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

estimation of states faults and unknown disturbances in non linear systems in this paper we extend existing theory on non linear unknown input observer design to a wider class of non linear systems where the systems are subject to unknown input and output disturbances and experience faults the approach used is to decouple the faults and unknown disturbances from the rest of the system through a series of transformations on state and output equations once total disturbance decoupling is achieved an appropriate observer for the disturbance free part of the non linear system is proposed and designed the designed observer is subsequently used for estimation of unknown inputs outputs and fault signals two examples are given for illustration

an observer design for linear systems with unknown inputs a method is presented for designing an observer for the state of a linear time invariant system with unknown inputs the structure algorithm developed by silverman is applied to obtain the observer which estimates the maximum estimable subspace of the state it is shown that the observer equation can be derived from the maximum uncontrollable subspace of the original system with the aid of a left inverse for a transposed linear system this leads us to the necessary and sufficient condition for the existence of a state observer an application to the insensitivity observer synthesis is also included

linear filtering for bilinear stochastic differential systems with unknown inputs investigates the problem of state estimation for bilinear stochastic multivariable differential systems in the presence of an additional disturbance whose statistics are completely unknown a linear filter is proposed based on a suitable decomposition of the state of the bilinear system into two components the first one is a computable function of the observations while the second component is estimated via a suitable linear filtering algorithm no a priori information on the disturbance is required for the filter implementation the proposed filter is robust with respect to the unknown input in that the covariance of the estimation error is not affected by such input numerical simulations show the effectiveness of the proposed filter

jacobi approximations in certain hilbert spaces and their applications to singular differential equations jacobi approximations in certain hilbert spaces are investigated several weighted inverse inequalities and poincare inequalities are obtained some approximation results are given singular differential equations are approximated by using jacobi polynomials this method keeps the spectral accuracy some linear problems and a nonlinear logistic equation are considered the stabilities and the convergences of proposed schemes are proved strictly the main idea and techniques used in this paper are also applicable to other singular problems in multiple dimensional spaces

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

closed loop state and input observer for systems with unknown inputs a closed loop observer that can identify states and inputs simultaneously is developed for linear time invariant systems with unknown inputs the necessary and sufficient conditions for the existence of the observer are derived and proved parameter identification of a system with a few unknown or time varying parameters is investigated by applying the observer technique developed in this paper potential usage in machine monitoring machine diagnostics appears promising

observation of the state vector of linear multivariable systems with unknown inputs the necessary and sufficient conditions for the existence of an observer for linear multivariable system with immeasurable arbitrary disturbances are formulated the theorem is a generalization of the observability conditions for linear systems based on the proof of the theorem the algorithm of an observer can be constructed a numerical example is given

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 novel approach to the design of unknown input observers a novel state estimator design scheme for linear dynamical systems driven by partially unknown inputs is presented it is assumed that there is no information available about the unknown inputs and thus no prior assumption is made about the nature of these inputs a simple approach for designing a reduced order unknown input observer uio with pole placement capability is proposed by carefully examining the dynamic system involved and simple algebraic manipulations it is possible to rewrite equations eliminating the unknown inputs from part of the system and to put them into a form where it could be partitioned into two interconnected subsystems one of which is directly driven by known inputs only this makes it possible to use a conventional luenberger observer with a slight modification for the purpose of estimating the state of the system as a result it is also possible to state similar necessary and sufficient conditions to those of a conventional observer for the existence of a stable estimator and also arbitrary placement of the eigenvalues of the observer the design and computational complexities involved in designing uios are greatly reduced in the proposed approach

on designing reduced order observers for linear time invariant systems subject to unknown inputs abstract using the simplest matrix generalized inverse the l inverse a procedure is developed for the construction of a reduced order luenberger observer for a linear time invariant system subjected to immeasurable input disturbances illustrative examples are included

state and unknown input estimation for linear discrete time systems in this paper a state and unknown input delayed estimator is designed for discrete time linear systems even if some well known matching condition does not hold this result is obtained using a constructive algorithm that analyzes the state observability and the left invertibility of the systems with unknown inputs and that provides a suitable canonical transformation for the design of the estimator

identification of systems with unknown inputs using indirect input measurements abstracta common issue with many system identification problems is that the true input to the system is unknown this paper extends a previously presented indirect modelling framework that deals with identification of systems where the input is partially or fully unknown in this framework unknown inputs are eliminated by using additional measurements that directly or indirectly contain information about the unknown inputs the resulting indirect predictor model is only dependent on known and measured signals and can be used to estimate the desired dynamics or properties since the input of the indirect model contains both known inputs and measurements that could all be correlated with the same disturbances as the output estimation of the indirect model has similar challenges as a closed loop estimation problem in fact due to the generality of the indirect modelling framework it unifies a number of already existing system identification problems that are contained as special cases for completeness

a behavioral approach to estimation and dead beat observer design with applications to state space models the observer design problem is investigated in the context of linear left shift invariant discrete behaviors whose trajectories have supports on z necessary and sufficient conditions for the existence of a dead beat observer of some relevant variables from some measured ones in the presence of some unmeasured and irrelevant variables are introduced and a complete parametrization of all dead beat observers is given equivalent conditions for the existence of causal dead beat observers are then derived finally several classical problems addressed for state space models like state estimation the design of unknown input observers or the design of fault detectors and identifiers possibly in the presence of disturbances are cast in this general framework and the aforementioned equivalent conditions and parametrizations are specialized to these cases

optimal filtering for systems with unknown inputs an optimal filtering formula is derived for linear time varying discrete systems with unknown inputs by making use of the well known innovations filtering technique the derivation is an extension of a new observer design method for time invariant deterministic systems with unknown inputs the systems under consideration have the most general form the derived optimal filter has a similar form to the standard kalman filter with some modified covariance and gain matrices

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

stable adaptive fuzzy control of nonlinear systems a direct adaptive fuzzy controller that does not require an accurate mathematical model of the system under control is capable of incorporating fuzzy if then control rules directly into the controllers and guarantees the global stability of the resulting closed loop system in the sense that all signals involved are uniformly bounded is developed the specific formula for the bounds is provided so that controller designers can determine the bounds based on their requirements the direct adaptive fuzzy controller is used to regulate an unstable system to the origin and to control the duffing chaotic system to track a trajectory the simulation results show that the controller worked without using any fuzzy control rules and that after fuzzy control rules were incorporated the adaptation speed became much faster it is shown explicitly how the supervisory control forces the state to remain within the constraint set and how the adaptive fuzzy controller learns to regain control

disturbance decoupled functional observers if a state observer does not exist it is possible to design a functional observer principally this is also true for systems with unknown inputs termed as disturbances necessary and sufficient conditions for the existence of disturbance decoupled functional observers for linear time invariant systems are provided a method for designing such observers is given the analysis and design are based on a matrix pencil approach the design can also be used to obtain functional observers for descriptor systems with or without unknown inputs

disturbance decoupled observer design a unified viewpoint this paper is concerned with the observer design for linear systems with unknown inputs an equivalent system which is free of unknown inputs is derived for the purpose of the observer design based on the equivalent system description one can design an observer full order reduced order minimal order or functional for linear systems with unknown inputs using well known techniques it is shown that the equivalent system exists as long as there exists a disturbance decoupled observer two sets of the known existence conditions of disturbance decoupled observers are proved to be equivalent

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

decentralized state estimation in large scale interconnected dynamical systems abstract a simple approach for decentralized state estimation in large scale control systems is proposed given that a large scale dynamical system can be decomposed into a number of interconnected input output decentralized subsystems a method for designing totally decentralized local reduced order estimators is proposed it is shown that totally decentralized state estimation may be possible as long as the number of the subsystem interaction inputs are less than or equal to the locally measured outputs here the interconnection effects among the subsystems are treated as totally unknown inputs to each subsystem the method builds upon a novel approach in designing reduced order unknown input observers uio for dynamical systems and it therefore results in totally decentralized estimators structure the pros and cons of the estimation scheme are pointed out and necessary and sufficient conditions for designing local estimators are stated finally the design approach is verified by a numerical example

a robust estimator for stochastic systems under unknown persistent excitation a robust estimator for uncertain stochastic systems under unknown persistent disturbance is presented the given discrete time stochastic formulation neither requires a known bound on the magnitude of the unknown excitation nor assumes stability of the system however the proposed estimator assumes certain structural conditions on system uncertainties though the proposed estimator is developed based on stochastic lyapunov analysis its structure and performance are comparable to that of unbiased minimum variance filters based on the disturbance decoupling technique unlike unbiased minimum variance filters implementation of the developed estimator only requires adding an auxiliary term to the nominal steady state kalman filter and it does not involve any similarity transformation or propagation of matrix difference equations

h synthesis of unknown input observers for non linear lipschitz systems the problem of unknown input observer design for non linear lipschitz systems is considered a new dynamic framework which is a generalization of previously used linear unknown input observers is introduced the additional degrees of freedom offered by this dynamic framework are used to deal with the lipschitz non linearity the necessary and sufficient condition that ensures asymptotic convergence of the new observer is presented and the equivalence between this condition and an h optimal control problem which satisfies the standard regularity assumptions in the h optimization theory is shown based on these results a design procedure that is solvable using commercially available software is presented a simulation example is given to illustrate the proposed design

stable adaptive fuzzy pd plus pi controller for nonlinear uncertain systems abstract this paper presents an improved version of the stable fuzzy adaptive control structure which comprises an approximation of the ideal controller and a supervisory controller wang 1993 2 the proposed adaptive controller cancels the nonlinear function using a fuzzy system whose inputs are the feedback error signals instead of the state variables by using the feedback errors as the inputs to the fuzzy system improved control and disturbance rejection performance may be achieved as the controller is made more sensitive to the presence of tracking errors another useful feature of this structure is that the supervisory controller can be designed without the need of prior knowledge about the plant furthermore the computational burden of on line tuning can be reduced by disabling on line adaptation without incurring stability problems the efficiency of the proposed adaptive fuzzy system is demonstrated through simulation studies

the state vector reconstruction for linear systems with unknown inputs necessary and sufficient conditions for the existence of an observer for linear multivariable systems with unknown inputs are presented in theorem 1 proof of the theorem gives an algorithm of full order observer matrices calculation

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

delayed unknown input observers for discrete time linear systems with guaranteed performance abstract in this paper we propose a state and unknown input observer for discrete time linear systems with bounded unknown inputs and measurement disturbances the design procedure is formulated using a set of linear matrix inequalities and leverages delayed or fixed lag estimates the observer error states and or user defined performance outputs are guaranteed to operate at certain performance bounds furthermore by employing sufficiently large delays the observer is guaranteed to provide exact asymptotic state and input estimates for minimum phase systems we demonstrate via numerical examples that the proposed observer can be used for a wider class of systems than those satisfying matching conditions

observers for linear systems with unknown inputs a direct design procedure of a full order observer for a linear system with unknown inputs is presented using straightforward matrix calculations some examples are given in these examples a reduced order observer is also derived it is shown that this may restrict the rate of convergence of some state estimates

disturbance decoupled observer design via singular value decomposition singular value decomposition is used to formulate a technique for the design of luenberger observers when there are completely unknown system inputs

kalman filter for discrete time stochastic linear systems subject to intermittent unknown inputs state estimation of stochastic discrete time linear systems subject to persistent unknown inputs has been widely studied but only few works have been dedicated to the case where unknown inputs may be simultaneously or sequentially active or inactive in this technical note a kalman filter approach is proposed for state estimation of systems with unknown intermittent inputs the design is based on the minimisation of the trace of the state estimation error covariance matrix under the constraint that the state estimation error is decoupled from the unknown inputs corrupting the system at the current time the necessary and sufficient stability conditions are established considering the upper bound of the prediction error covariance matrix

a unifying approach of lti discrete time state observers by means of complementary matrices this paper deals with the generalization of state observers in the framework of lti deterministic discrete time systems using complementary matrix formalism four necessary and sufficient general conditions have been established in the design of any type of state observer furthermore necessary sufficient intrinsic conditions have been deduced respecting these intrinsic conditions guarantees satisfaction of the preceding general conditions an illustrative example is also included

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

technical communique unbiased minimum variance input and state estimation for linear discrete time systems with direct feedthrough this paper extends previous work on joint input and state estimation to systems with direct feedthrough of the unknown input to the output using linear minimum variance unbiased estimation a recursive filter is derived where the estimation of the state and the input are interconnected the derivation is based on the assumption that no prior knowledge about the dynamical evolution of the unknown input is available the resulting filter has the structure of the kalman filter except that the true value of the input is replaced by an optimal estimate

fault detection and isolation observers a design of reduced order observers is proposed for linear time invariant systems with unknown inputs including unknown measurement disturbances based on the unknown input observer design a systematic treatment of designing fault detection and isolation fdi observers is provided the core of the fdi observer design is to find an observable subsystem where the faults of interest show up and the rest of the faults disappear the fdi observer design procedure has a clear physical meaning robust fdi observers for uncertain systems can also be obtained using the fdi observer design provided the uncertainties of the system can be formulated as unknown inputs it is shown that the parity equations of another important fdi method can be generated in an elegant way using a dead beat fdi observer scheme directly in the time domain examples are included to show some concepts and to illustrate the fdi observer design method