer gain matrix so as to achieve the objective of asymptotic stability

stability and bifurcation of delayed fractional order dual congestion control algorithms in this technical note fractional order congestion control systems are introduced for the first time in comparison with the conventional integer order dual congestion control algorithms the fractional control algorithms are more accurate and versatile bifurcation theory in fractional order differential equations is still an outstanding problem sufficient conditions for the occurrence of hopf bifurcations are extended from integer order dynamical systems to fractional order cases then these conditions are used to establish the existence of hopf bifurcations for the delayed fractional order model of dual congestion control algorithms proposed in this note finally the onsets of bifurcations are identified where hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium illustrative examples are also provided to demonstrate the theoretical results

comparison of several methods for calculating vibration mode shape derivatives four methods for the calculation of derivatives of vibration mode shapes eigenvectors with respect to design parameters are described these are finite difference method modal method a modified modal method and nelson s method the methods are implemented in a general purpose commercial finite element program and applied to the following test problems a cantilever beam and a stiffened cylinder with a cutout design variables are a beam tip mass a beam root height and specific dimensions of the cylinder model the methods are compared on the basis of central processor cp seconds required to obtain the derivatives and two of the methods are also evaluated for the rapidity of convergence data is presented showing the amount of cp time used to compute the first four eigenvector derivatives for each example problem a scalar measure of the error in the mode shape derivative is defined and numerical results illustrating the rapidity of convergence of the approximate derivative to the exact derivative are presented results indicate an advantage in using nelson s method because this method is exact and requires less cp time especially when derivatives with respect to several design variables are computed

stability preservation analysis for frequency based methods in numerical simulation of fractional order systems in this paper the frequency domain based numerical methods for simulation of fractional order systems are studied in the sense of stability preservation first the stability boundary curve is exactly determined for these methods then this boundary is analyzed and compared with an accurate ideal boundary in different frequency ranges also the critical regions in which the stability does not preserve are determined finally the analytical achievements are confirmed via some numerical illustrations

brief paper synthesis of fractional laguerre basis for system approximation fractional differentiation systems are characterized by the presence of non exponential aperiodic multimodes although rational orthogonal bases can be used to model any l2 0 system they fail to quickly capture the aperiodic multimode behavior with a limited number of terms hence fractional orthogonal bases are expected to better approximate fractional models with fewer parameters intuitive reasoning could lead to simply extending the differentiation order of existing bases from integer to any positive real number however classical laguerre and by extension kautz and generalized orthogonal basis functions are divergent as soon as their differentiation order is non integer in this paper the first fractional orthogonal basis is synthesized extrapolating the definition of laguerre functions to any fractional order derivative completeness of the new basis is demonstrated hence a new class of fixed denominator models is provided for fractional system approximation and identification

undamped oscillations generated by hopf bifurcations in fractional order recurrent neural networks with caputo derivative in this paper a fractional order recurrent neural network is proposed and several topics related to the dynamics of such a network are investigated such as the stability hopf bifurcations and undamped oscillations the stability domain of the trivial steady state is completely characterized with respect to network parameters and orders of the commensurate order neural network based on the stability analysis the critical values of the fractional order are identified where hopf bifurcations occur and a family of oscillations bifurcate from the trivial steady state then the parametric range of undamped oscillations is also estimated and the frequency and amplitude of oscillations are determined analytically and numerically for such commensurate order networks meanwhile it is shown that the incommensurate order neural network can also exhibit a hopf bifurcation as the network parameter passes through a critical value which can be determined exactly the frequency and amplitude of bifurcated oscillations are determined

computation of eigenpair partial derivatives by rayleigh ritz procedure based on rayleigh ritz procedure a new method is proposed for a few eigenpair partial derivatives of large matrices this method simultaneously computes the approximate eigenpairs and their partial derivatives the linear systems of equations that are solved for eigenvector partial derivatives are greatly reduced from the original matrix size and the left eigenvectors are not required moreover errors of the computed eigenpairs and their partial derivatives are investigated hausdorff distance and containment gap are used to measure the accuracy of approximate eigenpair partial derivatives error bounds on the computed eigenpairs and their partial derivatives are derived finally numerical experiments are reported to show the efficiency of the proposed method

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

stiffness matrix adjustment using mode data a procedure is introduced that uses in addition to mode data structural connectivity information to optimally adjust deficient stiffness matrices the adjustments performed are such that the percentage change to each stiffness coefficient is minimized the physical configuration of the analytical model is preserved and the adjusted model will exactly reproduce the modes used in the identification the theoretical development is presented and the procedure is demonstrated by numerical simulation of a test problem

fractional market dynamics a new extension of a fractality concept in nancial mathematics has been developed we have introduced a new fractional langevin type stochastic dierential equation that diers from the standard langevin equation i by replacing the rst order derivative with respect to time by the fractional derivative of order and ii by replacing white noise gaussian stochastic force by the generalized shot noise each pulse of which has a random amplitude with the stable levy distribution as an application of the developed fractional non gaussian dynamical approach the expression for the probability distribution function pdf of the returns has been established it is shown that the obtained fractional pdf ts well the central part and the tails of the empirical distribution of s p 500 returns c 2000 elsevier science b v all rights reserved

eigenvector derivatives of structures with rigid body modes by defining and solving a similar eigenvalue problem of a structure with rigid body modes eignevector derivatives can be accurately computed by using lower computed modes and a modified flexibility matrix

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

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

unknown input proportional multiple integral observer design for linear descriptor systems application to state and fault estimation in this note the problem of observer design for linear descriptor systems with faults and unknown inputs is considered first it is considered that the fault vector function f is s times piecewise continuously differentiable if the s th time derivative of f is null then s integral actions are included into a luenberger observer which is designed such that it estimates simultaneously the state the fault and its finite derivatives face to unknown inputs second when the fault is not time piecewise continuously differentiable but bounded like actuator noise or s th time derivative of fault is not null but bounded too a high gain observer is derived to attenuate the fault impact in estimation errors the considered faults may be unbounded may not be determinist and faults and unknown inputs may affect the state dynamic and plant outputs sufficient conditions for the existence of such observer are given results are illustrated with a differential algebraic power system

modal expansion method for eigensensitivity with repeated roots extensions are made to the modal expansion eigensensitivity procedure for self adjoint systems originally formulated by fox and kapoor these allow the computation of sensitivity information for mode shapes associated with repeated roots and repeated root derivatives the extensions follow a similar line to additions to nelson s direct method proposed first by ojalvo and later generalized independently by mills curran and dailey the formulation based on modal expansion is simpler and more computationally efficient than the direct method although some accuracy is sacrificed by modal truncation the method generally yields acceptable results for the primary application in optimization

observer design for unknown input nonlinear descriptor systems via convex optimization this paper treats the design problem of full order observers for nonlinear descriptor systems with unknown input ui depending on the available knowledge on the ui dynamics two cases are considered first a ui proportional observer uipo is proposed when the spectral domain of the ui is unknown second a pio is proposed when the spectral domain of the ui is in the low frequency range sufficient conditions for the existence and stability of such observers are given and proved based on the linear matrix inequality lmi approach an algorithm is presented to compute the observer gain matrix that achieves the asymptotic stability objective an example is included to illustrate the method

disturbance decoupled observer design for descriptor systems in this paper we study the observer design problem for descriptor systems with partly unknown inputs we give necessary and sufficient conditions for the existence of a solution to the disturbance decoupled estimation problem with or without stable error spectrum requiring at the same time that the resulting combined system is regular and of index at most one all results are proved based on a condensed form that can be computed using orthogonal matrix transformations i e transformations that can be implemented in a numerically stable way

nonlinear observer design by observer error linearization this paper studies the observer design problem by the observer error linearization approach for nonlinear systems with and without inputs necessary and sufficient conditions for the existence of the linearization transformation are derived for nonlinear systems without inputs the conditions are shown to be corrections to an existing result a computation procedure and a different set of necessary and sufficient conditions based on the computation procedure are presented

reduced order observer design for descriptor systems with unknown inputs a new method for the design of reduced order observers for descriptor systems with unknown inputs is presented the approach is based on the generalized constrained sylvester equation sufficient conditions for the existence of the observer are given

brief paper a proof for non existence of periodic solutions in time invariant fractional order systems the aim of this note is to highlight one of the basic differences between fractional order and integer order systems it is analytically shown that a time invariant fractional order system contrary to its integer order counterpart cannot generate exactly periodic signals as a result a limit cycle cannot be expected in the solution of these systems our investigation is based on caputo s definition of the fractional order derivative and includes both the commensurate or incommensurate fractional order systems

state observers for discrete time linear systems with unknown inputs in the paper the problem of designing a full order state observer for a general discrete time linear system with unknown inputs is analyzed necessary and sufficient conditions for the existence either of an asymptotic or of a deadbeat observer are provided and a constructive design procedure together with some examples are discussed finally the equivalence of these conditions for problem solvability with those derived in previous contributions by means of different approaches is explicitly proved

analysis of a system of nonautonomous fractional differential equations involving caputo derivatives abstract we discuss existence uniqueness and stability of solutions of the system of nonlinear fractional differential equations d i y i t f i t y 1 y n y i k c k i 1 i n 1 k m i where m i i m i 1 and d i denotes caputo fractional derivative linear and nonlinear systems have been solved using banach fixed point theorem

prediction error methods for limit cycle data prediction error methods are considered for identification of the forward linear dynamics of nonlinear feedback closed loop systems which operate in a perturbed stable limit cycle a model of the signals measured in a neighborhood of the limit cycle is presented and shown to satisfy a quasistationarity property quasistationarity is then used to prove that prediction error methods are both convergent and consistent for our data model

stability analysis and control synthesis for switched systems a switched lyapunov function approach this paper addresses the problem of stability analysis and control synthesis of switched systems in the discrete time domain the approach followed in this paper looks at the existence of a switched quadratic lyapunov function to check asymptotic stability of the switched system under consideration two different linear matrix inequality based conditions allow to check the existence of such a lyapunov function the first one is classical while the second is new and uses a slack variable which makes it useful for design problems these two conditions are proved to be equivalent for stability analysis investigating the static output feedback control problem we show that the second condition is in this case less conservative the reduction of the conservatism is illustrated by a numerical evaluation

adaptive observers for single output nonlinear systems an adaptive version of the nonlinear observer obtained by a j krener et al 1983 is presented this version involves the cancellation of nonlinear terms by output injection as an intermediate step necessary and sufficient conditions are given for transforming a nonlinear system by state space change of coordinates into the special adaptive observer form that was used by y bastin et al 1988 to design adaptive observers

chaotic attractors in incommensurate fractional order systems in this paper based on the stability theorems in fractional differential equations a necessary condition is given to check the existence of 1 scroll 2 scroll or multi scroll chaotic attractors in a fractional order system this condition is proposed for incommensurate order systems in general but in the special case it converts to the condition given in the previous works for the commensurate fractional order systems though the presented condition is only a necessary and not sufficient condition for the existence of chaos it can be used as a powerful tool to distinguish for what parameters and orders of a given fractional order system chaotic attractors can not be observed and for what parameters and orders the system may generate chaos it can also be used as a tool to confirm or reject results of a numerical simulation some of the numerical results reported in the previous literature are confirmed by this tool

on the state observation and output feedback problems for nonlinear uncertain dynamic systems abstract in this paper we examine the problems of state observation and state trajectory control by output feedback for the class of non linear systems in 3 11 we begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is globally exponentially stable ges we then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the ges sense specific time varying bounds on the observation error and the state trajectory are also developed revealing how the corresponding observer or control parameters can be adjusted to improve the system performance

a note on observers for lipschitz nonlinear systems this note deals with the design of reduced order observers for lipschitz nonlinear systems it shows that the conditions under which a full order observer exists also guarantee the existence of a reduced order observer a design method of the reduced order observer that is dependent on the solution of the riccati equation is then presented and an example is given to illustrate effects of the design method

full order observers for linear systems with unknown inputs this note presents a simple method to design a full order observer for linear systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are given

improvement of a large analytical model using test data a method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure the method directly identifies without iteration a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements an application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure the resulting changes in the model are judged to be small compared to expectations of error in the analysis thus the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics in addition it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structure nomenclature analytical matrix matrix of changes identity matrix full improved stiffness and mass matrices n x n full analytical k m matrices n x n partitions of ka ma corresponding to test coordinates partitions of ka ma corresponding to coupling elements partitions of ka ma corresponding to unmea sured coordinates number of measured modes number of degrees of freedom in the model measures of changes eqs 15 17 matrix norm sum of the squares of all the elements rectangular modal matrix normalized n x m th mode th column of measured and unmeasured partitions of diagonal matrix of measured natural frequencies m xm natural frequency of th mode 12 17 sum of the squares of all elements of matrix

delay independent criteria for exponential admissibility of switched descriptor delayed systems this paper deals with the uniform exponential admissibility problem for switched descriptor systems with time varying delays a criterion for regularity impulsiveness free of each subsystem is presented a solution to switching impulsiveness free for switched descriptor systems is provided a novel type of piecewise lyapunov functionals is introduced this type of lyapunov functionals can efficiently overcome the switching jump of adjacent lyapunov functionals at switching times by applying this type of lyapunov functionals and algebraic manipulations the delay independent conditions for uniform exponential admissibility is established on the minimum dwell time

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

submatrix approach to stiffness matrix correction using modal test data an efficient method six stiffness matrix correction to match modal testing data is presented significant reduction of unknown parameters is achieved by grouping the elements of the same stiffness characteristics and representing them as a multiplication of a scaling factor and a submatrix a concise formulation to identify the scaling factors is found by utilizing a least squares solution the formulation also incorporates a capability of reducing finite element mass and stiffness matrices to test degrees of freedom for a direct analysis experiment correlation

filtering and fault estimation of descriptor switched systems in this paper the problems of state and fault estimation are addressed for a class of switched descriptor systems subject to lipschitz nonlinearities and unknown inputs ui the ui appear both on the dynamic and on the measurement equations two problems are addressed by l 2 gain minimization with the use of switched lyapunov functions and formulated by lmi first a functional observer for switched lipschitz nonlinear descriptor system is proposed for robust state estimation second fault estimation is performed by filtering the output estimation error as usually done in the residual generation framework moreover frequency weighting functions can be used to shape the response to the fault and thus improve the estimation

eigenvector sensitivity when tracking modes with repeated eigenvalues abstract while eigenvalue optimization problems have been widely studied during the last three decades particularly for structural and topology optimization problems there are very few examples of problems involving mode shapes either in the cost or the constraints in this paper we propose a general framework for computing eigenvector sensitivity whenever tracking specific mode shapes selected beforehand of course the approach is valid for either non repeated or repeated eigenvalues but here the emphasis is placed on the multiple eigenvalues case both mathematical validity of the algorithm and numerical corroboration through several examples are included

a systematic approach to adaptive observer synthesis for nonlinear systems geometric techniques of controller design for nonlinear systems have enjoyed great success a serious shortcoming however has been the need for access to full state feedback this paper addresses the issue of state estimation from limited sensor measurements in the presence of parameter uncertainty an adaptive nonlinear observer is suggested for lipschitz nonlinear systems and the stability of this observer is shown to be related to finding solutions to a quadratic inequality involving two variables a coordinate transformation is used to reformulate this inequality as a linear matrix inequality a systematic algorithm is presented which checks for feasibility of a solution to the quadratic inequality and yields an observer whenever the solution is feasible the state estimation errors then are guaranteed to converge to zero asymptotically the convergence of the parameters however is determined by a persistence of excitation type constraint