continuous pole placement for delay equations in this paper we describe a stabilization method for linear time delay systems which extends the classical pole placement method for ordinary differential equations unlike methods based on finite spectrum assignment our method does not render the closed loop system finite dimensional but consists of controlling the rightmost eigenvalues because these are moved to the left half plane in a quasi continuous way we refer to our method as continuous pole placement we explain the method by means of the stabilization of a linear finite dimensional system in the presence of an input delay and illustrate its applicability to more general stabilization problems

on stability of lms methods and characteristic roots of delay differential equations we investigate the use of linear multistep lms methods for computing characteristic roots of systems of linear delay differential equations ddes with multiple fixed discrete delays these roots are important in the context of stability and bifurcation analysis we prove convergence orders for the characteristic root approximations and analyze under what condition for the steplength the discrete integration scheme retains certain delay independent stability properties of the original equations unlike existing results we concentrate on the recovery of both stability and instability we illustrate our findings with a number of numerical test results

simultaneous stabilization of discrete time delay systems and bounds on delay margin abstract this paper studies the delay margin problem of linear time invariant lti systems for discrete time systems this problem can also be posed as one of simultaneous stabilization of multiple unstable systems with different lengths of delay our contribution is threefold first for general lti plants with a number of distinct unstable poles and nonminimum phase zeros we employ analytic function interpolation and rational approximation techniques to derive bounds on the delay margin we show that readily computable and explicit lower bounds can be found by computing the real eigenvalues of a constant matrix and lti controllers potentially of a low order can be synthesized to achieve the bounds based on the h control theory second we show that these results can be coherently extended to systems with time varying delays also resulting in bounds on the delay range and delay variation that ensure simultaneous stabilization finally we investigate the delay margin problem in the context of pid control for first order unstable plants we obtain bounds achievable by pid controllers it is worth noting that unlike its continuous time counterpart the discrete time delay margin problem is fundamentally more difficult due to the intrinsic difficulty in simultaneously stabilizing several systems nevertheless while previous works on the discrete time delay margin led to largely negative results the bounds developed in this paper provide instead conditions that guarantee the simultaneous stabilization of multiple delay plants or ranges within which the delay plants can be robustly stabilized

penetration through slots in conducting cylinders part 2 tm case three methods for determining the penetration through small apertures in closed conducting surfaces are outlined and their salient features discussed these methods are designated 1 the scatterer method 2 the short circuit current method and 3 the equivalent current method they are implemented by integral equation techniques but are amenable to differential equation or hybrid methods procedures for applying each method are outlined as are schemes for repairing singular equations rendered invalid by the presence of false resonances reasons for inaccuracies in the three methods are also delineated data determined for a given structure by all three methods are presented and numerical examples that illustrate important features of the methods and their relative accuracies are described it is pointed out that some methods yield incorrect penetration data an outline is given of the integral equation formulations and numerical schemes needed to accurately determine the field that penetrates through a slot in a conducting cylinder excited by an axially independent te source

explicit bounds for guaranteed stabilization by pid control of second order unstable delay systems abstract in this paper we derive explicit lower bounds on the delay margin of second order unstable delay systems achievable by pid control which provide a priori a guaranteed range of delay values over which a second order delay plant can be stabilized by a pid and more generally a finite dimensional lti controller this is done by deriving lower bounds on the delay margin achievable by pd controllers whereas this margin constitutes a lower bound on that achievable by pid controllers analysis shows that in most cases our results can be significantly less conservative than the lower bounds obtained elsewhere using more sophisticated general lti controllers

linear multistep methods for impulsive delay differential equations abstract this paper deals with the convergence and stability of linear multistep methods for a class of linear impulsive delay differential equations numerical experiments show that the simpson s rule and two step bdf method are of order p 0 when applied to impulsive delay differential equations an improved linear multistep numerical process is proposed convergence and stability conditions of the numerical solutions are given in the paper numerical experiments are given in the end to illustrate the conclusion

asymptotic stability contractivity and dissipativity of one leg θ method for non autonomous delay functional differential equations abstract this paper focuses on asymptotic stability contractivity and dissipativity of non autonomous nonlinear delay functional differential equations with bounded lag and the corresponding dynamical properties of one leg method sufficient conditions for these delay functional differential equations to be dissipative asymptotically stable and contractive are established one leg method is constructed to solve such equations numerically an important result on the growth of solution of a class of difference inequalities with variable coefficients is obtained finally it is proved that the one leg method is asymptotically stable contractive and dissipative if and only if 1 numerical examples are given to confirm our theoretical results

memoryless approach to the lq and lqg problems with variable input delay this note studies the lq and lqg problems for linear time invariant systems with a single time varying input delay and instantaneous memoryless state feedback we extend the memoryless state feedback solution proposed in 1 in two directions we prove that in the deterministic case a memoryless state feedback can be in general optimal only up to a certain delay for which we provide a sufficient and sometimes strict bound moreover we show that this memoryless control is optimal also in the case of time varying delays and that the quadratic cost functional has the same value as in the case without delay for time varying delays the control law requires that the relationship between time points in which the input is generated and applied is known and invertible even if the delay function needs not to be differentiable or even continuous finally we prove that the cost functional is bounded also in the stochastic case for the same delay interval as in the deterministic case but with a larger cost than the delay less lqg solution

controller design for delay independent stability of linear time invariant vibration systems with multiple delays abstract one of the critical parameters that can deteriorate the effectiveness of active vibration control avc is the delay in sensors especially in remote sensing where delays are large and in high speed applications with even small delays instability can be inevitable this paper presents algebraic approaches to design controllers in order to achieve stability regardless of the amount of delays for avc applications modeled by linear time invariant systems with multiple constant delays the approaches are based on a nonconservative framework and can identify the regions in the controller gain space where delay independent stability dis is achievable with these controllers we demonstrate via simulations that vibration suppression within certain excitation frequency bands can be improved or be as effective as those in avc applications without delays

two examples of ill posedness with respect to time delays revisited we revisit two examples of elastic control systems which are stabilized by boundary feedback and then destabilized when time delays occur in the feedback in the first example a wave equation with a feedback gain greater than or equal to one arbitrary divergence rates are obtained for small time delays in the second example a euler bernoulli beam any time delay results in an arbitrary divergence rate

conditions for robustness and nonrobustness of thestability of feedback systems with respect to small delays inthe feedback loop it has been observed that for many stable feedback control systems the introduction of arbitrarily small time delays into the loop causes instability in this paper we present a systematic frequency domain treatment of this phenomenon for distributed parameter systems we consider the class of all matrix valued transfer functions which are bounded on some right half plane and which have a limit at spinfty along the real axis such transfer functions are called regular under the assumption that a regular transfer function is stabilized by unity output feedback we give sufficient conditions for the robustness and for the nonrobustness of the stability with respect to small time delays in the loop these conditions are given in terms of the high frequency behavior of the open loop system moreover we discuss robustness of stability with respect to small delays for feedback systems with dynamic compensators in particular we show that if a plant with infinitely many poles in the closed right half plane is stabilized by a controller then the stability is not robust with respect to delays we show that the instability created by small delays is itself robust to small delays three examples are given to illustrate these results

limitations of a class of stabilization methods for delay systems we investigate limitations of certain stabilization methods for time delay systems the class of methods under consideration implements the control law through a volterra integral equation of the second kind using as an example the pole placement approach of manitius and olbrot 1979 we illustrate how instability of the difference part of the control law leads to instability in the closed loop system in the case that implementation is done via numerical quadrature the outcome of our analysis provides computable limitations to stability and a maximum allowable size of the input delay

stability analysis of one step methods for neutral delay differential equations in this paper stability properties of one step methods for neutral functional differential equations are investigate stability regions are characterized for runge kutta methods with respect to the linear test equation begin gathered y left t right ay left t right by left t tau right cy left t tau right t geqq 0 hfill y left t right g left t right tau leqq t leqq 0 hfill end gathered 0 where a b andc are complex parameters in particular it is shown that everya stable collocation method for ordinary differential equations can be extended to a method for neutrals delay differential equations with analogous stability properties the so called np stable method we also investigate how the approximation to the derivative of the solution affects stability properties of numerical methods for neutral equations

testing hypotheses about the shape parameter of a gamma distribution the purpose of this expository article is to provide greater access to critical values for testing hypotheses about the shape parameter of a gamma distribution among the possible tests we consider tests of exponentiality against gamma increasing failure rate and or decreasing failure rate alternatives extensive tables of critical values are given for individual sample sizes from 2 to 30 and values of the shape parameter in half integer increments from i to 10 median unbiased estimators are also given for the shape parameter to avoid small sample complications with maximum likelihood methods power curves are given for testing exponentiality against gamma alternatives these curves illustrate certain advantages of this parametric test over nonparametric alternatives

the numerical stability of linear multistep methods for delay differential equations with many delays this paper deals with the stability analysis of linear multistep methods for the numerical solution of delay differential equations ddss with many delays we focus on the stability behaviour of such methods when they are applied to a scalar linear dde with many constant delays and complex coefficients the concept of gp m stability is introduced under a sufficient condition for the test equation to be stable the linear multistep method when combined with a certain lagrange interpolation must be stable for all stepsizes it is proven that a linear multistep method is gp m stable if and only if it is a stable for ordinary differential equations odes

input delay margin for consensusability of multi agent systems in this paper we are concerned with the consensus of multi agent systems with input delay among all standard static protocols that achieve the consensus for the multi agent system under no input delay we aim to find the maximum input delay such that the system remains consensusable under the same protocols in the case of continuous time systems in view of the continuity of stability with respect to the time delay the maximum delay margin for consensusability is given for scalar systems and vector systems with a single unstable open loop pole for scalar discrete time systems we show that the maximum delay margin for consensusability is strictly greater than zero if and only if the open loop pole of the system is located in a specified interval

on the stabilization and stability robustness against small delays of some damped wave equations in this paper we consider a system which can be modeled by two different one dimensional damped wave equations in a bounded domain both parameterized by a nonnegative damping constant we assume that the system is axed at one end and is controlled by a boundary controller at the other end we consider two problems namely the stabilization and the stability robustness of the closed loop system against arbitrary small time delays in the feedback loop we propose a class of dynamic boundary controllers and show that these controllers solve the stabilization problem when the damping coefficient is nonnegative and the stability robustness problem when the damping coefficient is strictly positive

predictor based control for an uncertain euler lagrange system with input delay controlling a nonlinear system with actuator delay is a challenging problem because of the need to develop some form of prediction of the nonlinear dynamics developing a predictor based controller for an uncertain system is especially challenging in this paper tracking controllers are developed for an euler lagrange system with time delayed actuation parametric uncertainty and additive bounded disturbances the developed controllers represent the first input delayed controllers developed for uncertain nonlinear systems that use a predictor to compensate for the delay the results are obtained through the development of a novel predictor like method to address the time delay in the control input lyapunov krasovskii functionals are used within a lyapunov based stability analysis to prove semi globally uniformly ultimately bounded tracking experimental results illustrate the performance and robustness of the developed control methods

nystrom solution to oblique scattering of arbitrarily polarized waves by dielectric filled slotted cylinders we investigate oblique diffraction of arbitrarily polarized waves by axially slotted dielectric filled perfectly conducting circular cylinders with infinitesimally thin walls the relevant 2 2 system of coupled singular integral integrodifferential equations is solved by a highly accurate nystrom method for enhanced efficiency several asymptotic terms are extracted from the kernels this helps isolate the inherent singularities and thus transform the initial slowly converging green function expansions into rapidly converging series as a consequence all elements of the resulting nystrom matrix take exact expressions in the form of very rapidly converging series of elementary terms numerical examples and case studies are presented that validate the algorithm illustrate its rapid convergence and bring to light the effect of changing several physical and geometrical parameters on the reflection transmission and absorption characteristics of the structure

not all feedback stabilized hyperbolic systems are robust with respect to small time delays in their feedbacks we present two examples of hyperbolic partial differential equations which are stabilized by boundary feedback controls and then destabilized by small delays in these controls we show that in a general case when the controls are distributed stabilized hyperbolic systems possess nontrivial periodic solutions if small time delays are introduced into their feedbacks we also indicate by means of an example that the general case of this phenomenon is harder to demonstrate for boundary control problems

stabilizing a first order system with an arbitrarily large time varying delay and an uncertain gain abstract handling delays and uncertain parameters in control systems is difficult and of long standing interest in this paper we consider the problem of stabilizing in a bounded input bounded output sense a first order linear time invariant plant with an arbitrarily large time varying delay and an arbitrarily large uncertain gain we propose the use of a mildly non linear periodic controller which is simple to implement we will derive a clear simple formula relating the maximum delay duration the location of the unstable plant pole and the bounds on the derivative of the delay for which our controller stabilizes the system

an eigenvalue based approach for the stabilization of linear time delay systems of neutral type an eigenvalue based approach for the stabilization of linear neutral functional differential equations is presented which extends the recently developed continuous pole placement method for delay equations of retarded type the approach consists of two steps first the stability of the associated difference equation is determined and a procedure is applied to compute the supremum of the real parts of its characteristic roots which corresponds to computing the radius of the essential spectrum of the solution operator of the neutral equation no restrictions are made on the dimension of the system and the number of delays also the effect of small delay perturbations is explicitly taken into account as a result of this first step the stabilization problem of the neutral equation is reduced to a problem involving only a finite number of characteristic roots as a second step stabilization is achieved by shifting the rightmost or unstable characteristic roots to the left half plane in a quasi continuous way by applying small changes to the controller parameters and meanwhile monitoring other characteristic roots with a large real part a numerical example is presented

when is the achievable discrete time delay margin nonzero this technical note considers the delay margin problem for discrete time finite dimensional linear time invariant fdlti single input single output siso systems this problem has been studied extensively in continuous time it is well known that given a fdlti plant and controller forming a strictly proper stable feedback connection closed loop stability will be maintained for small delays hence the achievable delay margin using fdlti control is strictly greater than zero in this work we show that this is not the case for discrete time systems indeed we show that a fdlti siso discrete time plant has an achievable delay margin strictly greater than zero if and only if it has no negative real unstable poles

robust stability optimization for linear delay systems in a probabilistic framework abstract this paper is concerned with an eigenvalue based stabilization method for linear autonomous delay systems with uncertain parameters modeled by a random vector the dependence of the characteristic matrix on the uncertain parameters can be nonlinear also delay values can be subject to uncertainty unlike the stability optimization methods for deterministic problems which minimize the spectral abscissa our approach shows better robust properties based on a more realistic model where the uncertainty is taken into account by minimizing an objective function consisting of the mean of the spectral abscissa with a variance penalty the properties of the spectrum of delay differential algebraic equations of retarded type are analyzed and an integration method to compute the mean and variance of the spectral abscissa which describes the stability property of the system is presented subsequently the analysis of the behavior of the gradient of the characteristic roots is addressed and a suitable explicit formula of the gradient of the objective function is presented finally for designing the controller a suitable optimization routine requiring the objective function and its gradient is presented the efficacy of the method is illustrated with numerical examples including a model of an experimental heat exchanger the algorithms developed are publicly available

prediction based control of lti systems with input and output time varying delays the stability of a prediction based controller is studied in presence of time varying delays both in the input and in the output thanks to the reduction method and a lyapunov krasovskii analysis stability conditions are derived a comparison is also made between the single input delay and single output delay cases it is shown that this method can be applied to stabilize output delay systems without restriction on the delay rate the results are illustrated numerically on a double integrator

an eigenvalue based approach for the robust stabilization of linear time delay systems we present a new numerical procedure for the robust stabilization of linear delay differential equations based on the position of the eigenvalues in the complex plane we assume static perturbations on the system matrices and express the robustness of the stability in terms of complex stability radii in the numerical procedure these stability radii are maximized as a function of the controller parameters this corresponds to a synthesis problem which is solved by a quasi continuous shaping of some frequency response plots the structure of the algorithm is analogous to the continuous pole placement algorithm for the non robust stabilization of linear delay differential equations

controller design for delay systems via eigenvalue assignment on a new result in the distribution of quasi polynomial roots this paper considers the eigenvalue distribution of a linear time invariant lti system with time delays and its application to some controllers design for a delay plant via eigenvalue assignment first a new result on the root distribution for a class of quasi polynomials is developed based on the extension of the hermite biehler theorem then such result is applied to proportional integral pi controller parameter design for a first order plant with time delay through pole placement the complete region of pi gains can be obtained so that the rightmost eigenvalues in the infinite eigenspectrum of the closed loop system with delay plant are assigned to desired positions in the complex plane furthermore on the basis of the previous result this paper also extended the pi control to the proportional integral derivative pid control it is worth pointing out that this work aims to improve the performance of the closed loop system on the premise of guaranteeing the stability

an accurate boundary value problem solver applied to scattering from cylinders with corners in this paper we consider the classic problem of scattering of waves from perfectly conducting cylinders with piecewise smooth boundaries the scattering problems are formulated as integral equations and solved using a nystrom scheme where the corners of the cylinders are efficiently handled by a method referred to as recursively compressed inverse preconditioning rcip this method has been very successful in treating static problems in nonsmooth domains and the present paper shows that it works equally well for the helmholtz equation in the numerical examples we focus on scattering of e and h waves from a cylinder with one corner even at a size kd 1000 where k is the wavenumber and d the diameter the scheme produces at least 13 digits of accuracy in the electric and magnetic fields everywhere outside the cylinder

estimations on numerically stable step size for neutral delay differential systems with multiple delays we derive two estimations of numerically stable step size for systems of neutral delay differential equations with multiple delays the stable step size for numerical integration of nddes with multiple delays can be easily selected by means of the logarithmic norm and the spectral radius of certain matrices both explicit linear multistep methods and explicit runge kutta methods are considered

spline collocation methods for solving delay differential equations the convergence and stability analysis of seventh c 3 spline collocation methods if applied to delay differential equations ddes will be considered letting the interior collocation points x i 1 c j x i 1 c jh j 1 3 be dependent on three parameters c 1 c 2 c email protected 0 1 it will be shown that these methods for ddes possess convergence rate of order seven if 0 7279115

asymptotic stability of numerical methods for linear delay parabolic differential equations this paper is concerned with the asymptotic stability property of some numerical processes by discretization of parabolic differential equations with a constant delay these numerical processes include forward and backward euler difference schemes and crank nicolson difference scheme which are obtained by applying step by step methods to the resulting systems of delay differential equations sufficient and necessary conditions for these difference schemes to be delay independently asymptotically stable are established it reveals that an additional restriction on time and spatial stepsizes of the forward euler difference scheme is required to preserve the delay independent asymptotic stability due to the existence of the delay term numerical experiments have been implemented to confirm the asymptotic stability of these numerical methods

destabilizing effects of small time delays on feedback controlled descriptor systems abstract in the last 15 years the problem of stabilizability and stabilization of descriptor systems have received considerable attention in this paper it is shown that if a descriptor system e x ax bu exhibits impulsive behavior then the stability of the closed loop system is extremely sensitive to small delays more precisely if f is the feedback which leads to a stable and impulsive free closed loop system then there exist numbers ej 0 and sj c with limj ej 0 and limj re sj and such that the delayed closed loop system obtained by applying the feedback u t fx t ej has a pole at sj moreover if the open loop system does not have impulsive behavior the same phenomenon occurs provided that the spectral radius of the matrix lim s f se a 1b is greater than 1 if this spectral radius is smaller than 1 it is shown that the closed loop stability is robust with respect to small delays

estimation of numerically stable step size for neutral delay differential equations via spectral radius we derive the estimates of numerically stable step size for systems of neutral delay differential equations nddes which only need to be calculated the spectral radius of the corresponding matrices the stable step size for numerical integration of nddes can be easily selected by means of the estimates the stability regions of both linear multistep methods and explicit runge kutta methods are presented

tail probabilities from observed likelihoods summary an exponential model not in standard form is fully characterized by an observed likelihood function and its first sample space derivative up to one one transformations of the observable variable this property is used to modify the lugannani rice 1980 tail probability approximation to make it parameterization invariant then for general continuous models a version of tangent exponential model is defined and used to derive a general tail probability approximation that uses only the observed likelihood and its first sample space derivative the analysis extends from density functions to distribution functions the tangent exponential model methods of fraser 1988 a related tail probability approximation has been reported barndorff nielsen 1988b in the discussion to reid 1988

stabilizing a chain of integrators using multiple delays this note addresses the output feedback stabilization problem of a chain of integrators using multiple delays we shall prove that either n distinct delays or a proportional delay compensator with n 1 distinct delays are sufficient to stabilize a chain including n integrators we present two different approaches both are constructive and rely on frequency domain techniques on a derivative feedback approximation idea and a pole placement idea respectively an illustrative example triple integrator is presented

inference on the gamma distribution this study develops inferential procedures for a gamma distribution based on the cornish fisher expansion and pivoting the cumulative distribution function an approximate confidence interval for

robustness with respect to delays for exponential stability of distributed parameter systems in this paper we address the question of whether the open loop exponential growth rate of a linear system can be improved by a feedback in such a way that this improvement is robust with respect to small delays in the feedback loop when the input operator is admissible and the class of possible feedbacks consists of compact operators we find that if a feedback can improve the exponential growth rate then it can do so robustly furthermore we find that if the control space is finite dimensional and a bounded feedback cannot be found to improve exponential stability then a large class of unbounded feedbacks cannot improve the exponential growth rate robustly even if such feedbacks can improve the exponential growth rate in the absence of delays

sensitivity to infinitesimal delays in neutral equations the stability of a steady state solution of a neutral functional differential equation can be sensitive to infinitesimal changes in the delays this phenomenon is caused by the behavior of the essential spectrum and is determined by the roots of an exponential polynomial avellar and hale j math anal appl 73 1980 pp 434 452 have considered the case of multiple fixed and nonzero delays in the first part of this paper their results are illustrated by means of spectral plots in the second part we extend the theory of avellar and hale to the limit case whereby some of the delays are brought to zero which may lead to characteristic roots with arbitrarily large real part necessary and sufficient conditions are provided using these results we show that the ratio of the delays plays a crucial role when several delays tend to zero simultaneously as an illustration of the theory we analyze the robustness of a boundary controlled pde in the presence of a small feedback delay

convergence of one leg methods for neutral delay integro differential equations the error analysis of one leg methods for a class of nonlinear neutral delay integro differential equations ndides is given it is proved that an a stable one leg method with an appropriate quadrature rule applied to ndides is convergent of order at least min p q 12 if the one leg method is consistent of order p2 in the classical sense for odes and the error order of the quadrature rule is o hq 1 numerical examples further confirm the theoretical results

exponentially converging nystro spl uml m s methods for systems of singular integral equations with applications to open closed strip or slot loaded 2 d structures this paper concerns the fast highly accurate and exponentially convergent solution of three sets of integral equations pertaining to two dimensional generalized microstrip or microslot structures the analysis relies on nystroumlm s method with due regard to all singular integrals and slowly converging series that appear in the kernels the sophisticated treatment and efficient computation of such series and integrals is of paramount importance entailing the use of advanced techniques as a result of our specialized treatment the discretization procedures developed herein a fully account for both the singular nature of the kernels and the singularities of the solution at the edges b obviate the need for taking inner products with testing functions c appear to converge exponentially versus matrix size and d enable expressing all matrix elements via single finite sums detailed numerical examples and case studies illustrate the simplicity flexibility and remarkable efficiency of the algorithms

inferences on the shape parameter of a gamma distribution a conditional approach a conditional method for inferences on the shape parameter of a two parameter gamma distribution is presented in this article a simple numerical implementation of this conditional method is developed this is a computer program that takes the observed data as input and produces the confidence distribution function for the shape parameter which in turn provides approximate observed significance levels and confidence intervals for that parameter as output these approximations are extremely accurate even for very small sample size and are numerically simple and easy to obtain

forwarding backstepping and finite spectrum assignment for time delay systems the nonlinear control ideas and results of forwarding and backstepping have been recently extended to systems with time delay in this paper we discuss how to apply these tools to design robust controls for linear delay systems we first show that the integral cross term forwarding produces a feedback law that achieves finite spectrum of the closed loop system combining it with backstepping provides a structured design method for a large class of systems with time delay robustness of the controller to uncertainties including uncertain time delay is illustrated by an example

convergence of runge kutta methods for neutral delay integro differential equations the present paper is concerned with the convergence of numerical methods to solve initial value problems of neutral delay integro differential equations ndides the error estimation of runge kutta methods for a class of nonlinear systems of ndides are derived some numerical experiments are given which confirm the theoretical results

predictor based stabilization of neutral type systems with input delay in this contribution we present an extension of the prediction scheme proposed in manitius and olbrot 1979 for the compensation of the input delay to the case of linear neutral type systems with input delay for simplicity of the presentation we treat the case of systems with one state delay

exponentially converging nystrom methods in scattering from infinite curved smooth strips part 1 tm case low order subdomain basis methods of moments provide little help when highly accurate electromagnetic computations are required high order modeling on the other hand can fill the need for enhanced accuracy but at the expense of greater implementation cost to supplement such methods this paper presents nystrom techniques both easily implemented and highly accurate relevant to te scattering by arbitrarily shaped smooth infinite curved strips the analysis takes full account of both the singular nature of the kernels and the singularities of the solution at the edges as a result the proposed solutions are exponentially converging in addition by eliminating inner product integrals closed form analytical expressions are obtained for all matrix elements thus our algorithms have very low implementation and computational cost detailed numerical examples and case studies amply demonstrate the efficiency stability and extremely high accuracy of the algorithms these algorithms apply uniformly from electrically small to electrically large conducting screens with only slight modifications the present analysis can be also used to obtain exponentially converging galerkin solutions

some special cases in the stability analysis of multi dimensional time delay systems using the matrix lambert w function this paper revisits a recently developed methodology based on the matrix lambert w function for the stability analysis of linear time invariant time delay systems by studying a particular yet common second order system we show that in general there is no one to one correspondence between the branches of the matrix lambert w function and the characteristic roots of the system furthermore it is shown that under mild conditions only two branches suffice to find the complete spectrum of the system and that the principal branch can be used to find several roots and not the dominant root only as stated in previous works the results are first presented analytically and then verified by numerical experiments

generic stabilizability for time delayed feedback control time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment this approach feeds back only terms that depend on the difference between the current output and the output from a fixed time t ago thus any periodic orbit of period t in the feedback controlled system is also a periodic orbit of the uncontrolled system independent of any modelling assumptions it has been an open problem whether this approach can be successful in general that is under genericity conditions similar to those in linear control theory controllability or if there are fundamental restrictions to time delayed feedback control we show that in principle there are no restrictions this paper proves the following for every periodic orbit satisfying a genericity condition slightly stronger than classical linear controllability one can find control gains that stabilize this orbit with extended time delayed feedback control while the paper s techniques are based on linear stability analysis they exploit the specific properties of linearizations near autonomous periodic orbits in nonlinear systems and are thus mostly relevant for the analysis of nonlinear experiments

an improved sufficient condition for stabilisation of unstable first order processes by observer state feedback this work considers the stabilisation and control of unstable first order linear systems subject to a relatively large i o time delay first it is proposed an observer strategy to predict a specific internal signal in the process the adequate prediction convergence is obtained and formally stated then it is proposed an estimated state feedback control necessary and sufficient stability conditions with respect to time delay size and unstable time constant are provided the proposed control strategy allows to address time delays as large as four times the unstable time constant of the open loop system in contrast with most of the reported related literature numerical examples are used for illustrating the parametric stabilisation region as a function of the time delay