norm based robust control of state constrained discrete time linear systems the author presents a theoretical framework for analyzing the stability properties of constrained discrete time systems in the presence of uncertainty and it is shown that this formalism provides a unifying approach including as a particular case the well known technique of estimating robustness bounds from the solution of a lyapunov equation these results are applied to the problem of designing feedback controllers capable of stabilizing a family of systems while at the same time satisfying state space constraints

quadratic stabilizability of uncertain systems a two level optimization setup abstract the problem of stabilizing linear systems subject to possibly fast time varying uncertainties is investigated necessary and sufficient conditions of quadratic stabilizability are discussed the design process is formulated as a two level optimization process which can be simplified if the uncertainty is bounded by a hyperpolyhedron

root locus approach to the stability analysis of interval matrices a new approach called the root locus approach is developed for the stability analysis of perturbed matrices the basic idea of this approach is to ensure that the root loci of a continuously perturbed matrix remain in the open left half complex s plane based on this approach new techniques are presented to analyse the stability of interval matrices examples are given to demonstrate the merit of the proposed theorems

a review of some methods for ranking fuzzy subsets this paper deals with the problem of ranking n fuzzy subsets of the unit interval a number of methods suggested in the literature is reviewed and tested on a group of selected examples where the fuzzy sets can be nonnormal and or nonconvex the ranking is obtained from i the index of strict preference defined by watson ii three indexes proposed by yager iii the algorithm used by chang iv three versions of the a preference index suggested by adamo v the index defined by baas and kwakernaak vi three modified versions used by baldwin and guild vii the method proposed by kerre viii three forms of the index suggested by jain ix the four grades of dominance studied by dubois and prade in simple cases the results are good for all the methods with some exceptions in questionable cases where the decision must be probably modelled in accordance with the context in which it is imbedded the best indexes seem to be the dominances suggested by dubois and prade these indexes do not force any particular choice but clearly describe the situation hence allowing the decision maker himself to make his best choice

the application of generalized diagonal dominance to linear system stability theory abstract this paper shows that the well known diagonal dominance condition associated with rosenbrock s stability theorems is unnecessary and can be replaced by a less restrictive generalized diagonal dominance condition similar results are derived for generalized block diagonally dominant systems whenever possible graphical interpretations are given to facilitate the implementation of these ideas in computer aided design packages

robust stability of interval matrices a computational approach a simple computational procedure is given to determine the robust stability of matrices containing interval parameter uncertainty the computation consists of determining the maximal phase difference of the characteristic polynomial evaluated over the vertices of the uncertain parameter set at each point of the stability boundary and verifying that this maximal phase difference is less than radians this follows as a direct application of the mapping theorem which allows us effectively to treat rank one perturbations of matrices we discuss the conservatism of the method and show how the solution may be improved to any desired level of accuracy we give several numerical examples of systems with state space perturbations and compare our results with those obtained by other methods

a fuzzy set preference model for consumer choice abstract a fuzzy set model for predicting consumer choice is developed by combining the vector conjoint model with fuzzy measurement in a new model that requires only ordinal data fuzzy set measurement of consumer preferences is examined by testing alternative set representations and an interactive set definition method a comparison test of predictive validity using identical data from 139 subjects showed large improvements in rank order prediction validity compared to a non fuzzy approach prediction improvements of 83 are attributable to the use of fuzzy set definitions for subject ratings with the first two of six ordered ranking predicted on average

stability analysis of gray discrete time systems the stability of discrete time system whose state matrix is an interval matrix is discussed in terms of lyapunov stability theory some sufficient conditions are obtained which guarantee the stability of gray discrete time systems or interval discrete time systems illustrative examples are given

robustness analysis with full structured uncertainties this paper deals with problems involving full structured rather than block diagonal uncertainty i e uncertainty blocks where each sub block or element may be an independent uncertainty rearranging this problem into standard block diagonal form results in an explosion in the required computation and so a number of researchers have proposed more efficient bounds in particular those based on non similarity scaling for such problems here we show how to map such problems into reduced size standard problems the standard bounds applied to the reduced size problem are then shown to be at least as accurate and require the same computational effort as earlier techniques with the added bonus that the standard upper bound is convex moreover this new approach is applicable in a much more general setting allowing one to efficiently compute both robust stability and robust performance for problems involving multiple real and complex uncertainty blocks any number of which may be full structured

improved stability robustness bounds using state transformation for linear discrete systems abstract sufficient condition bounds on the linear time varying perturbations for robust stability of an asymptotically stable linear time invariant discrete time system have been reported recently the development involves both schwartz and triangular inequalities and tends to give conservative results this paper uses state transformation to obtain improvement in these bounds both unstructured and structured perturbation bounds are shown to improve using transformations the proposed analysis is applied to a fourth order macroeconomic system model

stability robustness of interval matrices via lyapunov quadratic forms a sufficient condition for the robust stability of a class of interval matrices is derived using the lyapunov approach the matrices considered have elements which are nonlinear functions of a vector of independent and bounded parameters the robust stability condition requires that a quadratic form be positive definite in a finite number of conspicuous points of an enlarged parameter space

an approach to robust stability of matrix polytopes through copositive homogeneous polynomials an approach to guaranteeing the stability of a polytope of matrices is proposed previous results in the literature have made the obvious connection between various robust stability problems and a test for positivity of a multivariable polynomial such results are extended in order to demonstrate that all matrices within a polytope are stable is and only if an associated homogeneous polynomial is strictly copositive the additional structure obtained by exploiting homogeneity of this multivariable polynomial leads to several computationally tractable sufficiency tests for establishing either robust stability or instability of a polytope of matrices

a multirule base controller using the robust property of a fuzzy controller and its design method this paper suggests a new fuzzy adaptive controller which is able to solve the problems of classical adaptive controllers and conventional fuzzy adaptive controllers it explains the architecture of a fuzzy adaptive controller using the robust property of a fuzzy controller the basic idea of new adaptive control scheme is that an adaptive controller can be constructed with parallel combination of robust controllers this new adaptive controller uses a multirule base architecture which has several independent fuzzy controllers in parallel each with different robust stability area out of several independent fuzzy controllers the most suited one is selected by a system identifier which observes variations in the controlled system parameter here we propose a design procedure which can be carried out mathematically and systematically from the model of a controlled system related mathematical theorems and their proofs are also given the performance of the proposed adaptive control algorithm is analyzed through a design example and a dc motor control simulation

stability analysis of interval matrices another sufficient condition a sufficient condition for the stability of interval matrices is presented based on a lyapunov approach the condition while requiring the solution of a lyapunov matrix equation removes the restrictions imposed by heinen 1984 examples given illustrate the improvement of the proposed condition over the ones given by heinen and bialas 1983 and daoyi 1985

branch point placement abstract power series approximations to eigenvalue and eigenvector functions have a role to play in the design of multivariable feedback systems the convergence and sensitivity properties of these approximations depend on the positions of the branch points of the characteristic function of the appropriate rational transfer function this paper gives a quantitative treatment of this problem and proposes a set of suitable bounds for the case of isolated as well as latent branch points given the importance of the locations of the branch points from a practical viewpoint it is desirable to know whether it is possible to precondition the transfer function matrix so as to adjust the positions of the branch points to this end the paper proposes suitable algorithms and concludes with two simple design studies which demonstrate the benefits of preconditioning

characterization of robust controllers abstract this paper presents a procedure for designing a robust controller which is able to stabilize a multivariable system with interval uncertainties in the system parameters the uncertain parameters are assumed to lie within known intervals the fundamental idea behind the procedure is to characterize the set of robust controllers as a convex set by the new matrix inequalities result a suitable controller can then be chosen by means of an optimization algorithm the controller thus chosen will be able to ensure that the closed loop matrix lies within desired intervals for all the prescribed interval uncertainties in the system parameters

pedestrian movement analysis in transfer station corridor velocity based and acceleration based abstract in this paper pedestrians are classified into aggressive and conservative ones by their temper aggressive pedestrians walking through crowd in transfer station corridor is analyzed treating pedestrians as particles this paper uses the modified social force model msfm as the building block where forces involve self driving force repulsive force and friction force the proposed model in this paper is a discrete model combining the msfm and cellular automata ca model where the updating rules of the ca are redefined with msfm due to the continuity of values generated by the msfm we use the fuzzy logic to discretize the continuous values into cells pedestrians can move in one step with the observation that stimulus around pedestrians influences their acceleration directly an acceleration based movement model is presented compared to the generally reviewed velocity based movement model in the acceleration based model a discretized version of kinematic equation is presented based on the acceleration discretized with fuzzy logic in real life some pedestrians would rather keep their desired speed and this is also mimicked in this paper which is called inertia compared to the simple triangular membership function a trapezoidal membership function and a piecewise linear membership function are used to capture pedestrians inertia with the trapezoidal and the piecewise linear membership function many overlapping scenarios should be carefully handled and dubois and prade s four index method is used to completely describe the relative relationship of fuzzy quantities finally a simulation is constructed to demonstrate the effect of our model

pole assignment of linear uncertain systems in a sector via a lyapunov type approach the problem of designing robust control laws in performance and in stability for uncertain linear systems is considered performances are taken into account using root clustering of the closed loop dynamic matrix in a sector of the complex plane a synthesis procedure based on a sufficient condition for quadratic stabilization and root clustering such as stabilizability is given using an auxiliary convex problem the results are illustrated by a significant example from the literature

stability and performance robustness for multivariable linear systems abstract this paper deals with both aspects of stability and performance robustness of linear systems in the time domain a linear time invariant feedback control law which yields the largest set of parameter variations is first determined it is then used as an initial guess for designing a robust control law which produces satisfactory performance for each of several operating points of the system given a priori the stability robustness properties of the resulting control law is also studied the proposed approach is applied to an example yielding larger stability bounds including satisfactory performance in comparison with recently reported results

another sufficient condition for the stability of interval matrices a sufficient condition for the stability of interval matrices is presented which is based on the condition given by yedavalli 1985 b examples are given which illustrate the improvement of the proposed condition over that given by yedavalli 1986

robust control for linear systems with structured state space uncertainty abstract a recent sufficient condition for the stability robustness of linear systems with time varying norm bounded state space uncertainty is extended to include the structure of the uncertainty our new result requires that the nominal eigenvalues lie to the left of a vertical line in the complex plane which is determined by a norm involving the structure of the uncertainty and the nominal closed loop eigenvector matrix therefore this robustness result is especially well suited to the design of control systems using eigenstructure assignment when the uncertainty is time invariant our norm is also an upper bound on the incremental eigenvalue perturbations we also consider the use of perron weightings to reduce conservatism and the extension of the results to discrete time systems

structured singular values with nondiagonal structures i characterizations the purpose of this two part series is to provide a robustness analysis framework for a class of problems with highly structured modeling uncertainties this framework is more general than that of the usual block diagonally structured uncertainties and it corresponds to a structure consisting of block by block matrix perturbations we study the structured singular value with respect to this structure and we establish a number of novel results for this notion this paper contains a study on the properties of the structured singular value we give an alternative characterization of this notion as the solution of a smooth optimization problem furthermore we show that under a certain circumstance the structured singular value reduces to a vector induced matrix norm

robust control with structure perturbations the problem of making a given stabilizing controller robust so that the closed loop system remains stable for prescribed ranges of variations of a set of physical parameters in the plant the problem is treated in the state space and transfer function domains in the state space domain a stability hypersphere is determined in the parameter space using lyapunov theory the radius of this hypersphere is iteratively increased by adjusting the controller parameters until the prescribed perturbation ranges are contained in the stability hypersphere in the transfer function domain a corresponding stability margin is defined and optimized on the basis of the recently introduced concept of the largest stability hypersphere in the space of coefficients of the closed loop characteristic polynomial the design algorithms are illustrated by examples

improved measures of stability robustness for linear state space models in this paper the aspect of stability robustness of linear systems is analyzed in the time domain a bound on the structured perturbation of an asymptotically stable linear system is obtained to maintain stability using a lyapunov matrix equation solution the resulting bound is shown to be an improved bound over the ones recently reported in the literature also special cases of the nominal system matrix are considered for which the bound is given in terms of the nominal matrix thereby avoiding the solution of the lyapunov matrix equation examples given include comparison of the proposed approach with the recently reported results

on sufficient conditions for the stability of interval matrices abstract we investigate the hurwitz and schur stability of interval matrices using lyapunov s second method and interval analysis techniques previous results require a check of the definiteness of 2 n n 1 2 concerns of a certain interval matrix the present results require a check of the definiteness of only 2 n 1 corners

robustness analysis of matrices with highly structured uncertainties lyapunov s method is used to analyze the robustness of system matrices with structured uncertainties in particular the 2 norm matrix measure is used to give less conservative stability results

a hybrid approach to combine fuzziness and randomness in travel choice prediction abstract several approaches have been developed in order to deal with uncertainty in the prediction of travellers choices uncertainty almost always affects travel alternatives in several different choice contexts however the way in which this uncertainty affects choice options may consistently vary two main types of uncertainty can be identified randomness and fuzziness this paper discusses the use of a hybrid approach for choice modelling of travellers behaviour in choice contexts that involve conditions of high variability and uncertainty the aim of the work is to implement a hybrid methodology based on the use of a two term hybrid utility which allows taking into account at the same time the effects of both random and fuzzy uncertainty on travellers choice behaviour an application of the proposed methodology to a transit choice context is then presented

two undecidability results for chain code picture languages it is undecidable whether or not two 1 retreat bounded regular languages describe exactly the same set of pictures or they describe a picture in common

a new robust stability criterion for linear and non linear multivariable feedback systems earlier eigenvalue inclusion regions are replaced by new regions which are tight and thus lead to sufficient and necessary stability conditions for uncertain linear multivariate systems in the presence of unstructured perturbations the approach provides an exact and immediate assessment of gain and phase margins when applied to systems with sector bounded but unstructured non linearities the inclusion regions produce a necessary and sufficient test for the circle criterion conditions to hold in the multivariable case as such the resulting stability criterion gives the best possible nyquist type extension of the circle criterion to the multivariable case for unstructured non linearities

stability analysis of interval matrices improved bounds new sufficient conditions for the stability of interval matrices are presented based on the lyapunov stability approach as well as on the frequency domain approach the conditions help to overcome the conservatism of the existing criteria for the stability of interval matrices based on a matrix approach several numerical examples are given to demonstrate the new conditions and to compare them with results previously reported

stability analysis of dynamic interval systems abstract the stability analysis of interval matrices with certain stability margins is considered by means of similarity transformation and gershgorin s theorem new criteria are developed and illustrated by examples we also demonstrate a counter example to a recent result by argoun 1986

perturbation bounds for robust stability in linear state space models abstract this paper addresses the aspect of stability robustness of linear systems in the time domain upper bounds on the linear perturbation of an asymptotically stable linear system are obtained to maintain stability both for structured as well as unstructured perturbations using the lyapunov approach for structured perturbation the resulting bound is such that it garners the structural information about the nominal as well as the perturbation matrix into a single unified expression in the case of unstructured perturbations special features of the nominally stable matrix are exploited resulting in simpler expressions for the bound without the need to solve the lyapunov equation improvement of the proposed measures is illustrated with the help of examples

sufficient conditions for stability of interval matrices extremely simple sufficient conditions are presented for the stability of interval matrices these complement the necessary and sufficient conditions developed by bialas 1983 which become unwieldy for large matrices 4 4 and above

simple criteria for stability of interval matrices in this paper the simple sufficient conditions are presented for the stability of a constant real matrix whose elements are not known precisely but we know the upper and lower bounds of intervals in which the elements of matrix a are confined these conditions are also applied in determining the stability and the degree of stability of a matrix

characterization of allowable perturbations for robust stability the problem of determining stability for a closed loop linear multivariable process in the presence of ill defined process perturbations is considered it is shown that m matrices may be used to characterize a class of allowable perturbations

stability robustness analysis of digital control systems in state space models the stability robustness of discrete linear time invariant systems in state space models is analysed based on a root locus approach and from the stable eigenvalue viewpoint fundamental criteria for testing the stability robustness of autonomous systems are derived and applied to the robustness analysis of multivariable feedback systems both the norm bound and the element bounds for the allowed perturbations are obtained a stability robustness index is denned which is useful both for the analysis and synthesis of control systems

on the equivalence between similarity and nonsimilarity scaling in robustness analysis in the analysis of multivariable systems in the presence of structured uncertainties similarity scaling and nonsimilarity scaling techniques have been independently proposed as methods for obtaining nonconservative robustness measures in order to fully exploit the unique advantages of each method it is desirable to obtain the required nonsimilarity scaling matrices directly from the associated similarity scaling matrix and vice versa without the need for separate optimizations the authors present an explicit relationship developed between the similarity and nonsimilarity scaling matrices from the optimal similarity scaling several applications of the results are also presented

characterization of allowable perturbations of a closed loop system with pole placement controller the problem of determining stability of a closed loop transfer function in the presence of coefficient perturbations is considered the results of interval polynomial theory are used to characterize the allowable interval of variation

a necessary and sufficient condition for the stability of interval matrices consider the linear dynamical system described by the equation xdot t ax t where a is a constant real matrix with dimensions n n and the elements of matrix a are not known precisely we know only the upper and lower bounds of the intervals in which the elements of matrix a are confined in this paper there is proved a necessary and sufficient condition for the stability of solutions of eqn 1 with incomplete information about the elements of matrix a

robustness analysis of feedback systems with block diagonal structured uncertainties the results for magnitude bounded diagonal perturbation are extended to norm bounded block diagonal perturbation a useful consequence to this extension is that an easily computable upper bound for the structured singular value via suboptimal diagonal similarity scaling is obtained it is concluded that the results are applicable to a wider class of perturbations i e the norm which bounds the perturbation p in this study need not be the 2 norm maximum singular value in the scalar case this does not give much advantage as all pth norms reduce to the magnitude of the element however in the matrix case different norms would characterize different types of perturbations

rank preservation of matrices with structured uncertainties and its applications in robust control theory matrix rank is determined by the nonsingularity of its submatrices for matrices in which entries are quadratic functions of some uncertain parameters this paper derives sufficient conditions on parameters to that ensure the matrices preserve to some degrees the ranks they have when the parameters are all zero the rank preservation problem is converted to the nonsingularity analysis problem of the minors of the matrix in discussion and suitable tools such as the spl mu analysis method are used to solve the problem applications in robust control theory including tests for robust controllability observability minimum phaseness coprimeness and schur stability are given together with illustrative examples

improved quantitative measures of robustness for multivariable systems asymptotically stable linear systems subject to unstructured time varying perturbations are considered allowable perturbation bounds are obtained such that the perturbed systems remain stable these bounds are derived iteratively by means of adjusting a sequence of lyapunov matrices in comparison with existing methods less conservative quantitative measures of robustness are obtained

stability robustness of the discrete time lqg system under plant perturbation and noise uncertainty in this paper the robustness of discrete time lqg problems is studied the system to be controlled is described by the usual state space formulation but includes the structure of plant parameter perturbations and noise uncertainty a simple and direct way is given to derive a saddle point inequality of the closed loop system performance to cope with noise uncertainty and one sufficient condition for system stability robustness under plant perturbation is presented

perfectly quilted rectangular snake tilings we introduce a particular form of snake tilings to define picture languages and relate the obtained family to the recognizable picture languages as defined by wang tiles the correspondence for substitution tilings is even closer and hence is applicable to the hilbert curve

singular value and eigenvalue techniques in the analysis of systems with structured perturbations a new range of techniques is introduced for the purpose of exploiting information about the structure of the perturbation associated with uncertain linear multi variable feedback systems the class of perturbation considered is wide and ignores only the phase information of the individual elements of the perturbation matrix it encompasses diagonal block diagonal and other forms of block structured perturbations the techniques developed provide a means of assessing stability margins and also lead to an extension of the nyquist criterion

undecidability of existential properties in picture languages abstract we are interested in the description of a set of pictures by string languages by using several semantics segments 12 segments with blank moves 8 and pixels 10 we give a method to code the post correspondence problem in rational picture languages in order to show the undecidability of existence of words satisfying a given property in a rational language in particular we study the properties like is a self avoiding word is a minimal picture word or describes a connected picture

the e equilibrium in transportation networks abstract the principle of traffic equilibrium wardrop 1952 demands that the trip makers have enough knowledge of transportation networks which needs to be attained by accumulating experiences for a long time because of the complexity of traffic situation in the networks the route choice decisions for trip makers are however not always optimal objectively as a consequence it is impossible to strictly attain wardrop equilibrium in this paper a new concept of equilibrium equilibrium is proposed under the realistic assumption i e the fuzzy road information and random route choices equilibrium in the network is discussed by adopting fuzzy set theory mixed stochastic games and brouwer fixed point theorem in topological space the conclusion is that there is equilibrium in the real transportation network and this equilibrium has some deviations from the strict wardrop equilibrium the notion of equilibrium extends the traditional notion of network equilibrium it shows that traffic flow in the network converges to a region rather than to the points

improved robust stability bounds for discrete time linear regulators with computational delays abstract recently obtained stability robustness bounds on linear time varying perturbations of an asymptotically stable linear time invariant discrete time system are applied to linear regulators with computational delays the bounds were developed using lyapunov theory and singular value decomposition for unstructured and structured time varying perturbations the new structured perturbation bound may provide improved results for the elemental perturbations over a bound based on the unstructured perturbation bound of ishihara 1988 automatica 24 696 700 as indicated both by an example and by sufficient conditions

complexity and decidability for chain code picture languages abstract a picture description is a word over the alphabet u d r l where u means go one unit line up from the current point and d r and l are interpreted analogously with down right and left instead of up by this a picture description describes a walk in the plane its trace is the picture it describes a set of picture descriptions describes a chain code picture language this paper investigates complexity and decidability questions for these picture languages thus it is shown that the membership problem is np complete for regular picture languages i e picture languages described by regular languages of picture descriptions and that it is undecidable whether two regular picture description languages describe a picture in common after this we investigate so called stripe picture languages all pictures are within a stripe defined by two parallel lines providing better complexity and decidability results membership is decidable in linear time for regular stripe picture languages emptiness of intersection and equivalence is decidable for regular stripe picture languages

robust stability analysis of linear continuous discrete time systems with output feedback controllers the robust stability of linear systems with output feedback controllers and time varying uncertain parameters is considered the robust stability bounds for time varying uncertain parameters are given using the lyapunov method when there are no uncertain parameters in the input and or output matrices it is shown that the result for continuous time systems is the same as that presented by k m zhou and p p khargonekar 1987 and the result for discrete time systems is better than that of s r kolla 1989 for the same example

eigenvalue assignment robustness the analysis for autonomous system matrices abstract new techniques are presented for the analysis of eigenvalue assignment robustness the basic idea is to use a root locus approach to ensure that the eigenvalues of a dynamic system under parameter perturbations are restricted in the distinct desired regions no restriction is imposed on the shapes of the specified regions both the norm bound and the element bound for the allowable perturbations are obtained scaling techniques are proposed to increase the allowable element bound the proposed methods are applicable to the continuous time case as well as to the discrete time case when the eigenvalues are just required to locate in the stable region the proposed criteria will become the stability robustness criteria

generalized nyquist bands for structured and highly structured uncertainty additive uncertainty of multivariable systems is often assumed to be either unstructured or structured depending on whether the size or uncertainty is defined in terms of maximum singular value bounds or bounds on the moduli of individual elements in many practical situations however more information is available and in particular the frequency response of the elements of uncertainty often display directionality to exploit this directionality the present paper adopts elliptical rather than circular bounds on the elements of uncertainty and derives an algorithm that generates exact eigenvalue regions which in turn can be deployed in the construction of exact generalized nyquist bands with the aid of such bands it is possible to get an exact non conservative assessment of the stability margins and of other aspects of the dynamic performance of a much wider class of uncertain multivariable systems

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

fuzzy route choice model for traffic assignment abstract in order to represent traffic assignment on a road network we propose a new route choice model taking account of the imprecisions and the uncertainties lying in the dynamic choice process this model makes possible a more accurate description of the process than those deterministic or stochastic used in the literature we assume that drivers choose a path all the more than it is foreseen to have a lesser cost the predicted cost for each path is modelled by a fuzzy subset which can represent imprecision on network knowledge e g length of links as well as uncertainty on traffic conditions e g congested or uncongested network incident the costs of all possible paths are compared and result in an attractiveness degree for each path various comparison indices can be used to represent the different possible natures of drivers when making their decisions pessimistic optimistic risk taking risk averting the fuzzy choice model was compared with the logit model a widely used stochastic discrete choice model and has been proved to be able to find the same results the effect of advanced travellers information systems atis on drivers is modeled as a modification of the imprecision or the uncertainty of the predicted cost of a route

a note on robust stability bounds the authors comment on stability robustness bounds for linear systems with multiple uncertain parameters which were obtained by means of lyapunov functions results obtained with quadratic and with vector lyapunov functions are compared simple examples are used to illustrate the effects of the choice of functions corresponding majorizations and system decompositions

the majorant lyapunov equation a nonnegative matrix equation for robust stability and performance of large scale systems a new robust stability and performance analysis technique is developed the approach involves replacing the state covariance by its block norm matrix i e the nonnegative matrix whose elements are the norms of subblocks of the covariance matrix partitioned according to subsystem dynamics a bound i e majorant for the block norm matrix is given by the majorant lyapunov equation a lyapunov type nonnegative matrix equation existence uniqueness and computational tractability of solutions to the majorant lyapunov equation are shown to be completely characterized in terms of m matrices two examples are considered for a damped simple harmonic oscillator with uncertain but constant natural frequency the majorant lyapunov equation predicts unconditional stability and for a pair of nominally uncoupled oscillators with uncertain coupling the majorant lyapunov equation shows that the range of nondestabilizing couplings is proportional to the frequency separation between the oscillators a result not predictable from quadratic or vector lyapunov functions

handling uncertainty in route choice models from probabilistic to possibilistic approaches abstract in order to design effective advanced traffic information systems atis suitable mathematical models have to be defined to simulate the effects of information on users route choice behaviour and then to incorporate it into traffic assignment models to estimate how traffic demand loads the roads network to face this problem it is necessary to deal with uncertainty that plays a crucial role in the users decision making processes to this purpose this paper first analyses how uncertainty affects users route choice process and how traffic assignment models may take it into account in literature route choice behaviour modelling is widely solved within the random utility theory framework but we show in this paper that such an approach only considers one type of uncertainty more precisely the consideration of randomness of traffic by drivers is for example hardly ever represented in classical models in spite of its importance in the management of information by drivers starting from the presented analysis a new route choice model is also proposed to represent explicitly the uncertainty lying in users route choice behaviour it is based on recent developments in possibility theory which is an alternate way to probability theory in order to represent or measure uncertainty

convergence property of interval matrices and interval polynomials in association with robust control system design and analysis the hurwitz property of interval matrices and interval polynomials has recently been actively investigated however its discrete counterpart the convergence property has seemingly not been much discussed in this paper this property is studied in comparison with the hurwitz counterpart some conditions under which interval matrices or interval polynomials are convergent are derived

improved stability robustness bounds for digital control systems in state space models this paper presents stability robustness bounds for linear discrete time systems with time invariant perturbations these bounds extend the previous investigations for independent perturbations to dependent perturbations and provide improved results it is shown that the dependent perturbation bound includes an independent perturbation bound previously reported as a special case these results are illustrated with simple examples

normality scaling and eigenvalue inclusion regions one approach to establishing eigenvalue inclusion regions for robust stability analysis of uncertain linear multivariable feedback systems involves replacing the nominal plant matrix by an approximating normal one this approach incurs additional uncertainty but has the advantage that the resulting regions are insensitive to small perturbations these regions are obviously conservative and it is shown in this paper how this conservatism may be reduced by utilizing the eigenvalue preserving operation of similarity scaling

robust eigenvalue clustering in a specified circular region for linear uncertain discrete singular systems with state delay in this paper the robust eigenvalue clustering in a specified circular region problem i e the robust d stability problem of linear discrete singular time delay systems with structured elemental parameter uncertainties is investigated under the assumptions that the linear nominal discrete singular time delay system is regular and causal and has all its finite eigenvalues lying inside a specified circular region a new sufficient condition is proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time delay system when all the finite eigenvalues are just required to locate inside the unit circle of the z plane the proposed criterion will become the stability robustness criterion the presented criterion is mathematically proved to be less conservative than the existing ones reported very recently in the literature

an algorithm for the computation of the structured complex stability radius abstract perturbed state space models of the form x a bdc x are considered where a b c are given matrices a is stable and d is an unknown complex perturbation matrix a reliable and efficient algorithm for the computation of the norm of the minimal norm destabilizing matrix d is presented the performance of the algorithm and possible applications are illustrated

the membership and equivalence problems for picture languages abstract the paper describes two principal results 1 there is a nondeterministic polynomial time algorithm to determine whether an arbitrary picture is a member of a context free picture language and 2 the equivalence problem for regular picture languages is not decidable not even partially decidable this solves open questions described in earlier publications furthermore these results are best possible that is the membership problem for context free picture languages was earlier shown to be np hard and the complement of the equivalence problem for regular picture languages is easily seen to be partially decidable

necessary and sufficient stability criterion for systems with structured uncertainties the major principal direction alignment principle a necessary and sufficient stability criterion is proved for multivariable systems in the presence of element by element bounded perturbations the result constitutes a solution to the problem of computing the function for this class of perturbations and the paper also provides an explicit approximation to the exact criterion

necessary and sufficient conditions for stability of time varying discrete interval matrices sufficient conditions for the stability of time varying discrete interval systems are presented the spectral radius of the maximum absolute matrix of all interval matrices is employed as opposed to utilizing the matrix norm or lyapunov theorem for special cases our result becomes a necessary and sufficient condition for stability furthermore the proposed conditions are inclusive of the previous results of stability of time invariant interval systems

reduced order dynamic compensator design for stability robustness of linear discrete time systems a reduced order dynamic compensator design is presented with stability robustness for linear discrete systems by including a stability robustness component in addition to the standard quadratic state and control terms in the performance criterion the robustness component is based on an unstructured perturbation stability bound for time varying perturbations the controller design is developed by the parameter optimization technique and involves the solution of five algebraic matrix equations four of which are discrete time lyapunov matrix equations

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

robust multivariable feedback design a primary role of feedback design is to enable a system to cope with the inevitable uncertainly associated with its description although it is often the case that we have at hand a practical description of both the size and structure of the expected uncertainty simple multivariable design strategies which effectively incorporate this information have been slow to appear a rigorous development of the uncertainly problem for linear multivariable feedback systems is presented utilizing the characteristic locus framework and then a simple geometric alignment property is exploited in order to formulate a systematic design strategy focusing on a pi implementation for the resulting controllers

a method for estimating upper and lower bounds of eigenvalues of closed loop systems with uncertain parameters using the convex model theory the vibration control problem of structures with uncertain parameters is discussed which is approximated by a deterministic one a method for estimating the upper and lower bounds of eigenvalues of the closed loop systems is presented by combining the matrix perturbation and optimization the present method is applied to a vibration system to illustrate the application the numerical results show that the present method is effective

using string languages to describe picture languages a picture is a set of unit lines from the cartesian plane considered as a square grid a word over the alphabet l r u d is a picture description in the sense that it represents a traversal of a picture where the interpretation of the symbols l r u d is l go one unit line to the left of the current point r go one unit line to the right of the current point u go one unit line up from the current point and d go one unit line down from the current point a set of picture descriptions forms a picture description language this paper investigates the basic properties of pictures and picture description languages from the formal language theory point of view

interval finite element method for dynamic response of closed loop system with uncertain parameters in practical engineering it is difficult to obtain all possible solutions of dynamic responses with sharp bounds even if an optimum scheme is adopted where there are many uncertain parameters in this paper using the interval finite element ife method and precise time integration pti method we discuss the dynamic response of vibration control problem of structures with interval parameters with matrix perturbation theory and interval arithmetic the algorithm for estimating upper and lower bounds of dynamic response of the closed loop system is developed directly from the interval parameters two numerical examples are given to illustrate the application of the present method the example 1 is used to show the applicability of the present method the example 2 is used to show the validity of the present method by comparing the results with those obtained by the classical random perturbation method copyright 2006 john wiley sons ltd

reduced conservatism in stability robustness bounds by state transformation this note addresses the issue of conservatism in the time domain stability robustness bounds obtained by the lyapunov approach a state transformation is employed to improve the upper bounds on the linear time varying perturbation of an asymptotically stable linear time invariant system for robust stability this improvement is due to the variance of the conservatism of the lyapunov approach with respect to the basis of the vector space in which the lyapunov function is constructed improved bounds are obtained using a transformation on elemental and vector norms of perturbations i e structured perturbations as well as on a matrix norm of perturbations i e unstructured perturbations for the case of a diagonal transformation an algorithm is proposed to find the optimal transformation several examples are presented to illustrate the proposed analysis