convex conditions for robust stability analysis and stabilization of linear aperiodic impulsive and sampled data systems under dwell time constraints stability analysis and control of linear impulsive systems is addressed in a hybrid framework through the use of continuous time time varying discontinuous lyapunov functions necessary and sufficient conditions for stability of impulsive systems with periodic impulses are first provided in order to set up the main ideas extensions to the stability of aperiodic systems under minimum maximum and ranged dwell times are then derived by exploiting further the particular structure of the stability conditions the results are non conservatively extended to quadratic stability analysis of linear uncertain impulsive systems these stability criteria are in turn losslessly extended to stabilization using a particular yet broad enough class of state feedback controllers providing then a convex solution to the open problem of robust dwell time stabilization of impulsive systems using hybrid stability criteria relying finally on the representability of sampled data systems as impulsive systems the problems of robust stability analysis and robust stabilization of periodic and aperiodic uncertain sampled data systems are straightforwardly solved using the same ideas several examples are discussed in order to show the effectiveness and reduced complexity of the proposed approach

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

improved results on stability of continuous time switched positive linear systems in this paper the problems of stability for switched positive linear systems splss under arbitrary switching are investigated in a continuous time context the so called copositive polynomial lyapunov function cplf giving a generalization of copositive types of lyapunov function is first proposed which is formulated in a higher order form of the positive states of the underlying systems it is illustrated in this paper that some classical types of lyapunov functions can be seen as special cases of the proposed cplf then new stability conditions are developed by the new lyapunov function approach it is also proved that the conservativeness of the obtained criteria can be further reduced as the degree of the lyapunov function increases a numerical example is given to demonstrate the effectiveness and less conservativeness of the developed techniques

granular variable precision l fuzzy rough sets based on residuated lattices abstract firstly as for the beginning of this paper we introduce the granular variable precision l fuzzy rough sets based on residuated lattices with arbitrary l fuzzy relations and then the equivalent expressions for the lower and upper approximation operators are given with l fuzzy implications and l fuzzy coimplications on arbitrary l fuzzy relations which can calculate the lower and upper approximation operators efficiently finally some basic properties of the granular variable precision l fuzzy rough sets on residuated lattices are investigated and the conclusions on the granular variable precision fuzzy rough sets are generalized into the situations of the truth values set becoming residuated lattices

type 2 fuzzy rough sets based on extended t norms a type 2 fuzzy rough set based on extended t norms is investigated from constructive and axiomatic approaches an approximation algorithm of type 2 fuzzy rough sets is listed based on cut sets weak type 2 fuzzy topologies are proposed to investigate the topological properties of type 2 fuzzy rough sets an interval valued type 2 fuzzy rough set is proposed and investigated this paper is devoted to investigate type 2 fuzzy rough sets based on extended t norms with respect to type 2 fuzzy relations with convex normal fuzzy truth values type 2 fuzzy rough sets are proposed on two finite universes of discourse and characterized from both constructive and axiomatic approaches in the constructive approach different classes of type 2 fuzzy rough sets are investigated an approximate algorithm of type 2 fuzzy rough sets based on cut sets is given with numerical examples in the axiomatic approach the axiomatic characterizations of type 2 fuzzy rough approximation operators are studied moreover the topological properties of type 2 fuzzy rough sets are discussed in the end this paper introduces interval valued type 2 fuzzy rough sets and discusses their properties

weighted ordinal means the concept of weighted ordinal arithmetic means and other related weighted ordinal means is studied based on the relevant results on the scale 0 1 new types of weighted ordinal means are proposed in some cases these ordinal means coincide with those proposed by godo and torra but not in the case when ordinal means introduced by them are not idempotent based on divisible ordinal t conorms and modifying the approach of godo and torra we show how the previously introduced weighted ordinal means can be obtained without exploiting the formal similarity of the structure of continuous t conorms on 0 1 and divisible ordinal t conorms

stabilization of switched continuous time systems with all modes unstable via dwell time switching stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems in this brief paper a sufficient condition ensuring the asymptotic stability of switched continuous time systems with all modes unstable is proposed the main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes then by using a discretized lyapunov function approach a computable sufficient condition for switched linear systems is proposed in the framework of dwell time it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability based on derived results an algorithm is proposed to compute the stability region of admissible dwell time a numerical example is proposed to illustrate our approach

communicating between information systems communication between information systems is a basic problem in granular computing the concept of homomorphism is a useful mathematical tool to study the communication between two information systems in this paper some properties of information systems under homomorphisms are investigated the concepts of consistent functions are first introduced and their properties are investigated the concepts of relation mappings between two universes are then proposed in order to construct a binary relation on one universe according to the given binary relation on the other universe the main properties of the mappings are studied finally the notions of homomorphisms of information systems based on arbitrary binary relations are proposed and it is proved that attribute reductions in the original system and image system are equivalent to each other under the condition of homomorphism

on several definitions of the differential of a fuzzy mapping abstract several definitions of the differential of a fuzzy function are discussed in the restricted framework of fuzzy mappings from r to r

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

a fuzzy logic based approach to qualitative modeling this paper discusses a general approach to quali tative modeling based on fuzzy logic the method of qualitative modeling is divided into two parts fuzzy modeling and linguistic approximation it proposes to use a fuzzy clustering method fuzzy c means method to identify the structure of a fuzzy model to clarify the advantages of the proposed method it also shows some examples of modeling among them a model of a dynamical process and a model of a human operator s control action

a parametric model for fusing heterogeneous fuzzy data presented is a model that integrates three data types numbers intervals and linguistic assessments data of these three types come from a variety of sensors one objective of sensor fusion models is to provide a common framework for data integration processing and interpretation that is what our model does we use a small set of artificial data to illustrate how problems as diverse as feature analysis clustering cluster validity and prototype classifier design can all be formulated and attacked with standard methods once the data are converted to the generalized coordinates of our model the effects of reparameterization on computational outputs are discussed numerical examples illustrate that the proposed model affords a natural way to approach problems which involve mixed data types

nonquadratic lyapunov functions for robust stability analysis of linear uncertain systems in this note we derive conditions of existence of a homogeneous polynomial lyapunov function of an arbitrary even degree establishing global asymptotic stability of linear system with box bounded uncertainty verification of these conditions is reduced to solving a convex minimization problem we produce numerical examples that demonstrate significant improvement in estimates of admissible uncertainty bounds compared with estimates obtained via the most commonly used quadratic lyapunov functions

nonconservative lifted convex conditions for stability of discrete time switched systems under minimum dwell time constraint in this note a novel conception called virtual clock which is defined by an artificial timer over a finite cycle is introduced for stability analysis of discrete time switched linear systems under minimum dwell time constraint two necessary and sufficient conditions associated with a virtual clock with a sufficient length are proposed to ensure the global uniform asymptotic stability of discrete time switched linear systems for the two nonconservative stability criteria the lifted version maintains the convexity in system matrices based on the lifted convex conditions the extensions to ell 2 gain computation and mathcal h infty control problems are presented in the sequel in particular a novel virtual clock dependent controller is designed which outperforms the traditional mode dependent and common gain controllers several numerical examples are provided to illustrate our theoretic results

stability analysis of discrete time switched systems a switched homogeneous lyapunov function method abstractthis paper addresses the stability issue of discrete time switched systems with guaranteed dwell time the approach of switched homogeneous lyapunov function of higher order is formally proposed by means of this approach a necessary and sufficient condition is established to check the exponential stability of the considered system with the observation that switching signal is actually arbitrary if the dwell time is one sample time a necessary and sufficient condition is also presented to verify the exponential stability of switched systems under arbitrary switching signals using the augmented argument a necessary and sufficient exponential stability criterion is given for discrete time switched systems with delays a numerical example is provided to show the advantages of the theoretical results

granular variable precision fuzzy rough sets with general fuzzy relations the variable precision fuzzy rough sets were proposed to remedy the defects of preexisting fuzzy rough set models however the variable precision fuzzy rough sets were only defined and investigated on fuzzy similarity relations in this paper the granular variable precision fuzzy rough sets with general fuzzy relations are proposed on arbitrary fuzzy relations the equivalent expressions of the approximation operators are given with fuzzy co implications on arbitrary fuzzy relations which can calculate efficiently the approximation operators the granular variable precision fuzzy rough sets are characterized from the constructive approach which are investigated on different fuzzy relations the conclusions on the variable precision fuzzy rough sets are generalized into the granular variable precision fuzzy rough sets

toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic there are three basic concepts that underlie human cognition granulation organization and causation informally granulation involves decomposition of whole into parts organization involves integration of parts into whole and causation involves association of causes with effects granulation of an object a leads to a collection of granules of a with a granule being a clump of points objects drawn together by indistinguishability similarity proximity or functionality for example the granules of a human head are the forehead nose cheeks ears eyes etc in general granulation is hierarchical in nature a familiar example is the granulation of time into years months days hours minutes etc modes of information granulation ig in which the granules are crisp c granular play important roles in a wide variety of methods approaches and techniques crisp ig however does not reflect the fact that in almost all of human reasoning and concept formation the granules are fuzzy f granular the granules of a human head for example are fuzzy in the sense that the boundaries between cheeks nose forehead ears etc are not sharply defined furthermore the attributes of fuzzy granules e g length of nose are fuzzy as are their values long short very long etc the fuzziness of granules their attributes and their values is characteristic of ways in which humans granulate and manipulate information

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

a parametric representation of fuzzy numbers and their arithmetic operators abstract direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex implementation of the extension principle is equivalent to solving a nonlinear programming problem to overcome this difficulty many applications limit the membership functions to certain shapes usually either triangular fuzzy numbers tfn or trapezoidal fuzzy numbers trfn then calculation of the extended operators can be performed on the parameters defining the fuzzy numbers thus making the calculations trivial unfortunately the tfn shape is not closed under multiplication and division the result of these operators is a polynomial membership function and the triangular shape only approximates the actual result the linear approximation can be quite poor and may lead to incorrect results when used in engineering applications we analyze this problem and propose six parameters which define parameterized fuzzy numbers pfn of which tfns are a special case we provide the methods for performing fuzzy arithmetic and show that the pfn representation is closed under the arithmetic operations the new representation in conjunction with the arithmetic operators obeys many of the same arithmetic properties as tfns the new method has better accuracy and similar computational speed to using tfns and appears to have benefits when used in engineering applications

a t sum bound of lr fuzzy numbers abstract in this paper we provide an upper bound and a lower bound of t sum of lr fuzzy numbers with different spreads where t is archimedean t norm and also show in three examples how close they are to actual membership functions furthermore we study when the membership function of t sum achieves the upper bound

meta clustering of possibilistically segmented retail datasets this paper proposes a possibilistic meta clustering algorithm the possibility theory is used for possibilistic segmentation of the input data as well as for determining the possibilistic membership of objects to multiple clusters the meta clustering uses connections between information granules to send clustering knowledge from one granule to another the approach is demonstrated with the help of the k modes clustering algorithm for a real world retail store where a customer is connected to the products bought and products are connected to customers who buy them the meta clustering approach uses the results from clustering of customers as an input to cluster the products and recursively uses clustering of products as input to the clustering customers the customer granule is represented using static information from the database and dynamic information from the clustering of the products bought similarly a product granule is represented by static information from the database and dynamic part from the clustering of the customers who buy the product the static information from the database is represented using possibilistic segments

communication between information systems with covering based rough sets communication between information systems is considered as an important issue in granular computing the concept of homomorphism is an effective mathematical tool to study information exchange between information systems this paper provides a study on some basic properties of covering information systems and decision systems under homomorphisms first we define consistent functions related to coverings and covering mappings between two universes and study their properties then we introduce the notions of homomorphisms of covering information systems and point out that a homomorphism is a special covering mapping between information systems furthermore we investigate some important properties of homomorphisms in covering information systems and decision systems it is proved that some basic properties of original systems such as set approximations attribute reductions can be reserved under the condition of homomorphisms in both covering information systems and covering decision systems

common polynomial lyapunov functions for linear switched systems in this paper we consider linear switched systems dot x t a u t x t x in r n u in u a u u in u compact and the problem of asymptotic stability for arbitrary switching functions uniform with respect to switching uas given a uas system it is always possible to build a common polynomial lyapunov function our main result is that the degree of that common polynomial lyapunov function is not uniformly bounded over all the uas systems this result answers a question raised by dayawansa and martin a generalization to a class of piecewise polynomial lyapunov functions is given

a characterization of the extension principle abstract we provide an alternative characterization of the extension principle of fuzzy sets this characterization is based upon using relations to represent mappings we apply this new characterization to develop an extension for non deterministic mappings

methods for decision making with cardinal numbers and additive aggregation abstract for multi attribute decision making with cardinal numbers and additive aggregation the methods additive aggregation and outranking for crisp and fuzzy numbers are connected with the concept of linguistic variables preference ranking a generalization of outranking and preference ranking organization methods such as electre and promethee can be divided into three phases where each of them is defined completely by linguistic variables the derived method preference ranking with additive weighting and individual fuzziness has an improved selectivity or discrimination compared to conventional methods moreover the method fulfils four important requirements preference only for sufficiently large weights considering evaluation differences outside of thresholds and regarding aggregational and substitutional properties the simplified method preference ranking with additive weighting and general fuzziness allows a reduction of computational resources

fuzzy information systems and their homomorphisms abstract with the arrival of the information age information acquisition and communication have become more and more important in the field of information technology this paper uses the concept of homomorphism as a basic tool to study the communication between fuzzy information systems the concepts of consistent and compatible mappings with respect to fuzzy sets are firstly defined and their basic properties are studied then a pair of lower and upper rough fuzzy approximation operators is constructed by means of the concept of fuzzy mappings basic invariant properties of the approximation operators are investigated finally the concepts of fuzzy information system and its homomorphism are introduced and some invariant properties of fuzzy information systems under homomorphisms are examined it is proved that the attribute reductions of an original information system and its image system are equivalent to each other in the context of fuzzy attributes these results may have potential applications in attribute reduction and classification issues

a converse lyapunov theorem for linear parameter varying and linear switching systems we study families of linear time varying systems where time variations have to satisfy restrictions on the dwell time that is on the minimum distance between discontinuities as well as on the derivative in between discontinuities such classes of systems may be formulated as linear flows on vector bundles the main objective of this paper is to construct parameter dependent lyapunov functions which characterize the exponential growth rate this is possible in the generic irreducible case as an application the gelfand formula is generalized to the class of systems studied here in other words the maximal exponential growth rate may be approximated by only considering the periodic systems in the family of time varying systems a perspective on the question of continuous dependence of the exponential growth rate on the data is given

complementably universal banach spaces ii the two main results are a if a banach space x is complementably universal for all subspaces of c0 which have the bounded approximation property then x is non separable and hence x does not embed into c0 b there is no separable banach space x such that every com pact operator between banach spaces factors through x theorem b solves a problem that dates from the 1970s

generalized rough sets based on relations rough set theory has been proposed by pawlak as a tool for dealing with the vagueness and granularity in information systems the core concepts of classical rough sets are lower and upper approximations based on equivalence relations this paper studies arbitrary binary relation based generalized rough sets in this setting a binary relation can generate a lower approximation operation and an upper approximation operation but some of common properties of classical lower and upper approximation operations are no longer satisfied we investigate conditions for a relation under which these properties hold for the relation based lower and upper approximation operations

necessary and sufficient stability condition for second order switched systems a phase function approach abstractto find a unified approach for the stability analysis of second order switched system the concept of phase function is proposed in this paper first the basic properties of phase function are explored following this concept and its properties the phase based stability criterion is investigated based on the lyapunov theory and a necessary and sufficient stability condition is obtained in the phase function approach moreover the connection between phase based stability conditions and algebraic condition of system matrices is also discussed finally numerical examples are provided to exemplify the main result and make necessary comparisons with the existing methods

stability and stabilization of continuous time switched linear systems this paper addresses two strategies for the stabilization of continuous time switched linear systems the first one is of open loop nature trajectory independent and is based on the determination of a minimum dwell time by means of a family of quadratic lyapunov functions the relevant point on dwell time calculation is that the proposed stability condition does not require the lyapunov function to be uniformly decreasing at every switching time the second one is of closed loop nature trajectory dependent and is designed from the solution of what we call lyapunov metzler inequalities from which the stability condition including chattering is expressed being nonconvex a more conservative but simpler to solve version of the lyapunov metzler inequalities is provided the theoretical results are illustrated by means of examples

mode identifying time estimation and switching delay tolerant control for switched systems in this paper an elementary time unit etu method is proposed to study the problem of estimating the admissible delay in the identification of the active mode in the analysis and design of switched systems the activation interval of a subsystem is considered to consist of a finite time number of segments called etus by which a novel class of time scheduled lyapunov function is used to estimate the admissible delay in mode identification for switched systems further the etu method is applied for switching delay tolerant control problem and a class of time scheduled state feedback controllers are designed to achieve the exponentially stability several numerical examples are presented to validate the theoretic findings

fuzzy numbers from raw discrete data using linear regression this paper focuses on modelling fuzzy numbers with meaningful membership functions more precisely it proposes a method to construct trapezoidal fuzzy number approximations from raw discrete data in many applications input information is numerical and therefore particular fuzzy sets such as fuzzy numbers hold great interest and relevance in managing data imprecision and vagueness the proposed technique provides an efficient way to obtain trapezoidal numbers using linear regression the technique is simple fast and effective preliminary tests are performed using different types of input data a gaussian function a sigmoidal function three datasets of synthetic discrete data and an histogram obtained from a colour satellite image

improvements and critique on sugeno s and yasukawa s qualitative modeling investigates sugeno s and yasukawa s 1993 qualitative fuzzy modeling approach we propose some easily implementable solutions for the unclear details of the original paper such as trapezoid approximation of membership functions rule creation from sample data points and selection of important variables we further suggest an improved parameter identification algorithm to be applied instead of the original one these details are crucial concerning the method s performance as it is shown in a comparative analysis and helps to improve the accuracy of the built up model finally we propose a possible further rule base reduction which can be applied successfully in certain cases this improvement reduces the time requirement of the method by up to 16 in our experiments

regranulation a granular algorithm enabling communication between granular worlds abstract in this paper we describe a granular algorithm for translating information between two granular worlds represented as fuzzy rulebases these granular worlds are defined on the same universe of discourse but employ different granulations of this universe in order to translate information from one granular world to the other we must regranulate the information so that it matches the information granularity of the target world this is accomplished through the use of a first order interpolation algorithm implemented using linguistic arithmetic a set of elementary granular computing operations we first demonstrate this algorithm by studying the common fuzzy pd rulebase at several different granularities and conclude that the 3 3 granulation may be too coarse for this objective we then examine the question of what the natural granularity of a system might be this is studied through a 10 fold cross validation experiment involving three different granulations of the same underlying mapping for the problem under consideration we find that a 7 7 granulation appears to be the minimum necessary precision

the structure of decomposable indistinguishability operators decomposable fuzzy relations are studied symmetric fuzzy relations are proved to be generated by a single fuzzy subset for archimedean t norms decomposable indistinguishability operators generate special kinds of betweenness relations that characterize them a new way to generate indistinguishability operators coherent with the underlying ordering structure of the real line is given in the sense that this structure is compatible with the betweenness relation generated by the relation is developed

two nonparametric models for fusing heterogeneous fuzzy data two models are discussed that integrate heterogeneous fuzzy data of three types real numbers real intervals and real fuzzy sets the architecture comprises three modules 1 an encoder that converts the mixed data into a uniform internal representation 2 a numerical processing core that uses the internal representation to solve a specified task and 3 a decoder that transforms the internal representation back to an interpretable output format the core used in this study is fuzzy clustering but there are many other operations that are facilitated by the models two schemes for encoding the data and decoding it after clustering are presented one method uses possibility and necessity measures for encoding and several variants of a center of gravity defuzzification method for decoding the second approach uses piecewise linear splines to encode the data and decode the clustering results both procedures are illustrated using two small sets of heterogeneous fuzzy data

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

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

extended results on the relationship between information systems the relationship between information systems is an important topic in rough set field and it is studied through mappings many kinds of consistent functions have been proposed and they can be used to describe the invariance of attribute reducts between two information systems efficiently however they cannot reflect relationships between neighborhoods generated from two information systems in this paper to achieve this aim firstly we introduce a neighborhood continuous function that is inspired by the concept of continuous function in topology then we address its properties and discuss relationships between neighborhood continuous functions and several kinds of existing consistent functions furthermore we investigate some important properties of neighborhood continuous function with respect to relation mappings finally based on neighborhood continuous functions the notion of a neighborhood homomorphism between different information systems is proposed it is noted that the reduct feature of a single information system can be described by neighborhood continuous functions while the reduct invariance of two different information systems can be described by neighborhood homomorphisms

disturbance decoupling with closed loop modes stability in switched linear systems this work deals with the problem of rendering the output of a switched linear system insensitive to a disturbance input with the requirement that the dynamics of the closed loop system be exponentially stable for all switching signals with a sufficiently large dwell time a necessary and sufficient condition for the problem to have a solution is shown a complete computational procedure to check the solvability condition and to synthesize the compensation scheme is provided a worked out example is presented with the aim of showing the effectiveness of the devised method

lmi techniques for optimization over polynomials in control a survey numerous tasks in control systems involve optimization problems over polynomials and unfortunately these problems are in general nonconvex in order to cope with this difficulty linear matrix inequality lmi techniques have been introduced because they allow one to obtain bounds to the sought solution by solving convex optimization problems and because the conservatism of these bounds can be decreased in general by suitably increasing the size of the problems this survey aims to provide the reader with a significant overview of the lmi techniques that are used in control systems for tackling optimization problems over polynomials describing approaches such as decomposition in sum of squares positivstellensatz theory of moments polya s theorem and matrix dilation moreover it aims to provide a collection of the essential problems in control systems where these lmi techniques are used such as stability and performance investigations in nonlinear systems uncertain systems time delay systems and genetic regulatory networks it is expected that this survey may be a concise useful reference for all readers

a converse lyapunov theorem for a class of dynamical systems which undergo switching the authors investigate the stability of a system in which the dynamics at any instant in time will follow one of a fixed set of vector fields they allow switching between members of the family of vector fields to be completely random the focus of this paper is to prove a converse lyapunov theorem for this class of systems

a formal model of computing with words classical automata are formal models of computing with values fuzzy automata are generalizations of classical automata where the knowledge about the system s next state is vague or uncertain it is worth noting that like classical automata fuzzy automata can only process strings of input symbols therefore such fuzzy automata are still abstract devices for computing with values although a certain vagueness or uncertainty are involved in the process of computation we introduce a new kind of fuzzy automata whose inputs are instead strings of fuzzy subsets of the input alphabet these new fuzzy automata may serve as formal models of computing with words we establish an extension principle from computing with values to computing with words this principle indicates that computing with words can be implemented with computing with values with the price of a big amount of extra computations

necessary and sufficient condition for stability of switched uncertain linear systems under dwell time constraint in this technical note a necessary and sufficient stability criterion for switched linear systems under dwell time constraint is proposed by employing a class of time scheduled homogeneous polynomial lyapunov functions with a sufficiently large degree the key feature of this nonconservative condition lies in its convexity in the system matrices which explicitly facilitates its further extension to uncertain systems then in order to obtain numerically testable condition a family of lmi conditions are presented with the aid of the idea of dividing the dwell time interval into a finite number of segments it is proved that the non conservativeness can be maintained with a sufficiently large interval dividing parameter in the end the result is straightforwardly extended to the uncertain case in virtue of the convexity in the system matrices numerical examples are presented to illustrate our findings

communication between information systems using fuzzy rough sets communication between information systems is a basic problem in granular computing and the concept of homomorphism is a useful mathematical tool to study this problem in this paper some properties of communication between information systems based on fuzzy rough sets are investigated the concepts of fuzzy relation mappings between universes are first proposed in order to construct a fuzzy relation of one universe according to the given fuzzy relation on the other universe the main properties of the mappings are studied the notions of homomorphism of information systems based on fuzzy rough sets are then proposed and it is proved that properties of relation operations in the original information system and structural features of the system such as approximations of arbitrary fuzzy sets and attribute reductions are guaranteed in its image system under the condition of homomorphism

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

granular computing and dual galois connection a covering model for granular computing in a set theoretic setting is studied in this paper under this model a zooming in operator is redefined combinations of the zooming in and zooming out operators form two pairs of approximation operators of the original and the granulated universe of discourse their properties are examined in detail for the two pairs of lower and upper approximation operators it is proved that the duality is always true for a generalized approximation space the approximation representations are just the combination operators formed on the basis of the zooming out and zooming in operators relationships between these combination operators and the dual galois connection are also analyzed

a nonconservative lmi condition for stability of switched systems with guaranteed dwell time ensuring stability of switched linear systems with a guaranteed dwell time is an important problem in control systems several methods have been proposed in the literature to address this problem but unfortunately they provide sufficient conditions only this technical note proposes the use of homogeneous polynomial lyapunov functions in the non restrictive case where all the subsystems are hurwitz showing that a sufficient condition can be provided in terms of an lmi feasibility test by exploiting a key representation of polynomials several properties are proved for this condition in particular that it is also necessary for a sufficiently large degree of these functions as a result the proposed condition provides a sequence of upper bounds of the minimum dwell time that approximate it arbitrarily well some examples illustrate the proposed approach

convex conditions for robust stabilization of uncertain switched systems with guaranteed minimum and mode dependent dwell time abstract alternative conditions for establishing dwell time stability properties of linear switched systems are considered unlike the hybrid conditions derived in geromel and colaneri 2006 the considered ones are affine in the system matrices allowing then for the consideration of uncertain switched systems with time varying uncertainties the low number of decision variables moreover permits to easily derive convex stabilization conditions using a specific class of state feedback control laws the resulting conditions are enforced using sum of squares programming which are shown to be less complex numerically that approaches based on piecewise linear functions or looped functionals previously considered in the literature the sums of squares conditions are also proven to 1 approximate arbitrarily well the conditions of geromel and colaneri 2006 and 2 be invariant with respect to time scaling emphasizing that the complexity of the approach does not depend on the size of the dwell time several comparative examples illustrate the efficiency of the approach

convex lifted conditions for robust l 2 stability analysis and l 2 stabilization of linear discrete time switched systems with minimum dwell time constraint stability analysis of discrete time switched systems under minimum dwell time is studied using a new type of lmi conditions these conditions are convex in the matrices of the system and shown to be equivalent to the nonconvex conditions proposed in geromel and colaneri 2006b the convexification of the conditions is performed by a lifting process which introduces a moderate number of additional decision variables the convexity of the conditions can be exploited to extend the results to uncertain systems control design and 2 gain computation without introducing additional conservatism several examples are presented to show the effectiveness of the approach

analysis and efficient implementation of a linguistic fuzzy c means the paper is concerned with a linguistic fuzzy c means fcm algorithm with vectors of fuzzy numbers as inputs this algorithm is based on the extension principle and the decomposition theorem it turns out that using the extension principle to extend the capability of the standard membership update equation to deal with a linguistic vector has a huge computational complexity in order to cope with this problem an efficient method based on fuzzy arithmetic and optimization has been developed and analyzed we also carefully examine and prove that the algorithm behaves in a way similar to the fcm in the degenerate linguistic case synthetic data sets and the iris data set have been used to illustrate the behavior of this linguistic version of the fcm

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