performance comparison of numerical inversion methods for laplace and hankel integral transforms in engineering problems abstract different methods for the numerical evaluations of the inverse laplace and inverse of joint laplace hankel integral transforms are applied to solve a wide range of initial boundary value problems often arising in engineering and applied mathematics the aim of the paper is to present a performance comparison among different numerical methods when they are applied to transformed functions related to actual engineering problems found in the literature most of our selected test functions have been found in the solution of boundary value problems of applied mechanics such as those related to transient responses of isotropic and transversely isotropic half space to concentrated impulse or those related to viscoelastic wave motion in layered media these classes of test functions are frequently encountered in similar problems such as those in boundary element or boundary integral equations theoretical seismology soil structure interaction in time domain and so on therefore their behavior with different numerical inversion algorithms could make a useful guide to a precise choice of more suitable inversion method to be used in similar problems some different methods are also investigated in detail and compared for the inversion of the joint hankel laplace transforms where more sophisticated integrand functions are encountered it is shown that durbin crump d amore fixed talbot gaver whyn rho gwr and direct integration methods have excellent performance and produce good results when applied to the same problems on the contrary gaver stehfest and piessens methods furnish results not very reliable for almost all classes of transformed functions and they seem good only for simple transformed functions particularly the performance of gwr algorithm is very good even for transformed functions with infinite number of singularities where the other methods fail in addition in case of double integral transforms only the fixed talbot durbin and weeks methods are recommended

exponential stabilization of nonholonomic chained systems this paper presents a feedback control scheme for the stabilization of two input driftless chained nonholonomic systems also called chained form these systems are controllable but not asymptotically stabilizable by a smooth static state feedback control law in addition exponential stability cannot be obtained with a smooth time varying feedback control law here global asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth time varying feedback control law the control law depends in addition to the state and time on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state the inputs are differentiable with respect to time and tend exponentially toward zero for use in the analysis a lemma on the exponential convergence of a stable time varying nonlinear system perturbed by an exponentially decaying signal is presented simulation results are also shown

a necessary condition for feedback stabilization abstract we give a new necessary condition for the existence of a static or dynamic continuous asymptotically stabilizing feedback control for the system x dot f x u we apply our condition to give an example of a system in r 3 which is small time locally controllable satisfies brockett s second and third condition and cannot be locally asymptotically stabilized by employing a static or dynamic continuous feedback law

numerical simulation for non linear thermal wave the present work applies the hybrid method of the laplace transform technique and a modified discretization scheme to analyze the non linear hyperbolic heat conduction problems in a semi infinite domain with either linearly or exponentially temperature dependent thermal conductivity the laplace transform method is used to remove the time dependent terms in the governing differential equation and the boundary conditions and then the transformed equations are discretized by a modified discretization scheme to show the rationality and reliability of the present results a comparison between the present numerical results and those in the literature is made results show the behavior of hyperbolic heat conduction is sensitive to the function form of thermal conductivity the speed of heat propagation changes for the variation of thermal conductivity

nilpotent and high order approximations of vector field systems this paper is concerned with the study of structurally stable properties associated with systems described by one or several real analytic vector fields via approximating systems which retain inf

a general theorem on local controllability we prove a general sufficient condition for local controllability of a nonlinear system at an equilibrium point earlier results of brunovsky hermes jurdjevic crouch and byrnes sussmann and grossmann are shown to be particular cases of this result also a number of new sufficient conditions are obtained all these results follow from one simple general principle namely that local controllability follows whenever brackets with certain symmetries can be neutralized in a suitable way by writing them as linear combinations of brackets of a lower degree both the class of symmetries and the definition of degree can be chosen to suit the problem

necessary conditions for stability and attractivity of continuous systems considered in this paper are control systems of the form f x u for such systems a number of related necessary conditions for various forms of stability and attractivity are presented the paper starts by showing that brockett s necessary condition for stabilizability via smooth feedback still persists if is continuous and the class of allowable u increased to include continuous feedbacks using similar ideas to those used to prove the continuous brockett result again only assuming continuity of f and u necessary conditions are then derived for global attractivity and for ultimate boundedness

on the existence of local smooth repulsive stabilizing feedbacks in dimension three abstract given an affine control system in r 3 subject to the hormander s condition at the origin we prove the existence of a local smooth repulsive stabilizing feedback at the origin our construction is based on the classical homogenization procedure on the existence of a semiconcave control lyapunov function and on the classification of singularities of semiconcave functions in dimension two

behavior of micropolar cubic crystal due to various sources the response of a micropolar cubic crystal due to various sources acting at the free surface has been studied the eigenvalue approach using integral transforms has been employed and the transforms have been inverted by using a numerical technique the displacement stress and microrotation components in the physical domain are obtained numerically the results of displacement and stresses have been compared for micropolar cubic crystal and micropolar isotropic solid the numerical results are illustrated graphically for a particular model

improvement of accuracy in numerical methods for inverting laplace transforms based on the post widder formula abstract the paper proposes a new computational version for numerical inversion of laplace transforms at a point and on an interval based on the post widder formula in this version the original sequence of post widder approximants is calculated using operations on series and the approximate value of the sought function is constructed as a limit of this sequence using polynomial and rational extrapolation to the limit some procedures are proposed for improvement of accuracy in the problem of inversion at equidistant points of an interval without computing additional approximants an extension of the method to the two dimensional case is discussed the one dimensional version is illustrated with some probabilistic examples involving both explicit and implicit functions the accuracy achieved in these examples with using the standard double precision arithmetic evaluated in terms of relative errors is about 10 10 10 14 even in case of out of scale parameters computational aspects are discussed in comparison with previously known realizations of the post widder method

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

lyapunov design of stabilizing controllers for cascaded systems the design of a state feedback law for an affine nonlinear system to render a as small as possible compact neighborhood of the equilibrium of interest globally attractive is discussed following z artstein s theorem 1983 the problem can be solved by designing a so called control lyapunov function for systems which are in a cascade form a lyapunov function meeting artstein s conditions is designed assuming the knowledge of a control law stabilizing the equilibrium of the head nonlinear subsystem in particular for planar systems this gives sufficient and necessary conditions for a compact neighborhood of the equilibrium to be stabilized

linear prediction maximum flatness maximum entropy and ar polyspectral estimation the authors present a theoretical foundation for polyspectral estimation and modeling of non gaussian autoregressive ar processes which includes a new higher order statistics hos based linear prediction error filter and associated linear prediction polyspectral estimator and a maximum higher order entropy polyspectral estimator and considers the equivalences among these polyspectral estimators

a laplace transorm potential theoretic method for acoustic propagation in subsonic flows this paper introduces a competitive computational approach for determining time dependent far field sound generated by subsonic flows around lifting airfoils the procedure assumes the linearity of the sound field away from a bounded region surrounding the airfoil it is assumed that the sound pressure on the boundary of this enclosed region referred to as the kirchhoff surface is specified possibly by another procedure such as solving the full euler equations away from the kirchhoff surface the euler equations are linearized about a uniform mean flow it is well known that linearized euler equations can be uncoupled into a scalar convective wave equation however due to the anisotropy present in the convective wave equation it is difficult to compute solutions in this context direct numerical simulation of the convective wave equation requires proper numerical descriptions of far field boundary conditions which is a non trivial task moreover if accurate far field conditions can be formulated the computational cost of direct simulation can be prohibitive even in a modest computational domain in this paper we present an alternate solution procedure first the problem is transformed via the laplace transform with appropriate initial conditions into a reduced wave equation the convective term in the reduced wave equation is removed using a dependent variable transformation then we use gothert s rule to obtain a helmholtz like equation with complex wave number which is subsequently solved using double layer potential theory finally upon application of numerical inverse laplace transform techniques far field acoustic pressure is obtained as a function of space and time

sampled data state feedback stabilization of boolean control networks in this letter we investigate the sampled data state feedback control sdsfc problem of boolean control networks bcns some necessary and sufficient conditions are obtained for the global stabilization of bcns by sdsfc different from conventional state feedback controls new phenomena observed the study of sdsfc based on the controllability matrix we derive some necessary and sufficient conditions under which the trajectories of bcns can be stabilized to a fixed point by piecewise constant control pcc it is proved that the global stabilization of bcns under sdsfc is equivalent to that by pcc moreover algorithms are given to construct the sampled data state feedback controllers numerical examples are given to illustrate the efficiency of the obtained results

asymptotically stabilizing feedback controls abstract the problem considered is the existence and construction of an asymptotically stabilizing feedback control for a rest solution of an n dimensional single input affine control system the method is to construct high order homogeneous approximations of the vector fields defining the control system which then describe an approximating control system such that an asymptotically stabilizing control of the latter system is a local asymptotically stabilizing control of the original system unlike linear approximations there are many possible nonlinear homogeneous approximations these are constructed from lie algebra filtrations obtained by assigning various weights to the defining vector fields one seeks a weighting hence an approximating system which satisfies the various known necessary conditions for the existence of an asymptotically stabilizing feedback control and for which such a control can be constructed as the solution to a homogeneous hamilton jacobi bellman equation associated with an optimization regulator problem

lie brackets and local controllability a sufficient condition for scalar input systems we develop a general formalism based on exponential lie series which can be used to study control variations we apply the formalism to prove a result conjectured by h hermes that gives a sufficient condition for small time local controllability for single input systems

a method for the numerical inversion of laplace transforms abstract in this paper a numerical inversion method for laplace transforms based on a fourier series expansion developed by durbin 5 is presented the disadvantage of the inversion methods of that type the encountered dependence of discretization and truncation error on the free parameters is removed by the simultaneous application of a procedure for the reduction of the discretization error a method for accelerating the convergence of the fourier series and a procedure that computes approximately the best choice of the free parameters suitable for a given problem the inversion method allows the adequate application of these procedures therefore in a big range of applications a high accuracy can be achieved with only a few function evaluations of the laplace transform the inversion method is implemented as a fortran subroutine

on the design of nonlinear discrete time predictors corresp the problem of minimum mean squared error prediction of a discrete time random process using a nonlinear filter consisting of a zero memory nonlinearity followed by a linear filter is studied classes of random processes for which the best predictor is realizable using a nonlinear filter of the above form are discussed for those random processes for which the best predictor is not realizable using the above nonlinear filter an iterative procedure is presented for finding a suboptimal nonlinear filter special attention is directed to the case where the nonlinearity is a polynomial also a noniterative approach based on nonlinear regression is presented

second order statistics of complex signals the second order statistical properties of complex signals are usually characterized by the covariance function however this is not sufficient for a complete second order description and it is necessary to introduce another moment called the relation function its properties and especially the conditions that it must satisfy are analyzed both for stationary and nonstationary signals this leads to a new perspective concerning the concept of complex white noise as well as the modeling of any signal as the output of a linear system driven by a white noise finally this is applied to complex autoregressive signals and it is shown that the classical prediction problem must be reformulated when the relation function is taken into consideration

stabilization of nonlinear systems in the plane abstract it is shown that every small time locally controllable system in the plane can locally be asymptotically stabilized by employing locally holder continuous feedback laws as essentially was conjectured by e sontag an explicit algorithm for the construction of such feedback laws is given

hybrid laplace transform finite difference method for transient heat conduction problems the new method involving the combined use of the laplace transform and the finite difference method is applicable to the problem of time dependent heat flow systems the present method removes the time derivatives from the governing differential equation using the laplace transform and then solves the associated equation with the finite difference method the transformed temperature is inverted numerically by the method of honig and hirdes to obtain the result in the physical quantities the present results are compared in tables with exact solutions and those obtained from the combined use of the laplace transform and the finite element method it is found that the present method is reliable and efficient

mechanical and thermal sources in a micropolar generalized thermoelastic medium abstract the disturbance due to mechanical and thermal sources in a homogeneous isotropic micropolar generalized thermoelastic half space is investigated by the use of laplace fourier transform technique the analytical expressions of displacement components normal force stress tangential force stress and temperature field so obtained have been inverted by using a numerical technique numerical results are presented graphically for a magnesium crystal like material

nonlinear infinite extent interpolation of stationary processes the problem of minimum mean square interpolation of discrete time stationary stochastic processes using a system consisting of a finite number p of nonlinear instantaneous transformations followed by a p input one output infinite extent linear filter is studied the expressions of the optimal interpolator and of the approximation error are derived and generalize the corresponding relations known in linear interpolation theory some extensions including the estimation problem with several missing observations are also investigated

a numerical treatment to the solution of quasiparabolic partial differential equations this paper presents results obtained by the implementation of a hybrid laplace transform finite element method to the solution of quasiparabolic problem the present method removes the time derivatives from the quasiparabolic partial differential equation using the laplace transform and then solves the associated equation with the finite element method the numerical inverse of the laplace transform is realized by solving linear overdetermined systems and a polynomial equation of the kth order test examples are used to show that the numerical solution is comparable to the exact solution of the initial boundary value problem at the given grid points

magnetohydrodynamic unsteady free convection flow of a couple stress fluid with one relaxation time through a porous medium the method of the matric exponential which constitutes the basis of the state space approach of modern control theory is applied to the non dimensional equations of a magnetohydrodynamic unsteady free convection flow of a couple stress fluid through a porous medium with one relaxation time the resulting formulation together with laplace transform technique is applied to a thermal shock problem also a problem with distribution of heat sources is considered numerical results for the velocity induced magnetic field angular velocity and temperature distributions are given and illustrated graphically for each problem

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

asymptotic stabilization of a generic class of three dimensional homogeneous quadratic systems abstract we give necessary and sufficient conditions for the asymptotic stabilizability of a generic class of single input three dimensional homogeneous quadratic systems

asymptotically stabilizing feedback controls and the nonlinear regulator problem continuous asymptotically stabilizing feedback controls are constructed for two dimensional and certain three dimensional small time locally controllable affine systems the lie products which de

state space approach of two temperature generalized thermoelasticity of one dimensional problem abstract in this paper we will consider a half space filled with an elastic material which has constant elastic parameters the governing equations are taken in the context of the two temperature generalized thermoelasticity theory youssef h 2005a the dependence of the modulus of elasticity and the thermal conductivity on the reference temperature in generalized thermoelasticity for an infinite material with a spherical cavity j appl math mech 26 4 4827 youssef h 2005b theory of two temperature generalized thermoelasticity ima j appl math 1 8 the medium is assumed initially quiescent laplace transform and state space techniques are used to obtain the general solution for any set of boundary conditions the general solution obtained is applied to a specific problem of a half space subjected to thermal shock and traction free the inverse laplace transforms are computed numerically using a method based on fourier expansion techniques some comparisons have been shown in figures to estimate the effect of the two temperature parameter

explicit design of time varying stabilizing control laws for a class of controllable systems without drift abstract this paper gives a systematic way to design time variant feedback control laws for a class of controllable nonlinear systems this class contains a lot of systems which cannot be stabilized via a time invariant feedback control law the interest of this work lies in the design method since a general existence results is already available the techniques employed here are basic they mainly involve classical lyapunov analysis

uniqueness analysis of non unitary matrix joint diagonalization matrix joint diagonalization mjd is a powerful approach for solving the blind source separation bss problem it relies on the construction of matrices which are diagonalized by the unknown demixing matrix their joint diagonalizer serves as a correct estimate of this demixing matrix only if it is uniquely determined thus a critical question is under what conditions is a joint diagonalizer unique in the present work we fully answer this question about the identifiability of mjd based bss approaches and provide a general result on uniqueness conditions of matrix joint diagonalization it unifies all existing results which exploit the concepts of non circularity non stationarity non whiteness and non gaussianity as a corollary we propose a solution for complex bss which can be formulated in closed form in terms of an eigen and a singular value decomposition of two matrices

elastodynamics of an axisymmetric problem in an anisotropic liquid saturated porous medium the laplace and hankel transforms have been employed to find the general solution to the field equations in an anisotropic liquid saturated porous medium for plain axisymmetric problem in the transformed form an application of an infinite space with impulsive force at the origin has been considered to show the utility of the solution obtained the results of the corresponding problem in isotropic liquid saturated porous medium can be derived as a special case to get the solutions in the physical form a numerical inversion technique has been applied the results in the form of displacement and stress components have been obtained numerically and discussed graphically for a particular model

a two dimensional thermoelasticity problem for thermomechanical shock with two relaxation times in this work a two dimensional problem of thermoelasticity with two relaxation times is introduced laplace and fourier transform techniques are used the resulting formulation is applied to a thermomechanical shock half space problem the solution in the transformed domain obtained by using a direct approach numerical inversion of both transforms is carried out to obtain the temperature stress and displacement distributions in the physical domain numerical results are represented graphically

receding horizon control and discontinuous state feedback stabilization this paper addresses three aspects of receding horizon control in discrete time 1 feedback stabilization of general nonlinear systems with receding horizon control 2 the generation of stabili

piecewise constant stabilization with the help of topological necessary conditions for continuous stabilization it is shown that in general in order to stabilize continuous and discrete time systems one has to use time dependent or discontinuous feedback controls on the other hand the criterion of stabilization in the class of piecewise constant feedbacks is established in the context of this paper a piecewise constant feedback is associated with a piecewise constant function of the form u u x where x in rm r n x the piecewise constant feedback synthesis outlined here has several attractive features first it can be effectively applied to design feedback stabilizers subjected to control constraints second the designed feedback laws do not cause sliding mode or chattering behavior in the closed loop system i e on a finite interval of time the control in the closed loop system may have only a finite number of jump discontinuities

optimal linear quadratic systems for detection and estimation the problem of linear quadratic systems for detection has long been solved by assuming the deflection criterion and gaussian noise it is shown here that the gaussian assumption can be removed and a complete solution is presented for an arbitrary probability distribution with finite fourth order moments the optimal solution can always be obtained by solving a linear system of equations some properties of the optimal systems are developed for particular examples of nongaussian noise it is shown that there is a strong relationship between linear quadratic optimal detection and optimal estimation which extends results known for the purely linear case

local asymptotic feedback stabilization to a submanifold topological conditions abstract we consider the problem of local asymptotic feedback stabilization of a control system x f x u defined in r n to a compact connected oriented embedded codimension one submanifold p of r n using a continuous feedback law this generalizes the problem of local asymptotic feedback stabilization to a point which has been previously considered in the control theory literature it is natural to expect the topology of p to play a role in deciding whether or not local asymptotic stabilization to p of the system x f x u is feasible via continuous feedback and our aim in this paper is precisely to outline necessary conditions on the topology of p for stabilization via continuous feedback to be achievable

a stochastic galerkin approach to uncertainty quantification in poroelastic media recent concerns over the safety of oil and natural gas extraction fracking and carbon sequestration have driven the need to develop methods for uncertainty quantification for coupled subsurface flow and deformation processes traditional monte carlo methods are versatile but exhibit prohibitively slow convergence in this work we develop an intrusive polynomial chaos expansion method for biot s poroelasticity equations based on the galerkin projection with uniform and log normally distributed material parameters we analyze accuracy and efficiency of our method and compare it to the monte carlo method we verify exponential convergence of the stochastic galerkin approach

flow stability of patchy vector fields and robust feedback stabilization the paper is concerned with patchy vector fields a class of discontinuous piecewise smooth vector fields that were introduced by the authors to study feedback stabilization problems we prove the stability of the corresponding solution set w r t a wide class of impulsive perturbations these results yield the robustness of patchy feedback controls in the presence of measurement errors and external disturbances

an application of the ltdrm to transient diffusion problems with nonlinear material properties and nonlinear boundary conditions in this paper we shall present an application of the laplace transform dual reciprocity method ltdrm to the solution of transient diffusion problems with nonlinear material properties and nonlinear boundary conditions two methods with and without utilizing the kirchhoff transformation will be discussed the nonlinear terms in both governing equation and boundary conditions are linearized first followed by the removal of the time variable from the linearized differential system with the laplace transformation and then the problem is solved by the dual reciprocity method as a result a solution at any specific time can be obtained without step by step calculations in time domain and computations of domain integrals to show the efficiency and accuracy of the present method several problems are analyzed and their solutions are compared with those obtained either analytically or numerically

polyspectrum modeling using linear or quadratic filters the polyspectrum modeling problem using linear or quadratic filters is investigated in the linear case it is shown that if the output pth order cumulant function of a filter driven by a white noise is of finite extent then the filter necessarily has a finite extent impulse response it is proved that every factorable polyspectrum with a non gaussian white noise can also be modeled with a quadratic filter driven by a gaussian white noise it is shown that if the quadratic filter has a finite extent impulse response then the output pth order cumulant function is of finite extent and if the output pth order cumulant function of a quadratic filter is of finite extent then the impulse response may or may not be of finite extent it is shown that there exist finite and infinite extent pth order cumulant functions that are not factorable but can be modeled with quadratic filters

asymptotic stabilization of two dimensional real analytic systems abstract we investigate the local asymptotic stabilizability of a real analytic control system around an equilibrium point and give necessary and sufficient conditions for local asymptotic stabilization using continuous feedback

stabilization by artificial wiener processes in this technical note we restage the positive effects of gaussian white noises for continuous time driftless input affine nonholonomic systems compared with previous studies we found that the positive effects are hidden in the shadows of nonuniqueness of stochastic integrals over multi dimensional wiener processes furthermore we found that the positive effects are artificially restaged by numerical calculations with use of euler scheme for ordinary differential equations our results demonstrate that the positive effects act as hidden independent control inputs for nonholonomic systems this implies that our results provide a constructive procedure for designing control inputs such that the origins become p th moment exponentially or finite time stable

the extended durbin method and its application for piezoelectric wave propagation problems abstract based on the well known durbin method an efficient numerical method was developed for the inversion of the two sided laplace transform the accuracy of the method was verified using examples as an application of the method transient elastic waves propagating in a two layered piezoelectric medium subjected to anti plane concentrated loading and in plane electric displacement loading were investigated one sided and two sided laplace transforms were applied to determine the shear stresses and electric displacements in the double laplace transform domain subsequently the durbin method for one sided laplace transform inversion and the extended durbin method for two sided laplace transform inversion were used to implement the numerical inversions additionally the numerical results of the transient stresses and electric displacements were evaluated and discussed it showed that the arrival time of transient waves satisfies physical phenomena and the transient solution oscillates near the static solution and rapidly approximates the static solution

volterra filtering and higher order whiteness some properties of volterra filtering are established finite order finite horizon volterra filtering is investigated as well as its asymptotic properties next the concepts of volterra unpredictability and uninterpolability lead to generalizations of the notion of white noise to higher orders these generalizations are introduced and relations are established between them

quadratic approximation and time varying feedback laws we present a method to construct stabilizing time varying feedback laws for a large class of systems we apply our technique to several classical examples which do not satisfy the necessary brockett condition or the coron condition for stabilization by means of continuous stationary feedback laws

state space approach to generalized thermoelastic problem with thermomechanical shock in this work the state space formulation for one dimensional problem of generalized thermoelasticity with one relaxation time is introduced the resulting formulation together with the laplace transform technique is applied to a thermomechanical shock half space problem the solution in the transformed domain is obtained the inverse laplace transforms is evaluated numerically the results are obtained and represented graphically

a simple and efficient algorithm to compute tail probabilities from transforms we present an algorithm to approximately compute the tail probability that a random variable exceeds a specified number given only an expression for its transform we also show that the problem is p hard more difficult than np hard suggesting that no efficient procedure can solve it exactly our method consists essentially of summing a power series and thus is easy to perform and requires little memory furthermore its computational effort is nearly linear in the reciprocal of a prespecified worst case error bound

control lyapunov functions and zubov s method for finite dimensional nonlinear control systems we study the relation between asymptotic null controllability and control lyapunov functions it is shown that control lyapunov functions clfs may be constructed on the domain of asymptotic null controllability as viscosity solutions of a first order pde that generalizes zubov s equation the solution is also given as the value function of an optimal control problem from which several regularity results may be obtained

conley index condition for asymptotic stability in this paper we use conley index theory to develop necessary conditions for stability of equilibrium and periodic solutions of nonlinear continuous time systems the conley index is a topological generalization of the morse theory which has been developed to analyze dynamical systems using topological methods in particular the conley index of an invariant set with respect to a dynamical system is defined as the relative homology of an index pair for the invariant set the conley index can then be used to examine the structure of the system invariant set as well as the system dynamics within the invariant set including system stability properties efficient numerical algorithms using homology theory have been developed in the literature to compute the conley index and can be used to deduce the stability properties of nonlinear dynamical systems

stabilizability conditions in terms of critical hamiltonians and symbols symmetric functions of critical hamiltonians called symbols were used in such problems of nonlinear control as the characterization of symmetries and feedback invariants we derive here a stabilizability condition in the class of almost continuous feedback controls based on symbols the methodology proposed consists of defining a selector of the multivalued covector field satisfying an extra degree condition on a sphere close to the origin then the above selector is extended to some neighborhood in order to get an exact differential form integration of that form gives us a control lyapunov function candidate theorem 3 1 the condition proposed is applied to the analysis of a planar control affine system with polynomial homogeneous vector fields unlike known results in the literature we consider the case when each vector field vanishes at the origin and the control is bounded we give stabilizability conditions explicitly in terms of the control system parameters theorem 4 1

topological necessary conditions of smooth stabilization in the large abstract topological necessary conditions of smooth stabilization in the large are obtained in particular if a smooth single input nonlinear system is smoothly stabilizable in the large at some point of a connected component of an equilibrium set then the connected component is an unbounded curve

stabilization of a class of nonlinear systems by a smooth feedback control we consider the stabilizability problem for systems of the form x f x ub in the neighborhood of an equilibrium point of f x first by means of center manifold theory a lower order system is introduced if this system is stabilizable then so is the original system results on the stabilization of the low order system are presented no resort is taken to liapunov theory the relation between stabilizability and controllability is discussed

a continuous feedback approach to global strong stabilization of nonlinear systems we present a continuous feedback approach to the problem of global strong stabilization for genuinely nonlinear systems that may not be stabilized even locally by any smooth feedback we describe conditions under which it is possible to prove while no smooth controllers exist the existence of continuous state feedback control laws that achieve global strong stability gss in the sense of kurzweil 1956 the proof is constructive and carried out by developing a machinery which combines the theory of homogeneous systems with the idea of adding a power integrator for the explicit construction of globally stabilizing continuous controllers we then illustrate by means of examples how this machinery can be used to overcome the topological obstruction caused by smooth feedback and hence resulting in new solutions to a variety of open control problems including global stabilization of an underactuated unstable two degree of freedom mechanical system

a problem of numerical inversion of implicitly defined laplace transforms abstract a procedure is proposed for numerical inversion of laplace transforms x s implicitly defined from the functional equation x s g a s cx s where a and g are known functions c is a known constant this equation is encountered in queueing inventory and insurance problems the procedure constructs coefficients of the laguerre series for the original in the laguerre series inversion method and a sequence of approximants in the post widder inversion method scalar and matrix cases are treated in the same fashion the numerical results are compared with those attainable with the fourier series method

asymptotic stabilizability of homogeneous polynomial systems of odd degree we give some tools for the construction of the homogeneous feedback witch stabilizes a generic class of single input two dimensional homogeneous systems

a general procedure for the derivation of principal domains of higher order spectra a general procedure to determine the principal domain i e nonredundant region of computation of any higher order spectrum is presented using the bispectrum as an example the procedure is then applied to derive the principal domain of the trispectrum of a real valued stationary time series these results are easily extended to compute the principal domains of other higher order spectra

feedback stabilization of homogeneous polynomial systems of odd degree in the plane in this paper we give some tools for the construction of homogeneous feedback which stabilizes homogeneous polynomial systems of odd degree in the plane

topological obstructions to submanifold stabilization we consider the problem of local asymptotic feedback stabilization via a continuously differentiable feedback law of a control system x f x u defined in euclidean space rn with f being continuously differentiable to a compact connected oriented m dimensional submanifold m of rn with codimension strictly larger than one we obtain necessary conditions on the topology of m for such a stabilizing feedback law to exist this extends the work done in where only the codimension one case was treated we also briefly discuss the case where the control is only assumed continuous

homogeneous feedback controls for homogeneous systems let x x j 2n aj x xj be a real analytic n dimensional vector field with x 0 0 which is homogeneous of degree m 0 with respect to a dilation erx er1x1 ernxn and y xj we show that control system x x x uy admits a continuous asymptotically stabilizing feedback control u x then a one dimensional dynamic extension of the system admits a homogeneous asymptotically stabilizing dynamic feedback control u x such that the vector field w x 1 m u x 1 j 2aj x xj describing the extended controlled system is homogeneous of degree m with respect to the extended dilation er x e er1x1 ernxn