eigenderivative analysis of asymmetric non conservative systems in general the damping matrix of a dynamic system or structure is such that it can not be simultaneously diagonalized with the mass and stiffness matrices by any linear transformation for this reason the eigenvalues and eigenvectors and consequently their derivatives become complex expressions for the first and second order derivatives of the eigenvalues and eigenvectors of these linear non conservative systems are given traditional restrictions of symmetry and positive definiteness have not been imposed on the mass damping and stiffness matrices the results are derived in terms of the eigenvalues and left and right eigenvectors of the second order system so that the undesirable use of the first order representation of the equations of motion can be avoided the usefulness of the derived expressions is demonstrated by considering a non proportionally damped two degree of freedom symmetric system and a damped rigid rotor on flexible supports copyright 2001 john wiley sons ltd

efficient computation of modal sensitivities for systems with repeated frequencies the physical origin and ambiguity of repeated frequency modes is discussed followed by a mathematical derivation of the governing equations for the partial derivatives of repeated eigenvalues with respect to changes in the system parameters this is followed by a derivation for the associated eigenvector derivative equations physical interpretations are included to help explain the analytical results an efficient computation procedure which preserves the bandwidth for very large systems is also proposed for systems with repeated or closely spaced eigenvalues two small examples to illustrate the solution procedure are presented 8 references

positive filtering for continuous time positive systems under l 1 performance in this paper we address the positive filtering problem for positive continuous time systems under the l1 induced performance a pair of positive filters with error bounding feature is proposed to estimate the output of positive systems a novel characterisation is first obtained to ensure that the filtering error system is asymptotically stable with a prescribed l1 induced performance then necessary and sufficient conditions for the existence of required filters are presented and the obtained results are expressed in terms of linear programming problems which can be easily checked by standard software finally a numerical example is given to illustrate the effectiveness of the proposed design procedures

absolute exponential l1 gain analysis and synthesis of switched nonlinear positive systems with time varying delay this paper investigates absolute exponential stability and stabilization with l1 gain performance of switched nonlinear positive systems with time varying delay nonlinear functions considered in the paper are located in a sector field and the time varying delay is unknown but bounded the notion of absolute exponential l1 stability of switched nonlinear positive systems is first introduced a nonlinear lyapunov krasovskii functional is constructed for the underlying systems by using the lyapunov krasovskii functional a sufficient condition for absolute exponential l1 stability of the systems is established in terms of linear programming then absolute exponential l1 control synthesis of the systems is addressed a feedback control law containing nonlinear functions and a state feedback control law are designed respectively by comparing with existing results it is shown that the present design is less conservative finally an illustrative example is provided to illustrate the effectiveness of the results

mpeg vbr video traffic modeling and classification using fuzzy technique we present an approach for mpeg variable bit rate vbr video modeling and classification using fuzzy techniques we demonstrate that a type 2 fuzzy membership function i e a gaussian mf with uncertain variance is most appropriate to model the log value of i p b frame sizes in mpeg vbr video the fuzzy c means fcm method is used to obtain the mean and standard deviation std of t p b frame sizes when the frame category is unknown we propose to use type 2 fuzzy logic classifiers flcs to classify video traffic using compressed data five fuzzy classifiers and a bayesian classifier are designed for video traffic classification and the fuzzy classifiers are compared against the bayesian classifier simulation results show that a type 2 fuzzy classifier in which the input is modeled as a type 2 fuzzy set and antecedent membership functions are modeled as type 2 fuzzy sets performs the best of the five classifiers when the testing video product is not included in the training products and a steepest descent algorithm is used to tune its parameters

on l1 gain control of 2 d positive roesser systems with directional delays necessary and sufficient conditions abstract in this paper the problem of l 1 gain control is addressed for two dimensional 2 d positive roesser systems with directional delays a complete solution to the design problem is presented for the first time specifically by exploiting a new approach based on 2 d z transform an exact value of l 1 induced norm of the input output operator is obtained this analytical result is utilized to derive necessary and sufficient conditions under which a 2 d positive system with delays is asymptotically stable with a prescribed l 1 gain performance then by utilizing a vertex optimization approach necessary and sufficient conditions are established for the existence of a state feedback controller sfc that makes the closed loop system positive and stable subject to l 1 induced performance the proposed synthesis conditions are formulated in terms of linear programming lp which can be effectively solved by various convex algorithms to minimize the l 1 performance index

pattern recognition using markov random field models in this paper we propose markov random field models for pattern recognition which provide a flexible and natural framework for modelling the interactions between spatially related random variables in their neighbourhood systems the proposed approach is superior to conventional approaches in many aspects this paper introduces the concept of states into markov random filed models presents a theoretic analysis of the approach discusses issues of designing neighbourhood system and cliques and analyses properties of the models we have applied our method to the recognition of unconstrained handwritten numerals the experimental results show that the proposed approach can achieve high performance

t s fuzzy control of positive markov jump nonlinear systems the positive stochastic stabilization issue is investigated for markov jump nonlinear systems the nonlinear systems in the absence and presence of uncertainties are considered and modeled into markov jump fuzzy systems with known and partially known membership functions respectively for the former the parallel distributed compensator pdc controllers are designed to realize the positive stochastic stabilization besides an additional criterion is derived to reduce the number of linear inequalities for the latter namely some elements of membership functions are unavailable and the pdc strategy is infeasible then a switching controller whose structure is parallel to that of fuzzy model is constructed to achieve the corresponding positivity and stability all the conditions are transformed to standard form of linear programming problem which is solved with the help of linprog toolbox finally the feasibility of the obtained results is illustrated by a pest s structured population model

a constrained approach to multifont chinese character recognition the constraint graph is introduced as a general character representation framework for recognizing multifont multiple size chinese characters each character class is described by a constraint graph model sampling points on a character skeleton are taken as nodes in the graph connection constraints and position constraints are taken as arcs in the graph for patterns of the same character class the model captures both the topological invariance and the geometrical invariance in a general and uniform way character recognition is then formulated as a constraint based optimization problem a cooperative relaxation matching algorithm that solves this optimization problem is developed a practical optical character recognition ocr system that is able to recognize multifont multiple size chinese characters with a satisfactory performance was implemented

internal positivity preserved model reduction this article studies model reduction of continuous time stable positive linear systems under the hankel norm h norm and h 2 norm performance the reduced order systems preserve the stability as well as the positivity of the original systems this is achieved by developing new necessary and sufficient conditions of the model reduction performances in which the lyapunov matrices are decoupled with the system matrices in this way the positivity constraints in the reduced order model can be imposed in a natural way as the model reduction performances are expressed in linear matrix inequalities with equality constraints the desired reduced order positive models can be obtained by using the cone complementarity linearisation iterative algorithm a numerical example is presented to illustrate the effectiveness of the given methods

exponential stability and l1 gain analysis for positive time delay markovian jump systems with switching transition rates subject to average dwell time abstract the paper deals with the problems of exponential stability and l 1 gain analysis for positive time delay markovian jump systems mjss with switching transition rates another set of useful regime switching model is given which extends fixed transition rates to time varying transition rates by resorting to the linear co positive lyapunov function and average dwell time sufficient conditions for exponential stability are proposed in terms of standard linear programming based on the obtained results l 1 gain performance is analyzed finally an example is proposed to illustrate the validity of the main results

performance optimization over positive l cones abstract in this paper we study linear systems with positivity type of constraints first we consider the case where the input to a system is restricted to be in the positive cone of l denoted by l and seek to characterize the system s induced norm from l to l we obtain an exact characterization of this norm which is particularly easy to calculate in the case of lti systems furthermore we consider and solve the model matching problem and show that time varying linear or nonlinear control filtering does not improve the performance with respect to this norm for lti systems in the second part of the paper we consider the case when the output is forced to be in the positive l cone when the input is in this cone we show if internal positivity is sought a dynamic optimal controller offers no advantage over a static one also if the measurement matrix satisfies certain conditions synthesizing an optimal static output feedback controller reduces to a linear program

l1 induced norm and controller synthesis of positive systems in this paper the problem of 1 1 induced controller design for discrete time positive systems is investigated with the use of linear lyapunov function an analytical method to compute the exact value of 1 1 induced norm is first presented then a novel characterization for stability and 1 1 induced performance is proposed based on the characterization a necessary and sufficient condition for the existence of desired controllers is derived and an iterative convex optimization approach is developed to solve the condition in addition the synthesis of the state feedback controller for single input multiple output simo positive systems is investigated for this special case an analytic solution is established to show how the optimal 1 1 induced controller can be designed and some links to the spectral radius of the closed loop systems are provided finally the theoretical results are illustrated through a numerical example

h_ infty positive filtering for positive linear discrete time systems an augmentation approach in this note we address the reduced order positive filtering problem of positive discrete time systems under the h performance commonly employed approaches such as linear transformation and elimination technique may not be applicable in general due to the positivity constraint of the filter to cope with the difficulty we first represent the filtering error system as a singular system by means of the system augmentation approach which will facilitate the consideration of the positivity constraint two necessary and sufficient conditions are obtained in terms of matrix inequalities under which the filtering error system has a prescribed h performance then a necessary and sufficient condition is proposed for the existence of the desired positive filters and an iterative linear matrix inequality lmi algorithm is presented to compute the filtering matrices which can be easily checked by standard software finally a numerical example to illustrate the effectiveness of the proposed design procedures is presented

a linear framework on the distributed model predictive control of positive systems abstract this paper investigates the distributed model predictive control dmpc for positive systems with interval and polytopic uncertainties respectively different from the traditional quadratic dmpc a new linear dmpc framework is established for positive systems first a linear cooperative cost function performance index function is introduced for the dmpc of positive systems accordingly some linear constraint conditions are imposed on the systems then a linear co positive lyapunov function is constructed using the linear lyapunov function the dmpc controllers are designed for interval positive systems and polytopic positive systems respectively the controller of each subsystem contains not only the state information of the subsystem but also the state information of other correlated subsystems linear programming based optimization algorithm is addressed to compute the controller parameters to guarantee the feasibility and stability of the systems a cone invariant set is proposed finally two case studies are provided to illustrate the effectiveness of the theoretical findings

sensitivity analysis of non conservative eigensystems an expression for the derivatives of eigenvalues and eigenvectors of non conservative systems is presented contrary to previous methods that use state space form 2n space to consider damping proposed method solves the eigenpair derivatives of damped system explicitly the computation size of n order is maintained and the eigenpair derivatives are obtained simultaneously from one equation so that it is efficient in cpu time and storage capacity moreover this method can be extended to asymmetric non conservative damped systems although additional problems are generated contrary to the eigenpair sensitivity methods of symmetric systems in asymmetric case an algebraic method for the eigenpair derivatives can be obtained through similar procedure the proposed expression is derived by combining the differentiations of the eigenvalue problem and normalization condition into one linear algebraic equation the numerical stability is proved by showing non singularity of the proposed equation and the efficiency of the derived expression is illustrated by considering a cantilever beam with lumped dampers and a whirling beam

a comparison between hankel norms and induced system norms a general definition is formulated for the hankel norms as the induced norms of a strictly proper stable linear time invariant lti system mapping vector valued l sup p past inputs to vector valued l sup q future outputs some hankel norms are derived by the maximum principle and duality a property termed the system integral invariance is introduced by the derivation of those hankel norms furthermore the norm induced initial conditions and the comparison between the hankel norms and the induced system norms are also presented

stability and l1 gain analysis of linear periodic piecewise positive systems this paper investigates the stability stabilization and l1 gain of linear periodic piecewise positive systems the monotonicity of linear periodic piecewise positive systems is first studied then a time varying co positive lyapunov function for periodic piecewise positive systems is employed and a sufficient condition for the asymptotic stability of the system is established based on the provided co positive lyapunov function and the sufficient stability condition a state feedback periodic piecewise controller to stabilize the system is formed and an upper bound of l1 gain of the system is given finally numerical examples are given to illustrate the theoretical results

on reachable sets for positive linear systems under constrained exogenous inputs this paper focuses on positive linear time invariant systems with constant coefficients and specific exogenous disturbance the problem of finding a hyper pyramid to bound the set of the states that are reachable from the origin in the euclidean space is addressed subject to inputs whose 1 1 norm or 1 norm is bounded by a prescribed constant the lyapunov approach is applied and a bounding hyper pyramid is obtained by solving a set of inequalities iterative procedures with an adjustable parameter for reducing the hyper volume of the bounding hyper pyramid for the reachable set are proposed

derivatives of complex eigenvectors using nelson s method 6shyy w an adaptive grid method for navier stokes flow computation applied mathematics and computation vol 21 no 3 1987 pp 201 219 7jeng y n andliou s c modi edmultipleone dimensional adaptive grid method numerical heat transfer part b vol 15 no 2 1989 pp 241 247 8jeng y n and lee z s revisit to the modi ed muliple onedimensional adaptive grid method numerical heat transfer part b vol 29 no 3 1996 pp 305 323 9bockelie m j and smith r e an adaptive grid method for computing the high speed 3d viscous flow about a re entry vehicle aiaa paper 92 2685 june 1992 10yee h c and harten a implicit tvd schemes for hyperbolic conservation laws in curvilinear coordinates aiaa journal vol 25 no 2 1987 pp 266 274 11jeng y n and liou y c adaptive grid generation by elliptic equations with grid control at all of the boundaries numerical heat transfer part b vol 23 no 2 1993 pp 135 151

perturbation technique for non self adjoint systems with repeated eigenvalues the reanalysis of non self adjoint systems is computationally very expensive in the design of structural dynamics an effective even if approximate evaluation of the eigensolutions of a modified system is valuable to designers in a paper by meirovitch and ryland meirovitch l and ryland g a perturbation technique for gyroscopic systems with small internal and external damping journal of sound and vibration vol 100 no 3 1985 pp 393408 a perturbation technique was used to derive the perturhed solutions of a damped gyroscopic system with distinct eigenvalues that approach is extended to the case of systems with repeated eigenvalues a numerical example is presented to verify the present method and satisfactory results are observed

natural frequency and mode shape sensitivities of damped systems part ii multiple natural frequencies abstract an efficient algorithm with proven numerical stability is derived for computation of eigenvalue and eigenvector derivatives of damped vibratory systems with multiple eigenvalues in the proposed method adjacent eigenvectors and orthonormal condition are used to compose an algebraic equation whose order is n m n m where n is the number of co ordinates and m the number of multiplicity of a multiple natural frequency the mode shape derivatives of the damped systems can be obtained by solving the algebraic equation the method can be consistently applied to both structural systems with structural design parameters and mechanical systems with lumped design parameters as an example of a structural system to demonstrate the theory of the proposed methods and its possibilities in the case of multiple eigenvalues the finite element model of the cantilever beam is considered and also a 5 dof mechanical system in the case of a non proportionally damped system the design parameter of the cantilever beam is its height and that of the 5 dof mechanical system is a spring

brief paper positivity preserving h model reduction for positive systems this paper is concerned with the model reduction of positive systems for a given stable positive system our attention is focused on the construction of a reduced order model in such a way that the positivity of the original system is preserved and the error system is stable with a prescribed h performance based upon a system augmentation approach a novel characterization on the stability with h performance of the error system is first obtained in terms of linear matrix inequality lmi then a necessary and sufficient condition for the existence of a desired reduced order model is derived accordingly furthermore iterative lmi approaches with primal and dual forms are developed to solve the positivity preserving h model reduction problem finally a compartmental network is provided to show the effectiveness of the proposed techniques

a finite element formulation for piezoelectric shell structures considering geometrical and material non linearities in this paper we present a non linear finite element formulation for piezoelectric shell structures based on a mixed multi field variational formulation an electro mechanical coupled shell element is developed considering geometrically and materially non linear behavior of ferroelectric ceramics the mixed formulation includes the independent fields of displacements electric potential strains electric field stresses and dielectric displacements besides the mechanical degrees of freedom the shell counts only one electrical degree of freedom this is the difference in the electric potential in the thickness direction of the shell incorporating non linear kinematic assumptions structures with large deformations and stability problems can be analyzed according to a reissner mindlin theory the shell element accounts for constant transversal shear strains the formulation incorporates a three dimensional transversal isotropic material law thus the kinematic in the thickness direction of the shell is considered the normal zero stress condition and the normal zero dielectric displacement condition of shells are enforced by the independent resultant stress and the resultant dielectric displacement fields accounting for material non linearities the ferroelectric hysteresis phenomena are considered using the preisach model as a special aspect the formulation includes temperature dependent effects and thus the change of the piezoelectric material parameters due to the temperature this enables the element to describe temperature dependent hysteresis curves copyright 2011 john wiley sons ltd

a direct algebraic method for eigensolution sensitivity computation of damped asymmetric systems in general the derivative of an eigenvector of a vibrating symmetric system is the solution of a singular problem further complications are encountered in dealing with asymmetric damped systems for which the left and right eigenvectors and their derivatives become distinct and complex several approaches have been proposed to overcome this singularity such as nelson s method and the modal method in the present work a new approach is presented for calculating simultaneously the derivatives of the eigenvalues and their associated derivatives of the left and right eigenvectors for asymmetric damped systems with the proposed method the exact eigenderivatives can be obtained by solving a first order linear algebraic system of equations the method is applied on a 104 dof ventilator rotor system which is used as an example of an asymmetric damped system with distinct eigenvalues the diameter of the shaft has been chosen as the design parameter the comparison of the computational time shows that the proposed method is more efficient than both nelson s approach and the modal method copyright 2006 john wiley sons ltd

positive filtering for positive takagi sugeno fuzzy systems under l 1 performance in this paper the positive filtering problem is addressed for positive takagi sugeno t s fuzzy systems under the 1 induced performance to estimate the output of positive t s fuzzy systems error bounding positive filters are constructed a new performance characterization is first established to guarantee the asymptotic stability of the filtering error system with the 1 induced performance moreover sufficient conditions expressed by linear programming problems are derived to design the required filters finally a numerical example is presented to show the effectiveness of the derived theoretical results

uncertainty bounds and their use in the design of interval type 2 fuzzy logic systems we derive inner and outer bound sets for the type reduced set of an interval type 2 fuzzy logic system fls based on a new mathematical interpretation of the karnik mendel iterative procedure for computing the type reduced set the bound sets can not only provide estimates about the uncertainty contained in the output of an interval type 2 fls but can also be used to design an interval type 2 fls we demonstrate by means of a simulation experiment that the resulting system can operate without type reduction and can achieve similar performance to one that uses type reduction therefore our new design method based on the bound sets can relieve the computation burden of an interval type 2 fls during its operation which makes an interval type 2 fls useful for real time applications

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

a tutorial on the positive realization problem this paper is a tutorial on the positive realization problem that is the problem of finding a positive state space representation of a given transfer function and characterizing existence and minimality of such representation this problem goes back to the 1950s and was first related to the identifiability problem for hidden markov models then to the determination of internal structures for compartmental systems and later embedded in the more general framework of positive systems theory within this framework developing some ideas sprang in the 1960s during the 1980s the positive realization problem was reformulated in terms of a geometric condition which was recently exploited as a tool for finding the solution to the existence problem and providing partial answers to the minimality problem in this paper the reader is carried through the key ideas which have proved to be useful in order to tackle this problem in order to illustrate the main results contributions and open problems several motivating examples and a comprehensive bibliography on positive systems organized by topics are provided

iterative computation of eigenvector derivatives for middle eigenvalues the computation of eigenvector derivatives for middle eigenvalues in the real symmetric eigensystems is discussed based on finite element modeling the coefficient matrices of the governing equations for eigenvector derivatives are singular this work concentrates on a new method for such computations the method is based on an iteration technique and its convergence is proved the number of iterations is adaptively determined based on some error estimation highly accurate approximations to eigenvector derivatives can be achieved with low computational cost the proposed method can deal with both cases of simple and repeated eigenvalues in a unified manner it is especially suitable for the large sparse matrices from finite element models finally three examples including an aircraft wing structure are used to demonstrate the effectiveness of the proposed method

type 2 fuzzy hidden markov models and their application to speech recognition this paper presents an extension of hidden markov models hmms based on the type 2 t2 fuzzy set fs referred to as type 2 fuzzy hmms t2 fhmms membership functions mfs of t2 fss are three dimensional and this new third dimension offers additional degrees of freedom to evaluate the hmms fuzziness therefore t2 fhmms are able to handle both random and fuzzy uncertainties existing universally in the sequential data we derive the t2 fuzzy forward backward algorithm and viterbi algorithm using t2 fs operations in order to investigate the effectiveness of t2 fhmms we apply them to phoneme classification and recognition on the timit speech database experimental results show that t2 fhmms can effectively handle noise and dialect uncertainties in speech signals besides a better classification performance than the classical hmms

type 2 fuzzy markov random fields and their application to handwritten chinese character recognition in this paper we integrate type 2 t2 fuzzy sets with markov random fields mrfs referred to as t2 fmrfs which may handle both fuzziness and randomness in the structural pattern representation on the one hand the t2 membership function mf has a 3 d structure in which the primary mf describes randomness and the secondary mf evaluates the fuzziness of the primary mf on the other hand mrfs can represent patterns statistical structurally in terms of neighborhood system and clique potentials and thus have been widely applied to image analysis and computer vision in the proposed t2 fmrfs we define the same neighborhood system as that in classical mrfs to describe uncertain structural information in patterns we derive the fuzzy likelihood clique potentials from t2 fuzzy gaussian mixture models the fuzzy prior clique potentials are penalties for the mismatched structures based on prior knowledge because chinese characters have hierarchical structures we use t2 fmrfs to model character structures in the handwritten chinese character recognition system the overall recognition rate is 99 07 which confirms the effectiveness of the proposed method

on the existence of a positive realization the positive realization problem for linear systems is to find conditions for a given transfer function with nonnegative impulse response to have a realization such that the resulting system is a positive system recently it has been shown that under a mild assumption on the long term behaviour of the impulse response this problem is related to the maximum modulus poles only in this paper necessary and sufficient conditions for positive realizability of discrete time systems are given they show that also nondominant poles play a role in the most general case positive realizability conditions for the continuous time case are also given

rates of change of eigenvalues and eigenvectors in damped dynamic system rates of change of eigenvalues and eigenvectors of a damped linear discrete dynamic system with respect to the system parameters are presented a nonproportional viscous damping model is assumed because of the nonproportional nature of the damping the mode shapes and natural frequencies become complex and as a consequence the sensitivities of eigenvalues and elgenvectors are also complex the results are presented in terms of the complex modes and frequencies of the second order system and the use of rather undesirable state space representation is avoided the usefulness of the derived expressions is demonstrated by considering an example of a nonproportionally damped two degree of freedom system

techniques for generating analytic covariance expressions for eigenvalues and eigenvectors one of the key problems in data fusion is the estimation of a parameter vector from a set of noisy measurements in many cases the optimal estimate of such a parameter vector can be solved through the least squares problem there are however a number of important problems whose solution instead takes the form of an eigenvalue eigenvector problem furthermore knowledge of the uncertainty of the optimal estimate is as important as the estimate itself for many practical applications and this uncertainty is typically captured in the form of a covariance matrix while the covariance matrix for a least squares estimate has been well studied there has been substantially less research on the covariance of an optimal estimate originating from an eigenvalue eigenvector problem in this paper we develop general expressions that determine the uncertainty in a vector estimate obtained from an eigenvalue eigenvector problem given the uncertainty of the matrix this includes developing expressions for the analytic derivatives of the eigenvalues and eigenvectors with respect to the matrix from which they come finally the techniques developed are numerically validated with forward finite differencing and a monte carlo analysis and then used to determine covariance expressions for an ellipse fitting technique and the estimation of attitude quaternions

on calculation of sensitivity for non defective eigenproblems with repeated roots methods of calculating eigensolution sensitivity have long been divided into two categories the modal methods and the direct methods this paper presents a unified theory for the calculation of derivatives of eigenvalues and eigenvectors where the most general case non defective eigenproblems with repeated roots is considered the intrinsic relation between these two methods is exposed the present modal method is shown to be actually the asymptotic expansion of a special direct method a numerical example is given to verify the validity of the presented formulae and the issue of computational efficiency is addressed

hierarchical collapsing method for direct defuzzification of general type 2 fuzzy sets abstract karnik mendel km and enhanced km ekm algorithms are proved to be efficient approaches when dealing with general type 2 fuzzy sets represented by their planes on the other hand collapsing method as a type reduction algorithm for interval type 2 fuzzy sets has shown to be an effectual type reduction method for interval type 2 fuzzy sets in this paper we aim at developing mathematical formulations based on collapsing procedure and plane decomposition in order to utilize geometric properties of general type 2 fuzzy sets for preparing a direct defuzzification procedure the proposed methods are fast and robust extensive simulations have shown that the proposed algorithm outperforms most of the existing approaches in this field and its results are closer to the exact optimal defuzzified values

sensitivity analysis of the scaled boundary finite element method for elastostatics abstract as a semi analytical structural analysis algorithm the scaled boundary finite element method sbfem only discretizes the boundary of the analyzed domain without the need of fundamental solutions which makes it powerful for problems with stress singularity or unbounded foundation media in this paper a sensitivity analysis method of sbfem is proposed for elastostatics through which the first order derivatives of the structural responses with respect to the design parameters can be obtained efficiently and accurately an approach is suggested to compute the eigenvalue and eigenvector sensitivities of the hamilton matrix which are then used to calculate the analytical derivative of the stiffness matrix based on these calculations the sensitivities of displacements and stresses are further obtained by a series of differential equations the proposed sensitivity analysis method is also applied to the fracture mechanics problems three numerical examples are investigated to demonstrate the validity of the proposed method

eigenvector derivatives with repeated eigenvalues in this paper an algorithm is derived for computing the derivatives of eigenvalues and eigenvectors for real symmetric matrices in the case of repeated eigenvalues where the matrices are functions of real parameters such as mass density or moment of inertia the algorithm is an extension of recent work by i u ojalvo the key step in this extended derivation is to differentiate the eigenvalue equation twice the algorithm preserves the symmetry and band structure of the matrices allowing efficient computer storage and solution techniques applications include sensitivity analysis and optimization of the normal modes of finite element modeled structures such as large space structures a cantilever beam finite element example is included

stability theory for nonnegative and compartmental dynamical systems with time delay abstract nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations and involve the exchange of nonnegative quantities between subsystems or compartments these models are widespread in biological and physical sciences and play a key role in understanding these processes a key physical limitation of such systems is that transfers between compartments is not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments in this paper we present necessary and sufficient conditions for stability of nonnegative and compartmental dynamical systems with time delay specifically asymptotic stability conditions for linear and nonlinear nonnegative dynamical systems with time delay are established using linear lyapunov krasovskii functionals

stability analysis of linear delay systems with cone invariance this paper is concerned with the stability and input output gain analysis of linear delay systems with cone invariance based on the partial ordering over a cone the monotonicity of the trajectory of the cone preserving systems with constant delays is first studied then by comparing the trajectory of the constant delay systems and that of time varying delay systems we prove that a cone preserving system with interval time varying delays is asymptotically stable if and only if the corresponding delay free system is asymptotically stable this implies that the stability of a cone preserving system is insensitive to the magnitude of the delays moreover based on the cone induced norms an explicit characterization on the cone induced gain of an input output cone preserving system is given in terms of system matrices finally numerical examples are provided to illustrate the theoretical results

reachability properties of continuous time positive systems in this technical note reachability properties of continuous time positive systems are introduced and characterized specifically first it is shown that reachability and strong reachability are equivalent properties and thus the characterization of strong reachability derived in is extended to the weaker notion of reachability in the second part of the technical note essential reachability is introduced and necessary and sufficient conditions for this property to hold are provided

investigating the effects of time delays on stochastic stability and designing l1 gain controllers for positive discrete time markov jump linear systems with time delay this paper is concerned with stochastic stability l1 gain performance analysis and positivity preserving l1 gain controller design for a positive discrete time markov jump linear system with time delay first necessary and sufficient conditions for stochastic stability of the system are derived by constructing a linear co positive stochastic lyapunov functional and establishing a system equation whose state variables consist of the mathematical expectation of the markovianized states and whose coefficient matrices depend on time delay and the transition probability it is revealed that stochastic stability of the positive discrete time markov jump linear system with time delay is influenced by the size of time delay and it is demonstrated by an example that the effect of time delay on stochastic stability can be either positive or negative second exact computation on an l1 gain index of a stochastically stable positive discrete time markov jump linear system with time delay is presented and a necessary and sufficient condition for the l1 gain performance is derived in the form of linear programming third an iterative algorithm is proposed to design a positivity preserving l1 gain controller and in single input case an optimal controller is obtained analytically such that the closed loop system achieves the minimal l1 gain performance then a modified pest s structured population dynamic model is developed to illustrate the effectiveness of the designed method

nonsingleton fuzzy logic systems theory and application in this paper we present a formal derivation of general nonsingleton fuzzy logic systems nsflss and show how they can be efficiently computed we give examples for special cases of membership functions and inference and we show how an nsfls can be expressed as a nonsingleton fuzzy basis function expansion and present an analytical comparison of the nonsingleton and singleton fuzzy logic systems formulations we prove that an nsfls can uniformly approximate any given continuous function on a compact set and show that our nsfls does a much better job of predicting a noisy chaotic time series than does a singleton fuzzy logic system fls

dynamic output feedback control for continuous time interval positive systems under l1 performance this paper is concerned with the design of l1 induced dynamic output feedback controller for continuous time positive systems with interval uncertainties a necessary and sufficient condition for stability and l1 induced performance of positive linear systems is proposed in terms of linear inequalities based on this conditions for the existence of robust dynamic output feedback controllers are established and an iterative convex optimization approach is developed to solve the conditions one illustrative example is provided to show the effectiveness and applicability of the theoretical results

eigensolutions sensitivity for quadratic eigenproblems abstract when a dynamic system to be analyzed is subjected to velocity dependent force s a quadratic eigenproblem arises this paper presents an efficient algorithm for the calculation of the eigensolutions sensitivity in quadratic eigenproblems the attention being focused on how to extract eigenvalue and eigenvector derivatives of a general non defective eigenpair directly in the configuration space the method preserves the banded nature of the structural matrices and requires knowledge of only the eigenvectors to be differentiated which makes it powerful in dealing with large scale systems

calculation of eigenvector derivatives for structures with repeated eigenvalues in structural optimization and system identification eigenvector derivatives provide important information for updating design model parameters when the current parameter values yield repeated eigenvalues it has not been possible previously to calculate unique eigenvector derivatives recent work has provided a method for determining unique eigenvalue derivatives for this case but methods for calculating the eigenvector sensitivities have been incomplete in this work a complete method for calculation of repeated root eigenvector derivatives is shown for the real symmetric structural eigenproblem the derivation is completed by using information from the second derivative of the eigen problem and is limited to the case of distinct eigenvalue sensitivities as an example the repeated root eigenvector sensitivities are calculated for a simple three degree of freedom beam grillage comparisons of linear approximations using these derivatives to the calculated eigenvectors support the accuracy of the formulation

technical communique analysis and design of aimd congestion control algorithms in communication networks we present a model of a network of synchronised sources operating additive increase multiplicative decrease aimd congestion control algorithms we show i that networks of such devices in the presence of a drop tail bottleneck buffer may be modelled as a positive linear system ii that such networks possess a unique stationary point and iii that this stationary point is globally exponentially stable we use these results to establish conditions for the fair co existence of traffic in networks employing heterogeneous aimd algorithms and to design a new protocol for operation over high speed and long distance links

second order eigensensitivity analysis of asymmetric damped systems using nelson s method first order eigensensitivity analysis using nelson s method is first reviewed then nelson s approach is extended to the computation of the second order derivatives of the eigenvalues and eigenvectors of symmetric and asymmetric damped systems the computation of second order derivatives may be required for large variation of design parameters and for some optimization algorithms nelson s method has the advantage of requiring only the knowledge of the eigenvector to be differentiated only systems with distinct eigenvalues are considered in this paper two numerical examples have been selected to illustrate the application and the utility of the derived expressions of the first and second order eigensensitivities a four degree of freedom symmetric damped system is chosen for the first example whereas a finite element asymmetric 20 dof damped rotor model is considered in the second example

technical communique static output feedback stabilization an ilmi approach in this note the static output feedback stabilization problem is addressed using the linear matrix inequality technique a necessary and sufficient condition for static output feedback stabilizability for linear time invariant systems is derived in the form of a matrix inequality the extension of the result to h control is studied an iterative lmi ilmi algorithm is proposed to compute the feedback gain numerical examples are employed to demonstrate the effectiveness and the convergence of the algorithm

stability analysis and control synthesis for positive semi markov jump systems with time varying delay abstract this paper deals with stability analysis and control synthesis for positive semi markov jump systems s mjss with time varying delay in which the stochastic semi markov process related to nonexponential distribution is considered the main motivation for this paper is that the positive condition sometimes needs to be considered in s mjss and the controller design methods in the existing have some conservation to deal with these problems the weak infinitesimal operator is firstly derived from the point of view of probability distribution under the constraint of positive condition then some sufficient conditions for stochastic stability of positive s mjss are established by implying the linear lyapunov krasovskii functional depending on the bound of time varying delay furthermore an improved stabilizing controller is designed via decomposing the controller gain matrix such that the resulting closed loop system is positive and stochastically stable in standard linear programming the advantages of the new framework lie in the following facts 1 the weak infinitesimal operator is derived for s mjss with time varying delay under the constraint of positive condition and 2 the less conservative stabilizing controller is designed to achieve the desired control performance finally three examples one of which is the virus mutation treatment model are given to demonstrate the validity of the main results

stability analysis and l1 gain characterization for switched positive systems under dwell time constraint abstract this paper deals with the problems of stability analysis and l 1 gain characterization for continuous time switched systems consisting of positive subsystems with the aid of a discretized copositive lyapunov function a sufficient condition ensuring the asymptotic stability of continuous time switched positive systems under dwell time constraint is obtained which can be checked via linear programming furthermore the conservatism of the proposed approach is studied and the result with least conservatism in the framework of discretized copositive lyapunov function is obtained the result is then extended to l 1 gain characterization for switched positive systems with a prescribed dwell time an unweighted l 1 gain can be computed via solving a linear programming problem a numerical example and a practical traffic example are given to illustrate our results

l induced output feedback controller synthesis for positive nonlinear systems via t s fuzzy model approach abstract this paper investigates the l induced output feedback controller synthesis problem for positive takagi sugeno t s fuzzy systems for positive t s fuzzy systems a sufficient condition for stability and l induced performance is first put forward using a group of linear inequalities then on the basis of these inequalities the conditions on which static output feedback controllers exist are set up and to solve these conditions a method of iterative convex optimization is provided moreover a complete solution to the synthesis problem of the controller is proposed based on linear programming for positive t s fuzzy systems with single output or input finally two examples are presented to illustrate and verify the effective and applicable methods derived in this paper

derivatives of complex eigenvectors with distinct and repeated eigenvalues in this paper we investigate the computation of the first order derivatives of complex eigenvectors for general non defective eigensystems a new normalization condition is proposed with which we can compute unique first order derivatives of arbitrary differentiable eigenvectors of systems with distinct and repeated eigenvalues we also present an efficient algorithm to compute the particular solutions to the governing equations of the first order derivatives of eigenvectors finally numerical examples are included to demonstrate the validity of the proposed method copyright 2007 john wiley sons ltd

frequency limited mmb h _ infty model reduction for positive systems in this paper the problem of frequency limited mmb h infty model reduction for positive linear time invariant systems is investigated specifically our goal is to find a stable positive reduced order model for a given positive system such that the mmb h infty norm of the error system is bounded over a frequency interval of interest a new condition in terms of matrix inequality is developed for characterizing the frequency limited mmb h infty performance then an equivalent parametrization of a positive reduced order model is derived based on which an iterative algorithm is constructed for optimizing the reduced order model the algorithm utilizes coarse reduced order models resulting from generalized balanced truncation as the initial value both continuous and discrete time systems are considered in the same framework numerical examples clearly show the effectiveness and advantages of the proposed model reduction method

neuro fuzzy clustering of radiographic tibia image data using type 2 fuzzy sets abstract this paper presents the results of using type 2 fuzzy sets to assist in the pre processing of data for use with neuro fuzzy clustering for classification of sports injuries in the lower leg this research is concerned with the analysis of bone scans from stress related injuries to the tibia of particular interest is whether neural network based clustering techniques can help the consultant in classifying the images the work was motivated by the situation where there is a relatively small amount of relevant data and difficulties are faced by consultants in classifying the various types of injuries for this particular problem the consultant s interpretation of the image lends itself to representation using type 2 fuzzy sets this research sets out to address whether with fuzzy neuro clustering techniques some insights may be provided to the consultant that they can use along with their experience and knowledge the results of this approach indicate that the use of neural clustering using a type 2 representation can improve the classification of shin images

second order design sensitivities to assess the applicability of sensitivity analysis a quality criterion based on the cauchy ratio test for convergence of infinite series is suggested to examine the liability of systems to perform poorly under extrapolation

sensitivity analysis of discrete structural systems methods for calculating sensitivity derivatives for discrete structural systems are surveyed primarily covering literature published during the past two decades methods are described for calculating derivatives of static displacements and stresses eigenvalues and eigenvectors transient structural response and derivatives of optimum structural designs with respect to problem parameters the survey is focused on publications developed in nonstructural fields such as electronics controls and physical chemistry which are directly applicable to structural problems most notable among the nonstructural based methods are the adjoint variable technique from control theory and the green s function and fast methods from physical chemistry

l1 gain analysis and model reduction problem for boolean control networks in this paper the weighted l1 gain analysis and l1 model reduction problem for boolean control networks are proposed and investigated via semi tensor product method first the input energy and output energy are described by pseudo boolean functions based on which the definition of the weighted l1 gain is introduced by constructing a co positive lyapunov function a sufficient condition is established to ensure that a boolean control network is not only internally asymptotically stable but also has an l1 gain no more than a given scalar along this line by virtue of the properties of semi tensor product the l1 model reduction problem of a boolean control network is defined and converted to the l1 gain problem of another boolean control network with more nodes a sufficient condition for the l1 model reduction problem is then derived immediately and an algorithm is presented to compute the matrices in the reduced order model finally two examples including the boolean model for biochemical oscillators in the cell cycle are displayed to show the feasibility of the theoretical results

derivatives of eigenvalues and eigenvectors of a general complex matrix a survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non hermitian matrices is presented in addition a modification of one method based on a better normalizing condition is proposed methods are classified as direct or adjoint and are evaluated for efficiency operation counts are presented in terms of matrix size number of design variables and number of eigenvalues and eigenvectors of interest the effect of the sparsity of the matrix and its derivatives is also considered and typical solution times are given general guidelines are established for the selection of the most efficient method

linear copositive lyapunov functions for continuous time positive switched systems continuous time positive systems switching among p subsystems are introduced and a complete characterization for the existence of a common linear copositive lyapunov function for all the subsystems is provided when the subsystems are obtained by applying different feedback control laws to the same continuous time single input positive system the above characterization leads to a very easy checking procedure

dissipativity theory for nonnegative and compartmental dynamical systems with time delay nonnegative and compartmental dynamical system models are derived from mass and energy balance considerations that involve dynamic states whose values are nonnegative these models are widespread in engineering and life sciences and typically involve the exchange of nonnegative quantities between subsystems or compartments wherein each compartment is assumed to be kinetically homogeneous however in many engineering and life science systems transfers between compartments are not instantaneous and realistic models for capturing the dynamics of such systems should account for material in transit between compartments including some information of past system states in the system model leads to infinite dimensional delay nonnegative dynamical systems in this note we develop dissipativity theory for nonnegative dynamical systems with time delay using linear storage functionals with linear supply rates these results are then used to develop general stability criteria for feedback interconnections of nonnegative dynamical systems with time delay

new method for eigenvector sensitivity analysis with repeated eigenvalues and eigenvalue derivatives this paper proposes a new method of eigenvector sensitivity analysis for real symmetric systems with repeated eigenvalues and eigenvalue derivatives the derivation is completed by using information from the second and third derivatives of the eigenproblem and is applicable to the case of repeated eigenvalue derivatives the extended systems with a nonsingular coefficient matrix are constructed to calculate the particular solutions an efficient approach is developed to compute the homogeneous solutions associated with the repeated eigenvalue derivatives different constraints for calculating the eigenvector sensitivities are derived and discussed four numerical examples are presented to demonstrate the validity of the proposed method

eigensensitivity analysis for asymmetric nonviscous systems t he eigensensitivities of mechanical systems with respect to structural design parameters have become an integral part of many engineering design methodologies including optimization structural health monitoring structural reliability model updating dynamic modification reanalysis techniques and many other applications fox and kapoor 1 computed the derivative of each eigenvector as a linear combination of all of the undamped eigenvectors later adhikari and friswell 2 and adhikari 3 extended the modal method to the more general asymmetric systems with viscous and nonviscous damping respectively nelson 4 presented a method which requires only the eigenvector of interest by expressing the derivative of each undamped eigenvector as a particular solution and a homogeneous solution later friswell and adhikari 5 extended nelson s method to symmetric and asymmetric systems with viscous damping recently adhikari and friswell 6 extendednelson s method to symmetric and asymmetric nonviscously damped systems fox and kapoor 1 also suggested a direct algebraic method to calculate the eigensensitivity for symmetric undamped systems by solving a nonsingular linear system of algebraic equations lee et al 7 derived an efficient algebraic method which has a compact linear system with a symmetric coefficient matrix for symmetric systems with viscous damping later guedria et al 8 extended the algebraic method to general asymmetric viscous damped systems chouchane et al 9 reviewed the algebraic method and extended their method to the second order and high order derivatives of eigensolutions li et al 10 extended the algebraic method to symmetric and asymmetric nonviscously damped systems xu andwu 11 proposed a new normalization and presented a method for the computation of eigensolution derivatives of asymmetric systemswith viscously damping recently mirzaeifar et al 12 proposed a new method based on a combination of algebraic and modal methods for generally asymmetric viscously damped systems more recently li et al 13 proposed a method of design sensitivity analysis of asymmetric viscously damped systems with distinct and repeated eigenvalues which can compute the left and right eigenvector derivatives separately and independently all of the methods mentioned previously compute the eigensensitivities of asymmetric damped systems by using the left eigenvector however these methods have disadvantages in computational cost and storage capacity for the left eigenvector should be calculated to avoid using the left eigenvector an algebraic method is presented 14 which does not require the left eigenvector for asymmetric damped systems but this method is restricted to the case of viscous damping it should be noted that the coefficientmatrices of the algebraicmethodmay be ill conditioned due to the components of the additional constraints and system matrices in the coefficient matrices are not all of the same order of magnitude in addition 15 the normalization adapted in 14 and 12 will fail in some cases because it can equal zero or a very small number this note will present a method which is well conditioned and can calculate the eigensensitivity of asymmetric nonviscous damped systems without using the left eigenvector considering an n degree of freedom linear system with nonviscous viscoelastic damping 3 6 10

l1 gain performance analysis and positive filter design for positive discrete time markov jump linear systems a linear programming approach abstract this paper is concerned with the l 1 gain performance analysis and positive filter design for a positive discrete time markov jump linear system mjls by using a linear programming lp approach first by constructing a linear stochastic lyapunov function and introducing an equivalent deterministic positive discrete time linear system necessary and sufficient conditions in the form of lp are derived for stochastic stability and l 1 gain performance of the positive discrete time mjls then a sufficient condition on the existence of the desired positive l 1 gain filter is provided the desired positive l 1 gain filter can be designed by solving a standard lp problem the pest s structured population dynamic model is employed to illustrate the effectiveness of the proposed method

robust h sub spl infin control of uncertain markovian jump systems with time delay this paper is concerned with the robust stochastic stabilizability and robust h sub spl infin disturbance attenuation for a class of uncertain linear systems with time delay and randomly jumping parameters the transition of the jumping parameters is governed by a finite state markov process sufficient conditions on the existence of a robust stochastic stabilizing and spl gamma suboptimal h sub spl infin state feedback controller are presented using the lyapunov functional approach it is shown that a robust stochastically stabilizing h sub spl infin state feedback controller can be constructed through the numerical solution of a set of coupled linear matrix inequalities

stability and l_1 gain analysis of boolean networks with markovian jump parameters this paper presents some results on stability and l 1 gain analysis of boolean networks with markovian jump parameters a necessary and sufficient condition for global stability of the concerned boolean networks is given in terms of linear programming by utilizing the semi tensor product of matrices and some properties of linear positive systems then the definition of lyapunov function for stochastic boolean networks is presented and lyapunov theorem is derived moreover an l 1 gain problem for stochastic boolean networks with external disturbances is formulated and solved by a sufficient condition examples are shown to illustrate the effectiveness of the obtained results

equilibria stability and reachability of leslie systems with nonnegative inputs leslie systems a particular class of positive systems used in population dynamics and control are defined and analyzed a simple property relating sign and stability of their equilibria and some geometric characteristics of their reachability set in cases of bounded and unbounded inputs are proved all the properties do not hold in general in other classes of positive systems it is shown that leslie systems have strictly positive equilibria if and only if they are asymptotically stable their reachability set in the case of unbounded inputs is the positive cone generated by the reachability vectors while in the case of bounded inputs it is a polyhedron whose vertices can be easily computed all of these properties follow from the nonpositiveness of the coefficients of the characteristic polynomial of the system

improved nelson s method for computing eigenvector derivatives with distinct and repeated eigenvalues t he computation of derivatives of eigenvalues and eigenvectors with respect to model parameters is crucial for many applications 1 nelson 2 proposed an approach for general real eigensystemswith distinct eigenvalueswhere only the eigenvector of interest was required ojalvo 3 mills curran 4 dailey 5 and shaw and jayasuriya 6 developed nelson s method for real symmetric eigensystems with repeated eigenvalues for computation of a particular solution themethods described in 3 5 may fail in some circumstances other methods have been suggested by millscurran 4 and song et al 7 but they are difficult to implement when a system of linear equations is solved one hopes that the calculated solution is a close representation of the true solution the computed solution for a system with a large condition number may be inexact due to extreme sensitivity of the solution to small changes in its coefficient matrix and right column vectors 8 because some diagonal elements in the coefficient matrix for particular solutions are set to units its coefficients are not all of the same order of magnitude so the coefficient matrix has a large condition number in this note nelson s method is first extended to the case of repeated eigenvalues for the symmetric real eigensystems and its improvements are then presented the condition number of the coefficient matrix of the improved method is considerably reduced