system analysis via integral quadratic constraints this paper introduces a unified approach to robustness analysis with respect to nonlinearities time variations and uncertain parameters from an original idea by yakubovich 1967 the approach has been developed under a combination of influences from the western and russian traditions of control theory it is shown how a complex system can be described using integral quadratic constraints iqc for its elementary components a stability theorem for systems described by iqcs is presented that covers classical passivity dissipativity arguments but simplifies the use of multipliers and the treatment of causality a systematic computational approach is described and relations to other methods of stability analysis are discussed last but not least the paper contains a summarizing list of iqcs for important types of system components

a fusion approach for managing multi granularity linguistic term sets in decision making the aim of this paper is to present a fusion approach of multi granularity linguistic information for managing information assessed in different linguistic term sets multi granularity linguistic term sets together with its application in a decision making problem with multiple information sources assuming that the linguistic performance values given to the alternatives by the different sources are represented in linguistic term sets with different granularity and or semantic in this context a decision process based on two steps is proposed with a view to obtaining the solution set of alternatives first the fusion of the multi granularity linguistic performance values is carried out in order to obtain collective performance evaluations in this step on the one hand the multi granularity linguistic information is made uniform using a linguistic term set as the uniform representation base the basic linguistic term set on the other hand the collective performance evaluations of the alternatives are obtained by means of an aggregation operator being fuzzy sets on the basic linguistic term set second the choice of the best alternative s from the collective performance evaluations is performed to do that a fuzzy preference relation is computed from the collective performance evaluations using a ranking method of pairs of fuzzy sets in the setting of possibility theory applied to fuzzy sets on the basic linguistic term set then a choice degree may be applied on the preference relation in order to rank the alternatives

affine parameter dependent lyapunov functions and real parametric uncertainty this paper presents new tests to analyze the robust stability and or performance of linear systems with uncertain real parameters these tests are extensions of the notions of quadratic stability and performance where the fixed quadratic lyapunov function is replaced by a lyapunov function with affine dependence on the uncertain parameters admittedly with some conservatism the construction of such parameter dependent lyapunov functions can be reduced to a linear matrix inequality lmi problem and hence is numerically tractable these lmi based tests are applicable to constant or time varying uncertain parameters and are less conservative than quadratic stability in the case of slow parametric variations they also avoid the frequency sweep needed in real spl mu analysis and numerical experiments indicate that they often compare favorably with spl mu analysis for time invariant parameter uncertainty

extensions of states on mv quantales abstract we consider the lattice of the ordered right continuous families of elements of a dual quantale with the index set 0 1 called its rc extension and the lattice of the ordered n 1 tuples with n 1 of elements of this dual quantale its n extension equipped with a dual quantale structure that generalizes the canonical extension proposed by hohle and weber of particular interest is the existence of states on n extensions of finite mv chains we generalize the recent results of weber by incorporating effectible girard quantales which are introduced by the author

lpv system analysis via quadratic separator for uncertain implicit systems this paper considers a class of linear systems containing time varying parameters whose behavior is not known exactly we assume that the parameters vary within known intervals and there are known bounds on their rates of variation our objective is to give a computationally verifiable condition that guarantees stability of the system for all possible parameter variations we first point out that the information on the rate bounds can be exploited by considering an augmented system described by an implicit model we then develop a tool called the quadratic separator for stability analysis of uncertain implicit systems using this tool a sufficient stability condition is obtained for the original linear parameter varying system moreover we show that the stability condition obtained is equivalent to the existence of a lyapunov function that depends on the parameters in a linear fractional manner finally the computational aspects of the proposed stability conditions are addressed

operators and comparisons of hesitant fuzzy linguistic term sets the theory of hesitant fuzzy linguistic term sets hfltss is very useful in objectively dealing with situations in which people are hesitant in providing linguistic assessments the purpose of this paper is to develop comparison methods and study the aggregation theory for hfltss we first define operations on hfltss and give possibility degree formulas for comparing hfltss we then define two aggregation operators for hfltss a hesitant fuzzy lwa operator and a hesitant fuzzy lowa operator in actual application we use these operators and the comparison methods to deal with multicriteria decision making problems with different situations in which importance weights of criteria or experts are known or unknown

group decision making with a fuzzy linguistic majority abstract the determination of solutions in group decision making is considered the point of departure is a collection of individual fuzzy preference relations a solution is derived either directly from the individual fuzzy preference relations or by constructing first a social fuzzy preference relation as opposed to conventional approaches in which a crisp threshold type majority rule is used we employ a fuzzy majority rule specified by a fuzzy linguistic quantifier e g most much more than 50 etc a calculus of linguistically quantified propositions is applied using the fuzzy majority various solution concepts are derived mainly of the type of core minimax opposition set and consensus winner

lmi characterization of structural and robust stability the discrete time case abstract this paper extends to the discrete time case some robust stability conditions recently obtained for continuous time systems those conditions are expressed in terms of linear matrix inequalities lmi being thus simply and efficiently computable as in the continuous time case parameter dependent lyapunov functions can be constructed and consequently the new approach can yield much sharper and less conservative results than the simultaneous stability approach in particular well known stability problems namely d stability and robust stability in the presence of diagonally structured uncertainty can be more efficiently addressed numerical examples are included to illustrate the advantages of the new stability conditions

measure free conditioning and extensions of additive measures on finite mv algebras using the well known representation of any finite mv algebra as a product of finite mv chains as factors we obtain a representation of its canonical extension as a girard algebra product of the canonical extensions of the mv chain factors based on this representation and using the results from our last paper we characterize the additive measures on any finite mv algebra resp the weakly and the strongly additive measures on its canonical girard algebra extension and that as convex combinations of the corresponding measures on the respective factors after that we apply the results to measure free defined conditional events which for this reason are considered as elements of the canonical extension of a finite mv algebra of events this definition for conditional events is naturally equivalent to the well known definition as lattice intervals of events here the weak additivity is considered as a reasonable notion for a global additivity property of a measure extension these extensions are essentially different from the measure extension which has a form analogous to the classical conditional probability but which is only levelwise additive moreover the measure free approach of this paper is completely different from the classical approach in which conditional measures of events given a fixed condition event are considered based on additive measures states of events without having defined conditional events

robust spl hscr sub spl infin filtering for discrete time linear systems with uncertain time varying parameters this paper deals with the problem of robust spl hscr sub spl infin filtering for linear discrete time state space models with uncertain time varying parameters the parameters enter affinely into the state space model matrices and their admissible values and variations are assumed to belong to given intervals a method is derived for designing a linear stationary asymptotically stable filter with a prescribed spl hscr sub spl infin performance in spite of large parameter uncertainty the proposed method incorporates information on available bounds on both the admissible values and variation of the uncertain parameters and is based on a lyapunov function with quadratic dependence on the parameters the filter design is given in terms of linear matrix inequalities

applying a direct multi granularity linguistic and strategy oriented aggregation approach on the assessment of supply performance supply performance has the active continuity behaviors which covers the past present and future of time horizons thus supply performance possesses distinct uncertainty on individual behavior which is inadequate to assess with quantification this study utilizes the linguistic variable instead of numerical variable to offset the inaccuracy on quantification and employs the fitting linguistic scale in accordance with the characteristic of supply behavior to enhance the applicability furthermore the uniformity is introduced to transform the linguistic information uniformly from different scales finally the linguistic ordered weighted averaging operator with maximal entropy applies in direct to aggregate the combination of linguistic information and product strategy to ensure the assessment results meeting the enterprise requirements and then to emulate mental decision making in humans by the linguistic manner

quadratic separation for feedback connection of an uncertain matrix and an implicit linear transformation topological separation is investigated in the case of an uncertain time invariant matrix interconnected with an implicit linear transformation a quadratic separator independent of the uncertainty is shown to prove losslessly the closed loop well posedness several applications for lti descriptor system analysis are then given first some known results for stability and pole location of descriptor systems are demonstrated in a new way second contributions to robust stability analysis and time delay systems stability analysis are exposed these prove to be new even when compared to results for usual lti systems not in descriptor form all results are formulated as linear matrix inequalities lmis

robust pole placement in lmi regions discusses analysis and synthesis techniques for robust pole placement in linear matrix inequality lmi regions a class of convex regions of the complex plane that embraces most practically useful stability regions the focus is on linear systems with static uncertainty on the state matrix for this class of uncertain systems the notion of quadratic stability and the related robustness analysis tests are generalized to arbitrary lmi regions the resulting tests for robust pole clustering are all numerically tractable because they involve solving linear matrix inequalities lmis and cover both unstructured and parameter uncertainty these analysis results are then applied to the synthesis of dynamic output feedback controllers that robustly assign the closed loop poles in a prescribed lmi region with some conservatism this problem is again tractable via lmi optimization in addition robust pole placement can be combined with other control objectives such as h sub 2 or h sub spl infin performance to capture realistic sets of design specifications physically motivated examples demonstrate the effectiveness of this robust pole clustering technique

direct approach processes in group decision making using linguistic owa operators abstract in a linguistic framework several group decision making processes by direct approach are presented these processes are designed using the linguistic ordered weighted averaging lowa operator to do so first a study is made of the properties and the axiomatic of lowa operator showing the rationality of its aggregation way and secondly we present the use of lowa operator to solve group decision making problems from individuals linguistic preference relations

robust performance analysis for structured linear time varying perturbations with bounded rates of variation the robust performance analysis problem is considered for linear time invariant lti systems subject to block diagonal structured and bounded linear time varying ltv perturbations with specified maximal rates of variation analysis methods are developed in terms of semidefinite programming for the computation of upper and lower bounds for the optimum robust performance level the upper bound computation is based on an integral quadratic constraint iqc test developed using a generalized version of the so called swapping lemma the lower bound computation method employs an extended version of the power distribution theorem together with a generalized version of the kalman yakubovich popov kyp lemma and serves as a means to assess the conservatism of the computed upper bounds in the case of dynamic ltv perturbations as corollaries of the underlying result for lower bound computation it is shown for general block diagonal uncertainty structures that thefrequency dependent constant d scaling tests are exact for robust performance analysis against arbitrarily slow fast dynamic ltv perturbations respectively

a new class of universal lyapunov functions for the control of uncertain linear systems the authors analyze the problem of synthesizing a state feedback control for the class of uncertain continuous time linear systems affected by time varying memoryless parametric uncertainties they consider as candidate lyapunov functions the elements of the class spl sigma sub p sup z which is formed by special homogeneous positive definite functions they show that this class is universal in the sense that a lyapunov function exists if and only if there exists a lyapunov function in spl sigma sub p sup z they prove this result in a constructive way showing that such a lyapunov function can always be obtained by smoothing a polyhedral function for which construction algorithms are available the authors show that unlike the polyhedral lyapunov functions these functions allow us to derive explicit formulas for the stabilizing controller

a fuzzy linguistic methodology to deal with unbalanced linguistic term sets many real problems dealing with qualitative aspects use linguistic approaches to assess such aspects in most of these problems a uniform and symmetrical distribution of the linguistic term sets for linguistic modeling is assumed however there exist problems whose assessments need to be represented by means of unbalanced linguistic term sets i e using term sets that are not uniformly and symmetrically distributed the use of linguistic variables implies processes of computing with words cw different computational approaches can be found in the literature to accomplish those processes the 2 tuple fuzzy linguistic representation introduces a computational model that allows the possibility of dealing with linguistic terms in a precise way whenever the linguistic term set is uniformly and symmetrically distributed in this paper we present a fuzzy linguistic methodology in order to deal with unbalanced linguistic term sets to do so we first develop a representation model for unbalanced linguistic information that uses the concept of linguistic hierarchy as representation basis and afterwards an unbalanced linguistic computational model that uses the 2 tuple fuzzy linguistic computational model to accomplish processes of cw with unbalanced term sets in a precise way and without loss of information

analytic properties of maximum entropy owa operators we discuss the maximum entropy approach to obtaining the weights associated with the ordered weighted averaging owa aggregation operator the resulting weights are called the meowa weights using the method of lagrange multipliers we obtain an analytic form for these weights and describe some of their properties the concept of immediate probabilities is introduced as being a transformation of a probability distribution based on a decision maker s degree of optimism this transformation which is affected by an owa operator is shown to result in a relationship between the transformed expected value and the degree of optimism that is monotone when the weights used are the meowa weights

computing the numerical scale of the linguistic term set for the 2 tuple fuzzy linguistic representation model when using linguistic approaches to solve decision problems we need the techniques for computing with words cw together with the 2 tuple fuzzy linguistic representation models i e the herrera and martinez model and the wang and hao model some computational techniques for cw are also developed in this paper we define the concept of numerical scale and extend the 2 tuple fuzzy linguistic representation models under the numerical scale we find that the key of computational techniques based on linguistic 2 tuples is to set suitable numerical scale with the purpose of making transformations between linguistic 2 tuples and numerical values by defining the concept of the transitive calibration matrix and its consistent index this paper develops an optimization model to compute the numerical scale of the linguistic term set the desired properties of the optimization model are also presented furthermore we discuss how to construct the transitive calibration matrix for decision problems using linguistic preference relations and analyze the linkage between the consistent index of the transitive calibration matrix and one of the linguistic preference relations the results in this paper are pretty helpful to complete the fuzzy 2 tuple representation models for cw

uncertainty measures problems concerning additivity additivity of an uncertainty measure on an mv algebra has a clear meaning if the divisibility is dropped we come up to a so called girard algebra there we discuss strong resp weak additivity based on so called divisible disjoint unions resp on additivity for all sub mv algebras we obtain a description of those extensions from additive measures on an mv algebra to the canonical girard algebra extension of pairs which are strongly additive and valuation measures finally we prove the non existence of strongly additive measure extensions if the underlying mv algebra is a finite chain with more than two non trivial elements

effectible residuated lattices and n th roots in this paper conditions are given on residuated lattices and on girard algebras in order for them to be generalized effect algebras and effect algebras respectively a new class of such effectible residuated lattices essentially enlarging mv algebras is defined of particular interest are pre radicable residuated lattices having all n th roots generalizing hohle s square roots to an arbitrary order n the existence of partial n th roots on effectible residuated lattices and girard algebras is related with the concept of divisible effect algebras

a sequential selection process in group decision making with a linguistic assessment approach in this paper a sequential selection process in group decision making under linguistic assessments is presented where a set of linguistic preference relations represents individuals preferences a collective linguistic preference is obtained by means of a defined linguistic ordered weighted averaging operator whose weights are chosen according to the concept of fuzzy majority specified by a fuzzy linguistic quantifier then we define the concepts of linguistic non dominance linguistic dominance and strict dominance degrees as parts of the sequential selection process the solution alternative s is obtained by applying these concepts

affine parameter dependent lyapunov functions for lpv systems with affine dependence this paper deals with the certification problem for robust quadratic stability robust state convergence and robust quadratic performance of linear systems that exhibit bounded rates of variation in their parameters we consider both continuous time ct and discrete time dt parameter varying systems in this paper we provide a uniform method for this certification problem in both cases and we show that contrary to what was claimed previously the dt case requires a significantly different treatment compared to the existing ct results in the established uniform approach quadratic lyapunov functions which are affine in the parameter are used to certify robust stability robust convergence rates and robust performance in terms of linear matrix inequality feasibility tests to exemplify the procedure we solve the certification problem for mathscr l 2 gain performance both in the ct and the dt cases a numerical example is given to show that the proposed approach is less conservative than a method with slack variables

a complete characterization of all weakly additive measures and of all valuations on the canonical extension of any finite mv chain we consider extensions of the unique additive measure on a finite mv chain to uncertainty measures on its canonical girard algebra extension if the underlying mv chain has more than two non trivial elements in a previous paper we have proved the non existence of strongly additive measure extensions where strong additivity is defined as additivity not for all disjoint unions but only restricted to the so called divisible disjoint unions this negative result motivates to look for weakly additive measure extensions which are defined to be additive only on all mv subalgebras of the canonical girard algebra extension we obtain a characterization of all such mv subalgebras which are in fact mv chains and using this result we come up to a characterization of all weakly additive measure extensions moreover we characterize also all the valuation extensions and we prove the incompatibility of these two types of measure extensions except for underlying mv chains with one or two or four non trivial elements

parameter dependent lyapunov functions for discrete time systems with time varying parametric uncertainties abstract in this paper we consider discrete time systems with polytopic time varying uncertainty we look for a class of parameter dependent lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter we show that extending the new discrete time stability condition proposed by de oliveira et al systems control lett 36 1999 135 to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a lyapunov function this allows to check asymptotic stability of the system under study the obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem