superconvergent explicit two step peer methods we consider explicit two step peer methods for the solution of nonstiff differential systems by an additional condition a subclass of optimally zero stable methods is identified that is superconvergent of order p s 1 where s is the number of stages the new condition allows us to reduce the number of coefficients in a numerical search for good methods we present methods with 4 7 stages which are tested in fortran90 and compared with dopri5 and dop853 the results confirm the high potential of the new class of methods

a class of implicit peer methods for stiff systems we present a class of s stage implicit two step peer methods for the solution of stiff differential equations using the function values from the previous step in addition to the new function values this allows to increase the order to p s and to ensure zero stability straightforwardly corresponding s stage methods for s 6 of order p s with optimal zero stability are presented and their stability is discussed under special conditions we prove that an optimally zero stable subclass of these methods is superconvergent of order p s 1 for variable step sizes numerical tests and comparison with ode15s show the high potential of this class of implicit peer methods

controllability properties of perturbed distributed parameter systems abstract we analyse the action of perturbations on controllable distributed parameter systems we show that the most common controllability properties are not preserved under the action of perturbations whose norm is smaller than any prescribed tolerance v 0 in particular we show that small perturbations of the values of the coefficients of a system with delays can destroy the property of modal controllability finally a positive result which is important for application to the stabilization problem is presented

numerical solution of implicit neutral functional differential equations this paper is concerned with the numerical solution of implicit neutral functional differential equations based on the continuous runge kutta method for ordinary differential equations and the collocation method for functional equations two general one step methods are formulated and their uniform order of approximation is discussed numerical stability of a class of runge kutta collocation methods is analyzed in the case where a neutral equation can be expressed in an explicit as well as an implicit form the advantage of constructing a numerical scheme directly from the implicit form is explained theoretically and demonstrated by a numerical example

a new method for computing delay margins for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems we consider delay systems of retarded type modeled both as a high order scalar differential difference equation and as a set of first order differential difference equations expressed in state space form we provide a computational method that can be used to compute a delay interval such that the system under consideration is stable for all delay values that lie in the computed interval this method requires computing only the eigenvalues and generalized eigenvalues of certain constant matrices and it can be implemented efficiently based on this method we further state a simple necessary and sufficient condition concerning stability independent of delay for each of the two types of the models

stability and stabilization of delay differential systems the delay systems considered here are represented by linear delay differential equations the system parameters and the delays are assumed to be imperfectly known the instantaneous state vector is perturbed by a bounded external disturbance vector the problem addressed is that of characterizing conditions that guarantee that the trajectory of the instantaneous state vector remains in a domain defined by a set of symmetrical linear constraints it is shown that the positive invariance property can be used to solve this problem and that positive invariance of a compact domain of the instantaneous state space implies delay independent asymptotic stability of the associated deterministic system the possible use of these results for the control of a multiple delay mimo differential model is then presented finally an example is given

null controllability of a class of functional differential systems we consider a class of functional differential equations with both discrete and distributed delays distributed delays are represented by integrals whose bounds are commensurate with the discrete delays and by weight functions which are impulse responses of finite dimensional time invariant linear systems the properties of such systems can be studied by using simple algebraic techniques polynomials in one variable under the natural assumption of spectral controllability we give an explicit algebraic algorithm to compute a control function which steers any given initial datum to the equilibrium position in finite time this algorithm also constitutes a direct constructive and simple proof that spectral controllability implies null controllability for the class of systems considered the algorithm requires after the computation of the roots of a polynomial in one variable a finite number of steps

function space null controllability of linear delay systems with limited power abstract it is shown that if the system x t l t x t b t u t is null controllable with square integrable controls and if the system x t l t x t is uniformly asymptotically stable then the control system is null controllable with square integrable controls which lie in a closed unit ball with zero in its interior this extends known results and it is useful in the time optimal control problem of delay equations

global behavior of linear retarded functional differential equations abstract this paper formulates necessary and sufficient conditions for a linear delay differential equation to be asymptotically stable for each delay considered we use a new approach of the notion of observability of linear systems to obtain easily checkable conditions a new invariance principle of haddock and terjeki is employed

constrained approximate boundary controllability in this paper constrained approximate boundary controllability for linear disturbed parameter dynamical systems described by partial differential equations of parabolic type with mixed boundary conditions is considered using methods of spectral analysis for linear self adjoint operators and general constrained controllability results given by son 1990 necessary and sufficient conditions for constrained approximate boundary controllability are formulated and proved moreover in illustrative examples the constrained approximate boundary controllability of 1d distributed parameter dynamical systems is investigated the constrained controllability conditions obtained represent an extension of the unconstrained controllability results given by glothin 1974

robust stability of quasi polynomials frequency sweeping conditions and vertex tests in this paper we study the robust stability of uncertain time delay systems we consider uncertain quasi polynomials whose coefficients may vary in a certain prescribed range our goal is to derive necessary and sufficient conditions for such uncertain quasi polynomials to maintain stability independent of delay parameters our primary contributions are frequency sweeping conditions for interval diamond and spherical quasi polynomial families which can be readily checked requiring only the computation of two simple frequency dependent functions additionally we also obtain vertex and edge type results in the spirit of the kharitonov approach known in robust stability analysis showing that the stability of interval and diamond quasi polynomials can be ascertained by checking the stability of certain special vertex and or edge members in those families both type of results provide necessary and sufficient conditions for the quasi polynomial families to be robustly stable independent of delay

exponential stability criteria of uncertain systems with multiple time delays the exponential stability with convergence rate of uncertain linear systems with multiple time delays is studied in this paper using the characteristic function of linear time delay system stability criteria are derived to guarantee stability sufficient conditions are also obtained for exponential stability of uncertain parametric systems with multiple time delays for two dimensional time invariant system with multiple time delays the proposed stability criteria are shown to be less conservative than those in the literature numerical examples are given to illustrate the validity of our new stability criteria

on the stability of linear systems with uncertain delay this paper focuses on the stability of some class of delay systems including uncertainty in the delays more precisely we are interested in guaranteeing the stability of perturbed delay systems by assuming the stability of the nominal system if the delay perturbation is constant necessary and sufficient conditions are derived in terms of generalized eigenvalue distribution of some finite dimensional constant matrix pencil if the delay perturbation is time varying some sufficient stability conditions are derived using exact lyapunov krasovskii functionals illustrative examples are also included

observability and observers for a class of linear systems with delays a brief description of observability detectability and spectral observability concepts for time delay systems is given and some results on relations between these concepts are presented another result of this correspondence is the derivation of constructive design procedures for dynamic observers for a large class of linear autonomous systems with time delays this class includes systems with arbitrary output measurement delays where the procedure is based on well known methods of spectrum assignment for a pair of real matrices it is also shown that the observer problem for general systems with delays can be reformulated so as to get an easier case without output delays

on globally defined semianalytic sets in this work we present the concept of c semianalytic subset of a real analytic manifold and more generally of a real analytic space c semianalytic sets can be understood as the natural generalization to the semianalytic setting of global analytic sets introduced by cartan c analytic sets for short more precisely s is a c semianalytic subset of a real analytic space x ox if each point of x has a neighborhood u such that s u is a finite boolean combinations of global analytic equalities and strict inequalities on x by means of paracompactness c emianalytic sets are the locally finite unions of finite boolean combinations of global analytic equalities and strict inequalities on x the family of c semianalytic sets is closed

bounds of imaginary spectra of lti systems in the domain of two of the multiple time delays the stability of linear time invariant lti systems with independent multiple time delays and the cluster treatment of characteristic roots ctcr paradigm are investigated from a new perspective it is known that for such systems all the imaginary characteristic roots can be detected completely on a small set of hypersurfaces in the domain of the delays sipahi and olgac 2006a they are called kernel hypersurfaces kh the complete description of kh is the only prerequisite for the ctcr stability assessment procedure as the number of delays increases however their evaluation becomes infeasible instead we present a procedure to extract the 2 d cross sections of these hypersurfaces in the domain of any two of the delays by fixing the remaining delays in the 2 delay domain of interest the exact upper and lower bounds of the imaginary spectra are determined for this a combination of half angle tangent representation of the characteristic equation and the dixon resultant theory is used as the main contributions of this paper the complete kh are obtained by sweeping the root crossing frequency in this interval using this knowledge ctcr creates the cross section of the stability map in the domain of the two arbitrarily selected delays we demonstrate the effectiveness of this methodology over an example case study with three independent delays and two commensurate ones

on computing the maximal delay intervals for stability of linear delay systems this note is concerned with stability properties of linear time invariant delay systems the authors consider delay systems of both retarded and neutral types expressed in state space forms the author s main goal is to provide a computation oriented method for computing the maximal delay intervals over which the systems under consideration maintain stability the author s results show that this can be accomplished by computing the generalized eigenvalues of certain frequency dependent matrices based on these results the author also states a necessary and sufficient condition concerning stability independent of delay for each of the retarded and neutral systems the author s results can be readily implemented and appear suitable for analyzing systems with high dimensions and many delay units

absolute stability in linear delay differential systems ill posedness and robustness the author considers matrix delay differential systems which are polynomial in several delay operators using a necessary and sufficient criterion for stability independent of delay or absolute stability the author shows that system stability for all values of the delay vector lying in a sector will imply absolute stability we then show that absolute stability is ill posed with respect to arbitrarily small perturbations of the delay ratios if a certain extended delay differential system which is formed from the original is not also absolutely stable

imaginary characteristic roots of neutral systems with commensurate delays abstract this paper concentrates on stability analysis of neutral linear time invariant lti delay systems with multiple commensurate time delays a new numerical procedure is offered for the determination of purely imaginary characteristic roots of neutral delay systems which plays a crucial role in assessing the system stability based on simple linear algebra it is shown that the imaginary characteristic roots of such a system can be found by calculating the generalized eigenvalues of an associated matrix pair if the system is of retarded type we just need to determine the eigenvalues of a single matrix the results extend previously known work on neutral delay systems subject to a single delay for neutral systems subject to multiple commensurate delays in the light of the main result of this paper we present a new method to determine the largest first time delay interval for which a neutral delay system preserves its stability the paper is closed by showing numerical examples that illustrate the applicability and effectiveness of the proposed method

stability criteria of linear neutral systems with a single delay this article studies the asymptotic stability of linear neutral delay differential systems using the characteristic equation of the system new simple delay independent stability criteria are derived in terms of the spectral radius of modulus matrices numerical examples are given to demonstrate the validity of our main criteria

stability analysis for lti systems with multiple time delays using the bounds of its imaginary spectra abstract the stability of linear time invariant lti systems with multiple independent time delays and the cluster treatment of characteristic roots ctcr paradigm are investigated from a new perspective any delay composition that results in an imaginary characteristic root lies either on a small number of kernel hypersurfaces kh or their infinitely many offspring hypersurfaces oh the complete description of kh is the only prerequisite for the ctcr based stability assessment procedure as the number of delays increases however the determination of these kh becomes computationally costly instead we present a practical procedure to extract the 2 d cross sections of the kh set in the domain of the two arbitrarily selected delays first we determine the exact upper and lower bounds of the imaginary spectra in this 2 d cross section of interest this process starts with a half angle tangent representation of the characteristic equation followed by the dixon resultant operation based on the full knowledge of kh the ctcr paradigm creates the complete stability map in the domain of these two arbitrarily selected delays we demonstrate the effectiveness of this methodology over an example case study

stability radius of linear parameter varying systems and applications abstract in this paper we present a unifying approach to the problems of computing of stability radii of positive linear systems first we study stability radii of linear time invariant parameter varying differential systems a formula for the complex stability radius under multi perturbations is given then under hypotheses of positivity of the system matrices we prove that the complex real and positive stability radii of the system under multi perturbations or affine perturbations coincide and they are computed via simple formulae as applications we consider problems of computing of strong stability radii of linear time invariant time delay differential systems and computing of stability radii of positive linear functional differential equations under multi perturbations and affine perturbations we show that for a class of positive linear time delay differential systems the stability radii of the system under multi perturbations or affine perturbations are equal to the strong stability radii next we prove that the stability radii of a positive linear functional differential equation under multi perturbations or affine perturbations are equal to those of the associated linear time invariant parameter varying differential system in particular we get back some explicit formulas for these stability radii which are given recently in p h a ngoc strong stability radii of positive linear time delay systems internat j robust nonlinear control 15 2005 459 472 p h a ngoc n k son stability radii of positive linear functional differential equations under multi perturbations siam j control optim 43 2005 2278 2295 finally we give two examples to illustrate the obtained results

on sufficient conditions for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems the specific notion under consideration is asymptotic stability independent of delay as an attempt to achieve a compromise between the complexity and tightness of various stability tests we present a number of sufficient stability conditions which improve several previously available sufficient conditions and which are also much easier to verify than the known necessary and sufficient conditions

delay independent stability test for systems with multiple time delays delay independent stability dis of a general class of linear time invariant lti multiple time delay system mtds is investigated in the entire delay parameter space stability of such systems may be lost only if their spectrum lies on the imaginary axis for some delays we build an analytical approach that requires the inspection of the roots of finite number of single variable polynomials in order to detect if the spectrum ever lies on the imaginary axis for some delays excluding infinite delays the approach enables to test the necessary and sufficient conditions of dis of lti mtds technically known as weak dis as well as the robust stability of single delay systems against all variations in delay ratios the proposed approach which does not require any parameter sweeping and graphical display becomes possible by establishing a link between the infinite spectrum and algebraic geometry case studies are provided to show the effectiveness of the approach

easily testable necessary and sufficient algebraic criteria for delay independent stability of a class of neutral differential systems this paper analyzes the eigenvalue distribution of neutral differential systems and the corresponding difference systems and establishes the relationship between the eigenvalue distribution and delay independent stability of neutral differential systems by using the complete discrimination system for polynomials easily testable necessary and sufficient algebraic criteria for delay independent stability of a class of neutral differential systems are established the algebraic criteria generalize and unify the relevant results in the literature moreover the maximal delay bound guaranteeing stability can be determined if the systems are not delay independent stable some numerical examples are provided to illustrate the effectiveness of our results c 2007 elsevier b v all rights reserved

asymptotic stability of neutral differential systems with many delays we are concerned with delay independent asymptotic stability of linear system of neutral differential equations we first establish a sufficient and necessary condition for the system to be delay independently asymptotically stable and then give some equivalent stability conditions this paper improves many recent results on the asymptotic stability in the literature one example is given to show that the sufficient and necessary condition is easy to verify

parallel two step w methods with peer variables a new class of methods for the solution of stiff initial value problems is introduced that is parallel by design it has a two step character and propagates s different peer solution variables with essentially identical characteristics from step to step the main work lies in the solution of s independent linear stage equations which may be solved in parallel convergence of order s 1 and stability for general stepsize sequences are proved conditions for order s and stronger stability criteria are addressed as well promising methods up to order 7 are identified by numerical tests with some widely used stiff test problems some of these are competitive with existing software even in sequential computations

parameter dependent lyapunov functions for robust stability of time varying linear systems under point delays abstract this paper investigates the stabilization dependent on the delays of in general time varying linear systems with multiple constant point time delays the matrices describing the state space dynamics are parameterized by in general time varying function matrices governed by coefficient functions in compact sets the closed loop sufficiency type stability conditions are obtained from lyapunov s stability theory by constructing parameter dependent candidates which satisfy in the most general case a riccati matrix differential inequality

technical communique on stability of second order quasi polynomials with a single delay in this note the stability of a second order quasi polynomial with a single delay is studied although there is a vast literature on this problem most available solutions are limited to some particular cases moreover some published results on this subject appear to contain imprecise or even wrong conditions the purpose of this note is to show that by accurate application of known theories a complete explicit characterization of stability regions can be derived in a most general case as a byproduct of the proposed analysis we show that in the high order case the quasi polynomial is delay independent unstable whenever its delay free version has an odd number of unstable roots or equivalently a negative static gain

stability conditions for linear retarded functional differential equations abstract the purpose of this note is to study the exponential stability for the linear retarded functional differential equation x t 1 0 d x t r where the delay function r 0 is continuous and is of bounded variation on the interval 1 0 it is shown that the spectral limit function for the equation above has a continuous dependence on the pair r the set of all functions of bounded variation for which the equation above is exponentially stable for every delay function r the so called region of stability globally in the delays is a cone therefore for a fixed r the set of all which make our equation exponentially stable that is the region of stability for the delay function r contains a cone a discussion of the characterization of these regions of stability as well as of the largest cone contained in each region of stability for a fixed delay function r is given some remarks are made with respect to a similar question for the equation x t ax t 1 0 d x t r where a is a real n by n matrix is bounded variation on 1 0 and r as before several examples illustrate the results obtained

frequency sweeping tests for stability independent of delay in this paper we study the stability properties of linear time invariant delay systems given in a state space form we consider specifically the notion of asymptotic stability independent of delay systems with both commensurate and noncommensurate delays are investigated we present for each class of systems a necessary and sufficient condition in terms of structured singular values and further we demonstrate how these conditions may be extended to study stability independent of delay for uncertain systems our results consist of several frequency sweeping tests that can be systematically implemented and that should complement the previous work

vibrational control of linear time lag systems with arbitrarily large but bounded delays it is shown that vibrational stabilization can be effective for linear systems with large bounded delays theorems are given that define the procedures for the search of the stabilizing vibrations robust oscillatory stabilization insensitive to the delay size is also shown to take place for some classes of systems

on controllability and observability of time delay systems this paper deals with controllability and observability properties of time delay systems in the state space r n times l p in particular we prove the equivalence of spectral controllability and approximate null controllability moreover it is shown that the necessary condition for approximate f controllability obtained recently by manitius is also sufficient and a verifiable and matrix type criterion for f controllability is derived for systems with commensurate delays finally we introduce the dual observability notion of approximate controllability and prove that the control system is exactly null controllable if and only if the transposed delay system tis continuously finally observable

doubly quasi consistent fixed stepsize numerical integration of stiff ordinary differential equations with implicit two step peer methods abstract the problem of accurate and efficient numerical integration of ordinary differential equations odes is a key issue of computation science which has a valued practical impact in various topics of research in this respect effective global error estimation and control strategies are of particular theoretical and practical significance they allow many applied dynamic systems to be treated numerically for user supplied accuracy conditions in automatic mode the property of double quasi consistency plays an outstanding role in the mentioned topic because the global or true error of a doubly quasi consistent method is asymptotically equal to its local error therefore this entails quite a nontrivial implication that the true error of numerical integration can be cheaply evaluated and regulated within a single solution run the latter was considered to be impossible for decades the property of double quasi consistency goes back to 2009 when kulikov studied it in the first time but failed to find doubly quasi consistent numerical methods among nordsieck formulas later on kulikov and weiner proved the existence of doubly quasi consistent numerical schemes among superconvergent explicit two step parallel peer methods and examined their practical efficiency in comparison to explicit matlab ode solvers in 2010 the focus of the present research is on accurate numerical integration formulas for treating stiff odes which often arise in practice and for which explicit methods are shown to be ineffective here we make the first step towards an accurate and efficient numerical solution of stiff odes and prove existence of implicit doubly quasi consistent formulas we fulfill our investigation of double quasi consistency within the family of fixed stepsize implicit two step peer schemes and construct two methods of convergence orders 3 and 4 which possess excellent stability properties our theoretical results are confirmed with numerical integration of both nonstiff and stiff test problems in this paper

combination of sign inverting and delay scheduling control concepts for multiple delay dynamics abstract in this paper we treat a novel combination of two controversial control concepts sign inverting control sic and delay scheduling ds for systems with multiple independent and large delays sic suggests the inversion of the control polarity and ds prolongs the existing delays the combined scheme functions with a single requirement that the union of the control schemes provides a larger stable operating region than each of its components does in the domain of the delays the critical knowledge that is needed to execute such a unified control strategy is the crisp description of these stable regions for each time delayed control scheme this need can be fulfilled using the recent cluster treatment of characteristic roots ctcr paradigm which establishes the stable regions exhaustively and non conservatively the resulting options in selecting operating modes render more robust control performance against much larger delay variations than each of the schemes we also investigate the disturbance rejection speeds within these enlarged stable regions in order to improve the control performance even further such multi faceted paradoxical combinations provide previously unexplored tools to control designers experimental validations of these novel concepts are presented on a simple setup with a single axis manipulator

a new delay dependent criterion for neural systems with multiple delays in this paper the problem of the stability analysis for neutral systems with multiple delays is investigated using lyapunov method we present a new delay dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities lmis which can be easily solved by various convex optimization algorithms a numerical example is given to illustrate the effectiveness of the proposed method

algebraic criteria for stability of linear neutral systems with a single delay abstract the stability of linear neutral delay differential systems with a single delay via routh hurwitz and schur cohn criteria is investigated some algebraic criteria for delay independent stability are presented these criteria may complement those reported in the literature finally two examples illustrate the criteria

stability of linear neutral time delay systems exact conditions via matrix pencil solutions in this note we study the stability properties of linear neutral delay systems we consider systems described by both neutral differential difference and state space equations and we seek to determine the delay margin of such systems that is the largest range of delay values for which a neutral delay system may preserve its stability in both cases we show that the delay margin can be found by computing the eigenvalues and generalized eigenvalues of certain constant matrices which can be executed efficiently and with high precision the results extend previously known work on retarded systems and demonstrate that similar stability tests exist for neutral systems in particular the tests require essentially the same amount of computation required for retarded systems

constrained approximate controllability in the paper constrained approximate controllability for linear dynamical systems described by abstract differential equations with unbounded control operator is considered using methods of spectral analysis for linear self adjoint operators and general constrained controllability results given by son 1990 necessary and sufficient conditions of the constrained approximate controllability for the piecewise polynomial controls with values in a given cone are formulated and proved moreover as illustrative examples constrained approximate boundary controllability of one dimensional distributed parameter dynamical systems described by partial differential equations of parabolic type with dirichlet and neumann boundary conditions are investigated the constrained controllability conditions obtained in the paper represent an extension of the unconstrained controllability results given by glothin 1974 and klamka 1991

stability analysis for delay differential equations with multidelays and numerical examples in this paper we are concerned with the asymptotic stability of the delay differential equation x t a 0 x t a k x t k where a 0 a k c d d are constant complex matrices and x t k x 1 t k1 x 2 t k2 x d t kd t kl 0 stand for n x d constant delays k 1 n i 1 d we obtain two criteria for stability through the evaluation of a harmonic function on the boundary of a certain region we also get similar results for the neutral delay differential equation x t lx t m i x t i n j x t j where l m i and nj e c d d are constant complex matrices and i j 0 stands for constant delays i 1 m j 1 n numerical examples on various circumstances are shown to check our results which are more general than those already reported

on stability crossing curves for general systems with two delays for the general linear scalar time delay systems of arbitrary order with two delays this article provides a detailed study on the stability crossing curves consisting of all the delays such that the characteristic quasipolynomial has at least one imaginary zero the crossing set consisting of all the frequencies corresponding to all the points in the stability crossing curves are expressed in terms of simple inequality constraints and can be easily identified from the gain response curves of the coefficient transfer functions of the delay terms this crossing set forms a finite number of intervals of finite length the corresponding stability crossing curves form a series of smooth curves except at the points corresponding to multiple zeros and a number of other degenerate cases these curves may be closed curves open ended curves and spiral like curves oriented horizontally vertically or diagonally the category of curves are determined by which constraints are violated at the two ends of the corresponding intervals of the crossing set the directions in which the zeros cross the imaginary axis are explicitly expressed an algorithm may be devised to calculate the maximum delay deviation without changing the number of right half plane zeros of the characteristic quasipolynomial and preservation of stability as a special case

brief a practical method for analyzing the stability of neutral type lti time delayed systems a new paradigm is presented for assessing the stability posture of a general class of linear time invariant neutral time delayed systems lti ntds the ensuing method which we name the direct method dm offers several unique features it returns the number of unstable characteristic roots of the system in an explicit and non sequentially evaluated function of time delay t consequently the direct method creates exclusively all possible stability intervals of t furthermore it is shown that this method inherently verifies a widely accepted necessary condition for the t stabilizability of a lti ntds in the core of the dm lie a root clustering paradigm and the strength of rekasius transformation in mapping a transcendental characteristic equation into an equivalent rational polynomial in addition we also demonstrate by an example that dm can tackle systems with unstable starting posture for t 0 only to stabilize for higher values of delay which is rather unique in the literature

connected components of global semianalytic subsets of 2 dimensional analytic manifolds let m be a connected paracompact real analytic manifold and s a semi analytic subset the following results are proved 1 if dim m 2 and s is globally semianalytic then every connected component of s is again globally semianalytic 2 s is globally semianalytic if and only if its boundary bd s is globally semianalytic

comments on robust tracking control for rigid robotic manipulators in the original paper by m zhihong and m palaniswami ibid vol 39 p 154 9 1994 a robust tracking control using a nominal feedback controller and a variable structure compensator for a rigid robotic manipulator with uncertain dynamics was presented it is assumed that the model uncertainty is bounded the author claims that this assumption is not necessarily correct and that the results obtained are therefore untenable

null controllability in function space of nonlinear retarded systems with limited control abstract the question of controlling both linear and nonlinear retarded functional differential equations from an initial function in a sobolev space w 2 1 to zero in w 2 1 is considered when the controls are square integrable with values in a compact subset u of m dimensional euclidean space with zero in its interior sufficient computable criteria for null controllability are given

lmi characterization of the strong delay independent stability of linear delay systems via quadratic lyapunov krasovskii functionals abstract in this note is proposed an analogue for linear delay systems of the characterization of asymptotic stability of the rational systems by the solvability of associated lyapunov equation it is shown that strong delay independent stability of delay system is equivalent to the feasibility of certain linear matrix inequality lmi related to quadratic lyapunov krasovskii functionals

finite spectrum assignment problem for systems with multiple commensurate delays in state variables abstract this paper is concerned with the finite spectrum assignment problem for systems with multiple commensurate delays in state variables the necessary and sufficient condition for finite spectrum assignability is clarified a systematic design procedure which can straightforwardly yield a control law is presented

efficient a stable peer two step methods abstract a stability is a desirable property for stiff integrators however it may be difficult to prove or implement in an automated search for multi stage multi step methods requiring eigenvalue computations on complex sets of parameters in this paper we apply a purely algebraic criterion for a stability of peer two step methods requiring only the solution of algebraic equations and combine it with a new criterion for zero stability of peer methods on general time grids both criteria lead to formulations solvable by standard numerical methods and are easily verifiable by anyone if sufficient data are provided several 4 stage methods of order 3 and 4 are constructed and compared with existing methods on a few standard test problems

stability of functional partial differential equations on etablit des conditions necessaires et suffisantes pour qu une classe d equations aux derivees partielles fonctionnelles soit asymptotiquement stable pour toutes les valeurs des retards

neurocomputing with time delay analysis for solving convex quadratic programming problems this paper presents a neural network computational scheme with time delay consideration for solving convex quadratic programming problems based on some known results a delay margin is explicitly determined for the stability of the neural dynamics under which the states of the neural network does not oscillate the configuration of the proposed neural network is provided operational characteristics of the neural network are demonstrated via numerical examples

null controllability of nonlinear infinite delay systems with distributed delays in control abstract sufficient conditions for the null controllability of nonlinear infinite delay systems with distributed delays in the control are developed namely if the uncontrolled system is uniformly asymptotically stable and if the linear control system is proper then conditions are obtained that imply the nonlinear infinite delay system is null controllable

a convex approach to robust stability for linear systems with uncertain scalar parameters in this paper robust stability for linear systems with several uncertain complex and or real scalar parameters is studied a countable family of conditions sufficient for robust stability is given in terms of solvability of some simple linear matrix inequalities lmis these conditions are of increasing precision and it is shown conversely that robust stability implies solvability of these lmis from a certain rank and beyond this result constitutes an extension of the characterization by solvability of lyapunov inequality of the asymptotic stability for usual linear systems it is based on the search of parameter dependent quadratic lyapunov functions polynomial of increasing degree in the parameters

stability of linear neutral systems with multiple delays boundary criteria the stability of linear neutral delay differential systems with multiple delays is investigated the delay dependent stability criteria are presented through the evaluation of the corresponding harmonic functions on the boundary of a certain half circular region and such criteria are extensions of some results in literature an example is given to illustrate the stability criteria

stability and bifurcation analysis for a delayed lotka volterra predator prey system the present paper deals with a delayed lotka volterra predator prey system by linearizing the equations and by analyzing the locations on the complex plane of the roots of the characteristic equation we find the necessary conditions that the parameters should verify in order to have the oscillations in the system in addition the normal form of the hopf bifurcation arising in the system is determined to investigate the direction and the stability of periodic solutions bifurcating from these hopf bifurcations to verify the obtained conditions a special numerical example is also included

some simple criteria for stability of neutral delay differential systems this paper deals with the stability of linear neutral delay differential systems some simple criteria for delay independent stability of this class of problems which are described by evaluating the measure and norm of corresponding matrices are presented the main results proposed in this study are sharper than those reported in the literature

brief paper a discrete delay decomposition approach to stability of linear retarded and neutral systems this paper is concerned with stability of linear time delay systems of both retarded and neutral types by using some new simple quadratic lyapunov krasovskii functionals these lyapunov krasovskii functionals consist of two parts one part comes from some existing lyapunov krasovskii functionals employed in han q l 2005a absolute stability of time delay systems with sector bounded nonlinearity automatica 41 2171 2176 han q l 2005b a new delay dependent stability criterion for linear neutral systems with norm bounded uncertainties in all system matrices international journal of systems science 36 469 475 the other part is constructed by uniformly dividing the discrete delay interval into multiple segments and choosing proper functionals with different weighted matrices corresponding to different segments then using these new simple quadratic lyapunov krasovskii functionals some new discrete delay dependent stability criteria are derived for both retarded systems and neutral systems it is shown that these criteria for retarded systems and neutral systems are always less conservative than the ones in han 2005a and han 2005b cited above respectively numerical examples also show that the results obtained in this paper significantly improve the estimate of the discrete delay limit for stability over some other existing results

stability in linear delay equations abstract for linear autonomous differential difference equations of retarded or neutral type necessary and sufficient conditions are given for the zero solution to be stable hyperbolic for all values of the delays

optimal sign inverting control for time delayed systems a concept study with experiments an intriguing control logic sign inverting control sic is considered for control systems with delayed feedback it starts with a nominal control law formulated for non delayed case and simply inverts the sign of the control gains for some surprising benefits when used with the delays this operation sounds paradoxical as the sign inversion potentially harms the stability of the non delayed dynamics however sic with large delays may yield some complementary benefits to the nominal control logic from delay robustness perspective the main question we address in this paper is how to select the nominal control law so that such a contribution can be a feasible b optimal in some sense a structured methodology is proposed to achieve this starting with a linear quadratic regulator based controller a single scaling factor on the corresponding control gains is used for one dimensional optimisation experimental validation of the concept of this optimal sic procedure is also reported on a single axis

polynomial two parameter eigenvalue problems and matrix pencil methods for stability of delay differential equations several recent methods used to analyze asymptotic stability of delay differential equations ddes involve determining the eigenvalues of a matrix a matrix pencil or a matrix polynomial constructed by kronecker products despite some similarities between the different types of these so called matrix pencil methods the general ideas used as well as the proofs differ considerably moreover the available theory hardly reveals the relations between the different methods in this work a different derivation of various matrix pencil methods is presented using a unifying framework of a new type of eigenvalue problem the polynomial two parameter eigenvalue problem of which the quadratic two parameter eigenvalue problem is a special case this framework makes it possible to establish relations between various seemingly different methods and provides further insight in the theory of matrix pencil methods we also recognize a few new matrix pencil variants to determine dde stability finally the recognition of the new types of eigenvalue problem opens a door to efficient computation of dde stability

stability of non linear delay systems delay independent small gain theorem and frequency domain interpretation of the lyapunov krasovskii method the purpose of this note is to study the relationship between a certain stability criterion for non linear delay systems obtained via the lyapunov krasovskii method and a delay independent version of the small gain theorem we show that contrary to the delay free case in which the kalman yakubovich popov lemma ensures the equivalence of the two approaches the first method assumes stronger hypothesis than the second one however numerical verification of the former is in general np hard whereas the latter leads to linear matrix inequalities the difference between the two approaches is precisely stated and among other benefits this permits to exhibit classes of problems for which the lyapunov krasovskii method is not conservative

robust stability of neutral delay differential systems abstract in this paper we consider the robust stability problem for a neutral delay differential system where the characteristic equations involve a polytope of quasi polynomials first the edge theorem is developed for robust stability analysis of a polytope of neutral quasi polynomials based on the edge theorem the robust stability of neutral systems with commensurate delays will be reduced to the checking of the h hurwitz stability of all the edges of a polytope of quasi polynomials and the schur stability of all the edges of the subpolytope of neutral terms then an effective graphical test is made for checking the robust stability of a polytope of neutral quasi polynomials finally we show that checking vertic quasi polynomials is sufficient for the asymptotic stability of the entire family of first order quasi polynomials of the neutral type

on approximate and exact null controllability of delay systems approximate and exact null controllability of linear delay equations with a constant delay and scalar control are shown to be equivalent the main tool is a recent result on equivalence between spectral controllability and finite spectrum assignability

controllability of semilinear impulsive nonautonomous systems in this paper we apply rothe s type fixed point theorem to prove the controllability of the following semilinear impulsive nonautonomous systems of differential equations where a t b t are continuous matrices of dimension n n and n m respectively the control function u belongs to and k 1 2 3 p under additional conditions we prove the following statement if the linear is controllable on 0 then the semilinear impulsive system is also controllable on 0 moreover we could exhibit a control steering the nonlinear system from an initial state z0 to a final state z1 at time 0

a comparison of amf and krylov methods in matlab for large stiff ode systems for the efficient solution of large stiff systems resulting from semidiscretization of multi dimensional partial differential equations two methods using approximate matrix factorizations amf are discussed in extensive numerical tests of reaction diffusion type implemented in matlab they are compared with integration methods using krylov techniques for solving the linear systems or to approximate exponential matrices times a vector the results show that for low and medium accuracy requirements amf methods are superior for stringent tolerances peer methods with krylov are more efficient

punctuated evolution due to delayed carrying capacity a new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems a detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a population in the four main regimes dominated respectively by i gain and competition ii gain and cooperation iii loss and competition and iv loss and cooperation our delay equation may exhibit bistability in some parameter range as well as a rich set of regimes including monotonic decay to zero smooth exponential growth punctuated unlimited growth punctuated growth or alternation to a stationary level oscillatory approach to a stationary level sustainable oscillations finite time singularities as well as finite time death

stability of the radau ia and lobatto iiic methods for delay differential equations recently we have proved that the radau ia and lobatto iiic methods are p stable i e they have an analogous stability property to a stability with respect to scalar delay differential equations ddes in this paper we study stability of those methods applied to multidimensional ddes we show that they have a similar property to p stability with respect to multidimensional equations which satisfy certain conditions for asymptotic stability of the zero solutions the conditions are closely related to stability criteria for ddes considered in systems theory

critical effects of the polarity change in delayed states within an lti dynamics with multiple delays this note concerns the polarity inversion of the delayed states in linear time invariant multiple time delay systems lti mtds to start with for such systems the assessment of asymptotic stability is complicated due to the infinite dimensionality introduced by the delays it is shown that the mentioned polarity inversion influences the respective delay dependent stability maps in interesting ways there are some intriguing invariant characteristics and correspondences between the original and inverted systems which form the primary contributions of this note these findings are shown to be the enabling features to relate the stability maps of the two systems the cluster treatment of characteristic roots ctcr paradigm is utilized to identify these features an example case study is provided to illustrate the claims

stability of stochastic systems with uncertain time delays abstract for linear delay systems with bilinear noise sufficient conditions are given for the global asymptotic stochastic stability independent of the length of the delay s for linear stochastic noise terms sufficient conditions for the existence of an invariant distribution for all values of the delay are given it is shown that the gaussian distribution is the unique invariant distribution the covariance and correlation matrix function of the resulting stationary process are completely characterized by a lyapunov type equation all these sufficient conditions are obtained in the form of the existence of some positive definite matrices satisfying certain riccati type equations

stability of retarded dynamical systems a lyapunov function approach four new stability theorems for general classes of retarded dynamical systems are established by using the lyapunov function approach in this paper a new technique is proposed for estimating the derivative of the lyapunov function along the solution of a system at some specific instant it is remarked that the stability conditions obtained by the established stability theorems together with the proposed technique are less conservative than those obtained by the existing razumikhin type theorems and techniques in the literature four illustrative examples and two corollaries for systems with a single time varying delay or multiple time varying delays are given to show the applications of the established stability theorems and the proposed technique

generalization of integral constraints on sensitivity to time delay systems extends results on integral constraints to time delay systems key technical issues in this extension include properties of nonminimum phase zeros the convergence of blaschke products and the poisson integral the results have implications for scalar and multivariable control system design as well as in filtering problems

stability criteria for linear time invariant systems with multiple delays two new asymptotic stability criteria for linear time invariant systems with multiple delays are established by using a quadratic inequality lemma together with frequency domain techniques one criterion is for delay dependent stability and another is for delay independent asymptotic stability each of them has only one tuning parameter matrix p 0 as the lyapunov type stability criteria for the corresponding linear time invariant systems without delays do both of the established stability criteria are given in the form of lmi problems and hence are very easy to use in applications in addition it is remarked that the established delay independent asymptotic stability criterion with one tuning parameter matrix p 0 improves and simplifies the existing criterion with more than one tuning parameter matrix in the literature

explicit two step peer methods we present a new class of explicit two step peer methods for the solution of nonstiff differential systems a construction principle for methods of order p s s the number of stages with optimal zero stability is given two methods of order p 6 found by numerical search are tested in matlab on several representative nonstiff problems the comparison with ode45 confirms the high potential of the new class of methods

delay independent stability criteria for a class of retarded dynamical systems with two delays in this paper sufficient and necessary delay independent stability criteria are given for a class of retarded dynamical systems with two discrete time delays and parameters the delay independent stability problem of the system is discussed in terms of the stability of the characteristic function which is determined by checking the existence of real roots for some polynomials the criteria are also illustrated by examples

lyapunov equation for the stability of linear delay systems of retarded and neutral type in this note the delay independent stability of delay systems is studied it is shown that the strong delay independent stability is equivalent to the feasibility of certain linear matrix inequality lmi that is to the existence of a quadratic lyapunov krasovskii functional independent of the nonnegative value of the delay this constitutes the analogue of some well known properties of finite dimensional systems this result is then applied to study delay independent stability of systems with polytopic uncertainties

stability regions for linear equations with piecewise continuous delay in this article stability results are obtained for equations of the form x t ax t nj 0 ajx t rj r where a and aj are real constants r 0 and the symbol t r is the function with value n on the interval nr nr r r n 0 1 2 for the first order equation x t ax t a0 x t r the exact region of stability in the a a0 parameter plane is found the region of stability for all delays r is found and compared with that for the analogous differential difference equation

robust stabilization of a class of polytopic linear time varying continuous systems under point delays and saturating controls abstract this paper investigates the stabilization dependent on the delays of in general time varying linear systems with multiple constant point time delays under saturating state feedback controls the matrices describing the state space dynamics and control belong to polytopes also the controller gain matrix is characterized as belonging to another polytope whose vertices are computed from the knowledge of a closed bounded ball containing a set of values of the state norm and also the component wise saturating gains and saturation parameterizations this knowledge defines the polytope vertices through scaling diagonal matrices being associated with the various operation modes in the linear and saturated zones of each input component in these conditions the resulting closed loop system is of polytopic nature whose whole number of vertices is at most equal to the product of both numbers of vertices of the above two polytopes characterizing the plant parameterization and the saturation the closed loop sufficiency type stability conditions are obtained from lyapunov s stability theory by constructing candidates for each vertex of the polytopic closed loop system each satisfying in the most general case a riccati matrix differential inequality some conditions guaranteeing the stability conditions are obtained from a general kalman yakubovitch popov kyp lemma and some weaker stability conditions are also obtained for the time invariant case from a set of linear matrix inequalities associated with the set of vertices

on the irreducible components of globally defined semianalytic sets in this work we present the concept of amenablec semianalytic subset of a real analytic manifold m and study the main properties of this type of sets amenable c semianalytic sets can be understood as globally defined semianalytic sets with a neat behavior with respect to zariski closure this fact allows us to develop a natural definition of irreducibility and the corresponding theory of irreducible components for amenable c semianalytic sets these concepts generalize the parallel ones for complex algebraic and analytic sets c analytic sets nash sets and semialgebraic sets