eigenvalue based algorithms for testing positive realness of siso systems a computational test for scalar positive real and strictly positive real functions is proposed in this paper the input for this algorithm is state space representation not necessarily minimal it is derived for the discrete time problem based on numerical stable eigenvalue computations the test can be used in the continuous counterpart which is in fact an improvement of an algorithm posed by bai and freund differences between the discrete and continuous time problems are also pointed out

positive real control of two dimensional systems roesser models and linear repetitive processes this paper considers the problem of positive real control for two dimensional 2 d discrete systems described by the roesser model and also discrete linear repetitive processes which are another distinct sub class of 2 d linear systems of both systems theoretic and applications interest the purpose of this paper is to design a dynamic output feedback controller such that the resulting closed loop system is asymptotically stable and the closed loop system transfer function from the disturbance to the controlled output is extended strictly positive real we first establish a version of positive realness for 2 d discrete systems described by the roesser state space model then a sufficient condition for the existence of the desired output feedback controllers is obtained in terms of four lmis when these lmis are feasible an explicit parameterization of the desired output feedback controllers is given we then apply a similar approach to discrete linear repetitive processes represented in their equivalent 1 d state space form finally we provide numerical examples to demonstrate the applicability of the approach

control design for large scale lur e systems with arbitrary information structure constraints abstract in this paper an lmi based approach is proposed for the design of static output feedback for multi nonlinear lur e postnikov systems the resulting control laws ensure absolute stability and at the same time maximize the size of the nonlinear sectors the proposed method is computationally efficient and can accommodate feedback laws with arbitrary information structure constraints the effectiveness of this approach is demonstrated on a large scale example with 100 state variables

large rotatory oscillations of transversely isotropic rods spatio temporal symmetry breaking bifurcation time periodic motions of an initially straight transversely isotropic cantilever rod modeled as a general nonlinearly elastic cosserat curve are considered by inspection the problem possesses o 2 spatial symmetry and due to the requirement of time periodicity o 2 temporal symmetry invariance under time shifts modulo the period and time reversal first the mathematical realization of these symmetries is investigated in terms of transformation groups acting on the governing partial differential equations pdes which ultimately simplifies the task of finding special classes of solutions the main point of this paper is twofold the process just described i is difficult to implement in this problem we provide an unconventional reformulation of the cosserat model that mitigates the difficulty and ii uncovers new solutions more specifically the existence of solutions invariant under a certain twisted subgroup of the spatio temporal symmetry group is established these solution

a kyp lemma and invariance principle for systems with multiple hysteresis non linearities absolute stability criteria for systems with multiple hysteresis non linearities are given in this paper it is shown that the stability guarantee is achieved with a simple two part test on the linear subsystem if the linear subsystem satis es a particular linear matrix inequality and a simple residue condition then as is proven the non linear system will be asymptotically stable the main stability theorem is developed using a combination of passivity lyapunov and popov stability theories to show that the state describing the linear system dynamics must converge to an equilibrium position of the non linear closed loop system the invariant sets that contain all such possible equilibrium points are described in detail for several common types of hystereses the class of non linearities covered by the analysis is very general and includes multiple slope restricted memoryless non linearities as a special case simple numerical examples are used to demonstrate the e ectiveness of the new analysis in comparison to other recent results and graphically illustrate state asymptotic stability

absolute stability criteria for multiple slope restricted monotonic nonlinearities absolute stability criteria such as the classical popov criterion guarantee stability for a class of sector bounded nonlinearities although the sector restriction bounds the admissible class of the nonlinearities the local slope of the nonlinearity may be arbitrarily large in this paper the authors derive absolute stability criteria for multiple slope restricted time invariant monotonic nonlinearities like the popov criterion in the single input single output case the authors results provide a simple graphical interpretation involving a straight line in a modified popov plane

b r s algebras analysis of the consistency equations in gauge theory we compute all possible anomalous terms in quantum gauge theory in the natural class of polynomials of differential forms by using the appropriate cohomological and algebraic methods we do it for all dimensions of spacetime and all structure groups with reductive lie algebras

passivity analysis and passification for uncertain signal processing systems the problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers decision feedback equalizers and digital and analog filters equally important is the problem of passification where a compensator needs to be designed for a given system to become passive this paper considers these two problems for a large class of systems that involve uncertain parameters time delays quantization errors and unmodeled high order dynamics by characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints iqcs we present solutions to the problems of robust passivity analysis and robust passification more specifically for the analysis problem we determine if a given uncertain system is passive for all admissible uncertainty satisfying the iqcs similarly for the problem of robust passification we are concerned with finding a loop transformation such that a particular part of the uncertain signal processing system becomes passive for all admissible uncertainty the solutions are given in terms of the feasibility of one or more linear matrix inequalities lmis which can be solved efficiently

robust stabilization with positive real uncertainty beyond the small gain theory in many applications of feedback control phase information is available concerning the plant uncertainty for example lightly damped flexible structures with colocated rate sensors and force actuators give rise to positive real transfer functions closed loop stability is thus guaranteed by means of negative feedback with strictly positive real compensators in this paper the properties of positive real transfer functions are used to guarantee robust stability in the presence of positive real but otherwise unknown plant uncertainty these results are then used for controller synthesis to address the problem of robust stabilization in the presence of positive real uncertainty one of the principal motivations for these results is to utilize phase information in guaranteeing robust stability in this these sense results go beyond the usual limitations the small gain theorem and quadratic lyapunov functions which may be conservative when phase information is available the results of this paper are based upon a riccati equation formulation of the positive real lemma and thus are in the spirit of recent riccati based approaches to bounded real h control

new results for strict positive realness and feedback stability proposes an algorithm which enables the authors to characterize positive realness and three different classes of strict positive realness in terms of riccati equations and inherent integrations it has been an open question whether or not the feedback system consisting of a weakly strict positive realness and a nonlinear passivity is asymptotically stable the paper also shows that the statement is indeed the case

equivalence between positive real and norm bounded uncertainty this paper focuses on a linear time invariant system with positive real uncertainty and shows an equivalence between positive real and norm bounded uncertainty resulting in transformation of a proper transfer function with positive real uncertainty directly to a strictly proper transfer function with norm bounded uncertainty which is different from the result obtained by using bilinear transform this paper also shows a secondary result relations between the quadratic and robust stability of a system with positive real uncertainty

a unified theory for the cgt approach to adaptive control the command generator tracker cgt approach to model reference adaptive control of linear time invariant multi input multi output plants which are not almost strictly positive real aspr is considered three new algorithms are proposed which are characterized by the insertion of supplementary dynamics in i feedback with the plant ii in parallel with the plant and iii in cascade with the plant respectively the three different implementations are shown to be special cases of a metasystem representation for the adaptive system the new algorithms extend earlier results by introducing adaptive gains for the supplementary dynamics in addition to adaptive gains for the controller a stability proof is presented which shows that the error between the plant and model outputs is bounded in the presence of bounded input and output disturbances if the model input is constant for t t 1 and no disturbances exist then conditions are obtained for the choice of the design parameters in the parallel suppl

the exterior conic sector lemma the conic sector theorem is a powerful input output stability analysis tool providing a fine balance between generality and simplicity of system characterisations that is conducive to practical stability analysis and robust controller synthesis without means to systematically identify and impose exterior conic properties existing analysis and synthesis methods are limited to employing a special case of the conic sector theorem which may prove overly conservative when considering very strictly passive plants this paper removes the current limitation by establishing the exterior conic sector lemma which provides matrix inequalities equivalent to exterior conic bounds for linear time invariant systems

on the characterization of strict positive realness for general matrix transfer functions we present conditions which are necessary and sufficient for a transfer function or transfer function matrix to be strictly positive real a counter example is given to illustrate that the conditions presented here differ from those previously presented in the literature the proof of our results differs from previous related proofs in that it only uses properties of analytic functions and matrices and does not require state space realizations also the results are not restricted to rational transfer functions with real coefficients

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

strictly positive real transfer functions revisited the two most commonly used definitions of strictly positive real spr transfer functions are reviewed contrary to what has been suggested in the literature it is proven that the least restrictive weak definition of the two is clearly related to the yacubovich kalman lemma the relationship between time and frequency domain conditions pertaining to the weak definition of spr systems is established

frequency domain conditions for strictly positive real functions frequency domain conditions for strictly positive real spr functions which appear in literature are often only necessary or only sufficient this point is raised in 1 2 where necessary and sufficient conditions in the s domain are given for a transfer function to be spr in this note the points raised in 1 i2 are clarified further by giving necessary and sufficient conditions in the frequency domain for transfer functions to be spr these frequency domain conditions are easier to test than those given in the s domain or time domain 1 2

low order multivariable adaptive control with application to flexible structures all adaptive controllers require a certain amount of prior information regarding the plant to be controlled to achieve the desired control objectives in the context of multivariable adaptive control not only is the prior information quite significant but also the complexity of the adaptive controller is too high in this paper we introduce a low order multivariable adaptive controller that is easy to implement and requires less prior information than most other adaptive controllers

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

on the algebraic structure of covariant anomalies and covariant schwinger terms the algebraic structure of covariant anomalies and covariant schwinger terms in an anomalous yang mills theory is investigated a cohomological characterization is formulated and geometrically interpreted a new method of determining covariant anomalies and covariant schwinger terms based on the brs anti brs complex is presented

time domain and frequency domain conditions for strict positive realness the author states various time domain and frequency domain conditions pertaining to multivariate strict positive real systems and establishes the relationship between these conditions their relationship is clarified by means of a three tier diagram each tier represents a set of equivalent conditions successively stronger than the lower tier the main theorem in the present study can be considered as the positive realness lemma for strictly positive real systems

on a class of marginally stable positive real systems a class of marginally stable positive real systems is defined which is less restrictive than the previously published definitions of strictly positive real systems a minimal realization and state space characterization of such systems are presented and it is proven that controllers belonging to this class robustly stabilize positive real plants

passivity and disturbance attenuation via output feedback for uncertain nonlinear systems the authors address the problem of disturbance attenuation with internal stability via output feedback for a class of passive systems with uncertainties the problem is approached by means of adaptive output feedback control which does not require any state observer the results obtained extend an earlier result of steinberg and corless 1985 sufficient conditions are proposed under which a nonlinear system can be made locally or globally passive via output feedback

on relationships among passivity positive realness and dissipativity in linear systems the notions of passivity and positive realness are fundamental concepts in classical control theory but the use of the terms has varied for lti systems these two concepts capture the same essential property of dynamical systems that is a system with this property does not generate its own energy but only stores and dissipates energy supplied by the environment this paper summarizes the connection between these two concepts for continuous and discrete time lti systems beyond that relationships are provided between classes of strictly passive systems and classes of positive real systems the more general framework of dissipativity is introduced to connect passivity and positive realness and also to survey other energy based results the frameworks of passivity indices and conic systems are discussed to connect to passivity and dissipativity after surveying relevant existing results some clarifying results are presented these involve connections between classes of passive systems and finite gain l2l2 stability as well as asymptotic stability additional results are given to clarify some of the more subtle conditions between classes of these systems and stability results this paper surveys existing connections between classes of passive and positive real systems and provides results that clarify more subtle connections between these concepts

some remarks on brs transformations anomalies and the cohomology of the lie algebra of the group of gauge transformations we show that ghosts in gauge theories can be interpreted as maurer cartan forms in the infinite dimensional group of gauge transformations we examine the cohomology of the lie algebra of and identify the coboundary operator with the brs operator we describe the anomalous terms encountered in the renormalization of gauge theories triangle anomalies as elements of these cohomology groups

higher order nonlinear complementary filtering on lie groups nonlinear observer design for systems whose state space evolves on lie groups is considered the proposed method is similar to previously developed nonlinear observers in that it involves propagating the state estimate using a process model and corrects the propagated state estimate using an innovation term on the tangent space of the lie group in the proposed method the innovation term is constructed by passing the gradient of an invariant cost function resolved in a basis of the tangent space through a linear time invariant system the introduction of the linear system completes the extension of linear complementary filters to nonlinear lie group observers by allowing higher order filtering in practice the proposed method allows for greater design freedom and with the appropriate selection of the linear filter the ability to filter bias and noise over specific bandwidths a disturbance observer that accounts for constant and harmonic disturbances in group velocity measurements is also considered local asymptotic stability about the desired equilibrium point is demonstrated a numerical example that demonstrates the desirable properties of the observer is presented in the context of pose estimation

technical communique mitigation of symmetry condition in positive realness for adaptive control feasibility of nonlinear and adaptive control methodologies in multivariable linear time invariant systems with state space realization a b c is apparently limited by the standard strictly positive realness conditions that imply that the product cb must be positive definite symmetric this paper expands the applicability of the strictly positive realness conditions used for the proofs of stability of adaptive control or control with uncertainty by showing that the not necessarily symmetric cb is only required to have a diagonal jordan form and positive eigenvalues the paper also shows that under the new condition any minimum phase systems can be made strictly positive real via constant output feedback the paper illustrates the usefulness of these extended properties with an adaptive control example

a note on the covariant anomaly as an equivariant momentum mapping we show that there is a natural gauge invariant presymplectic structure on the spacea of all vector potentials the covariant axial anomaly tilde g is found to be the essentially unique infinitestimally equivariant momentum mapping for the action of the group of gauge transformations on a the infinitesimal equivariance of tilde g is shown to be equivalent to the wess zumino consistency condition for the consistent axial anomalyg we also show that thex operator of bardeen and zumino which relatesg and tilde g corresponds to the one form ona of the presymplectic structure

characterizing families of positive real matrices by matrix substitutions on scalar rational functions abstract this paper concerns the characterization of positive real pr matrices generated by substitutions of the laplace variable s in scalar rational transfer functions by matrix pr functions our main results are restricted to both strongly strictly pr matrices sspr and strictly bounded real matrices as a way to illustrate our main results we also include here a partial extension of both the kalman yakubovich popov lemma for sspr systems of zero relative degree and the circle criterion for strictly pr systems of zero relative degree

strictly positive real matrices and the lefschetz kalman yakubovich lemma the authors give necessary and sufficient conditions in the frequency domain for rational matrices to be strictly positive real based on this result the matrix form of the lefschetz kalman yakubovich lemma is proved which gives necessary and sufficient conditions for strictly positive real transfer matrices in the state space realization form