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

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

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

kalman filtering and riccati equations for descriptor systems a general formulation of a discrete time filtering problem for descriptor systems is considered it is shown that the nature of descriptor systems leads directly to the need to examine singular estimation problems using a dual approach to estimation the authors derive a so called 3 block form for the optimal filter and a corresponding 3 block riccati equation for a general class of time varying descriptor models which need not represent a well posed system in that the dynamics may be either over or under constrained specializing in the time invariant case they examine the asymptotic properties of the 3 block filter and in particular analyze in detail the resulting 3 block algebraic riccati equation the noncausal nature of discrete time descriptor dynamics implies that future dynamics may provide some information about the present state a modified form for the descriptor kalman filter that takes this information into account is presented

solving second kind fredholm integral equations by periodic wavelet galerkin method in this paper we use the periodized daubechies wavelets based galerkin method pwgm to solve linear nonlinear and singular fredholm integral equations of the second kind a main advantage of the present pwgm over the existing wavelet galerkin methods lies in that the wavelet expansion coefficients are exactly obtained without calculating the wavelet integrations therefore the computational cost is low whereas the accuracy is high after discretization the linear and nonlinear integral equations is converted into a system of linear and nonlinear equations respectively and for the linear case the matrix can be converted into a sparse and symmetrical one by fast wavelet transform fwt numerical experiments show that the pwgm has a good degree of accuracy

impulse controllability and observability of rectangular descriptor systems the presence of impulsive responses in descriptor systems and how it relates to impulse controllability and impulse observability is considered it is shown that the equivalence between impulse controllability observability and the existence of an impulse eliminating semistate feedback output injection gain although true for square descriptor systems does not hold for rectangular descriptor systems in general hence necessary and sufficient conditions for the existence of an impulse eliminating semistate feedback output injection gain are presented

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

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

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

reduced order h filtering for singular systems abstract this paper solves the problem of reduced order h filtering for singular systems the purpose is to design linear filters with a specified order lower than the given system such that the filtering error dynamic system is regular impulse free or causal stable and satisfies a prescribed h performance level one major contribution of the present work is that necessary and sufficient conditions for the solvability of this problem are obtained for both continuous and discrete singular systems these conditions are characterized in terms of linear matrix inequalities lmis and a coupling non convex rank constraint moreover an explicit parametrization of all desired reduced order filters is presented when these inequalities are feasible in particular when a static or zeroth order h filter is desired it is shown that the h filtering problem reduces to a convex lmi problem all these results are expressed in terms of the original system matrices without decomposition which makes the design procedure simple and directly last but not least the results have generalized previous works on h filtering for state space systems an illustrative example is given to demonstrate the effectiveness of the proposed approach

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

kalman filtering for general discrete time linear systems recursive state estimation problems for explicit and implicit time invariant linear systems both for systems with and without unknown inputs can be formulated as a single problem usually referred to as descriptor kalman filtering solutions to this problem have been proposed in the literature however these solutions either neglect possible contributions of future dynamics to the current estimate or make unnecessary assumptions on the structure of the system in this paper the authors propose a solution to this problem which leads to a constructive method lifting these unnecessary assumptions this method uses a generalization of the shuffle algorithm

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

optimal unbiased filtering via linear matrix inequalities abstract solutions to the optimal h and l2 l unbiased reduced order filtering problems are obtained in terms of linear matrix inequalities lmis the order of the optimal filter is equal to the number of measurements both continuous and discrete time results are presented an explicit parametrization of all optimal unbiased filters is provided in terms of a free contractive matrix

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

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

h sub spl infin filtering for singular systems this note considers the h sub spl infin filtering problem for linear continuous singular systems the purpose is the design of a linear filter such that the resulting error system is regular impulse free and stable while the closed loop transfer function from the disturbance to the filtering error output satisfies a prescribed h sub spl infin norm bound constraint without decomposing the original system matrices a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities lmis when these lmis are feasible an explicit expression of a desired filter is given finally an illustrative example is presented to demonstrate the applicability of the proposed approach

technical communique robust admissibility of time varying singular systems with commensurate time delays this paper addresses the problem of admissibility of time varying singular systems with commensurate time delays by introducing a new method to study the convergence of the fast sub system an admissibility condition is obtained in terms of linear matrix inequalities which guarantees the considered time varying singular delay system to be regular impulse free and stable furthermore a robust admissibility condition is proposed for the case when the time varying system matrices admit the usual constant plus norm bounded structure it is theoretically established that the proposed robust admissibility condition is less conservative than the existing one in the literature one of the important features of the results is that the inferred admissibility condition coincides with the usual stability condition for state space delay systems moreover the results are also applicable to the multiple rational delay case

stability and error analysis for a diffuse interface approach to an advection diffusion equation on a moving surface in this paper we analyze a fully discrete numerical scheme for solving a parabolic pde on a moving surface the method is based on a diffuse interface approach that involves a level set description of the moving surface under suitable conditions on the spatial grid size the time step and the interface width we obtain stability and error bounds with respect to natural norms furthermore we present test calculations that confirm our analysis

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

robust normalization and stabilization of uncertain descriptor systems with norm bounded perturbations this note is concerned with the problem of the so called quadratic normalization and stabilization via both proportional and derivative state feedback pdsf and proportional and derivative output feedback pdof for uncertain descriptor systems with norm bounded perturbations necessary and sufficient conditions are presented in terms of linear matrix inequalities lmis or quadratic matrix inequalities qmis by using a simple idea of changing the problem to the corresponding stabilization problem of an augmented uncertain system