on multiple solutions for berman s problem we study berman s problemsubjects to the conditions f 0 f 0 f 1 f 1 1 0 which arises from the study of laminar flows in channels with porous walls positive negative re denotes the case of suction injection flows preliminary numerical studies indicated the existence of three different types of solutions and a small portion of mathematical evidence was provided in this paper we are able to show that there exist connected sets in the re k plane on which different types of solutions occur in particular our result verifies that the problem possesses all three types of suction solutions for sufficiently large re moreover the limiting injection solution is also obtained

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

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

circle criterion based ℋ observer design for lipschitz and monotonic nonlinear systems enhanced lmi conditions and constructive discussions a new lmi design technique is developed to address the problem of circle criterion based mathcal h infty observer design for nonlinear systems the developed technique applies to both locally lipschitz as well as monotonic nonlinear systems and allows for nonlinear functions in both the process dynamics and output equations the lmi design condition obtained is less conservative than all previous results proposed in the literature for these classes of nonlinear systems by judicious use of a modified young s relation additional degrees of freedom are included in the observer design these additional decision variables enable improvements in the feasibility of the obtained lmi several recent results in the literature are shown to be particular cases of the more general observer design methodology developed in this paper illustrative examples are given to show the effectiveness of the proposed methodology the application of the method to slip angle estimation in automotive applications is discussed and experimental results are presented

the renormalization group and the implicit function theorem for amplitude equations this article lays down the foundations of the renormalization group rg approach for differential equations characterized by multiple scales the renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation chen et al phys rev e 54 376 1996 are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem developing the theoretical framework that underlies the rg approach leads to a systematization of the renormalization process and to the derivation of explicit closed form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well known results from the literature as special cases

on steady rotational high speed flows the compressible taylor culick profile we consider the compressible flow analogue of the well known taylor culick profile we first present the compressible euler equations for steady axisymmetric isentropic flow assuming uniform injection of a calorically perfect gas in a porous chamber we then apply the rayleigh janzen expansion in powers of m 2 w where mw is the wall mach number we solve the ensuing equations to the order of m 4 w and apply the results up to the sonic point in a nozzleless chamber area averaging is also performed to reconcile with one dimensional theory our solution agrees with the existing theory to the extent that it faithfully captures the steepening of the taylor culick profile with downstream movement based on the closed form expressions that we obtain the main flow attributes are quantified parametrically and compared to the existing incompressible and quasi one dimensional theories verification by computational fluid dynamics is also undertaken comparison with two turbulent flow models shows excellent agreement particularly in retracing the streamwise evolution of the velocity regardless of the mach number we observe nearly identical trends in chambers that are rescaled by the critical sonic length ls using a suitable transformation we prove the attendant similarity and provide universal criteria that can be used to assess the relative importance of gas compression in solid rocket motors owing to sharper velocity gradients at the wall we find that an incompressible model underestimates the skin friction along the wall and underpredicts the centreline speed by as much as 13 at the sonic point in practice such deviations become appreciable at high injection rates or chamber aspect ratios

on global identifiability for arbitrary model parametrizations it is a fundamental problem of identification to be able even before the data have been analyzed to decide if all the free parameters of a model structure can be uniquely recovered from data this is the issue of global identifiability in this contribution we show how global identifiability for an arbitrary model structure basically with analytic non linearities can be analyzed using concepts and algorithms from differential algebra it is shown how the question of global structural identifiability is reduced to the question of whether the given model structure can be rearranged as a linear regression an explicit algorithm to test this is also given furthermore the question of persistent excitation for the input can also be tested explicitly is a similar fashion the algorithms involved are very well suited for implementation in computer algebra one such implementation is also described

observer design for autonomous discrete time nonlinear systems abstract we obtain a necessary and sufficient condition for a discrete time nonlinear system to be locally state equivalent to the nonlinear observer form the result looks similar to the continuous counterpart except for the fact that ad operation is utilized instead of ad operation

observers for lipschitz non linear systems in an interesting paper r rajamani and y m cho have proposed a systematic methodology to design observers they have introduced a new problem relation between distance to unobservability and convergence of luenberger like observers a result for the convergence of the observer has also been given they have presented a quantity denoted by i claimed as the distance to unobservability we show that this number is not actually the distance from the system to the set of unobservable systems moreover the result for the observer is incorrect we provide a counterexample for the result of convergence in this paper results for convergence are obtained with additional strengthened hypothesis to correct rajamani and cho s result the results are used to design an observer for a now classical single link flexible robot joint the behaviour of the observer to noisy output is quite satisfactory

complex scaling circle criteria for lure systems abstractthis study reports alternative frequency domain interpretation and implementation of the circle criteria for absolute stability in lure systems by means of complex scaling and the argument principle by lure system a feedback configuration with a nominal lti model subject to sector nonlinearities is meant as usual firstly the complex scaling stability criterion is proved for asymptotic stability in lti feedback connections which dispenses open loop poles and contour locus pre orientation and possesses bounded loci without prior frequency sweeping secondly a novel frequency domain interpretation for positive realness of transfer functions is developed and employed for claiming the complex scaling circle criteria which accommodate various sector nonlinearities with unified conditions the new circle criteria are conformable in both multivariable and scalar cases implementable graphically and tractable numerically besides being a frequency complex domain analytical technique thirdly the re

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

analysis of steady flow in a channel with one porous wall or with accelerating walls a similarity solution of the navier stokes equations that describes the two dimensional flow of a viscous incompressible fluid through a channel with one porous wall is analysed the analysis which determines the number and character of solutions in various cases according to the higher order boundary conditions at the impermeable wall of the channel agrees with asymptotic results in the limits of small and large reynolds numbers flow in a channel with one or two accelerating walls is similarly analysed

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

on the asymptotic solution of a high order nonlinear ordinary differential equation we examine berman s similarity solution for steady flow of a viscous incompressible fluid in a channel driven by suction or injection of the fluid through the channel walls we convert the two point boundary value problem for the similarity function into an initial value problem in which the position of the upper channel wall and the reynolds number are determined as part of the solution and consider two cases in the first case equal suction or injection takes place at each wall and solutions are sought that are symmetrical about the mid line of the channel in the second case fluid can pass through only the upper channel wall in each case analysis of a single initial value problem yields two distinct solutions one corresponding to injection the other to suction and our analysis is valid in the limit of large suction or injection the injection solutions are well known for the first symmetrical case the suction solution has previously been given only incompletely while for the second case the asymptotic structure of the solution for large suction has been an open problem we complement our asymptotics with numerical integrations of the ordinary differential equation governing the similarity function and find excellent agreement between the two

stability of discrete time systems with quantized input and state measurements this note focuses on linear discrete time systems controlled using a quantized input computed from quantized measurements nominally stabilizing but otherwise arbitrary state feedback gains could result in limit cycling or nonzero equilibrium points although a single quantizer is a sector nonlinearity the presence of a quantizer at each state measurement channel makes traditional absolute stability theory not applicable in a direct way a global asymptotic stability condition is obtained by means of a result which allows us to apply discrete positive real theory to systems with a sector nonlinearity which is multiplicatively perturbed by a bounded function of the state the stability result is readily applicable by evaluating the location of the polar plot of a system transfer function relative to a vertical line whose abcissa depends on the one norm of the feedback gain a graphical method is also described that can be used to determine the equilibrium points of the closed loop system for any given feedback gain

on the existence of solutions of an equation arising in the theory of laminar flow in a uniformly porous channel with injection we establish the existence of concave solutions of berman s equation which describes the laminar flow in channels with injection through porous walls it is found that the unique concave solutions exist for all injection reynolds number r 0

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

two dimensional viscous flow between slowly expanding or contracting walls with weak permeability abstract since the transport of biological fluids through contracting or expanding vessels is characterized by low seepage reynolds numbers the current study focuses on the viscous flow driven by small wall contractions and expansions of two weakly permeable walls the scope is limited to two dimensional symmetrical solutions inside a simulated channel with moving porous walls in seeking an exact solution similarity transformations are used in both space and time the problem is first reduced to a nonlinear differential equation that is later solved both numerically and analytically the analytical procedure is based on double perturbations in the permeation reynolds number r and the wall expansion ratio results are correlated and compared via variations in r and under the auspices of small r and the analytical result constitutes a practical equivalent to the numerical solution we find that when suction is coupled with wall contraction rapid flow turning is precipitated near the wall where the boundary layer is formed conversely when injection is paired with wall expansion the flow adjacent to the wall is delayed in this case the viscous boundary layer thickens as injection or expansion rates are reduced furthermore the pressure drop along the plane of symmetry increases when the rate of contraction is increased and when either the rate of expansion or permeation is reduced as nonlinearity is retained our solutions are valid from a large cross section down to the state of a completely collapsed system

a framework for nonlinear sampled data observer design via approximate discrete time models and emulation we study observer design for sampled data nonlinear systems using two approaches i the observer is designed via an approximate discrete time model of the plant ii the observer is designed based on the continuous time plant model and then discretized for sampled data implementation emulation we investigate under what conditions and in what sense these designs achieve convergence for the unknown exact discrete time model we present examples which show that designs that violate our conditions may indeed lead to instability when implemented on the exact model

vortical and acoustical mode coupling inside a two dimensional cavity with transpiring walls in a long low aspect ratio two dimensional cavity where gaseous motion is permitted along transpiring walls a time dependent field is established when low amplitude sinusoidal pressure oscillations with nonzero mean are introduced an accurate solution is extracted here for the time dependent field by way of small parameter perturbations contingent upon small pressure wave amplitudes navier stokes equations are linearized to the order of the mean flow mach number to furnish interaction equations governing the unsteady field the latter is decomposed into acoustic and solenoidal fields coupled through dirichlet type boundary conditions solving for the solenoidal field from the momentum equation employs separation of variables and multiple scale expansions based on a careful choice of an inner scale in fact the unique inner scale used in the two variable derivative expansion method is original in the sense that it stems from an unconventional nonlinear variable transformation a uniformly valid s

coherence for monoidal g categories and braided g crossed categories abstract we prove a coherence theorem for actions of groups on monoidal categories as an application we prove coherence for arbitrary braided g crossed categories

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

how much uncertainty can be dealt with by feedback feedback is used primarily for reducing the effects of the plant uncertainty on the performance of control systems and as such understanding the following questions is of fundamental importance how much uncertainty can be dealt with by feedback what are the limitations of feedback how does the feedback performance depend quantitatively on the system uncertainty how can the capability of feedback be enhanced if a priori information about the system structure is available as a starting point toward answering these questions a typical class of first order discrete time dynamical control systems with both unknown nonlinear structure and unknown disturbances is selected for our investigation and some concrete answers are obtained in the paper in particular we find that in the space of unknown nonlinear functions the generalized lipschitz norm is a suitable measure for characterizing the size of the structure uncertainty and that the maximum uncertainty that can be dealt with by the feedback mechanism is described by a ball with radius 3 2 spl radic 2 in this normed function space

on lmi conditions to design observers for lipschitz nonlinear systems this paper addresses the problem of observer design for lipschitz nonlinear systems via lmi the goal of this note is to clarify some recent results and to propose a new design methodology this is based on the reformulation of the lipschitz property using some mathematical tools this reformulation is a relevant and useful lipschitz condition which leads to less restrictive lmi conditions to show the superiority of this latter two numerical examples are presented

new algebraic geometric conditions for the linearization by input output injection the goal of this paper is twofold it unifies and generalizes existing results on input output injection linearization of nonlinear systems the problem is solved as a realization problem since it is based on the analysis of the structure of the input output differential equation the necessary and sufficient conditions are derived from a simplified and constructive procedure for clarity the paper is limited to the case of single output systems exterior differential systems are extensively used throughout the paper giving constructive conditions

brief paper circle criterion approach to discrete time nonlinear observer design this paper addresses the design of discrete time nonlinear observers through the circle criterion the new design method is mainly devoted to either globally lipschitz systems or bounded state systems whose nonlinearities can be decomposed into a linear combination of positive slope nonlinearities the observer design is not restricted to systems with positive slope nonlinearities but it encompasses systems with non positive slope nonlinearities too stability conditions of the observation error are given in terms of numerically tractable linear matrix inequalities illustrative examples are presented in order to highlight the main features and advantages of the new proposed technique over some classical designs

on the lagrangian optimization of wall injected flows from the hart mcclure potential to the taylor culick rotational motion the taylor culick solution for a porous cylinder is often used to describe the bulk gas motion in idealized representations of solid rocket motors however other approximate solutions may be found that satisfy the same fundamental constraints in this vein steeper or smoother profiles may be observed in either experimental or numerical tests particularly in the presence of intense levels of acoustic energy in this study we use the lagrangian optimization principle to arrive at multiple solutions that can help to explain the practically observed motions we then search for the extreme states that display either the least or the most kinetic energy these are derived and found to be dependent on the chamber s aspect ratio by assuming a slender case simple expressions are retrieved from which both the rotational taylor culick and the irrotational hart mcclure solutions are recovered as special cases at the outset a new family of flow approximations is derived extending from purely potential to highly rotational fields these are constructed verified and catalogued based on their kinetic energies to help understand the tendency of a motion to shift energy states a second law analysis is performed and used to rank these solutions based on their entropy content interestingly the taylor culick profile is found to represent an equilibrium state entailing the most energy and entropy among those starting from the rest a formal extension of kelvin s minimum energy theorem to an open region is then pursued followed by a direct implementation to the problem at hand three other flow motions with open boundaries are examined to further exemplify the application of kelvin s extended criteria our efforts illustrate the overarching harmony that exists between lagrange s minimization principle and kelvin s minimum energy theorem both converge on the potential solution as the least kinetic energy bearer even when the velocity at the open barrier is finite

reflection fusion categories abstract we introduce the notion of a reflection fusion category which is a type of a g crossed category generated by objects of frobenius perron dimension 1 and p where p is an odd prime we show that such categories correspond to orthogonal reflection groups over f p this allows us to use the known classification of irreducible reflection groups over finite fields to classify irreducible reflection fusion categories

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

a new renormalization method for the asymptotic solution of weakly nonlinear vector systems this paper considers the asymptotic integration of a special class of initial value problems involving a nonlinear regular perturbation scaled by a small parameter epsilon 0 for t mathcal o 1 epsilon these problems were classically solved using either the method of averaging or of multiple scales to remove secular terms that arise in the natural power series procedure our new ansatz is straightforward and effective moreover it indicates when problems might occur in providing the asymptotic solution on very long time intervals other closely related problems are also attacked using renormalization

transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input abstract the transformation of nonlinear multi input multi output systems x f x u y h x u into an observer canonical form with reduced dependency on derivatives of the input is studied necessary and sufficient conditions for its existence and a straightforward algorithm for obtaining the canonical model are derived the proposed method involves the solution of a nonlinear algebraic equation system and systems of first order linear partial differential equations the nonlinear canonical form obtained permits global observer error linearization and it is a stage in the design of nonlinear observers the method is illustrated by an example

the extended luenberger observer for nonlinear systems abstract for nonlinear single input single output systems dot x f x u y h x u the relationships for a state transformation into the nonlinear observer canonical form are developed it is possible to dimension a nonlinear observer by an eigenvalue assignment without solving the nonlinear partial differential equations for the transformation if the transformed nonlinearities are linearized about the reconstructed state with reference to the extended kalman filter algorithm this nonlinear observer design is called the extended luenberger observer

a multivariable extension of the tsypkin criterion using a lyapunov function approach for analyzing the stability of discrete time systems containing a feedback nonlinearity the tsypkin criterion is the closest analog to the popov criterion which is used for analyzing such systems in continuous time traditionally the proof of this criterion is based upon input output properties and function analytic methods in this paper we extend the tsypkin criterion to multivariable systems containing an arbitrary number of monotonic sector bounded memoryless time invariant nonlinearities along with providing a lyapunov function proof for this classical result

observers for discrete time nonlinear systems abstract the problem of observers for discrete time nonlinear systems has been considered and a simple easy to implement algorithm is given whose convergence properties are guaranteed for autonomous and forced systems some numerical examples show the effectiveness of the proposed observer

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

existence and design of observers for nonlinear systems relation to distance to unobservability this paper presents a systematic design methodology and some fundamental insights into observer design for the class of lipschitz nonlinear systems the existence of an asymptotically stable observer is shown to be guaranteed when the distance to unobservability is larger than the lipschitz constant of the nonlinear system an analytical solution for the observer is provided in this case a methodology for the use of a coordinate transformation is then developed so as to reduce the lipschitz constant and increase the distance to unobservability in the new coordinates the methodology is directly applicable to the important class of feedback linearizable systems the developed theory is used successfully in the design of an observer for a flexible joint robotic system

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

symmetric solutions for the oscillatory channel flow with arbitrary suction this paper considers a porous channel in which a suction driven flow is modulated by arbitrary levels of fluid extraction acting uniformly along its porous boundaries when small longitudinal oscillations are enabled a rotational wave motion is established that this study attempts to analyse for an elongated channel two asymptotic methods are used the first technique is based on a two variable multiple scale expansion that takes into account the thin boundary layer near the wall while retaining generality of expression the multiple scale procedure is carried out until a closed form solution for the velocity field is obtained for an arbitrary mean flow function an alternative approach based on wkb exponentials is also employed the wkb expansion is then pursued to arbitrary order these asymptotic formulations are shown to agree with one another and with numeric simulations of the problem for three specific mean flow functions

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

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

state observers for systems subject to bounded disturbances using quadratic boundedness quadratic boundedness is adopted to construct state observers for linear piecewise linear and lipschitz nonlinear systems subject to bounded disturbances upper bounds on the estimation error are derived by exploiting quadratic boundedness and a design method based on linear matrix inequalities is proposed to minimize such bounds simulation results are provided to show the effectiveness of the proposed approach

online exact differentiation and notion of asymptotic algebraic observers in recent years the availability of computer based methods has created a revival of interests in exploring algebraic methods in nonlinear context this paper proposes a new approach to algebraic nonlinear observer design after giving the notion of algebraic observability and based on a novel algorithm of exact differentiation the formulation of the nonlinear observer is realized via the construction of a set of linear time varying differentiators an example of a chemical reaction is given to show the effectiveness of our approach

on fusion categories using a variety of methods developed in the literature in particular the theory of weak hopf algebras we prove a number of general results about fusion categories in characteristic zero we show that the global dimension of a fusion category is always positive and that the s matrix of any not necessarily hermitian modular category is unitary we also show that the category of module functors between two module categories over a fusion category is semisimple and that fusion categories and tensor functors between them are undeformable generalized ocneanu rigidity in particular the number of such categories functors realizing a given fusion datum is finite finally we develop the theory of frobenius perron dimensions in an arbitrary fusion category at the end of the paper we generalize some of these results to positive characteristic

the oscillatory channel flow with large wall injection in the presence of smallamplitude pressure oscillations the linearized navierstokes equations are solved to obtain an accurate description of the timedependent field in a channel having a rectangu

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

stochastic stability of the discrete time extended kalman filter the authors analyze the error behavior for the discrete time extended kalman filter for general nonlinear systems in a stochastic framework in particular it is shown that the estimation error remains bounded if the system satisfies the nonlinear observability rank condition and the initial estimation error as well as the disturbing noise terms are small enough this result is verified by numerical simulations for an example system

picard iteration algorithm combined with gauss seidel technique for initial value problems abstract in this paper we introduce and implement a relatively new improvement for the well known picard s method for studying linear and nonlinear systems of ordinary differential equations in this method the solution takes the form of a rapidly convergent series with easily computable components a mathematica computer algebra system mathematica 5 1 is used to introduce a code which generates the series different illustrative examples have been considered as well as different comparison criterion between the proposed method and modern reliable and conventional methods the deeply mathematical roots of the method fixed point theorem and the correspondence with the theory of algebraic systems makes it is very interesting theoretical considerations are being discussed and convergence of the method is addressed other extensions and applications for further work are mentioned

a technique for the numerical verification of asymptotic expansions a technique is presented that uses numerical solutions to verify the order of the accuracy of an asymptotic expansion for several types of problems this technique may be introduced in any beginning course on asymptotic or perturbation methods but is equally suited to verifying advanced asymptotic results

on the observer design in discrete time abstract the paper deals with the equivalence under coordinates change and output transformation of a discrete time nonlinear system to observer canonical forms necessary and sufficient conditions for local equivalence to these forms are given

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

two families of semiglobal state observers for analytic discrete time systems two families of observers for discrete time nonlinear systems are presented in this paper whose design is based on the taylor approximation of the inverse of the observation map semiglobal convergence results are provided under the assumption that the system observation map is a globally analytic diffeomorphism the performances of the observers in the two families are compared both from theoretical and practical points of view

higher mean flow approximation for solid rocket motors with radially regressing walls the bulk gas motion in a circular port rocket motor is described using a rotational incompressible and viscous flow model that incorporates the effect of wall regression the mathematical idealization developed is also applicable to semi open porous tubes with expanding walls based on mass conservation a linear variation in the mean axial velocity is ascertained this relationship suggests investigating a spatial transformation of the proudman johnson form with the use of similar arguments a temporal transformation is also introduced when these transformations are applied in both space and time the navier stokes equations are reduced to a single nonlinear fourth order differential equation following this exact navier stokes reduction the resulting problem is solved using variation of parameters and small parameter perturbations the asymptotic solutions for the velocity pressure vorticity and shear are obtained as function of the injection reynolds number re and the dimensionless regression ratio a by way of verification it is shown that as re 0 yuan and finkelstein s solutions can be restored from ours similarly as re 0 culick s inviscid profile is recovered it is demonstrated that for a range of small re inviscid solutions are practical however for fast burning propellants under development the inviscid assumption deteriorates because it is applicable over a broader range of operating parameters the current analysis leads to a closed form mean flow solution that can be used instead of the inviscid profile to 1 prescribe an adjusted aeroacoustic field 2 describe the so called acoustic boundary layer 3 evaluate the viscous and rotational contributions to the acoustic stability growth rate factor 4 track the evolution of hydrodynamic instability and 5 accurately simulate the internal gasdynamics in rapidly regressing motors and cold flow experiments with medium to high levels of injection

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

discrete time implementation of high gain observers for numerical differentiation high gain observers have been used in non linear control to estimate derivatives of the output in this paper we study discrete time implementation of high gain observers and their use as numerical differentiators in noise free as well as noisy measurements we show that discretization using the bilinear transformation method gives better results than other discretization methods we also show that many of the available numerical differentiators are special cases of the bilinear discrete time equivalents of full order or reduced order high gain observers

observer based control of discrete time lipschitzian non linear systems application to one link flexible joint robot the problem of designing asymptotic observers along with observer based feedbacks for a class of discrete time non linear systems is considered we assume that the system non linearity is globally lipschitz and the system is supposed to be stabilizable by a linear controller sufficient linear matrix inequality condition is derived to ensure the stability of the considered system under the action of feedback control based on the reconstructed states a numerical example of a single link flexible joint robot is presented to illustrate the efficacy of the theoretical developments

the oscillatory pipe flow with arbitrary wall injection the linearized navierstokes equations play a central role in describing the unsteady motion of a viscous fluid inside a porous tube asymptotic solutions of these equations have been found and here

tensor categories with fusion rules of self duality for finite abelian groups abstract semisimple tensor categories with fusion rules of self duality for finite abelian groups are classified as an application we prove that the tannaka duals of the dihedral and the quaternion groups of order 8 and the eight dimensional hopf algebra of kac and paljutkin are not isomorphic as abstract tensor categories whereas they have the same fusion rule

singularly perturbed linear two point boundary value problems finding asymptotic solutions to two point boundary value problems for linear singularly perturbed second order ordinary differential equations is now quite well understood troublesome exceptions involving turning points known as problems of boundary layer resonance have been studied by many experts since the initial work of ackerberg and o malley stud appl math 49 1970 pp 277 295 this significant work is surveyed here closely related literature involves the canard phenomena new generally more geometric approaches including gevrey asymptotics and blowup promise improved understanding of such sensitive asymptotics and their generalizations

semi global observer for multi output nonlinear systems abstract we present an explicit form of nonlinear observers for a class of multi input multi output systems observer construction for multi output nonlinear systems is not a trivial extension of single output case especially when the global error convergence is of interest in this paper we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself and the overall system has a block triangular form for each subsystem hence the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed the construction is based on the saturation of some estimates which is originated by khalil and esfandiari for the use of semi global output feedback control

vortical and acoustical mode coupling inside a porous tube with uniform wall suction this paper considers the oscillatory motion of gases inside a long porous tube of the closed open type in particular the focus is placed on describing an analytical solution for the internal acoustico vortical coupling that arises in the presence of appreciable wall suction this unsteady field is driven by longitudinal oscillatory waves that are triggered by small unavoidable fluctuations in the wall suction speed under the assumption of small amplitude oscillations the time dependent governing equations are linearized through a regular perturbation of the dependent variables further application of the helmholtz vector decomposition theorem enables us to discriminate between acoustical and vortical equations after solving the wave equation for the acoustical contribution the boundary driven vortical field is considered the method of matched asymptotic expansions is then used to obtain a closed form solution for the unsteady momentum equation developing from flow decomposition an exact series expansion is also derived and shown to coincide with the numerical solution for the problem the numerically verified end results suggest that the asymptotic scheme is capable of providing a sufficiently accurate solution this is due to the error associated with the matched asymptotic expansion being smaller than the error introduced in the navier stokes linearization a basis for comparison is established by examining the evolution of the oscillatory field in both space and time the corresponding boundary layer behavior is also characterized over a range of oscillation frequencies and wall suction velocities in general the current solution is found to exhibit features that are consistent with the laminar theory of periodic flows by comparison to the sexl profile in nonporous tubes the critically damped solution obtained here exhibits a slightly smaller overshoot and depth of penetration these features may be attributed to the suction effect that tends to attract the shear layers closer the wall