some new results in the theory of negative imaginary systems with symmetric transfer matrix function abstract this note represents a first attempt to provide a definition and characterisation of negative imaginary systems for not necessarily rational transfer functions via a sign condition expressed in the entire domain of analyticity along the same lines of the classic definition of positive real systems under the standing assumption of symmetric transfer functions we then derive a necessary and sufficient condition that characterises negative imaginary transfer functions in terms of a matrix sign condition restricted to the imaginary axis once again following the same line of argument of the standard positive real case using this definition even transfer functions with a pole at the origin with double multiplicity as well as with a possibly negative relative degree can be negative imaginary

negative imaginary lemmas for descriptor systems this technical note studies the negative imaginary properties of descriptor linear systems based on state space realizations under the assumption of a minimal realization necessary and sufficient conditions are established to characterize the negative imaginary properties of descriptor systems in terms of linear matrix inequalities with equality constraints in particular a negative imaginary lemma a strict negative imaginary lemma and a lossless negative imaginary lemma are developed a multiple input and multiple output rlc circuit network is used as an illustrative example to validate the developed theory

bilinear transformation for discrete time positive real and negative imaginary systems this paper studies the connection between discrete time and continuous time negative imaginary systems first we analyze differences between two statements that are claimed to provide equivalent conditions for systems to be discrete time positive real our conclusion is that one is equivalent to the definition of discrete time positive real transfer matrices the other is not second by means of the bilinear transformation a connection between discrete time and continuous time negative imaginary transfer matrices is established third the concept of discrete time lossless negative imaginary systems is introduced and a discrete time lossless negative imaginary lemma is developed to characterize the lossless negative imaginary properties in terms of minimal state space realization some properties of discrete time lossless negative imaginary transfer matrices are also studied several numerical examples illustrate the developed theory

damage tensors and the crack density distribution abstract the paper presents an algorithm for the derivation of damage tensors emphasizing its relationship with the actual and approximate crack density distributions the proposed model is illustrated using scalar second and fourth order continuous tensor approximations of some typical two and three dimensional crack distributions it is also shown that the occurrence of regions with negative crack density anticrack regions is in many cases a common and as yet unexplored feature of the approximate solutions

strain localization in elastic micro cracked bodies elastic micro cracked bodies are analyzed within the setting of multifield theories the presence of micro cracks is evaluated through a vector order parameter describing the perturbation induced by the micro cracks on the displacement field numerical analyses are developed in two dimensions they show localization phenomena induced by micro cracks even in the case of linear constitutive equations which have been deduced from a lattice model by means of an equivalence procedure in terms of power

on decentralized integral controllability of stable negative imaginary systems and some related extensions abstract this paper exploits the decentralized integral controllability dic of stable negative imaginary ni systems with non singular dc gain matrix to develop a constant input tracking framework with failure tolerance property in the event of sensor and or actuator faults by virtue of the dic property of ni systems it is shown that a positive feedback interconnection of two ni systems of which one is a decentralized integrator system with non negative gains and the other one is a stable ni system having negative definite dc gain matrix is internally stable this is in contrast to the existing results where for internal stability at least one of the systems needs to be strictly negative imaginary sni further it is shown that in a positive feedback interconnection stable ni systems with negative definite dc gain matrix exhibit integral controllability ic property for any positive value of the integral gain k which is a distinct property of stable ni systems having negative definite dc gain matrix since the existing notion of ic for lti systems offers only a finite range of k using the dic property and the eigenvalue loci technique some new results and research directions for the ni systems have also been presented in this paper

comment on absolute stability analysis for negative imaginary systems automatica 67 2016 107 113 abstract this note provides the connection between the paper absolute stability analysis for negative imaginary systems and classical results in absolute stability strictly negative imaginary systems satisfy the aizerman conjecture

brief paper on lossless negative imaginary systems the paper is concerned with the notion of lossless negative imaginary systems and their stabilization using strictly negative imaginary controllers through positive feedback firstly the concept of lossless negative imaginary transfer functions is introduced and some properties of such transfer functions are studied secondly a lossless negative imaginary lemma is given which establishes conditions on matrices appearing in a minimal state space realization that are necessary and sufficient for a transfer function to be lossless negative imaginary thirdly a necessary and sufficient condition is provided for the stabilization of a lossless negative imaginary system by a strictly negative imaginary controller finally a flexible structure example is presented to illustrate the theory

global solutions for the ultra relativistic euler equations abstract a front tracking scheme for the ultra relativistic euler equations is introduced this scheme is based on piecewise constant approximations to the front tracking riemann solutions where continuous rarefaction waves are approximated by finite collections of discontinuities so called non entropy shocks we study the interaction estimates of the generalized shocks entropy and nonentropy shocks of the ultra relativistic euler equations and the outcoming asymptotic riemann solution moreover we use a new function to measure the strengths of the waves of the ultra relativistic euler equations this function has the important implication that the strength is non increasing for the interactions of the generalized shocks this enables us to define a new kind of total variation of a solution the main application of this scheme is proving the global existence of weak solutions for the ultra relativistic euler equations

a symmetric nonlocal damage theory abstract the paper presents a thermodynamically consistent formulation for nonlocal damage models nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening the main features of the presented formulation are i relations derived by the free energy potential fully complying with nonlocal thermodynamic principles ii nonlocal integral operator which is self adjoint at every point of the solid including zones near to the solid s boundary iii capacity of regularizing the softening ill posed continuum problem restoring a meaningful nonlocal boundary value problem in the present approach the nonlocal integral operator is applied consistently to the damage variable and to its thermodynamic conjugate force i e nonlocality is restricted to internal variables only the present model when associative nonlocal damage flow rules are assumed allows the derivation of the continuum tangent moduli tensor and the consistent tangent stiffness matrix which are symmetric the formulation has been compared with other available nonlocal damage theories finally the theory has been implemented in a finite element program and the numerical results obtained for 1 d and 2 d problems show its capability to reproduce in every circumstance a physical meaningful solution and fully mesh independent results

output feedback negative imaginary synthesis under structural constraints the negative imaginary property is a property that many practical systems exhibit this paper is concerned with the negative imaginary synthesis problem for linear time invariant systems by output feedback control sufficient conditions are developed for the design of static output feedback controllers dynamic output feedback controllers and observer based feedback controllers based on the design conditions a numerical algorithm is suggested to find the desired controllers structural constraints can be imposed on the controllers to reflect the practical system constraints also the separation principle is shown to be valid for the observer based design finally three numerical examples are presented to illustrate the efficiency of the developed theory

on α and d negative imaginary systems this paper is concerned with and d negative imaginary systems the definition of negative imaginary transfer functions is firstly introduced then the relationship between negative imaginary and negative imaginary transfer functions is studied by means of the generalised inverse an negative imaginary lemma is proposed to test the negative imaginary property of transfer functions also a necessary and sufficient condition is provided for the stability of interconnection of negative imaginary systems a state feedback controller design condition is established such that the resulting system is negative imaginary moreover the concept of negative imaginary transfer functions is extended to that of d negative imaginary transfer functions finally the developed results are illustrated by numerical examples

on the front tracking algorithm in this paper we present an improved version of the front tracking algorithm for systems of conservation laws the formulation and the theoretical analysis are here somewhat simpler than in previous algorithms at the same time our version leads to a more efficient numerical scheme

stability robustness of a feedback interconnection of systems with negative imaginary frequency response a necessary and sufficient condition expressed simply as the dc loop gain i e the loop gain at zero frequency being less than unity is given in this note to guarantee the internal stability of a feedback interconnection of linear time invariant lti multiple input multiple output systems with negative imaginary frequency response systems with negative imaginary frequency response arise for example when considering transfer functions from force actuators to colocated position sensors and are commonly important in for example lightly damped structures the key result presented here has similar application to the small gain theorem which refers to the stability of feedback interconnections of contractive gain systems and the passivity theorem which refers to the stability of feedback interconnections of positive real or passive systems a complete state space characterization of systems with negative imaginary frequency response is also given in this note and also an example that demonstrates the application of the key result is provided

foundations of not necessarily rational negative imaginary systems theory relations between classes of negative imaginary and positive real systems in this technical note we lay the foundations of a not necessarily rational negative imaginary systems theory and its relations with positive real systems theory in analogy with the theory of positive real functions in our general framework negative imaginary systems are defined in terms of a domain of analyticity of the transfer function and of a sign condition that must be satisfied in such domain in this way we do not require to restrict the attention to systems with a rational transfer function in this work we also define various grades of negative imaginary systems and aim to provide a unitary view of the different notions that have appeared so far in the literature within the framework of positive real and in the more recent theory of negative imaginary systems and to show how these notions are characterized and linked to each other

forward action to make a system negative imaginary abstract in this letter a strategy to make a system negative imaginary is introduced we prove that a dynamical forward action is effective to do it for lyapunov stable systems and discuss how to design the forward compensator for siso and mimo systems some numerical examples are also included

an observer based control scheme using negative imaginary theory this paper presents a full order state observer based scheme that transforms a causal lti minimally realized system into a strongly strict negative imaginary system by defining an auxiliary output based on the observed states the auxiliary output is used for closed loop control with positive feedback invoking the internal stability condition of negative imaginary theory a set of lmi conditions is derived that determines the value of a design parameter required for the proposed scheme to transform a given system with a minimal state space realization into a strongly strict negative imaginary system the proposed scheme is applicable for both stable unstable and square non square systems in this paper the framework is further explored for robustness analysis of uncertain systems and numerical examples are given to elucidate effectiveness of the proposed results

absolute stability analysis for negative imaginary systems this paper deals with absolute stability of a lur e system with positive feedback where the linear subsystem exhibits negative imaginary frequency response and the nonlinearity connected in feedback is time invariant memoryless and slope restricted the proposed absolute stability criterion requires the linear subsystem to belong to the strongly strict negative imaginary class along with that positive definiteness of a symmetric matrix needs to be ensured where the symmetric matrix is obtained by subtracting the dc gain matrix of the linear subsystem from a strictly positive diagonal matrix with elements indicating the reciprocal of the maximum slope bounds of the nonlinearities the stability criterion is proved using a lur e postnikov type lyapunov function numerical examples are presented to demonstrate the proposed results

local existence of weak solutions to the quasi linear wave equation for large initial values on considere le probleme aux valeurs initiales hyperbolique quasilineaire suivant u t f u x x r t 0 u x o u x avec u u 1 u 2 r r 0 r 2 u u u 2 r r 2 f u u 2 u 1

the interaction of waves for the ultra relativistic euler equations abstract the interactions between nonlinear waves for the ultra relativistic euler equations for an ideal gas are studied these equations are described in terms of the pressure p and the spatial part u r 3 of the dimensionless four velocity a new function which measures the strengths of the waves of the ultra relativistic euler equations is presented and sharp estimates for these strengths are derived the interpretation of the strength for the riemann solution is given this function has the important implication that the strength is non increasing for the interactions of waves for the system this study of interaction estimates also allows to determine the type of the outgoing riemann solutions

a generalized negative imaginary lemma and riccati based static state feedback negative imaginary synthesis abstract in this paper we present a generalized negative imaginary lemma based on a generalized negative imaginary system definition then an algebraic riccati equation method is given to determine if a system is negative imaginary also a state feedback control procedure is presented that stabilizes an uncertain system and leads to the satisfaction of the negative imaginary property the controller synthesis procedure is based on the proposed negative imaginary lemma using this procedure the closed loop system can be guaranteed to be robustly stable against any strict negative imaginary uncertainty such as in the case of unmodeled spill over dynamics in a lightly damped flexible structure a numerical example is presented to illustrate the usefulness of the results

minimal representations of continuous time processes having spectral density with zeros in the extended imaginary axis given a process y with stationary increments and rational incremental spectral density s we parametrize minimal state space representations of dy we consider the case when s may have zeros on the imaginary axis including infinity and we analyze the zero structure of each state space representation

a negative imaginary lemma and the stability of interconnections of linear negative imaginary systems the note is concerned with linear negative imaginary systems first a previously established negative imaginary lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis this result is achieved by suitably extending the definition of negative imaginary transfer function matrices secondly a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems meanwhile some properties of linear negative imaginary systems are developed finally an undamped flexible structure example is presented to illustrate the theory

a general approach to the eigenstructure assignment for reachability and stabilizability subspaces abstract this paper is concerned with the problem of determining basis matrices for the supremal output nulling reachability and stabilizability subspaces and the simultaneous computation of the associated friends that place the assignable closed loop eigenvalues at desired locations our aim is to show that the moore laub algorithm in moore and laub 1978 for the computation of these subspaces was stated under unnecessary restrictive assumptions we prove the same result under virtually no system theoretic hypotheses this provides a theoretical foundation to a range of recent geometric techniques that are more efficient and robust and as general as the standard ones based on the computation of sequences of subspaces

positive real lemma necessary and sufficient conditions for the existence of solutions under virtually no assumptions in this note the celebrated positive real lemma equations are considered with the purpose of obtaining necessary and sufficient conditions for the existence of solutions under the mildest system theoretic assumptions more precisely necessary and sufficient conditions are established under the very weak assumption of sign controllability it is then shown that the order of the equations may be suitably reduced by restricting attention to a subspace related to a certain observable subsystem this reduction beside being interesting per se permits us to weaken the assumption of sign controllability finally the assumptions are further weakened as to include the case when the state matrix has uncontrollable eigenvalues on the imaginary axis

strictly negative imaginary state feedback control with a prescribed degree of stability abstract this paper presents conditions for the synthesis of a strictly negative imaginary closed loop system with a prescribed degree of stability under the assumption of full state feedback a perturbation method is used to ensure the closed loop system has both the strict negative imaginary property and a prescribed degree of stability this approach involves the real schur decomposition of a matrix followed by the solution to two lyapunov equations also we present and clarify the perturbation properties of strictly negative imaginary systems

on non proper negative imaginary systems abstract this paper studies non proper negative imaginary systems first the concept of negative imaginary transfer functions that may have poles at the origin and infinity is introduced then a generalized lemma is presented to provide a sufficient condition to characterize the non proper negative imaginary properties of systems the generalized lemma is given in terms of complex variable s in the quarter domain of analyticity compared to previous results our result removes the symmetric restriction also a new relationship is established between lossless negative imaginary and lossless positive real transfer function matrices by using a minor decomposition the results in this paper give us the possibility to address non proper and non symmetric descriptor systems with negative imaginary frequency response several examples are presented to illustrate the results

robust stability conditions for feedback interconnections of distributed parameter negative imaginary systems sufficient and necessary conditions for the stability of positive feedback interconnections of negative imaginary systems are derived via an integral quadratic constraint iqc approach the iqc framework accommodates distributed parameter systems with irrational transfer function representations while generalising existing results in the literature and allowing exploitation of flexibility at zero and infinite frequencies to reduce conservatism in the analysis the main results manifest the important property that the negative imaginariness of systems gives rise to a certain form of iqcs on positive frequencies that are bounded away from zero and infinity two additional sets of iqcs on the dc and instantaneous gains of the systems are shown to be sufficient and necessary for closed loop stability along a homotopy of systems

finite frequency negative imaginary systems this technical note is concerned with finite frequency negative imaginary ffni systems firstly the concept of ffni transfer function matrices is introduced and the relationship between the ffni property and the finite frequency positive real property of transfer function matrices is studied then the technical note establishes an ffni lemma which gives a necessary and sufficient condition on matrices appearing in a minimal state space realization for a transfer function to be ffni also a time domain interpretation of the ffni property is provided in terms of the system input output and state finally an example is presented to illustrate the ffni concept and the ffni lemma

on the factorization of rational discrete time spectral densities in this paper we consider an arbitrary matrix valued rational spectral density phi z we show with a constructive proof that phi z admits a factorization of the form phi z w top z 1 w z where w z is stochastically minimal moreover w z and its right inverse are analytic in regions that may be selected with the only constraint that they satisfy some symplectic type conditions by suitably selecting the analyticity regions this extremely general result particularizes into a corollary that may be viewed as the discrete time counterpart of the matrix factorization method devised by youla in his celebrated work 48

on positive realness negative imaginariness and h control of state space symmetric systems this paper studies positive realness and negative imaginariness of state space symmetric systems first a necessary and sufficient condition is provided for a state space symmetric system to be respectively positive real and negative imaginary then an explicit formulation for the infimum of h norm under a mixed h and negative imaginary performance and an explicit solution for the associated optimal static output feedback control gain are developed based on symmetric negative imaginary theorem finally three examples are provided to illustrate the main results of the paper

an improved front tracking method for the euler equations an improved front tracking method for hyperbolic conservation laws is presented the improved method accurately resolves discontinuities as well as continuous phenomena the method is based on an improved front interaction model for a physically more accurate modeling of the euler equations as compared to standard front tracking methods the resulting algorithm is also more efficient than existing front tracking methods the improved front tracking method is applied to the euler equations for one dimensional unsteady flow and two dimensional steady supersonic flow the results are compared to results of a standard front tracking method and a finite volume method

damage gradient of damage and principle of virtual power a theory of continuum damage mechanics is developed within the framework of the principle of virtual power because the damage in a solid results from microscopic movements we decided to include the power of these microscopic movements in the power of the internal forces the microscopic velocities are related to the damage rate the power of the internal forces we choose depends on the damage velocity and its gradient to take into account the interactions models issued from this theory are presented they are coherent from the mechanical and mathematical points of view the numerical computations show no mesh sensitivity they describe with good agreement the main experimental properties concrete is chosen as an example to illustrate the theory a model using two damage quantities is also presented it yields the correct description of the unilateral phenomenon observed in concrete finally an extension of the existing models is proposed to describe the fatigue damage behaviour

necessary and sufficient conditions on negative imaginariness for interval siso transfer functions and their interconnection this article is concerned with the study of the negative imaginariness of interval transfer functions necessary and sufficient conditions for strictly negative imaginary interval transfer functions subject to parameter uncertainty are first derived based on kharitonov s theorem then certain properties of the interconnection system with negative imaginary interval transfer functions are analyzed finally an example is provided to illustrate the main results of the article

discrete time negative imaginary systems abstract in this paper we introduce the notion of a discrete time negative imaginary system and we investigate its relations with discrete time positive real system theory in the framework presented here discrete time negative imaginary systems are defined in terms of a sign condition that must be satisfied in a domain of analyticity of the transfer function in analogy with the case of discrete time positive real functions as well as analogously to the continuous time case this means in particular that we do not need to restrict our notions and definitions to systems with rational transfer functions we also provide a discrete time counterpart of the different notions that have appeared so far in the literature within the framework of strictly positive real and in the more recent theory of strictly negative imaginary systems and to show how these notions are characterized and linked to each other stability analysis results for the feedback interconnection of discrete time negative imaginary systems are also derived

a front tracking method for conservation laws in one dimension abstract we present a front tracking technique for conservation laws in one dimension the method is based on approximations to the solution of riemann problems where the solution is represented by piecewise constant states separated by discontinuities the discontinuities are tracked until they interact at this point a new riemann problem is solved and so on no finite differences are used this method is tested on the system of nonstationary gas dynamics defined by the euler equations and three test cases are presented

interactions in general continua with microstructure a satisfactory axiomatic treatment of the interaction among bodies modelled as standard continua was achieved by noll almost thirty years ago and was presented in the seminal paper 1 variously reprinted a full review of the matter is also available in the first chapters of the treatise 2

a new front tracking scheme for the ultra relativistic euler equations the ultra relativistic euler equations for an ideal gas are described in terms of the pressure p the spatial part email protected r 3 of the dimensionless four velocity and the particle density n two schemes for these equations are presented in one space dimension namely a front tracking and a cone grid scheme a new front tracking technique for the ultra relativistic euler equations is introduced which gives weak solutions the front tracking method is based on piecewise constant approximations to riemann solutions called front tracking riemann solutions where continuous rarefaction waves are approximated by finite collections of discontinuities so called non entropy shocks this method can be used for analytical as well as for numerical purposes a new unconditionally stable cone grid scheme is also derived in this paper which is based on the riemann solution for the ultra relativistic euler equations both schemes are compared by two numerical examples where explicit solutions are known

uniqueness and minimum theorems for a multifield model of brittle solids some minimum theorems potentially useful to construct numerical schemes related to quasi static evolution of damage in brittle elastic solids are proposed the approach is that of multifield theories with a second order damage tensor describing the microcrack density the use of damage entropy flux and damage pseudo potential are both investigated

feedback stability of negative imaginary systems this paper extends the robust feedback stability theorem of negative imaginary systems by removing restrictive assumptions on the instantaneous gains of the systems that were imposed in the earlier literature and it further generalizes this robust analysis result into the case that allows negative imaginary systems to have poles at the origin in doing so we extend the class of negative imaginary systems for which this robust stability theorem is applicable we also show that this new generalized necessary and sufficient result specializes to the earlier theorems under the same assumptions we additionally prove that the previously known dc gain condition is not only necessary and sufficient for robust feedback stability under the earlier specified instantaneous gain assumptions but is also necessary and sufficient for robust feedback stability under new different and equally simple assumptions the general robust feedback stability theorem for negative imaginary systems with free body dynamics i e poles at the origin derived in this paper also specializes to the case that is only applicable for the negative imaginary system without poles at the origin since the results for negative imaginary systems with free body dynamics developed in this paper depend on the existence of a matrix psi with certain properties we also propose a systematic construction of this matrix psi and show that construction of one such psi is sufficient for determining the feedback stability of the closed loop system finally examples are used to demonstrate the applicability of the results

second order front tracking for the euler equations a second order front tracking method is developed for solving the hyperbolic system of euler equations of inviscid fluid dynamics numerically meshless front tracking methods are usually limited to first order accuracy since they are based on a piecewise constant approximation of the solution here second order convergence is achieved by deriving a piecewise linear reconstruction of the piecewise constant front tracking solution the linearization is performed by decomposing the front tracking solution into its wave components and by linearizing the wave solutions separately in order to construct a physically correct linearization the physical phenomena of the front are taken into account in terms of the front types of the previously developed improved front interaction model this front interaction model is also extended to include front numbers used in the wave decomposition it is illustrated numerically for sod s riemann problem the two interacting blast waves problem and a two dimensional supersonic airfoil flow validation study that the proposed front tracking method achieves second order convergence also in the presence of strong discontinuities and their interactions