a note on stabilization by dynamic high gain output feedback in this note we study the problem of stabilization by dynamic output feedback for a certain class of linear systems we establish the existence of pairs of subspaces im upsilon a where im is a minimum phase input subspace contained in an almost stabilizability snbspace upsilon a by applying a recent theorem by sehumacber this result leads to the existence of stabilizing high gain compensators for the linear systems under consideration in particular it will be shown that invertible minimum phase systems can always be stabilized by dynamic compensators of dynamic order equal to the excess of poles over zeros minus the number of inputs

mathematical analysis and numerical solution of models with dynamic preisach hysteresis abstract hysteresis is a phenomenon that is observed in a great variety of physical systems which leads to a nonlinear and multivalued behavior making their modeling and control difficult even though the analysis and mathematical properties of several rate independent and rate dependent hysteresis models are known this is not the case for the bertotti s rate dependent extension of the classical preisach model the so called dynamic preisach model for which current approaches lack a proper functional analytic framework which is essential to formulate optimization problems and develop stable numerics both being crucial in practice this paper deals with the description and mathematical analysis of the dynamic preisach hysteresis model toward that end we complete a widely accepted definition of the dynamic model commonly used to describe the constitutive relation between the magnetic field h and the magnetic induction b in which the values of b not only depends on the present values of h but also on the past history and its velocity we first analyze mathematically some important properties of the model and compare them with known results for the static preisach model then we consider a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations under suitable assumptions we prove the existence of a solution of a weak formulation of the problem and solve it numerically finally we report a numerical test in order to assess the order of convergence and to illustrate the behavior of the numerical solution for different configurations of the dynamic preisach model

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

stabilization of uncertain systems via linear control this note considers the problem of stabilizing a linear dynamical system whose state equation includes a time varying uncertain parameter vector q cdot given the dynamics dot x t a q t x t b q t u t and a bounding set q for the values q t the objective is to choose a control law u t p x t guaranteeing uniform asymptotic stability for all admissible variations of q cdot our results differ from previous work in one fundamental way that is we show that when working with linear controllers it is possible to dispense with all assumptions on b cdot which have been made by previous authors e g see 1 9 this elimination of hypotheses on b cdot is accomplished roughly as follows the system sigma underline underline delta a q b q is shown to be equivalent to another system sigma underline underline delta a q b as far as stabilization is concerned since b is a constant matrix independent of q the desired result is readily obtained

global stabilization with almost disturbance decoupling of a class of uncertain non linear systems in this paper we study the global stabilization of a class of non linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy the class of non linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order although the plants considered are non linear the compensator developed here is linear our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so called matching conditions and or by treating a family of plants for which a single controller simultaneously globally exponentially stabilizes all the plants in while achieving almost disturbance decoupling of the output

brief further results on almost disturbance decoupling with global asymptotic stability for nonlinear systems as a complement to some new breakthroughs on global almost disturbance decoupling problem with stability for nonlinear systems in a recent note we identified a class of unstable zero dynamics that are allowed to be affected by disturbances the class of the unstable zero dynamics identified in that note is linear and have all the poles at the origin in this paper we enlarge such a class of zero dynamics to include any linear system with all its poles in the closed left half plane the condition on the way the disturbance affects this part of zero dynamics is also identified this enlargement is due to a new scaling technique that views each pair of jw axis zeros as a generalized integrator and transforms the zero dynamics into a number of chains of generalized integrators

new relationships between input output and lyapunov stability in this note we define a concept called small signal l p stability and show its relationship to lyapunov stability

algebraic design techniques for reliable stabilization in this paper we study two problems in feedback stabilization the first is the simultaneous stabilization problem which can be stated as follows given plants g 0 g 1 g l does there exist a single compensator c that stabilizes all of them the second is that of stabilization by a stable compensator or more generally a least unstable compensator given a plant g we would like to know whether or not there exists a stable compensator c that stabilizes g if not what is the smallest number of right half place poles counted according to their mcmillan degree that any stabilizing compensator must have we show that the two problems are equivalent in the following sense the problem of simultaneously stabilizing l 1 plants can be reduced to the problem of simultaneously stabilizing l plants using a stable compensator which in turn can be stated as the following purely algebraic problem given 2l matrices a 1 a l b 1 b l where a i b i are right coprime for all i does there exist a matrix m such that a i mb i is unimodular for all i conversely the problem of simultaneously stabilizing l plants using a stable compensator can be formulated as one of simultaneously stabilizing l 1 plants the problem of determining whether or not there exists an m such that a bm is unimodular given a right coprime pair a b turns out to be a special case of a question concerning a matrix division algorithm in a proper euclidean domain we give an answer to this question and we believe this result might be of some independent interest we show that given two n times m plants g 0 and g 1 we can generically stabilize them simultaneously provided either n or m is greater than one in contrast simultaneous stabilizability of two single input single output plants g 0 and g 1 is not generic

adaptive thinning algorithm of nonsingular triangulation this paper studies adaptive thinning strategies for the non singular triangulation of scattered data by c 1 rational spline function given a set of points in r 2 luo liu and chen have presented a triangulation algorithm which ensures the non singularity of s 2 1 and s 3 1 spaces in this paper we improve the algorithm to reduce the number of knots of the triangulation within a given tolerance while the non singularity of s 2 1 and s 3 1 spaces is ensured our strategies presented here depend on both the locations of the data points in the plane and the data values at these points we give the definition of discrete norm for c 1 rational spline function by using its coefficients then a weight is assigned to each knot which is a measure of the importance of knot in the representation of spline when the weight of the knot is less than the given tolerance its influence is regarded negligible then it can be removed it s a discrete method in the end of this paper several numerical examples are presented to show the feasibility and validity of our algorithm

almost stabilizability subspaces and high gain feedback the class of almost stabilizability subspaces is introduced as the state space analog of the class of stable but not necessarily proper transfer functions almost stabilizability subspaces can be considered as candidate closed loop eigenspaces associated with infinitely fast and stable modes we derive the basic properties of these subspaces and show that they can be approximated by regular stabilizability subspaces the relation with high gain feedback is elaborated upon in a number of applications

progressive scattered data filtering given a finite point set z rd the covering radius of a nonempty subset x z is the minimum distance r x z such that every point in z is at a distance of at most r x z from some point in x this paper concerns the construction of a sequence of subsets of decreasing sizes such that their covering radii are small to this end a method for progressive data reduction referred to as scattered data filtering is proposed the resulting scheme is a composition of greedy thinning a recursive point removal strategy and exchange a postprocessing local optimization procedure the paper proves adaptive a priori lower bounds on the minimal covering radii which allows us to control for any current subset the deviation of its covering radius from the optimal value at run time important computational aspects of greedy thinning and exchange are discussed the good performance of the proposed filtering scheme is finally shown by numerical examples

special coordinate basis for multivariable linear systems finite and infinite zero structure squaring down and decoupling abstract a special coordinate basis for multivariable linear systems is introduced here several fundamental properties of linear systems regarding controllability stabiliza bility observability detectability invariant zeros decoupling zeros infinite zero structure effect of feedback on zero structure squaring down diagonal and triangular decoupling etc can be directly displayed in terms of the special coordinate basis moreover connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions

direct singular perturbation analysis of high gain and cheap control problems a new and direct approach to the analysis and design of high gain feedback and cheap control problems is developed transformation of such singular problems to singular perturbation models of conventional type early at the onset of analysis or design allows a direct application of the readily available singular perturbation literature the approach permits a simple characterization of a multivariable root loci under a high gain feedback and b asymptotic behavior of optimal closed loop poles state and control trajectories performance index and optimal transfer function as the control cost coefficient in the performance index goes to zero

almost disturbance decoupling with global asymptotic stability for nonlinear systems with disturbance affected unstable zero dynamics the problem of global almost disturbance decoupling problem with stability for nonlinear system is revisited and is shown to be solvable for a class of nonlinear systems whose zero dynamics contains a chain of integrators affected by disturbance this result complements some recent work on the topic where unstable zero dynamics is not allowed to be affected by the disturbances

adaptive thinning for bivariate scattered data this paper studies adaptive thinning strategies for approximating a large set of scattered data by piecewise linear functions over triangulated subsets our strategies depend on both the locations of the data points in the plane and the values of the sampled function at these points adaptive thinning all our thinning strategies remove data points one by one so as to minimize an estimate of the error that results by the removal of a point from the current set of points this estimate is termed anticipated error the thinning process generates subsets of most significant points such that the piecewise linear interpolants over the delaunay triangulations of these subsets approximate progressively the function values sampled at the original scattered points and such that the approximation errors are small relative to the number of points in the subsets we design various methods for computing the anticipated error at reasonable cost and compare and test the performance of the methods it is proved that for data sampled from a convex function with the strategy of convex triangulation the actual error is minimized by minimizing the best performing measure of anticipated error it is also shown that for data sampled from certain quadratic polynomials adaptive thinning is equivalent to thinning which depends only on the locations of the data points nonadaptive thinning based on our numerical tests and comparisons two practical adaptive thinning algorithms are proposed for thinning large data sets one which is more accurate and another which is faster

simultaneous stabilization with almost disturbance decoupling uniform rank system abstract in this paper we study the problem of stabilization with almost disturbance decoupling for a family of linear time invariant finite dimensional uniform rank plants with a fixed controller it is shown that for a family of minimum phase plants which have the same order of infinite zeros and have high frequency gain matrices satisfying a certain condition such a fixed controller exists the restriction on the high frequency gain matrices is equivalent to requiring that the sign of high frequency gain for siso plants be known

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

almost disturbance decoupling for a class of high order nonlinear systems the problem of almost disturbance decoupling with internal stability add is formulated in terms of an l sub 2 l sub 2p instead of an l sub 2 gain for a class of high order nonlinear systems which consist of a chain of power integrators perturbed by a lower triangular vector field a significant feature of the systems considered in the paper is that they are neither feedback linearizable nor affine in the control input which have been two basic assumptions made in all the existing add nonlinear control schemes using the technique of adding a power integrator we solve the add problem via static smooth state feedback under a set of growth conditions that can be viewed as a high order version of the feedback linearization conditions we also show how to explicitly construct a smooth state feedback controller that attenuates the disturbance s effect on the output to an arbitrary degree of accuracy with internal stability

h sub spl infin almost disturbance decoupling with internal stability for linear systems subject to input saturation for a linear system subject to input saturation and input additive disturbances we show that 1 the h sub spl infin almost disturbance decoupling problem with local asymptotic stability is always solvable via state feedback as long as the system in the absence of saturation is stabilizable no matter where the open loop poles are and 2 the h sub spl infin almost disturbance decoupling problem with semiglobal asymptotic stability is solvable via state feedback as long as the system in the absence of saturation is stabilizable with all its open loop poles located in the closed left half plane the results generalize those in lin et al 1996 by not requiring the disturbance to be bounded by a known bound or even bounded

a new systematic design of high gain feedback for nonlinear systems with unmatched uncertainties the systematic design of a robust output tracking algorithm for a feedback linearizable system with unmatched uncertainties is presented the proposed technique is based on a backstepping procedure to construct a time varying singularly perturbed system and the underlying theoretical approach by the lyapunov theory the main result is that a dynamically parametrized state feedback is developed to cancel the output tracking error finally an illustrative example through a chemical reactor system is given to demonstrate the utilization of the approach developed in this paper

a flexible content adaptive mesh generation strategy for image representation based on the greedy point removal gpr scheme of demaret and iske a simple yet highly effective framework for constructing triangle mesh representations of images called gprfs is proposed by using this framework and ideas from the error diffusion ed scheme for mesh generation of yang a highly effective mesh generation method called gprfs ed is derived and presented since the ed scheme plays a crucial role in our work factors affecting the performance of this scheme are also studied in detail through experimental results our gprfs ed method is shown to be capable of generating meshes of quality comparable to and in many cases better than the state of the art gpr scheme while requiring substantially less computation and memory furthermore with our gprfs ed method one can easily trade off between mesh quality and computational memory complexity a reduced complexity version of the gprfs ed method called gprfs med is also introduced to further demonstrate the computational memory complexity scalability of our gprfs ed method

the almost disturbance decoupling problem with internal stability for linear systems subject to input saturation state feedback case abstract we consider the almost disturbance decoupling problem addp and or almost d bounded disturbance decoupling problem addp d with internal stability for linear systems subject to input saturation and input additive disturbance via linear static state feedback we show that the almost d bounded disturbance decoupling problem with local asymptotic stability addp las d is always solvable via linear static state feedback as long as the system in the absence of input saturation is stabilizable no matter where the poles of the open loop system are and the locations of these poles play a role only in the solution of addp gas d addp sgas d or addp gas where semi global or global asymptotic stability is required

systematic design of robust controllers for nonlinear uncertain systems the design problem of robust stabilizing controllers for nonlinear uncertain systems is considered in this paper the nominal system is input output linearizable and the uncertainty is assumed to be either generalized matching or mismatched the control design combines differential geometric feedback linearization with the deterministic approach in which no statistical property of the uncertainty is assumed and used the only information on the uncertainty which is needed for the design is its possible bound two robust stabilizing controllers for generalized matching uncertain systems are given for mismatched uncertain systems a systematic design procedure is first presented then four robust stabilizing controllers are given the robust controllers which are given in forms of explicit feedback laws based on the nominal system and are parametrized by the robust design parameters related to the bounds of uncertainties are more practicable than the existing ones in the literature numerical example

multistep scattered data interpolation using compactly supported radial basis functions a hierarchical scheme is presented for smoothly interpolating scattered data with radial basis functions of compact support a nested sequence of subsets of the data is computed efficiently using successive delaunay triangulations the scale of the basis function at each level is determined from the current density of the points using information from the triangulation the method is rotationally invariant and has good reproduction properties moreover the solution can be calculated and evaluated in acceptable computing time

distance functions and geodesics on submanifolds of r d and point clouds a theoretical and computational framework for computing intrinsic distance functions and geodesics on submanifolds of bbb r d given by point clouds is introduced and developed in this paper

singularly perturbed zero dynamics of nonlinear systems stability properties of zero dynamics are among the crucial input output properties of both linear and nonlinear systems unstable or nonminimum phase zero dynamics are a major obstacle to input output linearization and high gain designs an analysis of the effects of regular perturbations in system equations on zero dynamics shows that whenever a perturbation decreases the system s relative degree it manifests itself as a singular perturbation of zero dynamics conditions are given under which the zero dynamics evolve in two time scales characteristic of a standard singular perturbation form that allows a separate analysis of slow and fast parts of the zero dynamics the slow part is shown to be identical to the zero dynamics of the unperturbed system while the fast part represented by the so called boundary layer system describes the effects of perturbation

a relationship between sensitivity and stability of multivariable feedback systems both comparison sensitivity and robust stability analysis attempt to extend concepts which are well understood in scalar feedback systems to multivariable control system design although the two bodies of work have developed about a decade apart the basic philosophies are similar both attempt to maintain a system property sensitivity reduction versus stability in the presence of plant modeling errors this paper demonstrates how the similarity in philosophy translates into a similarity in results and interpretations

on a numerical method for 2d magnetic field computations in a lamination with enforced total flux the paper deals with a numerical method for the evaluation of the electromagnetic loss in a lamination of an electric machine based upon the maxwell equations the underlying problem consists in the computation of the unidirectional magnetic field in a cross section of the laminate orthogonal to the enforced flux the method starts from a suitable variational formulation of the governing parabolic problem with a nonlocal neumann boundary condition accompanied by a dirichlet side condition involving nonlinear and hysteresis effects through the differential permeability coefficient the variational problem is solved numerically by a finite element method combined with a finite difference technique which is deviced so as to take into account the nonlinear and hysteresis behaviour of the material the numerical method is found to be effective and reliable

global output feedback control with disturbance attenuation for minimum phase nonlinear systems abstract this paper deals with the problem of disturbance attenuation with stability for a class of minimum phase nonlinear uncertain systems by output feedback in contrast to the state feedback case a nonlinear not necessarily linear l 2 gain is employed to characterize the disturbance rejection level a constructive output feedback design is described to achieve global asymptotic stability while the effect of the disturbance on the output is diminished to an arbitrary degree of accuracy sufficient conditions are additionally provided to yield a nonlinear output feedback solving the standard l 2 gain disturbance attenuation problem with internal stability

complementary 2 d finite element procedures for the magnetic field analysis using a vector hysteresis model the main purpose of this paper is to incorporate a rened hysteresis model viz a vector preisach model in 2 d magnetic eld computations two complementary formulations based either on the scalar or on the vector potential are considered the governing maxwell equations are rewritten in a suitable way that allows to take into account the proper magnetic material parameters and moreover to pass to a variational formulation the variational problems are solved numerically by a finite element approximation using a quadratic mesh followed by a time discretization method based upon a modied cranck nicholson algorithm finally the eectiveness of the presented mathematical tools have been conrmed by several numerical experiments comparing the complementarity of the two procedures 1998 john wiley sons ltd

nonlinear output feedback tracking with almost disturbance decoupling addresses the design of global output feedback controls for a class of uncertain nonlinear single input single output systems which are globally transformable into an observable minimum phase system whose nonlinearities depend on the output only they may be affected by unknown time varying disturbances or parameter variations entering linearly in the state equations the proposed dynamic controller is of order spl rho 1 spl rho is the relative degree of the given system and ensures that the closed loop system enjoys for any initial condition and for any smooth bounded output reference signal with bounded time derivatives up to order spl rho the following properties input to state stability with respect to disturbance inputs and almost disturbance decoupling i e the influence of disturbances both on the l sub 2 and on the l sub spl infin norm of the output tracking error is arbitrarily attenuated by increasing a positive scalar control parameter when disturbances are zero the reference signal is exponentially tracked by the output and the equilibrium point corresponding to the reference signal is globally asymptotically stable

design for h almost disturbance decoupling problem with internal stability via state or measurement feedback singular perturbation approach an almost disturbance decoupling technique guaranteeing internal stability of a linear system while using either state feedback or only measurement feedback is considered under a set of necessary and sufficient conditions a state feedback controller is explicitly constructed similarly a full or reduced order observer based measurement feedback controller is explicitly constructed under a set of necessary and sufficient conditions all the developed controllers guarantee the asymptotic stability of the closed loop system in the absence of disturbances furthermore they can reduce h norm of the transfer function from the external disturbance to the controlled output to any arbitrarily specified value unlike other methods which merely give the solvability conditions our method explictly constructs them also our controllers are parametrized in terms of tuning parameters by the tuning of which the disturbance reflected in the output can be attenuated to any desired degree of accuracy