partial stability and boundedness of general dynamical systems on metric spaces we develop new results for partial stability of invariant sets and boundedness of motions for dynamical systems defined on metric space using stability preserving mappings our results are applicable to a much larger class of systems than existing results including dynamical systems that cannot be determined by the usual classical differential equations and inequalities in contrast to existing results which pertain primarily to the analysis of equilibria present results apply to invariant sets including equilibria as a special case we apply our results in the analysis of a class of discrete event systems a computer load balancing problem we are not aware of existing results on partial stability that apply to this class of systems

strong detectability and observers conditions are given for the existence of observers that estimate unmeasured outputs on the basis of partial information on the input and the state the concepts of strong detectability and strong observability introduced before in the literature for discrete time systems only are defined and studied for continuous time systems it is shown that there are two different concepts of strong detectability which coincide for discrete time systems algebraic conditions for either concept are given it is shown that these concepts are intimately related to the existence of strong observers i e observers that only use the output of the plant

eigenvalue assignment by minimal state feedback gain in lti multivariable systems in this article an improved method for eigenvalue assignment via state feedback in the linear time invariant multivariable systems is proposed this method is based on elementary similarity operations and involves mainly utilisation of vector companion forms and thus is very simple and easy to implement on a digital computer in addition to the controllable systems the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs moreover two types of state feedback gain matrices can be achieved by this method 1 the numerical one which is unique and 2 the parametric one in which its parameters are determined in order to achieve a gain matrix with minimum frobenius norm the numerical examples are presented to demonstrate the advantages of the proposed method

survey paper static output feedback a survey this paper reviews the static output feedback problem in the control of linear time invariant lti systems it includes analytical and computational methods and presents in a unified fashion the knowledge gained in the decades of research into this important open problem the paper shows that although many approaches and techniques exist to approach different versions of the problem no efficient algorithmic solutions are available

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

nonlinear decoupling via feedback a differential geometric approach the paper deals with the nonlinear decoupling and noninteracting control problems a complete solution to those problems is made possible via a suitable nonlinear generalization of several powerful geometric concepts already introduced in studying linear multivariable control systems the paper also includes algorithms concerned with the actual construction of the appropriate control laws

grassmannian central projection and output feedback pole assignment of linear systems a sufficient rank condition for arbitrary pole assignability by static output feedback of m input p output linear systems of mcmillan degree n mp is given this condition is easy to check and is satisfied by the generic system an effective computational method to compute the feedback laws assigning any self conjugate set of closed loop poles is also given

pole placement by static output feedback for generic linear systems we consider linear systems with m inputs p outputs and mcmillan degree n such that n mp if both m and p are even we show that there is a nonempty open in the usual topology subset u of such systems where the real pole placement map is not surjective it follows that for each system in u there exists an open set of pole configurations symmetric with respect to the real line which cannot be assigned by any real static output feedback

adaptive systems and time varying plants abstract the behaviour of four adaptive algorithms lms equation error output error identification and the goodwin ramadge caines adaptive control algorithm are examined in the face of plant parameter variations the key point to note is that persistency of excitation conditions in the time invariant parameter case guarantees exponential convergence then standard and newly developed lyapunov stability results allow us to guarantee tracking error and parameter error boundedness when the plant parameters are actually time varying

a new approach to adaptive nonlinear regulation this paper shows how the theory of adaptive observers can be effectively used in the design of internal models for nonlinear output regulation the main result obtained in this way is a new method for the synthesis of adaptive internal models which substantially enhances the existing theory of adaptive output regulation by allowing nonlinear internal models and more general classes of controlled plants

an iterative algorithm for pole placement by output feedback an iterative algorithm is proposed for solving the pole assignment by output feedback problem for an nth order l input m output linear system the algorithm uses a full rank feedback gain matrix and requires only linear equations of low dimension to be solved at each iteration application of the proposed algorithm allows all n closed loop poles to be almost exactly assigned provided that the iterations converge so that deviations of the resulting closed loop poles from the respective desired values become less than some user specified tolerance and m spl times t spl ges n examples are provided to illustrate the applicability of the proposed method

adaptive observers with arbitrary exponential rate of convergence for nonlinear systems concerns the same class of linearly parameterized single output nonlinear systems that the authors previously identified in 1992 in terms of differential geometric conditions when persistency of excitation conditions are satisfied the adaptive observers presented in this note guarantee arbitrarily fast exponential convergence both of parameter and state estimates to actual parameters and states while previous adaptive observers guarantee only exponential not arbitrarily fast convergence this extends earlier results for linear systems

observer based adaptive stabilization for a class of non linear systems abstract we determine via geometric conditions a class of single input single output non linear systems linear with respect to an unknown constant parameter vector which are globally stabilizable by an adaptive observer based control the only restriction on the non linearities is the dependence in suitable coordinates on the output only they are not restricted by sector or global lipschitz conditions when the parameter vector is known we obtain as a special case new sufficient conditions for global output feedback stabilization

brief paper adaptive observers for nonlinearly parameterized class of nonlinear systems in this paper one proposes adaptive observers for a class of uniformly observable mimo nonlinear systems with general nonlinear parameterizations the state and the unknown parameters of the considered systems are supposed to lie in bounded domains which size can be arbitrarily large and the exponential convergence of the observers is shown to result under a well defined persistent excitation condition moreover the gain of the observers involves a design function that has to satisfy a simple condition which is given different expressions of such a function are proposed and it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function the theory is supported by simulation results related to the estimation of the biomass concentration and the contois model parameters in a bioreactor

some remarks on real and complex output feedback we provide some new necessary and sufficient conditions which guarantee arbitrary pole placement of a particular linear system over the complex numbers we exhibit a nontrivial real linear system which is not controllable by real static output feedback and discuss a conjecture from algebraic geometry concerning the existence of real linear systems for which all static feedback laws are real

design of observers for linear systems with unknown inputs with a straightforward treatment a design of reduced order observers is presented for linear systems with unknown inputs the observers are derived with a physical meaning some explanations are given within the framework of descriptor system observer design principles the conditions for the existence of the observers are presented some illustrative examples are included

a complex variable form of the heg technique a previously reported simple method for calculating complex matrix eigenvalues is modified to incorporate the traditional heg approach for the case of even parity potentials two examples of resonance calculations are given our matrix and perturbation results agree with each other but are not in full accord with previously published results for one of the test potentials new results are given for the resonances of the inverted gaussian potential

functional unknown input reconstruction of descriptor systems the problem of finding conditions for the reconstruction of a linear combination of the vector of unknown inputs is tackled appropriate definitions are given in order to address formally the analysis thus necessary and sufficient conditions are obtained for two cases when the reconstruction may be achieved in finite time and when it is possible to do it asymptotically the results are applied for the fault detection with the respective deduction of analogous conditions

a geometric approach to the synthesis of failure detection filters a geometric formulation of beard s failure detection filter problem is stated using the concepts of c a invariant and unobservability subspaces the notions of output separable and mutually detectable families of subspaces introduced by beard are also clarified it is shown that mutual detectability is a necessary and sufficient condition for the existence of a detection filter with arbitrarily assignable spectrum moreover it is shown that the failure detection falter problem has a computationally simple solution when the failure events satisfy some mild restrictions finally the complete duality between a generalization of beard s detection filter problem and the restricted control decoupling problem is illustrated

unknown input observer for state affine systems a necessary and sufficient condition the problem of designing an unknown input observer for linear systems and its application to fault detection is widely studied in the literature for nonlinear systems only subclasses of nonlinear systems and sufficient conditions have been stated in this paper an unknown input observer design for state affine systems is considered based on the geometric approach a necessary and sufficient condition is given for the existence of an unknown input observer

design of a unified adaptive fuzzy observer for uncertain nonlinear systems this paper presents an adaptive fuzzy observer for a class of uncertain nonlinear systems more precisely we propose a unified approach for designing such an observer with some design flexibility so that it can be easily adaptable and employed either as a high gain or a sliding mode observer by selecting its gain appropriately additionally we derive a suitable parameter adaptation law so that the proposed observer is robust with respect to ubiquitous fuzzy approximation errors and external disturbances we also show that the observation error is ultimately bounded using a lyapunov approach without having recourse to the usual strictly positive real spr condition or a suitable observation error filtering the effectiveness of the proposed observers is illustrated through two simulation case studies taken from the adaptive fuzzy control literature

robust adaptive observers for nonlinear systems with bounded disturbances since existing adaptive observers for nonlinear systems may generate unbounded parameter estimates in the presence of bounded disturbances robust adaptive observers are presented which prevent parameter estimate drift in addition the input to state stability of the error dynamics with respect to disturbances and parameter time derivatives is guaranteed by generalizing a persistency of excitation result asymptotic convergence of state estimation errors is still achieved for systems in adaptive observer form when disturbances are not present by a suitable extension of barbalat s lemma

persistent excitation in bilinear systems discrete time systems described by difference equations which are polynomial in the input and linear in the output are discussed bilinear systems are special members of this class two issues are examined first a multidimensional polynomial based algebraic condition which is necessary and sufficient for such systems to be identifiable is given second subject to an identifiability assumption a condition on the input sequence which guarantees persistent excitation is given the principle analytic tool used in this study involves multidimensional polynomials

adaptive state observer for lipschitz nonlinear systems abstract the problem of adaptive observer synthesis for lipschitz nonlinear systems is addressed in the case of known parameters the convergence property of state observer is first discussed based on a generalized lipschitz condition the sufficient conditions to ensure the stability of observer error dynamics are presented in terms of some lmis in the case of system dynamics with some unknown parameters the proposed conditions along with an equality constraint are then employed to guarantee the convergence property of an adaptive state observer moreover an adaptive observer form is derived which can be utilized in designing the reduced order state observer the simulation results are finally given to exhibit the effectiveness of proposed synthesis approaches in dealing with the practical systems

unknown input observer design for fuzzy systems with uncertainties this paper investigates the problem of unknown input observer design for both discrete and continuous time t s fuzzy systems with uncertainties after doing appropriate processing to the model and reasonable analysis to the error expression of the system the observer design conditions are proposed in lmi form based on lyapunov theory more important is the introduction of a new decoupling method which can further reduce the conservatism the idea can eliminate the influence of the unknown inputs and guarantee the error of the state estimation is bounded when the uncertainties are nonzero finally an appropriate example is given to show the effectiveness of the algorithm especially the excellent estimate ability of the observer in initial time

on the observability codistributions of a nonlinear system abstract the purpose of this is to introduce the notion of observability codistribution for a nonlinear system which extends the dual of the notion of unobservability subspace then we study its properties which bear important similarities with a number of properties which render the notion of unobservability subspace powerful in the solution of certain design problems

detection filter design for lpv systems a geometric approach this paper investigates fault detection and isolation of linear parameter varying lpv systems by using parameter varying c a invariant subspace and parameter varying unobservability subspaces the so called detection filter approach formulated as the fundamental problem of residual generation fprg for linear time invariant lti systems is extended for a class of lpv systems the question of stability is addressed in the terms of lyapunov quadratic stability by using linear matrix inequalities the results are applied to the model of a generic small commercial aircraft

black box identification of a class of nonlinear systems by a recurrent neurofuzzy network this brief presents a structure for black box identification based on continuous time recurrent neurofuzzy networks for a class of dynamic nonlinear systems the proposed network catches the dynamics of a system by generating its own states using only input and output measurements of the system the training algorithm is based on adaptive observer theory the stability of the network the convergence of the training algorithm and the ultimate bound on the identification error as well as the parameter error are established experimental results are included to illustrate the effectiveness of the proposed method

stable adaptive observers for nonlinear time varying systems an adaptive observer identifier for single input single output observable nonlinear systems that can be transformed to a certain observable canonical form is described sufficient conditions for stability of this observer are provided these conditions are in terms of the structure of the system and canonical form the boundedness of the parameter variations and the sufficient richness of some signals the scope of the canonical form and the use of the observer identifier is motivated by the presentation of applications to time invariant bilinear systems nonlinear systems in phase variable form a biotechnological process and a robot manipulator in each case the specific stability conditions are presented

output regulation for linear minimum phase systems with unknown order exosystem under the assumption that the regulation error is the only feedback signal it is shown how to design a global regulator capable of rejecting and or tracking signals made of at most m sinusoidal terms with unknown frequencies magnitudes and phases for linear observable minimum phase systems the asymptotic convergence of the tracking error to zero is guaranteed provided that an upper bound is known on the number of sinusoidal terms even though the values of the unknown frequencies may not be recovered exponential convergence is achieved if all the exosystem frequencies are excited

generic eigenvalue assignment by memoryless real output feedback by extensive use of methods from algebraic geometry x wang proved that arbitrary pole placement by static output feedback is generically possible for strictly proper plants with n states m inputs and p outputs if n mp here we show the same result using no more of algebraic geometry than the definition of genericity

global observability and detectability analysis of uncertain reaction systems and observer design observation issues are of fundamental importance for reaction systems due to the limited availability of on line sensors and the uncertainties related to the mathematical model the objective of this work is to propose a methodology to make a global analysis of observability and detectability of such systems with a particular concern about the design of robust observers for this the uncertainties of the reaction system are modelled as arbitrary unknown inputs these results include and generalize the standard asymptotic observers well known in the biotechnology moreover the observability properties required for the existence of such observers and for the assignability of their convergence dynamics are clarified

pole placement via static output feedback is np hard this note proves that the problem of pole placement via static output feedback for linear time invariant systems is np hard

computing dynamic output feedback laws the pole placement problem asks to find laws to feed the output of a plant governed by a linear system of differential equations back to the input of the plant so that the resulting closed loop system has a desired set of eigenvalues converting this problem into a question of enumerative geometry efficient numerical homotopy algorithms to solve this problem for general multiple input multiple output systems have been proposed recently despite the wider application range of dynamic feedback laws the realization of the output of the numerical homotopies as a machine to control the plant in the time domain has not been addressed before in this note we present symbolic numeric algorithms to turn the solution to the question of enumerative geometry into a useful control feedback machine we report on numerical experiments with our publicly available software phcpack and illustrate its application on various control problems from the literature

adaptive observers for a class of uniformly observable systems with nonlinear parametrization and sampled outputs in this paper we propose an adaptive observer for a class of uniformly observable nonlinear systems with nonlinear parametrization and sampled outputs a high gain adaptive observer is first designed under the assumption that the output is continuously measured and its exponential convergence is investigated thanks to a well defined persistent excitation condition then we address the case where the output is available only at non uniformly spaced sampling instants to this end the continuous time output observer is redesigned leading to an impulsive observer with a corrective term involving instantaneous state impulses corresponding to the measured samples and their estimates moreover it is shown that the proposed impulsive observer can be put under the form of a hybrid system composed of a continuous time observer coupled with an inter sample output predictor two design features are worth to be emphasized firstly the observer calibration is achieved through the tuning of a scalar design parameter secondly the exponential convergence to zero of the observation and parameter estimation errors is established under a well defined condition on the maximum value of the sampling partition diameter more specifically the observer design is firstly carried out in the case of linear parametrization before being extended to the nonlinear one the theoretical results are corroborated through simulation results involving a typical bioreactor

krein space based h adaptive smoother design for a class of lipschitz nonlinear discrete time systems in this paper the problem of h adaptive smoother design is addressed for a class of lipschitz nonlinear discrete time systems with l2 bounded disturbance input by comprehensively analyzing the h performance lipschitz conditions and unknown parameter s bounded condition a positive minimum problem for an indefinite quadratic form is introduced such that the h adaptive smoothing problem is achieved a krein space stochastic system with multiple fictitious outputs is constructed by associating with the minimum problem of the introduced indefinite quadratic form the minimum of indefinite quadratic form is derived in the form of innovations through utilizing krein space orthogonal projection and innovation analysis approach via choosing the suitable fictitious outputs to guarantee the minimum of indefinite quadratic form is positive the existence condition of the adaptive smoother and its analytical solutions are obtained in virtue of nonstandard riccati difference equations the quality of the estimator is checked on an example

brief paper robust adaptive observer for nonlinear systems with unmodeled dynamics unmodeled dynamics exist in almost all applications of observers due to the impossibility of using exact and detailed models it is highly desired that the observers can dominate the effects of unmodeled dynamics independently to prevent the state estimations from diverging and to get the precise estimations based on adaptive nonlinear damping this paper presents a robust adaptive observer for multiple input multiple output nonlinear systems with unknown parameters uncertain nonlinearities disturbances and unmodeled dynamics the observer only has one adaptive parameter no matter how high the order of the system is and how many unknown parameters there are with the proposed observer neither estimating the unknown parameters or solving linear matrix inequalities is needed it is shown that the state estimation error is uniformly bounded and can be made arbitrarily small

a state observer for nonlinear dynamical systems the problem of state observation for nonlinear systems is of main importance in automatic control in recent years many contributions have been presented in literature that solve the design problem for classes of nonlinear systems most works can be roughly classi ed into two categories in one the geometrical properties of vector elds de ning the system are exploited and therefore mathematical tools of the di erential geometry are extensively employed in the other one the functional properties of the input state and state output maps which de ne the system are mainly used while the geometrical methods often provide a general solution of the problem for systems that belong to restricted classes characterized by geometrical properties 1 2 3 4 5 6 7 13 14 17 18 19 the second approach gives solutions for classes of nonlinear systems whose geometrical nature is not investigated and only macroscopic parameters norms gains lipschitz constants and so on are involved in the design procedure 8 9 11 12 21 one main problem in state observation for nonlinear systems is that the property of driftobservability does not imply observability for any input function as shown in 16 19 thus it is interesting to investigate when the drift observability property allows the solution of the state observation problem nding conditions that restricts the class of input functions due to the mathematical tools employed this work may be considered as belonging to both the categories above mentioned in this paper nonlinear systems of the form

global adaptive observers for nonlinear systems via filtered transformations the problem of determining global adaptive observers for a class of single output nonlinear systems which are linear with respect to an unknown constant parameter vector is addressed sufficient conditions are given to observe asymptotically an equivalent state without persistency of excitation under additional geometric conditions the original state can be observed as well the results obtained are based on a nonlinear change of coordinates driven by auxiliary filters filtered transformations

detectability of linear systems over a principal ideal domain with unknown inputs abstract observability and detectability conditions are obtained for a sort of linear time invariant systems affected by unknown inputs it is assumed that the system can be described using matrices whose elements are within a principal ideal domain pid it is shown that under suitable hypothesis the obtained conditions are necessary and sufficient the analysis is carried out by making use of the smith normal form of matrices over a pid the obtained conditions are a generalization of known conditions for particular sorts of systems which are included in those considered here

spectral properties of random non self adjoint matrices and operators i describe some numerical experiments which determine the degree of spectral instability of medium sized randomly generated matrices which are far from self adjoint the conclusion is that the eigenvalues are likely to be intrinsically uncomputable for similar matrices of a larger size i also describe a stochastic family of bounded operators in infinite dimensions for almost all of which the eigenvectors generate a dense linear subspace but the eigenvalues do not determine the spectrum my results imply that the spectrum of the non self adjoint anderson model changes suddenly on passing to the infinite volume limit

adaptive redesign of nonlinear observers to estimate unmeasured states in dynamical systems with parametric uncertainties one can use adaptive observers in this technical note a new method for adaptive redesign of reduced order observers for nonlinear systems is presented the redesign makes the observer robust as it guarantees that the state estimation error converges to zero in the presence of parametric uncertainties to enable parameter adaption a new type of update law is derived using lyapunov analysis and a nonlinear coordinate transformation the uniqueness of the approach is that it allows terms containing both uncertainty and nonlinearity in the unmeasured states to appear in the dynamics of the unmeasured states and still achieves convergence of the state estimate without requiring persistent excitation two examples are presented that demonstrate these properties

on eigenfunction approximations for typical non self adjoint schrodinger operators efficient approximations are constructed for the eigenfunctions of non self adjoint schrodinger operators in one dimension the same ideas also apply to the study of resonances of self adjoint schrodinger operators which have dilation analytic potentials in spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima we show that a suitable adaptation of the jwkb method is able to provide accurate global approximations to them

a necessary condition for pole assignment by constant output feedback in this paper we shall investigate the pole assignment problem by constant output feedback using transfer function techniques in particular a necessary condition is given for the existence of constant output feedback which assigns the eigenvalues of closed loop system to any desired positions

a geometric approach to nonlinear fault detection and isolation we present a differential geometric approach to the problem of fault detection and isolation for nonlinear systems a necessary condition for the problem to be solvable is derived in terms of an unobservability distribution which is computable by means of suitable algorithms the existence and regularity of such a distribution implies the existence of changes of coordinates in the state and in the output space which induce an observable quotient subsystem unaffected by all fault signals but one for this subsystem a fault detection filter is designed

global asymptotic linearisation of the pole placement map a closed form solution for the constant output feedback problem abstract the problem of pole assignment by constant output feedback controllers is studied for minimal systems described by a proper transfer function matrix g s r m p s with mcmillan degree n a new method is presented based on asymptotic linearisation around a degenerate point of the pole placement map related to the problem the essence of the present approach is to reduce the multilinear nature of the problem to one of solving a linear set of equations and this is achieved without losing any of the degrees of freedom in the controller the solution is given in closed form in terms of a one parameter family of static feedback compensators for which the closed loop poles approach the required ones as 0 conditions for the generic as well as exact solvability of the arbitrary pole placement problem are given in terms of the numbers m p n and the rank of a new system invariant the d restricted plucker matrix it is shown that the method works generically when mp n which along with the boundary case mp n is the best possible condition as far as the number of states of the open loop system is concerned for achieving arbitrary pole placement via constant output feedback

static output feedback pole placement via a trust region approach this technical note presents two closely related algorithms for the problem of pole placement via static output feedback the algorithms are based on two different trust region methods and utilize the derivatives of the closed loop poles extensive numerical experiments show the effectiveness of the algorithms in practice though convergence to a solution is not guaranteed for either algorithm while desired poles must be distinct strategies for dealing with repeated poles are also presented

identification of fault estimation filter from i o data for systems with stable inversion classical methods for estimating additive faults are based on state space models e g moving horizon estimation mhe and unknown input observers uios this paper contributes new direct design methods from closed loop i o data for systems with stable inversion which do not require building a state space model by first principles nor require identifying it inspired by subspace identification we use the input and output i o relationship of a plant in a vector arx varx form to parameterize least squares ls problems for estimating faults we prove that with the order of the varx descriptions tending to infinity the fault estimates are unbiased under lower relative degrees we prove that our new methods are equivalent to system inversion based estimation for both lti and ltv systems we will show more general unbiased estimation conditions for higher relative degrees these require that the underlying inverted system from faults to outputs is stable algorithms of identifying unbiased fault estimation filters from data will be developed in this paper based on single ls moreover covariance of the fault estimates can also be extracted from data

sampled data adaptive observer for a class of state affine output injection nonlinear systems the problem of observer design is addressed for output injection nonlinear systems a major difficulty with this class of systems is that the state equation involves an output dependent term that is explicitly dependent on unknown parameters as the output is only accessible to measurement at sampling times the output dependent term turns out to be almost all time subject to a double uncertainty making previous adaptive observers inappropriate presently a new hybrid adaptive observer is designed and shown to be exponentially convergent under ad hoc conditions

brief residual generator design for singular bilinear systems subjected to unmeasurable disturbances an lmi approach in this paper a method to design a bank of unknown input residual generator for fault detection and isolation is investigated the plant model is assumed to be a bounded control inputs singular bilinear systems subjected to unknown disturbances the measurements can be bilinear

output feedback eigenstructure assignment using two sylvester equations the eigenstructure assignment problem with output feedback is studied for systems satisfying the condition p m n the main tool used is the concept of c a b invariance and two coupled sylvester equations the solution of which leads to the computation of an output stabilizing feedback a computationally efficient algorithm for the solution of these two coupled equations which leads to the computation of a desired output feedback is presented

nonlinear observer for simultaneous states and unknown parameter estimation this paper presents the design of an observer for the simultaneous estimation of states and unknown parameter for a class of nonlinear systems whose nonlinearity satisfies a bounded jacobian condition the paper presents two alternate observers based on the structure of the system the conditions for the existence of these observers can be expressed as a linear matrix inequality and solved using standard solvers the case of time varying parameter and multiple unknown parameter have also been investigated the use of the developed methodology is demonstrated through illustrative examples

a luenberger like observer for nonlinear systems a state observer is proposed for nonlinear continuous time systems which extends the well known luenberger observer in particular on the basis of simple assumptions on the regularity of the system equations observability and the global holder condition for suitable functions which are generally satisfied for physically meaningful dynamic systems the global asymptotic convergence of the estimated state towards the true state is shown finally some examples of applications are also reported showing the effectiveness of the proposed observer

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

spectral instability for some schrodinger operators we show that the condition numbers of isolated eigenvalues of typical non self adjoint differential operators such as the harmonic oscillator may be extremely large we describe a stable procedure for computing the condition numbers for schrodinger operators in one dimension and apply it to the complex resonances of a typical operator with a dilation analytic potential

technical communique continuous discrete adaptive observers for state affine systems the observation of a class of multi input multi output mimo state affine systems with constant unknown parameters and discrete time output measurements is addressed assuming some persistent excitation conditions to hold and the sampling steps to satisfy some boundedness hypotheses system observability is ensured and a class of global exponential observers is synthesized

design of state observers from a drift observability property in this paper the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed for such an observer the drift observability property of the system i e observability for zero input together with an assumption on the input amplitude or on the observation relative degree are sufficient conditions for exponential convergence of the observation error the existence of an exponential observer is correlated to the existence of a solution for an h sub spl infin riccati like inequality global and semiglobal convergence results are presented

adaptive nonlinear observer for state and unknown parameter estimation in noisy systems this paper proposes a novel adaptive observer for lipschitz nonlinear systems and dissipative nonlinear systems in the presence of disturbances and sensor noise the observer is based on an h observer that can estimate both the system states and unknown parameters by minimising a cost function consisting of the sum of the square integrals of the estimation errors in the states and unknown parameters the paper presents necessary and sufficient conditions for the existence of the observer and the equations for determining observer gains are formulated as linear matrix inequalities lmis that can be solved offline using commercially available lmi solvers the observer design has also been extended to the case of time varying unknown parameters the use of the observer is demonstrated through illustrative examples and the performance is compared with extended kalman filtering compared to previous results on nonlinear observers the proposed observer is more computationally efficient and guarantees state

state estimation and decoupling of unknown inputs in uncertain lpv systems using interval observers abstractthis paper proposes a linear parameter varying lpv interval observer for state estimation and unknown inputs decoupling in uncertain continuous time lpv systems two different problems are considered and solved 1 the evaluation of the set of admissible values for the state at each instant of time and 2 the unknown input observation i e the design of the observer in such a way that some information about the nature of the unknown inputs affecting the system can be obtained in both cases analysis and design conditions which rely on solving linear matrix inequalities lmis are provided the effectiveness and appeal of the proposed method is demonstrated using an illustrative application to a two joint planar robotic manipulator

observer based parameter identifiers for nonlinear systems with parameter dependencies a class of nonlinear dynamical systems whose dynamics depend linearly on the unknown parameter vector is considered after reviewing a standard observer based identifier for estimating the unknown parameters we propose a family of new identifiers which exploit the a priori known parameter dependencies we then establish under mild assumptions on the dynamical system that 1 the proposed identifiers are stable and 2 the weighted norm of state parameter errors using the proposed identifiers are less than the corresponding errors using the standard identifier for a length of time after t 0 the main contribution of this paper is that it introduces a family of observer based identifiers which exhibit better transient performance than the standard identifier

bounded state reconstruction error for lpv systems with estimated parameters the note deals with the state reconstruction of a class of discrete time systems with time varying parameters while usually the parameters are assumed to be online available and exactly known the special and realistic situation when the parameters are known with a finite accuracy is considered the main objective of the note is to show that despite of the resulting mismatch between the true system and the model the state reconstruction error boundedness can be guaranteed and an explicit bound can be derived the proof is based upon the concept of input to state stability

adaptive observer for a class of parabolic pdes the problem of state observation based on spatially sampled output measurements is addressed for a class of infinite dimensional systems modelled by a semi linear heat equation augmented with a structured uncertain part involving a set of unknown parameters an adaptive observer is designed that provides online estimates of the system spatially distributed state and unknown parameters based on sampled data in space sufficient conditions for the observer to be exponentially convergent are established these include an ad hoc persistent excitation condition as well as a condition on how the observer gain must be selected in relation with the space sampling interval

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

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

a new approach to eigenstructure assignment by output feedback the eigenstructure assignment problem for a linear time invariant multi input multi output system using output feedback is considered a new approach is developed which identifies the eigenspaces for the desired set of all the closed loop eigenvalues for the assignment of this desired set necessary and sufficient conditions are established these conditions contain two coupled sylvester matrix equations one of which is proven to be a reduced order square sylvester matrix equation this results in an efficient analytical procedure numerically superior to known techniques for the determination of the output feedback gain matrix

on pole placement via eigenstructure assignment approach this note comes back to the hard problem of pole placement by static output feedback let a triplet of matrices a b c be given with n state variables m inputs and p ouputs find a matrix k such that the spectrum of a bkc equals a specified set when mp m p a simple noniterative technique based upon the notion of eigenstructure that in most cases assigns m p roots is proposed it therefore enables the designer to assign the whole of the desired spectrum when m p n mp

on nonlinear observers in this note we make some remarks about the general observer problem for nonlinear systems we show how the existence of a partial observer without stability requirements is locally equivalent to the existence of a conditioned invariant distribution we argue that by considering not only identity observers we can put the stability issue in a broader perspective

eigenvalue assignment by static output feedback on a new solvability condition and the computation of low gain feedback matrices in this article the static output feedback problem for linear time invariant systems is considered for arbitrary assignability of the roots of the characteristic polynomial by static output feedback a new necessary and sufficient condition is derived although the proof is based on simple analysis the known sufficient conditions derived by techniques of algebraic geometry are directly covered furthermore an algorithm for the calculation of feedback matrices assigning a desired set of eigenvalues is proposed this algorithm does not require the desired eigenvalues to be distinct and it explicitly exploits the available degrees of freedom for reducing the feedback gain the presented approach is illustrated on computational examples

remarks on nonlinear adaptive observer design abstract a solution to the problem of state estimation for systems with unknown parameters is to use some on line adaptation of the observer parameters on the basis of various existing results for such adaptive observer designs a unifying adaptive observer form is proposed in this paper this form indeed emphasizes properties allowing some asymptotic state estimation in spite of unknown parameters as well as additional properties which further allow parameter estimation as an example it is shown how an adaptive observer can be designed for a class of state affine systems

output regulation for linear systems via adaptive internal model given a stabilizable and detectable linear system with additive disturbances and output references generated by a linear stable exosystem with unknown parameters and known order the problem of designing a global output feedback regulator which asymptotically achieves output regulation and disturbance rejection is considered the system is assumed to be known while the frequencies of the exosystem are unknown all exosystem oscillatory modes are assumed to be excited by the initial condition a global solution is proposed consisting of a dynamic output feedback controller which includes exponentially convergent estimates of the unknown frequencies

failure detection and identification using the geometric concept of an unobservability subspace a solution is given to the problem of detecting and identifying control system component failures in linear time invariant systems conditions are developed for the existence of a causal linear time invariant processor that can detect and uniquely identify a component failure first for the case where components can fail simultaneously and then for the case where they fail only one at a time explicit design algorithms are provided when these conditions are satisfied in addition to time domain solvability conditions frequency domain interpretations of the results are given and connections are drawn with results already available in the literature