robust state estimation and unknown inputs reconstruction for a class of nonlinear systems multiobjective approach we consider a novel method to design h h observers for a class of uncertain nonlinear systems subject to unknown inputs first the main system dynamics are rewritten as an augmented system with state vector including both the state vector of the main system and the unknown inputs then we design a h h reduced order observer to estimate both state variables and unknown inputs simultaneously based on a lyapunov functional we derive a sufficient condition for existence of the designed observer which requires solving a nonlinear matrix inequality to facilitate the observer design the achieved condition is formulated in terms of a set of linear matrix inequalities lmi by extending the proposed method to a multiobjective optimization problem the maximum bound of the uncertainty and the minimum value of the disturbance attenuation level are found finally the proposed observer is illustrated with an example

observer based schemes for adaptive nonlinear state feedback control we combine recently proposed adaptive nonlinear controllers with two types of observer based identifiers the controllers guarantee an input to state stability property with respect to and and the observer based identifiers independently guarantee boundedness of a stability enhancement in the observer is crucial in establishing stability properties

design of sliding observers for lipschitz nonlinear system using a new time averaged lyapunov function abstractthis paper provides a procedure for designing a sliding mode observer for a nonlinear system in the presence of gaussian input disturbances and sensor noises the paper first proposes a nov

penalty approach to a nonlinear obstacle problem governing american put option valuation under transaction costs we propose a penalty method for a finite dimensional nonlinear complementarity problem ncp arising from the discretization of the infinite dimensional free boundary obstacle problem governing the valuation of american options under transaction costs in this method the ncp is approximated by a system of nonlinear equations containing a power penalty term we show that the mapping involved in the system is continuous and strongly monotone thus the unique solvability of both the ncp and the penalty equation and the exponential convergence of the solution to the penalty equation to that of the ncp are guaranteed by an existing theory numerical results will be presented to demonstrate the convergence rates and usefulness of this penalty method

adaptive observers for ts fuzzy systems with unknown polynomial inputs a large class of nonlinear systems can be well approximated by takagi sugeno ts fuzzy models with linear or affine consequents however in practical applications the process under consideration may be affected by unknown inputs such as disturbances faults or unmodeled dynamics in this paper we consider the problem of simultaneously estimating the state and unknown inputs in ts systems the inputs considered in this paper are 1 polynomials in time such as a bias in the model or an unknown ramp input acting on the model and 2 unmodeled dynamics the proposed observer is designed based on the known part of the fuzzy model conditions on the asymptotic convergence of the observer are presented and the design guarantees an ultimate bound on the error signal the results are illustrated on a simulation example

sontag s input to state stability condition and global stabilization using state detection this paper deals with the global stabilization problem for nonlinear system using state detection sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included these conditions are based to a version of a lyapunov like condition proposed by sontag which guarantees input to state stability

a unifying integral iss framework for stability of nonlinear cascades we analyze nonlinear cascades in which the driven subsystem is integral input to state stable iss and we characterize the admissible integral iss gains for stability this characterization makes use of the convergence speed of the driving subsystem and allows a larger class of gain functions when the convergence is faster we show that our integral iss gain characterization unifies different approaches in the literature which restrict the nonlinear growth of the driven subsystem and the convergence speed of the driving subsystem the result is used to develop a new observer based backstepping design in which the growth of the nonlinear damping terms is reduced

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

output feedback stabilization the stabilization of control systems using output feedback is addressed necessary and sufficient lyapunov conditions are established generalizing the artstein s stabilization theorem for linear control systems a necessary and sufficient lyapunov condition is provided for stabilization by means of a linear output feedback law

ℋ observers design for a class of nonlinear time delay systems in descriptor form in this article we address the problem of designing an observer for a class of nonlinear time delay systems in descriptor form in both discrete time and continuous time cases we propose an observer design method using a particular lyapunov function that leads to solve a linear matrix inequality condition ensuring the convergence of the estimation error indeed we use a lyapunov function depending on the disturbances in order to avoid a specific obstacle in the stability analysis finally three numerical examples are provided in order to show the validity of the proposed method

brief paper global nonlinear output regulation convergence based controller design in this paper we present output feedback controllers solving the global output regulation problem for a class of nonlinear systems the proposed controllers are based on the notion of convergent systems the presented solution extends well established results on the linear output regulation problem and the local nonlinear output regulation problem to the global case for lur e systems which are not necessarily in the output feedback form the proposed controllers can be found by solving the regulator equations and certain linear matrix inequalities for systems in the output feedback form with uncertain parameters and uncertain nonlinearities we provide a robust regulator that does not rely on the minimum phaseness assumption on the system which is crucial in the previous regulator designs for output feedback systems the results are illustrated by examples

velocity observers for non linear mechanical systems subject to non smooth impacts this paper is concerned with the estimation of the velocity variables when the position variables are the measured outputs for non linear mechanical systems subject to non smooth impacts both elastic and inelastic i e with coefficient of restitution e 1 and e 0 1 respectively a reduced order observer is proposed which guarantees that the corresponding error system despite the possible presence of an infinite sequence of non smooth impacts is locally exponentially stable an estimate of the basin of attraction is also given

on observers for nonlinear differential algebraic systems we extend a recent approach to observer design for linear differential algebraic systems to systems with lipschitz nonlinearities the observer design further extends the standard luenberger type observer design we show that the design parameters for the observer can be obtained by the solution of a riccati type inequality the solutions of the latter can in turn be obtained by solving a set of linear matrix inequalities lmis and bilinear matrix inequalities bmis which provides a computational procedure a feature of the presented observer design is the possibility of reformulation as an ordinary differential equation

generalised observer design for dissipative lipschitz nonlinear systems in the presence of measurement noise this paper presents two novel observer concepts first it develops a globally exponentially stable nonlinear observer for noise free dissipative nonlinear systems second for a dissipative nonlinear system with measurement noise the paper develops an observer to guarantee a desired performance namely an upper limit on the ratio of the square of the weighted l2 norm of the error to the square of the weighted l2 norm of the measurement noise the necessary and sufficient conditions for both observers are reformulated as algebraic riccati equations ares so that standard solvers can be utilised in addition the paper presents necessary and sufficient conditions to be satisfied by the nonlinear system in order to ensure that the are and hence the observer design problem has a solution the use of the methodology developed in this paper is demonstrated through illustrative examples in literature there is no previous observer for dissipative system that provides both necessary and sufficient condition

almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

european option pricing with transaction costs the authors consider the problem of pricing european options in a market model similar to the black scholes one except that proportional transaction charges are levied on all sales and purchases o

distributed robust filtering with h consensus of estimates the paper addresses a problem of design of distributed robust filters using the recent vector dissipativity theory the main result is a sufficient condition which guarantees a suboptimal h level of disagreement of estimates in a network of filters it involves solving a convex optimization feasibility problem subject to lmi constraints the special case of balanced interconnection graphs is also considered a gradient descent type algorithm is presented which allows the nodes to compute their estimator parameters in a decentralized manner the proposed approach is applied to the problem of observer based robust synchronization of a nonlinear network to an isolated node

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

state noise estimator for descriptor systems with application to sensor fault diagnosis for descriptor systems with measurement output noises input disturbances may exist at the same time a new descriptor estimator technique is developed the necessary and sufficient condition for the existence of the present estimator is derived and a systematic design approach is addressed the effect of uncertainties is decoupled completely and the asymptotic estimates of the descriptor system state and the output noise are obtained simultaneously furthermore a normal state disturbance estimator is also given for a class of nonlinear descriptor systems with both output noises and input uncertainties a nonlinear descriptor estimator is derived by using the proposed design approach together with the linear matrix inequality technique the existence and convergence of the nonlinear descriptor estimator is proven the asymptotic estimates of the descriptor nonlinear system state and the output noise are obtained at the same time the present estimators are applied to the sensor fault diagnosis and hence the sensor fault can be estimated asymptotically finally two numerical examples are included to illustrate the proposed design procedures and applications

input to error stable observer for nonlinear sampled data systems with application to one sided lipschitz systems in this paper the design of sampled data state observers for nonlinear plants is investigated under the effect of system and measurement disturbance signals we establish general design principles using the standard approaches of i direct discrete time design via approximation and ii discretization of a continuous time observer emulation by interpreting the disturbances as exogenous inputs affecting the error dynamics sufficient conditions are derived which ensure the input to state stability iss of the observer error system in a semiglobal practical sense for the unknown exact discrete time model next we focus on systems whose vector fields are one sided lipschitz to develop constructive design techniques via linear matrix inequalities lmis numerical simulations of an academic example and a chaotic attractor corroborate the effectiveness of the proposed sampled data estimators

iterative solutions to matrix equations of the form aixbi fi this paper is concerned with the numerical solutions to the linear matrix equations a 1xb 1 f 1 and a 2xb 2 f 2 two iterative algorithms are presented to obtain the solutions for any initial value it is proved that the iterative solutions obtained by the proposed algorithms converge to their true values finally simulation examples are given to verify the proposed convergence theorems

control strategy for state and input observer design in this note an alternative to classical methods for observer design is discussed based on a dual control approach it is indeed highlighted how an observer at least approximate can be obtained for a system by designing a control law for an auxiliary copy of this system so that it tracks the system output an important ingredient in this approach is the use of high gain in the control design the strategy is illustrated by various examples including the case of unknown input reconstruction

simultaneous input and state estimation for nonlinear systems with applications to flow field estimation this paper studies the problem of simultaneous input and state estimation sise for nonlinear dynamical systems with and without direct input output feedthrough we take a bayesian perspective to develop a sequential joint input and state estimation approach our scheme gives rise to a nonlinear maximum a posteriori optimization problem which we solve using the classical gauss newton method the proposed approach generalizes a number of sise methods presented in the literature we illustrate the effectiveness of the proposed scheme for nonlinear systems with direct feedthrough in an oceanographic flow field estimation problem involving submersible drogues that measure position intermittently and acceleration continuously

a common solution to a pair of linear matrix equations over a principal ideal domain abstract a necessary and sufficient condition for the existence of a common solution to a pair of linear matrix equations over a principal ideal domain is obtained the equations are of the type a i b i xc i for i 1 2 the solvability condition is that the equations each have a solution and a bilateral linear matrix equation made up of the matrices a i b i and c i has a solution

the matrix nearness problem for symmetric matrices associated with the matrix equation atxa btxb c d abstract a direct method based on the projection theorem in inner products spaces the generalized singular value decomposition and the canonical correlation decomposition is presented for finding the optimal approximate solution x in the set s e to a given matrix x where s e denotes the least squares symmetric solution set of the matrix equation atxa btxb c d the analytical expression of the optimal approximate solution x is obtained and an algorithm for finding this solution is also suggested

simultaneous input and state estimation for stochastic nonlinear systems with additive unknown inputs abstract this paper investigates simultaneous input and state estimation for a class of nonlinear stochastic systems we propose a recursive filter to concurrently estimate system states and unknown inputs we show that the estimation errors of the proposed filter are practically exponentially stable in probability and the estimation error covariance matrices are uniformly bounded

iterative algorithms for the minimum norm solution and the least squares solution of the linear matrix equations abstract in this paper two iterative algorithms are proposed to solve the linear matrix equations a 1 xb 1 c 1 x t d 1 m 1 a 2 xb 2 c 2 x t d 2 m 2 when the matrix equations are consistent by the first algorithm a solution x can be obtained within finite iterative steps in the absence of roundoff error for any initial value furthermore the minimum norm solution can be got by choosing a special kind of initial matrix additionally the unique optimal approximation solution to a given matrix x 0 can be derived by finding the minimum norm solution of a new matrix equations a 1 x b 1 c 1 x t d 1 m 1 a 2 x b 2 c 2 x t d 2 m 2 when the matrix equations are inconsistent we present the second algorithm to find the least squares solution with the minimum norm finally two numerical examples are tested by matlab the results show that these iterative algorithms are efficient

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

brief paper full order observer design for a class of port hamiltonian systems we consider a special class of port hamiltonian systems for which we propose a design methodology for constructing globally exponentially stable full order observers using a passivity based approach the essential idea is to make the augmented system consisting of the plant and the observer dynamics to become strictly passive with respect to an invariant manifold defined on the extended state space on which the state estimation error is zero we first introduce the concept of passivity of a system with respect to a manifold by defining a new input and output on the extended state space and then perform a partial state feedback passivation which leads to the construction of the observer we then illustrate this observer design procedure on two physical examples the magnetic levitation system and the inverted pendulum on the cart system

brief paper state and input observability for structured linear systems a graph theoretic approach this paper deals with the state and input observability analysis for structured linear systems with unknown inputs the proposed method is based on a graph theoretic approach and assumes only the knowledge of the system s structure using a particular decomposition of the systems into two subsystems we express in simple graphic terms necessary and sufficient conditions for the generic state and input observability these conditions are easy to check because they are based on comparison of integers and on finding particular subgraphs in a digraph therefore our approach is suited to study large scale systems

a sliding mode observer for infinitely unobservable descriptor systems in existing work of sliding mode observers smos for descriptor systems a necessary condition is that the system must be infinitely observable this paper presents a scheme that circumvents that condition by reformulating the system as a reduced order system where certain structures in the system matrix are manipulated and certain states are treated as unknown inputs following that an smo is implemented on the reduced order system where state and fault estimation can be achieved necessary and sufficient conditions of this scheme are also presented finally a simulation example shows the effectiveness of the proposed scheme

robust observer design for unknown inputs takagi sugeno models this paper deals with the observer design for takagi sugeno t s fuzzy models subject to unknown inputs and disturbance affecting both states and outputs of the system sufficient conditions to design an unknown input t s observer are given in linear matrix inequality lmi terms both continuous time and discrete time cases are studied relaxations are introduced by using intermediate variables extension to the case of unmeasured decision variables is also given a numerical example is given to illustrate the effectiveness of the given results

observer design for stochastic nonlinear systems via contraction based incremental stability this paper presents a new design approach to nonlinear observers for ito stochastic nonlinear systems with guaranteed stability a stochastic contraction lemma is presented which is used to analyze incremental stability of the observer a bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of the contraction rate and maximum noise intensity the observer design is based on a non unique state dependent coefficient sdc form which parametrizes the nonlinearity in an extended linear form the observer gain synthesis algorithm called linear matrix inequality state dependent algebraic riccati equation lmi sdare is presented the lmi sdare uses a convex combination of multiple sdc parametrizations an optimization problem with state dependent linear matrix inequality sdlmi constraints is formulated to select the coefficients of the convex combination for maximizing the convergence rate and robustness against disturbances two variations of lmi sdare algorithm are also proposed one of them named convex state dependent riccati equation csdre uses a chosen convex combination of multiple sdc matrices and the other named fixed sdare uses constant sdc matrices that are pre computed by using conservative bounds of the system states while using constant coefficients of the convex combination pre computed by a convex lmi optimization problem a connection between contraction analysis and l 2 gain of the nonlinear system is established in the presence of noise and disturbances results of simulation show superiority of the lmi sdare algorithm to the extended kalman filter ekf and state dependent differential riccati equation sddre filter

an iterative method for symmetric solutions and optimal approximation solution of the system of matrix equations a1xb1 c1 a2xb2 c2 abstract the symmetric solutions of the system of matrix equations a1xb1 c1 a2xb2 c2 are too difficult to be obtained by applying matrices decomposition in this paper an iterative method is applied to solve this problem with it the solvability of this system of matrix equations can be determined automatically when this system of matrix equations is consistent its solution can be obtained within finite iterative steps and its least norm solution can be obtained by choosing a special kind of initial iterative matrix furthermore its optimal approximation solution to a given matrix can be derived by finding the least norm symmetric solution of a new system of matrix equations a 1 x b 1 c 1 a 2 x b 2 c 2 finally numerical examples are given

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

simultaneous state and input estimation of hybrid systems with unknown inputs this paper addresses the problem of the simultaneous state and input estimation for hybrid systems when subject to input disturbances the proposed algorithm is based on the moving horizon estimation mhe method and uses mixed logical dynamical mld systems as equivalent representations of piecewise affine pwa systems so far the mhe method has been successfully applied for the state estimation of linear hybrid and nonlinear systems the proposed extension of the mhe algorithm enables the estimation of unknown inputs or disturbances acting on the hybrid system the new algorithm is shown to improve the convergence characteristics of the mhe method by reducing the delay of convergent estimates while assuring convergence for every possible sequence of input disturbances to ensure convergence the system is required to be incrementally input observable which is an extension to the classical incremental observability property

observer based control of systems with slope restricted nonlinearities an observer design is presented which makes use of bounds on the slope of system nonlinearities necessary and sufficient conditions are derived for the feasibility of the design a class of state feedback control laws are characterized which when implemented with the observer states ensure global asymptotic stability one such certainty equivalence design is illustrated on an active magnetic bearing example

sobolev norms based state estimation and input recovery for a class of nonlinear systems design and experimental results in this paper we address the problem of state estimation and input recovery for a class of nonlinear systems in the presence of disturbances in both the state and output equations indeed one of the main difficulties that arise when input recovery is considered is how to cope with the problem of disturbance s derivative for the filter design our contribution lies in the use of sobolev norms to develop a simple and useful observer we provide first the state filtering and input recovery equations after based on the lyapunov stability theory and some robustness criteria new sufficient synthesis conditions are given in terms of linear matrix inequalities lmis to show performances of the proposed method we considered the problem of simultaneous synchronization and decryption in chaotic communication systems with some experimental results

almost non interacting control by measurement feedback consider a linear system that apart from a control input and a measurement output has two exogeneous inputs and two exogenous outputs controlling such a system by means of a measurement feedback compensator c results in a closed loop system with two inputs and two outputs hence the closed loop transfer matrix can be partitioned as a two by two block matrix the problem addressed in this paper consists of the following given and any positive number ge is it possible to find c such that the off diagonal blocks of the closed transfer matrix in a suitable norm are smaller than for the solvability of this problem necessary and sufficient conditons will be derived

state and unknown input observers for nonlinear systems with bounded exogenous inputs a systematic design methodology for state observers for a large class of nonlinear systems with bounded exogenous inputs disturbance inputs and sensor noise is proposed the nonlinearities under consideration are characterized by an incremental quadratic constraint parameterized by a set of multiplier matrices linear matrix inequalities are developed to construct observer gains which ensure that a performance output based on the state estimation error satisfies a prescribed degree of accuracy furthermore conditions guaranteeing estimation of the unknown inputs to arbitrary degrees of accuracy are provided the proposed scheme is illustrated with a numerical example which does not satisfy the so called matching conditions

adaptive rejection of non linear disturbances in extended non linear output feedback systems this paper deals with asymptotic rejection of disturbances generated from non linear exosystems for uncertain nonlinear systems in an extended output feedback form which allows the vector field coupled with the system input to have different nonlinear functions of the system output as its elements a new internal model design is proposed to deal with nonlinear functions of the system output that are coupled with the input and the unknown disturbance adaptive control techniques are then used to deal with the uncertainty in the system the proposed adaptive disturbance rejection algorithm with the new internal model design ensures the asymptotic rejection of the unknown nonlinear disturbance and the boundedness of all the variables

pricing european options with proportional transaction costs and stochastic volatility using a penalty approach and a finite volume scheme abstract in this paper we propose a combination of a penalty method and a finite volume scheme for a four dimensional time dependent hamilton jacobi bellman hjb equation arising from pricing european options with proportional transaction costs and stochastic volatility the hjb equation is first approximated by a nonlinear partial differential equation containing penalty terms a finite volume method along with an upwind technique is then developed for the spatial discretization of the nonlinear penalty equation we show that the coefficient matrix of the discretized system is an m matrix an iterative method is proposed for solving the nonlinear algebraic system and a convergence theory is established for the iterative method numerical experiments are performed using a non trivial model pricing problem and the numerical results demonstrate the usefulness of the proposed method

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

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

a note on non linear observers a general non linear exponential observer is presented for non linearly perturbed nonlinear systems this is done by using the non linear variation of constants formula

state and input simultaneous estimation for a class of nonlinear systems this paper addresses the problem of estimating simultaneously the state and input of a class of nonlinear systems here the systems nonlinear part comprises a lipschitz nonlinear function with respect to the state and input and a state dependent unknown function including additive disturbance as well as uncertain nonlinear time varying terms upon satisfying some conditions the observer design problem can be solved via a riccati inequality or a lmi based technique with asymptotic estimation guaranteed a numerical example is included for illustration

robust output feedback guaranteed cost control of nonlinear stochastic uncertain systems via an iqc approach this technical note presents a new approach to constructive output feedback robust nonlinear controller design based on the use of iqcs and minimax lqg control the approach involves a class of controllers which include copies of the nonlinearities in the controller the linear part of the controller is synthesized using minimax lqg control theory which is closely related to h infin control theory

observer design for systems with multivariable monotone nonlinearities globally convergent observers are designed for a class of systems with multivariable nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a state dependent multivariable nonlinearity we first extend an earlier design automatica 37 12 2001 1923 to multivariable nonlinearities satisfying an analog of the scalar nondecreasing property next we exploit the structure of the nonlinearity to relax the positive real restriction on the linear part of the observer error system this relaxed design renders the feasibility conditions less restrictive and widens the applicability of the observer as illustrated with examples finally output nonlinearities are studied and the design is extended to be adaptive in the presence of unknown parameters

disturbance observer for estimating higher order disturbances in time series expansion in the note a generalized disturbance observer capable of estimating higher order disturbances in the time series expansion is newly proposed initiated from a constant disturbance observer we extend it systematically to cope with ramp disturbance and general order disturbances the generalized form for disturbance observer exhibits the novel structure incorporating the system model and integrals to be practical the noisy measurement and the performance in the frequency domain are addressed in addition for a class of linear systems an output based disturbance observer of reduce order is newly derived from the proposed full state disturbance observer and its potential applicability will be demonstrated by an example

vector least squares solutions for coupled singular matrix equations the weighted least squares solutions of coupled singular matrix equations are too difficult to obtain by applying matrices decomposition in this paper a family of algorithms are applied to solve these problems based on the kronecker structures subsequently we construct a computationally efficient solutions of coupled restricted singular matrix equations furthermore the need to compute the weighted drazin and weighted moore penrose inverses and the use of tian s work and lev ari s results are due to appearance in the solutions of these problems the several special cases of these problems are also considered which includes the well known coupled sylvester matrix equations finally we recover the iterative methods to the weighted case in order to obtain the minimum d norm g vector least squares solutions for the coupled sylvester matrix equations and the results lead to the least squares solutions and invertible solutions as a special case

a nonlinear small gain theorem for the analysis of control systems with saturation a nonlinear small gain theorem is presented that provides a formalism for analyzing the behavior of certain control systems that contain or utilize saturation the theorem is used to show that an iterative procedure can be derived for controlling systems in a general nonlinear feedforward form this result in turn is applied to the control of 1 linear systems stable and unstable with inputs subject to magnitude and rate saturation and time delays 2 the cascade of globally asymptotically stable nonlinear systems with certain linear systems those that are stabilizable right invertible and such that all of their invariant zeros have nonpositive real part 3 the inverted pendulum on a cart and 4 the planar vertical takeoff and landing aircraft

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

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

consensus of nonlinear multi agent systems with observer based protocols abstract this paper is concerned with distributed pinning consensus problem for a class of nonlinear multi agent system with observer based protocols two types of state observers including local observer and distributed pinning observer are proposed for the single nonlinear agent with the first one designed by the local output information and the second one designed via the relative output information of its neighboring agents according to the state information observed a distributed pinning observer based protocol is proposed for the leader following consensus of the multi agent system furthermore two multi step algorithms are presented to construct the observer gains and the protocol parameters for the proposed protocols respectively it is shown that under the condition that the pinning joint communication topology contains a directed spanning tree the sufficient criteria established can not only ensure the observation error to be globally asymptotically stable but also guarantee the consensus of the multi agent system to be solved asymptotically finally two numerical examples are provided to demonstrate the effectiveness of the observer based protocols

on the existence of a common solution x to the matrix equations aixbj cij i j γ in this paper conditions are derived for the existence of a common solution x to the matrix equations aixbj cij i j where the matrices ai bj cij and x have suitable dimensions and the i j s are index pairs in some set the purpose of this paper is to present for certain specific sets of index pairs verifiable necessary and sufficient solvability conditions that are stated directly in terms of the matrices and that do not use kronecker products

a unifying framework for global regulation via nonlinear output feedback from iss to iiss this paper presents a unifying framework for the problem of robust global regulation via output feedback for nonlinear systems with integral input to state stable inverse dynamics subject to possibly unknown control direction the contribution of the paper is two fold firstly we consider the problem of global regulation instead of global asymptotic stabilization gas for systems with generalized dynamic uncertainties it is shown by an elementary example that gas is not solvable using conventional smooth output feedback secondly we reduce the stability requirements for the disturbance and demand relaxed assumptions for the system using our framework most of the known classes of output feedback form systems are broadened in several directions unmeasured states and unknown parameters can appear nonlinearly restrictive matching and growth assumptions are removed the dynamic uncertainty satisfies the weaker condition of sontag s integral input to state stability and the sign of high frequency gain may be unknown a constructive strategy is proposed to design a dynamic output feedback control law that drives the state to the origin while keeping all other closed loop signals bounded

nonlinear observers a circle criterion design and robustness analysis globally convergent observers are designed for a class of systems with monotonic nonlinearities the approach is to represent the observer error system as the feedback interconnection of a linear system and a time varying multivariable sector nonlinearity using lmi software observer gain matrices are computed to satisfy the circle criterion and hence to drive the observer error to zero in output feedback design the observer is combined with control laws that ensure input to state stability with respect to the observer error robustness to unmodeled dynamics is achieved with a small gain assignment design as illustrated on a jet engine compressor example

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

least squares solution with the minimum norm for the matrix equation axb gxh c d based on the projection theorem in hilbert space by making use of the generalized singular value decomposition and the canonical correlation decomposition an analytical expression of the least squares solution for the matrix equation axb gxh c d with the minimum norm is derived an algorithm for finding the minimum norm solution is described and some numerical results have been given

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

on robustness of finite time stability of homogeneous affine nonlinear systems and cascade interconnections this paper investigates robustness of finite time stability property for a homogeneous nonlinear dynamical system with sufficiently small affine inputs in addition robust stability conditions are presented for the systems admitting homogeneous approximations at the origin or at infinity the effects of additional stable unmodeled dynamics in the input channel on robust stability are investigated the utility of the obtained results is illustrated via robustness analysis of homogeneous observer with time varying gains

discrete time dynamic systems synchronization information transmission and model matching some recently published results have highlighted the role of synchronization phenomena in recovering perturbation signals injected in nonlinear continuous time oscillators in the present contribution those results are extended to the realm of discrete time systems it is also shown that the synchronization of nonlinear discrete time systems provide very interesting ramifications to the problem of measuring the discrepancy between mathematical models and the corresponding original dynamical system from which the data were measured moreover the noise impact on the proposed approach is discussed

unknown input observer design for one sided lipschitz discrete time systems subject to time delay in this paper we address the problem of unknown input observer design which simultaneously estimates state and unknown input of a class of nonlinear discrete time systems with time delay a novel approach to the state estimation problem of nonlinear systems where the nonlinearities satisfy the one sided lipschitz and quadratically inner bounded conditions is proposed this approach also allows us to reconstruct the unknown inputs of the systems the nonlinear system is first transformed to a new system which can be decomposed into unknown input free and unknown input dependent subsystems the estimation problem is then reduced to designing observer for the unknown input free subsystem rather than full order observer design in this paper we propose observer design of reduced order which is more practical and cost effective by utilizing several mathematical techniques the time delay issue as well as the bilinear terms which often emerge when designing observers for nonlinear discrete time systems are handled and less conservative observer synthesis conditions are derived in the linear matrix inequalities form two numerical examples are given to show the efficiency and high performance of our results

a pair of simultaneous linear matrix equations a1xb1 c1 a2xb2 c2 and a matrix programming problem necessary and sufficient conditions are obtained for a pair of matrix equations a1xb1 c1 a2xb2 c2 on a general field f to have a common solution along with the expression for a general common solution when certain conditions hold common solutions of minimum rank are described a matrix programming problem is solved en route

a relaxed condition for stability of nonlinear observer based controllers we study certainty equivalence design of observer based controllers and present a new stability condition that exploits state dependent convergence properties of observers this result eliminates the conservatism of treating the observer error as an exogeneous disturbance as an application we show that the reduced order variant of the class of observers in automatica 37 2001 9231 preserves global asymptotic stability in a certainty equivalence implementation in another application we study a nonminimum phase system which cannot be stabilized with the existing output feedback designs

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

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

observer design for one sided lipschitz discrete time systems abstract this note focuses on state observer design for a general class of nonlinear discrete time systems that satisfies the one sided lipschitz condition it has been shown that this condition may encompass a large class of nonlinearities however challenging problems arise such as relevant choice of the lyapunov function or non convexity of the obtained stability conditions both full order and reduced order observer designs are considered in this work the main contribution is to provide first some mathematical artifacts on the lyapunov function to obtain simple and workable stability conditions furthermore we show how to obtain lmi conditions to ensure asymptotic convergence on the other hand we extend the obtained results to n p reduced order observer design high performances are shown through simulation results

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

a note on observer design for one sided lipschitz nonlinear systems in this note observer design of a class of nonlinear systems is considered based on the one sided lipschitz condition sufficient conditions for the existence of observers of the class of nonlinear systems are presented a design method of the observer that is dependent on the solution of the linear matrix inequality is then presented furthermore a gain matrix of the observer is given the method given in this note makes the applicable class larger than that given in the literature it should be noticed that the proposed method is applicable not only to the monotone nonlinearities and lipschitz nonlinearities but also to the one sided lipschitz nonlinearities which are neither monotone nonlinearities nor usual lipschitz nonlinearities finally we use the proposed method to design observers for three simulative examples and the effect of each state trajectory tracking is very satisfactory

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

reduced order disturbance observer for discrete time linear systems in the paper an output based disturbance observer of reduced order is presented for a class of discrete time linear systems first a general form of a disturbance observer is proposed when full states are available then by combining a state function estimator of minimal order an output based disturbance observer is derived the existence condition will be formulated in the form of a static output feedback through examples the effectiveness and advantages of the proposed approach will be demonstrated a servo control problem in practice is addressed to show the validity of the approach furthermore it will be shown that the proposed approach does provide a smaller order of disturbance observer than that of conventional approaches while maintaining satisfactory performances

state and input estimation for a class of uncertain systems we consider here the problem of state and input estimation for a class of uncertain systems which consist of a nominally linear part and an uncertain nonlinear time varying part which can be regarded as a state dependent time varying input we obtain a lyapunov type characterization of the assumptions commonly found in the literature on this problem using this characterization we obtain estimators which using only a measured output can asymptotically estimate to any desired accuracy the system state and the input

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

hamilton jacobi bellman quasi variational inequality arising in an environmental problem and its numerical discretization abstract a hamilton jacobi bellman quasi variational inequality hjbqvi for a river environmental restoration problem with wise use of sediment is formulated and its mathematical properties are analyzed a finite difference scheme with a penalization technique is then established for solving the hjbqvi the scheme is free from any iterative solvers and is unconditionally stable and convergent in the viscosity sense under certain conditions a demonstrative application example of the hjbqvi is finally presented

global stabilization by output feedback examples and counterexamples abstract we show by means of examples that global complete observability and global stabilizability by state feedback are not sufficient to guarantee global stabilizability by dynamic output feedback we show that a main obstruction is related to unboundedness unobservability this is that some unmeasured state components may escape in finite time whereas the measurements remain bounded

an iterative algorithm for solving a pair of matrix equations ayb e cyd f over generalized centro symmetric matrices a matrix email protected r n x n is said to be a symmetric orthogonal matrix if p p t p 1 a matrix email protected r n x n is said to be generalized centro symmetric generalized central anti symmetric with respect to p if a pap a pap the generalized centro symmetric matrices have wide applications in information theory linear estimate theory and numerical analysis in this paper we propose a new iterative algorithm to compute a generalized centro symmetric solution of the linear matrix equations ayb e cyd f we show when the matrix equations are consistent over generalized centro symmetric matrix y for any initial generalized centro symmetric matrix y 1 the sequence y k generated by the introduced algorithm converges to a generalized centro symmetric solution of matrix equations ayb e cyd f the least frobenius norm generalized centro symmetric solution can be derived when a special initial generalized centro symmetric matrix is chosen furthermore the optimal approximation generalized centro symmetric solution to a given generalized centro symmetric matrix can be derived several numerical examples are given to show the efficiency of the presented method

lsqr iterative common symmetric solutions to matrix equations axb e and cxd f abstract a new matrix based iterative method is presented to compute common symmetric solution or common symmetric least squares solution of the pair of matrix equations axb e and cxd f by this iterative method for any initial matrix x0 a solution x can be obtained within finite iteration steps if exact arithmetic was used and the solution x with the minimum frobenius norm can be obtained by choosing a special kind of initial matrix in addition the unique nearest common symmetric solution or common symmetric least squares solution x to given matrix x in frobenius norm can be obtained by first finding the minimum frobenius norm common symmetric solution or common symmetric least squares solution of the new pair of matrix equations the given numerical examples show that the matrix based iterative method proposed in this paper has faster convergence than the iterative methods proposed in 1 2 to solve the same problems