canonical forms for time delay systems polynomial transformations are considered for linear systems with time delays a technique for state reduction is given as well as schemes for obtaining other useful canonical forms the results are achieved using a combination of module theoretic ideas polynomial ring and functional analysis

delay independent stability analysis of linear time delay systems based on frequency discretization this paper studies strong delay independent stability of linear time invariant systems it is known that delay independent stability of time delay systems is equivalent to some frequency dependent linear matrix inequalities to reduce or eliminate conservatism of stability criteria the frequency domain is discretized into several sub intervals and piecewise constant lyapunov matrices are employed to analyze the frequency dependent stability condition applying the generalized kalman yakubovich popov lemma new necessary and sufficient criteria are then obtained for strong delay independent stability of systems with a single delay the effectiveness of the proposed method is illustrated by a numerical example

extended kronecker summation for cluster treatment of lti systems with multiple delays a new procedure is presented for determining the kernel and the offspring hypersurfaces for general linear time invariant lti dynamics with multiple delays these hypersurfaces as they have very recently been introduced in a concept paper r sipahi and n olgac automatica 41 2005 pp 1413 1422 form the basis of the overriding paradigm which is called the cluster treatment of characteristic roots ctcr in fact these two sets of hypersurfaces exhaustively represent the locations in the domain of the delays where the system possesses at least one pair of imaginary characteristic roots to determine the kernel and offspring we use the extraordinary features of the extended kronecker summation operation in this paper the end result is that the infinite dimensional problem reduces to a finite dimensional one and preferably into an eigenvalue problem following the procedure described in this paper we are able to shorten the computational time considerably in determining these hypersurfaces we demonstrate these concepts via some example case studies one of the examples treats a 3 delay system for this case another interesting perspective called the building block is also utilized to display the kernel in three dimensional space in the domain of spectral delays

local spectral properties of generators of c0 groups and bernstein type inequalities let t t t t r be a c0 group on a complex banach space x dominated by a weight function t 1 t 0 1 and let a be its generator with domain d a among other things it is shown that if the operator a has compact local spectrum at x x then x d a and there exist double sequences of real numbers cn n z and tn n z such that ax n zcnt tn x where n z cn ra x ra x is the local spectral radius of a at x as an application some inequalities of bernstein type in lp spaces are given

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

regulation of split linear systems over rings coefficient assignment and observers a theory of regulators is developed for finite free split linear systems over a commutative ring k this is achieved by developing a theory of coefficient assignment and observers it is shown that the problem of coefficient assignment can be solved for reachable systems by using dynamic state feedback for strongly observable systems it is shown that observers with arbitrary dynamics can be constructed internal stability of observer and state feedback configuration is considered explicitly some examples are given to illustrate these techniques

numerical simulation by cubic polynomial interpolation for unsteady incompressible viscous flow tuncer i h ekaterinaris j a and platzer m r a viscous inviscid interaction method for 2 d unsteady compressible flows aiaa paper 93 3019 june 1993 tuncer i h ekaterinaris j a and platzer m e a novel viscousinviscid interaction method with inviscid wake modeling aiaa paper 94 0178 jan 1994 ekaterinaris j a cricelli a and platzer m e a zonal method for unsteady viscous compressible airfoil flows journal of fluids and structures vol 8 jan 1994 pp 107 123 mcalister k w pucci s l mccroskey w j and carr l w an experimental study of dynamic stall on advanced airfoil sections pressure and force data vol 2 nasa tm 84245 sept 1982

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

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

transfer matrices realization and control of continuous time linear time varying systems via polynomial fractional representations abstract an algebraic theory of transfer matrices fractional representations and control for linear continuous time time varying systems based on the realization theory of input output maps is given it is shown for the first time that the realization of such systems specified by an abstract input output map as a module homomorphism over noncommutative polynomial rings can be established using an abstract kalman input output map defined over a ring of skew polynomials with time varying coefficients it is shown that in fact transfer matrices can be defined as formal power

differential inequalities in lp spaces abstract in this article we present inequalities related to the continuous representations of one parameter groups as an application we obtain some differential inequalities of bernstein type in l p spaces we define the spectrum f of f l p r 1 p as f k l q r sp b f k 1 p 1 q 1 where sp b is the beurling spectrum it is shown that if r satisfies the condition 0 then f l p r and f p 2 sin f f p where sup f some related problems are also discussed

finite spectrum assignment and observer for multivariable systems with commensurate delays this paper is concerned with control of multivariable systems with commensurate delays the purpose of this paper is to enlarge the class of finite spectrum assignable systems to spectrally controllable multivariable systems with commensurate delays by overcoming an infinite number of eigenvalues which are contained in the system and make control very complex it is proved that if the system is spectrally controllable there is a delayed feedback matrix such that the closed loop system is spectrally controllable through a single input combining this result with previous ones about single input systems it is verified that spectral controllability is equivalent to finite spectrum assignability for multivariable systems with commensurate delays an observer for the system with delayed outputs is presented by using these results the multivariable system can be regulated as desired without preliminary knowledge of open loop eigenvalues and a stability test of transcendental functions whenever the system is spectrally controllable and spectrally observable

linear systems with commensurate time delays stability and stabilization independent of delay notions of exponential stability independent of delay and stabilizability independent of delay are developed for the class of delay differential systems of the retarded type with commensurate time delays various criteria for exponential stability independent of delay with a given order are specified in terms of matrices whose entries are functions of a single real parameter and polynomials in one variable whose coefficients are functions of a single real parameter sufficient conditions and a necessary condition based on local stabilizability are given for stabilizability independent of delay using state feedback with commensurate time delays constructive methods for determining a stabilizing feedback are also presented the last part of the paper deals with a standard type of observer and regulator with the requirement that the closed loop system be stable independent of delay

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

finite difference method to solve incompressible fluid flow abstract a method to solve incompressible fluid flow is proposed the method uses primitive variables velocity and pressure of the fluid and introduces an idea that the discretized navier stokes equations have an invariant implicitly in each iteration at any time step as numerical examples transient two dimensional poiseuille flow and steady flow past a backward facing step are calculated it is shown that the method needs fewer iterations than the mac and the smac methods and the accuracy of the present method is guaranteed by comparison with the analytic solution and the existing methods

assessment of pressure strain models in predicting compressible turbulent ramp flows the study presented has the objective of isolating the effect of the pressure strain correlation term in the prediction of a compression ramp flow where shock boundary layer interaction had a significant effect on turbulence amplification variable density extensions of three incompressible pressure strain models were tested to assess their performance the study showed that all of the models had difficulty in predicting the rapid response of the turbulence to the presence of the shock and showed improper distribution among stress components these results imply that the variable density extensions of incompressible pressure strain correlation models are insufficient in themselves to properly account for the effects of turbulence amplification through a shock 14 refs

stabilization of linear distributed control systems with unbounded delay in this paper we study the asymptotic stabilization of linear distributed parameter control systems with unbounded delay assuming that the semigroup of operators associated with the uncontrolled and nondelayed equation is compact and that the phase space is a uniform fading memory space we characterize those systems that can be stabilized using a feedback control as consequence we conclude that every system of this type is stabilizable with an appropriated finite dimensional control

asymptotic tracking for 2 d and delay differential systems abstract a method for asymptotic tracking in 2 d systems is presented and is applied to discrete 2 d systems and delay differential systems the method consists of solving two linear equations in 2 d polynomials solvability conditions are derived and the questions of stability causality and properness are discussed

control of linear systems with fixed noncommensurate point delays the first solution is given to the fundamental open problem of stabilizability and detectability necessary sufficient conditions for internal stabilization by feedback of retarded and a large class of neutral delay differential systems with several fixed noncommensurate point delays using causal compensators observers and state feedback or dynamic output feedback which are also the same type of neutral or retarded delay differential systems with fixed point delays only our results are rank conditions on the system matrices zi f g and zif t h t evaluated at points in the complex plane and are the weakest possible generally applicable sufficient such rank conditions for stabilization of neutral systems in the light of what is known on the stability of such systems these conditions are necessary for most practical purposes the class of systems we consider includes all retarded delay differential systems with noncommensurate fixed point delays in the case of retarded systems these rank conditions are necessary and sufficient conditions for stabilization via compensators which are causal retarded delay differential systems with fixed point delays only these constitute the first full solution of these previously unsolved problems of stabilizability and detectability which together are necessary and sufficient conditions for internal stabilization by feedback for delay differential systems even in the retarded single fixed point delay case an application of our results to a problem of practical importance in control of linear systems with no delays provides a stabilization criterion interesting in itself

on the stabilization of linear neutral delay differential systems feedback feedforward stabilizers for linear neutral delay differential systems are proposed explicit conditions under which an adequate compensator yields a desired closed loop characteristic polynomial are given the relation between realizability properties such as causality of the compensator and structural properties of the system are also described an example is provided to illustrate the design technique

stabilization of time delay systems using finite dimensional compensators for linear time invariant systems with one or more noncommensurate time delays necessary and sufficient conditions are given for the existence of a finite dimensional stabilizing feedback compensator in particular it is shown that a stabilizable time delay system can always be stabilized using a finite dimensional compensator the problem of explicitly constructing finite dimensional stabilizing compensators is also considered

observability and related structural results for linear hereditary systems new results on the theory of observability and deterministic observers for linear time invariant systems with delays are presented the results have been established only for the case of point delays which are commensurable however most of the results can be generalized to the situation with distributed delays and to the ease with non commensurate delays

dynamic compensation of siso systems over a principal ideal domain the polynomial equation approach and some concepts from algebraic geometry are employed in compensator design for a class of linear single input single output siso systems with coefficients from a principal ideal domain pid

feedback stabilization of linear autonomous time lag systems a stabilization theory which employs well established finite dimensional control system tools is developed for the stabilization of linear autonomous time lag systems the main ideas include 1 a set whose elements are matrices each of which is a left zero of the system characteristic quasi polynomial matrix and 2 a linear transformation which reduces the delay system to a delay free system whose state matrix is a direct sum of n elements of the matrix set where n is some positive integer from the definition of this matrix set it is shown that each of its elements inherits its spectrum from that of the delay system so that by design the system unstable poles may be embedded in the spectrum of the delay free system under the assumption of spectral stabilizability it is then shown how to obtain a stabilizing feedback control law on the basis of the delay free system numerical examples are presented to confirm the theory

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

on matrix fraction representations for linear systems over commutative rings this paper deals with the problem of existence of polynomial matrix fraction representations for transfer matrices of linear systems over rings as well as the related realization theory these representations are then used in establishing new results for various classes of systems including split systems the relevance of these results to the regulation of various nonclassical classes of linear systems for example delay differential systems two dimensional systems etc is also discussed

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

pole placement for linear systems over bezout domains the problem of pole placement for linear systems over rings is considered for a class of rings our results show that one can construct reduced order dynamic output feedback compensators for pole placement our results also provide an alternative proof of some previously known results on the problem of pole placement by state feedback for a class of reachable pairs f g over bezout domains

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

on necessary and sufficient conditions for regulation of linear systems over rings necessary and sufficient conditions are given for regulation of linear systems over rings using observers and causal dynamic state feedback systems with the polynomial fractional representation property the results are then used to obtain stabilizability conditions for systems over integers delay differential systems systems over polynomial rings and to obtain conditions to make a 2 d system nonrecursive

a lyapunov theory for linear time delay systems some relationships between a lyapunov based stability test and linear control system models with time delays are explored the main result is a generalization of the result that if a b is a reachable pair of matrices then square a is a stability matrix if and only if there is a positive definite matrix k such that ak ka bb

delay independent stability of higher order systems global asymptotic stability of the equilibrium point of a delayed system given by a higher order delayed differential equation of retarded type with several time varying delays is considered for this purpose the given system is transformed to a multi variable first order system and then the previously obtained stability criterion is applied to this several illustrative examples are presented to show the stability region in the parameter spaces and they are compared to the cases with constant delays

regulation of linear systems over rings by dynamic output feedback abstract a general algebraic solution to the problem of regulation of linear systems over arbitrary commutative rings by dynamic output feedback is given which extends the theory of regulation for such systems furthermore the notion of row column regularity for polynomial matrices over a class of rings bezout domains is introduced this concept is shown to simplify the regulation problem considerably for these rings compared to the general case

stabilization of hereditary distributed parameter control systems abstract in this paper we study the asymptotic stabilization of semilinear distributed parameter control systems with delay assuming that the semigroup of operators associated with the uncontrolled and undelayed equation is compact we prove that a well known rank condition which implies the feedback stabilization for lumped systems can be extended to this type of systems

a note on dynamic output feedback for linear systems over rings it is shown that two previous regulation techniques one from systems over rings the other from systems over fields can be combined with a slight modification to obtain a dynamic output feedback compensator for regulating stabilizable and detectable systems over rings the advantage of the resulting technique is that it is a more direct and explicit output feedback technique than the available alternative technique of using observers and dynamic state feedback configuration and as such it brings more insight into regulation of linear systems over rings

output feedback stabilization of delay systems via generalization of the transformation method the left characteristic matrix equation l c m e of a delay system has been employed to develop a state feedback stabilization theory for delay systems analogously the right characteristic matrix equation r c m e has led to the development of an observer theory for this class of systems the characteristic matrix equation approach however only permits the relocation of integral multiples of n poles where n represents the system order this restriction is removed in this work through a generalization of the l c m e and r c m e in a manner which permits the stabilization of an arbitrary but finite number of unstable modes the resulting state feedback controller and state estimator permit the output feedback stabilization of the most general linear autonomous delay system under the minimal assumptions of spectral stabilizability and detectability

a method for computing the interval of delay values for which a differential delay system is stable a test for determining the interval of delay values for which delay differential system is asymptotically stable is presented i e an explicit method is given for calculating h such that for 0

coprime fraction computation of 2 d rational matrices this note presents a numerical method of computing a coprime fraction of a two dimensional 2 d rational matrix not necessarily proper it is achieved by searching the primary linearly dependent rows in order from top to bottom of the two generalized resultants the procedure can be extended to the three or higher dimensional case and the result can also be used to compute the greatest common divisor gcd of 2 d polynomial matrices without employing primitive factorizations which does not exist in the three or higher dimensional case

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

delay independent stability conditions and decay estimates for time varying functional differential equations this paper presents sufficient delay independent conditions that guarantee stability of nonlinear time varying functional differential equations fde s estimates on the rate of decay of solutions are also obtained

stability criteria for linear time invariant systems with point delays based on one dimensional routh hurwitz tests this brief deals with the asymptotic stability of a class of linear time invariant systems subject to point constant uncommensurate delays results are obtained dependent on and independent of the delays which may be tested be performing a finite set of 1 d routh hurwitz tests on a corresponding set of auxiliary delay free linear time invariant systems plus some supplementary conditions related to either commutation pairwise of the associate dynamics matrices or their norm closeness or some simple testable conditions if the matrices have particular forms and there is only one single delay the obtained results are applicable to the case when a finite set of matrices describing the dynamics of a set of delay free auxiliary dynamical systems are hurwitz and either commute pair wise or their norms are sufficiently close to each other some extensions are given to robust stability of point time delay time invariant systems with commensurate delays parametrized by an uncertain parameter vector whose components are in real intervals of known limits

stabilizability and stable proper factorizations for linear time varying systems the objective of this paper is to study in detail stabilizability and stable proper factorizations for linear time varying discrete time systems our main results are i if a linear time varying system can be stabilized by dynamic state feedback then it can also be stabilized by memoryless state feedback ii a complete characterization of the existence of stable proper factorizations for linear time varying input output operators this characterization is nontrivial there exist input output operators that do not admit stable proper factorizations

stability conditions for the general linear difference differential equation with constant coefficients and one constant delay abstract for the application low degree cases of the equations of the title are of special interest lag independent stability conditions are derived for all systems up to degree two inclusive some necessary stability conditions for large lags are expounded in the non neutral case left half planes depending on the lag and containing all zeros of the characteristic function are obtained a sufficient lag independent condition for the whole class considered is found special attention is devoted to the neutral case for that case a collection of disks covering all zeros of the characteristic function is given the result is illustrated by the example of the general neutral characteristic function with coalescing zeros finally zero free regions around the zeros of the coefficient polynomials are derived to derive the results conformal mappings are studied